PROBING ANISOTROPIC INTERMOLECULAR FORCES IN NEMATIC
LIQUID CRYSTALS USING N M R A N D C O M P U T E R SIMULATIONS
By
Raymond Thomas Syvitski
B.Sc, Lakehead University, 1991
M.Sc, Lakehead University, 1994
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
in
THE FACULTY OF GRADUATE STUDIES
DEPARTMENT OF CHEMISTRY
We accept this thesis as conforming
to the required standard
THE UNIVERSITY OF BRITISH COLUMBIA
April 2000
© Raymond Thomas Syvitski, 2000
In presenting this thesis in partial fulfilment of the requirements for an advanced degree at
the University of British Columbia, I agree that the Library shall make it freely available
for reference and study. I further agree that permission for extensive copying of this
thesis for scholarly purposes may be granted by the head of my department or by his
or her representatives. It is understood that copying or publication of this thesis for
financial gain shall not be allowed without my written permission.
Department of Chemistry
The University of British Columbia
2075 Wesbrook Place
Vancouver, Canada
V6T 1W5
Date:
Abstract
Molecules of similar size and shape, but with different electrostatic properties are used to
investigate the effects of molecular dipoles, quadrupoles and polarizabilities on the orientational ordering of several solutes co-dissolved in nematic liquid crystals. Permanent
dipoles have a negligible influence on solute orientational order and effects from molecular
polarizability interactions could not be separated from short-range interactions. Order
parameters predicted from strong, short-range repulsive forces coupled with interactions
between the solute quadrupole and the average electric field gradient felt by the solute
(EFG) are consistent with experimental values. For liquid crystals utilized in this study,
the calculated values of the (EFGys are the same sign and of similar magnitude to the
(_FG)'s determined previously from experiments on D and HD. However, in contradic2
tion to these experimental results, the (EFG)'s determined from computer simulations
of hard particles with embedded point quadrupoles is found to be very dependent on the
properties of the particle.
For a particular nematic liquid crystal (55 wt% ZLI 1132 in EBBA), the contribution
to solute ordering from long-range electrostatic interactions is found to be negligible.
This conclusion is supported by computer simulation studies of hard particles; models
for short-range interactions which bestfitthe NMR experimental solute order parameters
ii
also best fit the simulation results.
Experimentally determined second rank orientational order parameters and structural
parameters of solutes are calculated from vibrationally and non-vibrationally corrected
nuclear dipolar coupling constants; accurate dipolar couplings are obtained from analysis of the high-resolution nuclear magnetic resonance (NMR) spectra. For the more
complicated molecules spectral parameters arefirstestimated from analysis of multiple
quantum NMR spectra. In some cases, a modified version of a least-squares routine
which independently adjusts chemical shifts, order parameters, structural parameters
and/or dipolar couplings is used.
iii
Table of Contents
Abstract
ii
List of Tables
vii
List of Figures
ix
Acknowledgment
xi
Dedication
1
xii
Introduction
1
1.1
Liquid Crystals
1
1.1.1
General
1
1.1.2
Nematic Liquid Crystals
2
1.2
1.3
Orientational Ordering and Anisotropic Intermolecular Interactions . . .
3
1.2.1
Orientational Ordering from Experiments
3
1.2.2
Anisotropic Intermolecular Interactions
5
1.2.3
Calculating Order Parameters from Intermolecular Interactions .
5
Identifying Intermolecular Interactions that are Important for Orientational Ordering
6
iv
1.4
1.5
2
1.3.1
Some Key Experiments and Predictions from Theory/Model . . .
1.3.2
Computer Simulations
7
10
NMR Experiments and their Relation to Orientational Ordering
11
1.4.1
Dipolar Couplings and Orientational Order Parameters
11
1.4.2
NMR Theory
13
1.4.3
Simplifying NMR Spectra and Analysis by Multiple Quantum NMR 15
Outline of Thesis
17
21
N M R and Molecular Structure
2.1
Introduction
21
2.2
Experiment
25
2.3
Spectral Analysis and Strategy
28
2.4
Molecular Structure and Order Parameters
42
2.4.1
Calculations
42
2.4.2
Molecular Structure
46
2.4.3
Order Parameters . . .
47
2.5
Summary
48
3 Dipole-Induced Ordering in Nematic Liquid Crystals
49
3.1
Introduction
49
3.2
Experiments and Results
54
3.3
Mean-Field Models
55
v
4
5
3.4
Analysis and Discussion
61
3.5
Conclusions
78
Comparative Study Between M C and N M R Experiments
80
4.1
Introduction
80
4.2
Short-range Interactions
82
4.3
Long-range Interactions
88
4.4
Conclusions
95
Summary and Future Considerations
Bibliography
96
99
Appendixes
105
A Solutes
106
B Dipolar Couplings
108
C Structural Parameters
124
D Order Parameters
136
E
142
Scaled and Calculated Order Parameters
vi
List of Tables
2.1
Solute and Solvent Composition of Samples
26
2.2
Selected Dipolar Couplings
42
3.3
Molecular Parameters
63
3.4
Liquid Crystal Parameters
64
3.5
Adjusted Molecular Parameters
76
B.6 Fitting Parameters and RMS Errors from Analysis of High-Resolution and
MQ NMR Spectra
109
B. 7 Fitting Parameters and RMS Errors from Analysis of High-Resolution and
MQ NMR Spectra of Sample #25
122
C. 8 Molecular Parameters of Fits to Vibrationally Corrected Dipolar Couplings 125
C.9 Structural Parameters of Fits to Dipolar Couplings for chlorobenzene,
toluene and 1,3,5-trichlorobenzene
126
C.10 Structural Parameters of Fits to Dipolar Couplings for p-disubstituted
benzenes
128
C.ll Structural Parameters of Fits to Dipolar Couplings for o-disubstituted
benzenes
130
vii
C. 12 Structural Parameters of Fits to Dipolar Couplings for m-disubstituted
benzenes
133
D. 13 Order Parameters of Fits to Dipolar Couplings
137
D. 14 Order Parameters for solutes in Sample #25 of Fits to Dipolar Couplings 141
E. 15 Scaled and Calculated Order Parameters
viii
143
List of Figures
1.1
Molecular Structure of N-(4-ethoxybenzylidene)-4'-n-butylaniline
1.2
An example of angle and axes definitions for order parameters and dipolar
couplings
3
.
12
2.3
High-resolution spectrum of acetonitrile, propyne and 1,3,5-trichlorobenzene 30
2.4
High-resolution spectrum of Sample #11
32
2.5
7-quantum spectrum of Sample #11
34
2.6
Expansion of High-Resolution Spectrum of Sample #11
35
2.7 8-quantum spectrum of o-xylene
38
2.8
Spectral analysis strategy
40
2.9
Atom Numbering for p-, m- and o-xylene, and o-chlorotoluene
44
3.10 Coordinate System for Solutes
56
3.11 Sa p s for p- and mono substituted benzenes
67
3.12 S
68
C
led,
s for 1,3,5-trichlorobenzene, acetonitrile and propyne
s c aled,
z z
3.13 S^ s
for o- and m-disubstituted benzenes
69
s for o- and m-disubstituted benzenes
70
led,
3.14 S^
c aled,
3.15 S
z
s
scaled,
minus S^'s against S
's
scaled
ix
71
3.16 Experimentally determined Fzz's
74
4.17 Order Parameters from MC simulations of hard ellipsoids
85
4.18 Differences between calculated and experimental order parameters . . . .
86
4.19 Relative differences between calculated and experimental order parameters 89
4.20 Experimental and MC F z's
93
4.21 Relative difference between calculated and NMR solute order parameters
94
Z
A.22 Coordinate System and Atom Numbering of Solutes
x
107
Acknowledgment
My
gratitude
goes out to my
supervisor Dr. Elliott Burnell
for his constant coadjuvancy
and encouragement. I thank you for
putting up with me and allowing me
to redecorate the lab. I thank Dr. Thambirajah Chandrakumar for his useful suggestions when I was analyzing NMR spectra and Dr. James Poison who enlightened me
about NMR and computer simulations. Dr. Grenfell Patey must be recognized for his
stimulating and informative discussions. I congratulate the electronics shop for keeping the spectrometers operational; I did my best, but Tom and Milan were still able
to fix the spectrometers. Thanks to Dr. Nick Burlinson for helpful discussions regarding Bruker software. Karen Cheng, Ducky and other fuzzy critters (including
my sister Heather) must be acknowledged for their "intellectually stimulating"
conversations; sparkles, glow-in-the-dark stars, Teddy, and the couch also
helped with our creativity. I must recognize everyone else who kept me
(in)sane by either going for coffee, beer, lunch or breakfast with
me. Finally, I thank my sister Heather for the interesting
if not somewhat odd phone conversations, and
my family and my friends for their love,
support
and encourage-
ment. Thanks.
xi
Dedication
To my Grandmother
Mary Thomas
xii
Chapter 1
Introduction
1.1
1.1.1
Liquid Crystals
General
In 1888 Reinitzer[l] observed that a turbid liquid was formed when solid cholesteryl
benzoate was melted, and that a clear isotropic liquid was produced upon further heating.
The turbid liquid was characterized by Lehmann[2] and was found to be birefringent
and therefore anisotropic. Phases which are anisotropic and still exhibit some degree
of fluidity are described as "liquid-crystalline" or "mesomorphic." Transitions to the
liquid-crystalline phase can be induced either by thermal processes (thermotropic liquid
crystals) or by the influence of solvents (lyotropic liquid crystals). The main feature of
all liquid crystals is the orientational ordering of the component molecules; the molecules
of some liquid crystals are also positionally ordered. This study focuses on thermotropic
nematic liquid crystals which are the simplest of all the liquid crystals and which are
identified by having only orientational ordering.
1
Chapter 1. Introduction
1.1.2
2
Nematic Liquid Crystals
Typically, nematogens (the constituent molecules of a nematic phase) are elongated
molecules with semi-rigid cores, withflexiblealkyl chains, and with polar constituents
(see for example Fig. 1.1). The nematic phase is characterized by having no long-range
positional ordering, but there are "domains" of long-range orientational ordering which
can extend over distances of up to l/xm[3]. Orientational ordering describes the tendency
of the nematogen's long axis to be parallel to a common axis; the common axis is defined
as the nematic director. In the absence of external fields, the orientations of the nematic
directors vary through the sample. Since the dimensions of the domains are on the order
of the wavelength of visible light, the turbid appearance of the macroscopic sample arises
from the scattering of light as it propagates through the phase.
In the presence of a constant magnetic or electricfieldall the nematic directors align
either parallel or perpendicular with the applied field. The direction of the director
alignment depends on the magnetic or dielectric susceptibility anisotropy of the domain.
The magnetic or electric field has a negligible influence on the relative orientational
ordering of individual molecules; the interaction energy for the susceptibility anisotropy
coupled with thefieldis very small compared to the thermal energy [3]. However, over the
entire collection of molecules within the domain the energy is sufficient to cause alignment
of the directors. Since the current study is concerned with the intermolecular forces that
cause alignment of molecules in nematic phases and since the orientational ordering of
3
Chapter 1. Introduction
H
H C -0
5
2
'N
Figure 1.1: Molecular Structure of N-(4-ethoxybenzylidene)-4'-r^butylaniline. A collection of these molecules forms a stable nematic phase from 308 to 352 K.
the molecules is determined from analysis of nuclear magnetic resonance spectral data,
it is important to realize that the strong magneticfielddoes not significantly influence
the relative orientational ordering of molecules within the phase. For the liquid crystals
utilized in this study, the directors are aligned parallel with the main magnetic field.
1.2
1.2.1
Orientational Ordering and Anisotropic Intermolecular Interactions
Orientational Ordering from Experiments
The orientational ordering of an inflexible molecule is completely described by the orientational distribution function f(Q) where Q, denotes the Eulerian angles that describe
the orientations of the molecularfixedaxes relative to the nematic director. Since these
molecules are in a fluid phase /(fi) is an average over all molecular reorientations arid
/(fi)dfi is the probability offindingthe molecule in a small solid angle dfi at the direction
defined by fi. In principal, the complete distribution function can be assessed by X-ray
diffraction techniques[4]. Up to the fourth rank component of the distribution function
can be determined from neutron diffraction techniques [5]. However, poor resolution and
4
Chapter 1. Introduction
instrumental limitations make these tasks extremely difficult[5]. Nevertheless, the average second rank component S (the second rank orientational order parameter) of /(ft)
is readily accessible by analysis of nuclear magnetic resonance (NMR) spectral data (a
brief description of N M R theory is given later in this chapter and a detailed description
of spectral analysis and determining S from spectral data is the topic of Chapter 2). The
relationship between the experimentally determined S and /(ft) is given by:
S 0 = J/(ft) Q cos 9
a
aZ
cos 6p Z
dQ
(1.1)
where a and /3 are the molecular fixed axes (typically defined to be coincidental with
symmetry axes of the molecule), S p is the a(3 component of 5, and 9 z
a
a
and B$z are
the angles between the a and /3 axis and the nematic director defined to be parallel
to the laboratory fixed Z direction (see Fig. 1.2, page 12 for an example of axis and
angle definitions); for the nematic phases utilized in this study the nematic director
and magnetic field directions are coincidental with the laboratory fixed Z direction.
Since there is no positional ordering of the component molecules, the nematic phase is
cylindrically symmetric about the nematic director, and since there is an equal probability
of a molecule aligning parallel or anti-parallel with the laboratory fixed Z direction, the
nematic phase is apolar. Thus, measured properties are invariant to rotations about the
nematic director and all odd components of /(ft) (eg., components that are related to
cos 9, cos 6, etc.) are necessarily zero. The second rank orientational order parameter is
3
Chapter 1.
5
Introduction
the leading term in the expansion of the anisotropic components of / ( f i ) .
1.2.2
Anisotropic Intermolecular Interactions
Anisotropic intermolecular interactions are responsible for the orientational ordering of
liquid-crystal phases. The interactions can be characterized as anisotropic short-range
repulsive or as anisotropic long-range.
Short-range repulsive interactions depend on the details of the molecular structure,
such as size, shape and flexibility. Long-range interactions involve dipoles, quadrupoles,
polarizabilities and other properties that describe the distribution of charges over a
molecule and can be either attractive or repulsive.
1.2.3
Calculating Order Parameters from Intermolecular Interactions
The / ( f i ) and ultimately 5 j's can be calculated using statistical mechanics and a meanQ/
field anisotropic orientational interaction potential [/(fi) which is characterized by the
short-range repulsive and long-range interactions. It is currently impractical to completely define J7(fi); it would require a detailed understanding of all the interactions
present. The form of (7(fi) can be simplified by assuming that it is adequately described
either by a pair potential[6, 7] or by the interaction between a molecular property and
an average- or mean-field produced from the surrounding liquid crystal medium [8]. For
Chapter 1. Introduction
6
relatively inflexible molecules / ( f t ) can be calculated from [/(ft) using
exp(-c7(ft)/feT)
A
Jezp(-c7(ft)/A;T)dft'
;
1
Therefore, by defining C/(ft), a second rank order parameter S%$ can be calculated
c
calc
5_/3
—
1.3
/ (f cos 6
aZ
cos dffz - \5 )
aP
exp(-U(Q)/kT)dn
fexp(-U(n)/kT)dn
(1.3)
Identifying Intermolecular Interactions that are Important for Orientational Ordering
It is now recognized that for molecules w i t h a high degree of shape anisotropy, the orientational ordering m a i n l y arises from anisotropic short-range interactions [8-14]. Contributions from the long-range interactions may have a lesser influence on the orientational
ordering[6,15-17]. T h e importance of various long-range interactions is a matter of current controversy and is an important topic of this study.
A n important means of learning about f/(ft) is to compare real experimental S ps
a
w i t h those calculated (S%$ ) from theory or model, or w i t h those determined from comc
puter simulations. Orientational order parameters of the constituent molecules of a liquid
crystalline phase are difficult to study because these molecules are normally devoid of
symmetry and exist i n a number of symmetrically unrelated conformers. A proper description involves a plethora of orientational parameters as well as conformer probabilities
7
Chapter 1. Introduction
and it becomes essential to assume some model for the pair potential in order to relate
experimental measurements to single-molecule properties. However, by examining the
orientational ordering of small, well-characterized solutes, the role of the various contributions to the intermolecular potential can be investigated, for example, by choosing a
solute with particular properties [8], by choosing a set of solutes whose properties differ
in a well-defined manner[18,19] or by choosing a liquid crystal solvent that may have
special properties [8].
1.3.1
Some Key Experiments and Predictions from Theory/Model
D 2 and HD are special solutes; from the NMR spectral data of orientationally ordered D
2
and HD in various liquid crystals, it was determined that the orientational ordering of D
2
and HD is dominated by the interaction between the molecular electric quadrupole and
an average electric field gradient due to the liquid crystal environment (EFG)[20\. In
addition, the (EFGYs for various liquid crystals, a quantity that is not easily accessible
by experimental methods, was determined from the quadrupolar coupling constant of
the deuteron B
OBS
and the dipolar coupling constant between the deuterons D D (or the
D
deuteron and proton D H)- The experimentally measured value of B
D
OBS
B
obs
= -^(F
z z
-eqS)
is
(1.4)
Chapter 1.
8
Introduction
where eQo is the deuteron nuclear quadrupole moment, F
zz
is the ZZ component of
(EFG) parallel to the magnetic field direction Z, S is the solute order parameter, and eq
is the average electric field gradient due to the intramolecular charge distribution around
the deuteron nucleus. eQp was determined from molecular beam experiments and the
value of eq determined from quantum mechanical calculations.
For the various liquid crystals, the order parameter S of D or HD is directly mea2
sured from the DDD or D
DH
and the vibrationally averaged value of < r
- 3
>. The values
of the S's are found to be in excellent agreement with the S's calculated from an orientational potential that describes a molecular electric quadrupole moment/F
where the F
zz
zz
interaction
was determined from Eq. 1.4. The calculations incorporated the quantum
mechanical nature of D and employed no model or adjustable parameters[21-23].
2
In other studies acetylene, like D , was found to have a negative order parameter
2
in the nematic solvent N-(4-ethoxybenzylidene)-4'-n-butylaniline (EBBA; see Fig. 1.1,
page 3) [24,25]; EBBA is a solvent which was determined (from the D and HD studies)
2
to have a negative F .
zz
The counter-intuitive negative order parameter is the predicted
result for a positive quadrupole/negative F
zz
interaction. Similarly, order parameters for
benzene and hexafluorobenzene, molecules with very similar shapes but with quadrupole
moments of opposite signs, are in accordance with results predicted from the quadrupole
moment/F
zz
mechanism[26]. These experiments demonstrated that interactions involv-
ing molecular quadrupoles could provide an important orientational mechanism and that
for a particular liquid crystal, solutes experience at least the same sign F \
zz
from the
Chapter 1. Introduction
9
experiments mentioned above and other similar experiments[8] it was concluded that solutes experience roughly the same average environment regardless of the size, shape or
electrostatic properties.
The concept of a solute independent average environment has been criticized by Photinos et. al.[27] and Terzis et. al[Q]. They developed a theory to describe the effects from
short-range repulsive and long-range dipole and quadrupole interactions. Effects from
dipole-dipole interactions were inferred by comparing order parameters of a,w-dibromon-alkanes and n-alkanes[17]. The observed bias on the segmental orientational order of
the bromo-alkanes relative to the n-alkanes was ascribed to result from the interaction
of the local dipole moment with the local dipoles on the nematogens. The effect was explained qualitatively by the asymmetric arrangement which results from off-center local
dipoles on molecules with short-range repulsive cores. This results in strong short-range
correlations which contribute significantly to the orientational ordering. They concluded
that long-range interactions were comparable in magnitude to short-range interactions
and that long-range interactions were highly sensitive to the size, shape and electrostatic
properties of the solvent and solute molecules, i.e. solutes do not experience the same
environment.
Emsley et al. [16] have also examined the importance of dipoles, quadrupoles and the
concept of a solute independent average environment. They suggested that there is no
contribution to solute ordering from dipole interactions because in apolar nematic phases
the first rank order parameter of the liquid crystal is zero (i.e. the mean electric field of
10
Chapter 1. Introduction
the nematic phase is zero) and that the F^z's experienced by a solute are dependent on
the solvent quadrupole and the distribution of intermolecular vectors about the solute
particle; the solute properties influence the distribution of intermolecular vectors and thus
the F z is indirectly influenced by the solute. The distribution of intermolecular vectors
Z
is a property which is not easily determined by experimental methods. Nevertheless, the
orientational behavior of anthracene and anthraquinone, molecules that are claimed to
have similar shapes and polarizabilities but significantly different quadrupole moments,
was examined using the theory[28].
The distribution of solvent-solute intermolecular
vectors, and consequently the Fzz's, were found to be strongly dependent on both solvent
and solute molecular properties.
Hence, there is controversy over the importance of dipole and quadrupole interactions
and about the concept of a solute-independent average environment. The controversy is
an important aspect of this study and is discussed further in Chapters 3 and 4.
1.3.2
Computer Simulations
Experimentally determined values of S ps are often difficult to interpret unambiguously.
a
The orientational ordering of a molecule is governed by many interactions and models must be employed to extract the main contributions to the orientational ordering.
Computer simulations provide an effective complimentary method to the interpretation
of experimental data and can be used to test theories.
Specific interactions that are
thought to be important for orientational ordering such as short-range size and shape,
11
Chapter 1. Introduction
dipole or quadrupole interactions can be incorporated into the simulation algorithm. The
effect of each interaction on the ordering can be examined without interference from other
ordering mechanisms.
A simple but very useful computer simulation method is the Monte Carlo method
using the Metropolis algorithm [29]. In this study, a series of micro-states is generated
with the probability of a particular state being determined from a Boltzmann distribution.
The system is arranged in some initial configuration. One of the particles is randomly
chosen, and a repositioning (eg. translation, rotation) is attempted. The energy difference
between the initial i and final j states, AE = Ej — E{, is calculated. If AE < 0, then
the new position is accepted; if AE > 0, then the new position is accepted with the
probability given by Py = e~ .
0AE
The relationship between experiment, model and
computer simulations is examined in Chapter 4.
1.4
1.4.1
N M R Experiments and their Relation to Orientational Ordering
Dipolar Couplings and Orientational Order Parameters
The second rank orientational order parameters S ps can be determined from analysis of
a
NMR spectral data of orientationally ordered molecules. In particular, dipolar couplings
Dy's between spins i and j contain information on the relative orientation of the internuclear vector between i and j. Unlike NMR spectra of isotropic solutions, the proton NMR
spectra of orientationally ordered molecules contain information about nuclear dipolar
12
Chapter 1. Introduction
couplings between pairs of spins on the same molecule; random rapid translational motion of the molecules causes intermolecular dipolar couplings to be averaged to zero. The
anisotropic molecular reorientation causes the intramolecular dipolar couplings to be averaged to a non-zero value. For relatively inflexible molecules with no large amplitude
motions, S /?'s can be calculated using the relationship
Q
n
Voftlilj v-^
j'cos9gcos9 \
—
^
\—7
/
c
i j
=
P
Q/3
3
{
}
where /J,Q is the magnetic permeability of free space, h is Plank's constant, 7J and
7j are the gyromagnetic ratios of spins i and j, rij is the internuclear distance between nuclei i and j, 9 and 9p are the angles between the internuclear vector and
a
the molecular a and j3 axes (see Fig. 1.2 for an example of axis and angle definitions),
1
_
4
Z
J
Labortroy fixed Z direction
Figure 1.2: The nematic director and magnetic field direction are parallel to the laboratoryfixedZ direction, x, y, z refer to the molecular axis system. As an example, 9 z
is the angle between the molecularfixedx axis and the Z direction, and 9 is the angle
between the internuclear vector r - and the molecular fixed x direction. S /j's and Di/s
are averages over all molecular reorientations and thus 9 z and 9 only represent angles
at an instant in time.
x
X
a
y
x
X
13
Chapter 1. Introduction
and the angle brackets indicate a statistical average over all intramolecular motions.
For isotropic systems S p = 0 and thus Dij = 0. A detailed description of obtaining
a
S ps from Di/s is given in Chapter 2 and a description of basic NMR theory and the
a
application to oriented systems is given in the next section.
1.4.2
N M R Theory
In the highfieldlimit, where the chemical shift, and the direct and indirect dipolar interactions are small compared to the principal Zeeman interaction of the bare nucleus with
the external magnetic field, the proton (spin I = \) NMR spectrum of orientationally
ordered molecules is described by the spin Hamiltonian H,
H =H +H
Z
D
+ Hj
(1.6)
where H is the Zeeman Hamiltonian, Hj is the scalar coupling and HD is the dipolar
z
coupling Hamiltonian. The Zeeman Hamiltonian is given by
N
H = -^huilf
i=l
z
(1.7)
where If is the Z-component of the spin operator for the i spin and Vi are the chemically
14
Chapter 1. Introduction
shifted frequencies which are given by
*i = ^ ( l - * _ _ , , ) •
(1-8)
H is the static external magnetic field, defined to be along the Z-axis. The quantity
0
o~zz,i is the ZZ component of the chemical-shift tensor projected onto the external field
for spin i.
The indirect or scalar Hamiltonian is approximately given by
H = Y hJiiIi-h
J
(1-9)
J
i<j
—*
where
—*
is the scalar coupling constant between spins i and j, and Ii and Ij are the
spin operators for the i and j spins. The general form of this Hamiltonian includes an
anisotropic orientationally dependent component; however, for most couplings involving
protons, the anisotropy is small and is ignored.
The direct dipolar Hamiltonian is given by
H
D
= Y, hDij(3lfl?
i<j
- h • I,),
(1.10)
where Dy is the dipolar coupling constant between spins % and j (see Eq. 1.5, page 12).
For isotropic systems Dij is zero and only the Zeeman and indirect coupling terms are
observed.
Chapter 1. Introduction
15
The eigenstates \$A) and eigenvalues E are obtained from a diagonalization of the
A
Hamiltonian and are parameterized by <7zz,i, Dij and Jy. Thus, the associated spectral
transition frequencies and intensities are also a function of the coupling constants. Spectra are characterized by transitions between eigenstates \<&) and |$B) which, in the case
A
of infinitely sharp lines, is given by
(1.11)
A<B
where UAB — (EA — Eb)/h for eigenvalue energies E and E , I
+
A
I~ = I
x
- U.
Y
B
= I
x
+ U , and
Y
The main NMR selection rule is M - M = ±1 where M and M
A
B
A
B
are the total angular momenta of eigenstates |$^) and |$B). The order oi a particular
coherence is given by the value of MA — M , and the standard high-resolution NMR
B
spectrum (the Fourier transform of the free induction decay acquired after a single pulse)
is characterized by transitions of order ±1.
1.4.3
Simplifying N M R Spectra and Analysis by Multiple Quantum N M R
For simple molecules with < 7 spins the high-resolution NMR spectrum contains at most
a few hundred lines and is usually easy to analyze. For larger spin systems the number
of transitions increases dramatically and the high-resolution spectra become extremely
difficult to analyze. The analysis of spectra can be simplified by acquiring multiple
quantum (MQ) NMR spectra[30-32] (i.e. M - M
A
B
> ±1). The higher order MQ
16
Chapter 1. Introduction
spectra contain far fewer lines than the high-resolution spectra, but contain the same
information about the chemical shifts and coupling constants.
A basic 2D pulse sequence that may be used to generate and indirectly observe MQ
coherences is given by
t2(acquire). (1-12)
Prior to application of the pulse sequence the spin system is at equilibrium and only I
z
magnetization is present. Application of a 90° Y pulse (for example) converts I into
z
I.
x
I
x
evolves under the spin Hamiltonian into other one-quantum coherences during
the preparation time r. The second 90° Y pulse transforms the one-quantum coherences
into all possible MQ coherences. The MQ coherences evolve for the evolution time t\.
The third pulse partially converts the MQ coherences back into one-quantum coherences
which then evolve into the observable I
x
which is recorded as a function of i - Two2
dimensional Fourier transformation and a summed projection onto the / i axis yields a
spectrum of MQ transitions which corresponds to the time evolution of MQ coherences
during the evolution time t\.
During the ti evolution time the chemical shifts are modulated according to their MQ
coherence. Therefore, offsetting the carrier frequency from resonance will separate individual orders. Phase-cycling[33,34] or application offieldgradients[35,36] can selectively
detect particular orders of MQ spectra.
17
Chapter 1. Introduction
Although MQ spectra are easier to analyze and in principal contain the same information as the high-resolution spectrum, poor signal-to-noise and poor resolution (halfheight line-widths of 50Hz) cause the spectral parameters to be somewhat inaccurate.
Therefore the spectral parameters determined from MQ spectra are used only as initial
guesses when analyzing the well-resolved high-resolution spectra. The spectral analysis
using MQ and high-resolution spectra is discussed in Chapter 2.
1.5
Outline of Thesis
The understanding of the intermolecular forces within liquid crystals is not complete.
Short-range repulsive interactions which are based on the size and shape of the molecules
are an important ordering mechanism. Molecular quadrupoles are significant for the longrange contributions, but the form of the quadrupole potential is still much in debate[6,18].
From theory the F s
zz
are predicted to be dependent on the properties of the solute,
whereas from experimental results it is observed that at least the sign of the F
zz
is the
same for all solutes in a particular liquid-crystal solvent. The importance of dipoles for
the intermolecular potential is still uncertain.
One of the objectives of this study is to determine the effects of permanent quadrupoles, dipoles, and molecular polarizabilities on solute ordering. The choice of liquid
crystals and solutes is important to the understanding of orientational ordering mechanisms. From previous NMR studies of D and HD the F 's
2
1
zz
in ZLI 1132 and EBBA
1
M e r c k ZLI 1132 is a eutectic mixture of three irons-4-n-alkyl-(4-cyanophenyl)-cyclohexanes and
18
Chapter 1. Introduction
were found to be of opposite sign and in the special 55 wt% ZLI1132/EBBA mixture the
Fzz is zero. There is evidence that other solutes also experience similar F z^>
Z
m
these
three liquid crystal mixtures. Since the sign and approximate magnitude of the Fzz's
are known for these three liquid crystals, this may help with determining the influence
of dipoles and polarizabilities on orientational ordering.
Since orientational ordering is dominated by short-range interactions, if probe solutes
that have very similar sizes and shapes are compared, differences among orientational
order parameters might then reflect the effects of the additional, weak long-range interactions. It may therefore be possible to examine effects of long-range interactions on the
anisotropic intermolecular potential. Since methyl and chloro constituents have roughly
the same size and shape but different electrostatic properties[38], methyl and chloro substituted benzenes (as well as propyne and acetonitrile) can be used to distinguish between
steric and electrostatic effects on order parameters. Five sets of similar size and shape
molecules have been chosen; the short-range interactions for each set is assumed to be
similar but, due to the various constituent substitutions, the long-range interactions for
molecules within a set are different. Chlorobenzene and toluene represent a group with
dipoles of different magnitudes; p-dichlorobenzene, p-chlorotoluene and p-xylene represent a group in which the chlorotoluene has a dipole and the other two molecules have
no molecular dipole; ra- and o-dichlorobenzene, m- and o-chlorotoluene and m- and oxylene represent two groups where the dichlorobenzenes and xylenes have dipoles that
trans-4-7i-pentyl-(4'-cyanobiphenyl)-cyclohexcine. See Ref. [37] for chemical composition.
Chapter 1. Introduction
19
are collinear with the z molecular axis while the chlorotoluenes have dipoles that have
components along the molecular z and x axes. The last group, acetonitrile and propyne,
was chosen because these are small molecules with a large difference in the magnitude of
their dipoles; it would be expected that effects on the intermolecular potential from shape
anisotropy would be reduced and that the effects from long-range interactions would be
enhanced with these two molecules. See Fig. A.22, page 107 for a representation of the
molecular structure and axes definitions of the solutes.
Chapter 2 focuses on the experimental and analysis methods used to obtain spectral
parameters (and ultimately order and structural parameters) from the complicated NMR
spectra of the solutes co-dissolved in nematic liquid crystals. The spectra are complicated
by having more than one solute dissolved in the sample tube, and methods for disentangling spectra from different molecules are discussed. Structural and order parameters are
determined from vibrationally and non-vibrationally corrected dipolar couplings.
The vibrationally corrected order parameters are utilized in Chapter 3 to examine the
effects of size and shape dependent short-range interactions, and dipoles, quadrupoles
and polarizabilities on the second rank orientational order parameters of the molecules.
The average electricfield,average electric field gradient and the averagefieldsquared are
determined and compared to various theories and models. This is one of a few studies
that utilizes a self-consistent set of order parameters and that estimates the sign and
magnitude of the F z$Z
Chapter 1. Introduction
20
Chapter 4 compares computer simulation results[13,39] with NMR experimental results which were taken from previous studies [8] and from this study. Computer simulations which employed only short-range interactions are compared with NMR experiments
of solutes dissolved in a special liquid crystal mixture where all long-range interactions
seem to be negligible. Results from previous computer simulations using short-range
and point quadrupole interactions are compared with NMR results of solutes in liquid
crystals where long-range interactions are known to be important.
Chapter 2
Multiple Quantum and High—Resolution N M R , Molecular Structure, and
Order Parameters of Partially Oriented Solutes Co-dissolved in Nematic
Liquid Crystals
The material presented in this chapter has either been published in Refs. [40] and [41] or
has been submitted for publication[19].
2.1
Introduction
Nuclear magnetic resonance (NMR) spectroscopy of small molecules orientationally ordered in liquid-crystal solvents can yield precise information about the solute molecular
geometry and second rank orientational order parameters[42,43]. NMR spectroscopy is
one of the few techniques available for the determination of bond distances and bond
angles of molecules in condensed phases, and the method can be used to investigate
possible differences between gas and condensed phase structures. In addition, rotational
potential barriers in molecules such as butane[44] and biphenyl[45] can be examined.
Orientational order parameters are related to anisotropic intermolecular forces and
thus have been used to examine statistical theories of liquid crystals[6,8,14,16,18,20,46,
21
Chapter 2. NMR and Molecular Structure
22
47]. Instead of investigating the order parameters of the liquid-crystal molecules themselves, it is common to examine the orientational ordering of small probe solutes dissolved
in the liquid crystal phase; solutes are chosen so as to emphasize specific anisotropic interactions^, 17,18, 20]. There is general consensus that molecular size and shape dependent
short-range interactions represent the dominant mechanism that is responsible for orientational ordering in nematic liquid crystals. However, additional long-range interactions
are known to be present and since their precise description is a matter of current controversy^, 8,14,16,17,27], the order parameters determined in this study for molecules
of similar size and shape are quite useful for investigating intermolecular potentials (see
Chapter 3 and 4).
The differences among order parameters of solutes may be small and thus accurate
measurements are required. Order parameters determined for molecules in the same
liquid crystal should be measured under identical conditions. Ideally all solutes should
be co-dissolved in the same sample tube but, due to overlap of spectral lines, extracting information from the resultant NMR spectrum may be impractical. It is common
to dissolve solutes in different sample tubes and then to scale the results to account
for variation in the solvent orientational order that results from different sample conditions^, 17, 27,46,48,49]. In an effort to alleviate the problem of scaling, in this study
three or four fully protonated solutes are co-dissolved in the same sample tube. Some
interesting NMR and spectral analysis tricks are developed to disentangle the resultant
complicated proton NMR spectra.
Chapter 2. NMR and Molecular Structure
23
The complexity of high-resolution NMR spectra of partially oriented molecules, and
thus the ability to accurately determine spectral parameters such as chemical shifts and
nuclear coupling constants from such spectra, depends on theflexibilityand symmetry of
the molecules and on the number and type of nuclear spins. For example, the proton NMR
spectrum of complex liquid crystal molecules is typically broad and featureless and therefore impossible to analyze accurately; the rolling base line in the experimental spectrum
of Fig. 2.3 (page 30) is from the liquid crystal. Unfortunately, even with small solutes
that contain « 6 spins, determining spectral parameters from high-resolution spectra can
be extremely difficult. In such cases, the use of two-dimensional multiple-quantum (MQ)
NMR spectroscopy[30-32] is very helpful since there are comparatively fewer lines in the
spectra[44,45,50-53]; for example, compare the high-resolution spectrum of p-xylene
(Fig. 2.4C; page 32) with the 7Q spectrum (Fig. 2.5A; page 34). However, the use of
MQ spectra is not entirely straightforward; the intensities depend on both spectral and
experimental parameters in such a complicated manner that they are unreliable and are
not normally used in the analysis. In addition, care must be taken to avoid an incorrect
and therefore a meaningless "fit." Nevertheless, the analysis is far easier than for the
normal high-resolution spectra.
An additional problem with MQ NMR is the technical limitations that lead to spectra
with broad peaks and poor resolution. Although the relatively few number of lines in
the MQ spectrum can be advantageous, spectral parameters are not determined with
high accuracy. Therefore, parameters determined from MQ spectra are used only as a
24
Chapter 2. NMR and Molecular Structure
starting point when analyzing high-resolution spectra. Despite the poor resolution of
the MQ spectra, often only minor adjustments to parameters determined from such
spectra are required in order to obtain a "fit" to the high-resolution spectrum (see
Refs. [44,45, 52,53]). High-resolution spectra can have many hundreds of lines and thus
obtaining erroneous spectral parameters from a well "fit" spectrum is extremely unlikely.
In this chapter, a strategy for the analysis of high-resolution NMR spectra which
contain resonances from many partially oriented solutes is developed. In some cases 2D
multiple quantum (MQ) NMR spectra are analyzed first. Spectral parameters determined from the analysis of MQ spectra are used as initial estimates in the analysis of
the complex high-resolution spectra which contain resonances from other solutes. The
resultant analyzed spectrum is subtracted from the experimental one and resonances
corresponding to the other solutes are readily visible. From analysis of proton NMR
spectra of the partially oriented solutes propyne, acetonitrile, chlorobenzene, toluene,
p, m- and o-xylene, p, m- and o-chlorotoluene, and p, m- ando-dichlorobenzene, the
chemical shifts, dipolar couplings and for most solutes the indirect scalar couplings were
determined. The dipolar couplings were used to calculate molecular order parameters,
and internuclear distances including the vibrationally corrected r structures.
Q
Chapter 2. NMR and Molecular Structure
2.2
25
Experiment
The nematic liquid crystal Merck ZLI 1132 (see Ref. [37] for chemical composition) and
all solutes were used without further purification. The liquid crystal solvent N-(p-ethoxybenzylidene)-p'-n-butylaniline (EBBA) was synthesized[54] and purified by recrystallization from cold methanol. The composition of each sample is given in Table 2.1. Samples #1-3 were prepared by dissolving 1,3,5-trichlorobenzene and acetonitrile in one of
the liquid crystal solvents: ZLI 1132; 55 wt% ZLI 1132/EBBA; or EBBA. Approximately
400mg of the mixture was transfered into a medium-walled 5mm o.d. NMR tube and thoroughly degassed by several freeze-pump-thaw cycles. Propyne was condensed into the
NMR tube at liquid nitrogen temperature to achieve approximately 5 mol% of propyne
in the mixture. The tube was thenflamesealed under vacuum. Samples #4-25 were prepared by dissolving three or four solutes in one of the liquid crystal solvents mentioned
above. All samples were repeatedly heated to the isotropic phase and thoroughly mixed.
The total solute concentration was « 10 mol%. The solute 1,3,5-trichlorobenzene which
was added to each sample was used as an internal orientational standard.
Proton NMR spectra of Samples #4-25 were acquired at 299.6 ±0.5 K on a Bruker
AMX-500 spectrometer. Acetone-d in a coaxial capillary provided the deuterium lock.
6
Proton NMR spectra of Samples #1-3 were acquired unlocked at 300 ±1 K on a Bruker
CXP-200 spectrometer. For high-resolution proton NMR spectra, 32K point free induction decays were acquired after a single pulse, zerofilledto 64K points and processed
26
Chapter 2. NMR and Molecular Structure
Table 2.1: Solute" and Solvent Composition of Samples
a
6
c
d
Sample #
1
2
3
Solutes
acetonitrile / propyne
acetonitrile/propyne
acetonitrile/propyne
Liquid Crystal Solvent
ZLI 1132
55 wt% ZLI 1132/EBBA
EBBA
4
5
6
chlorobenzene/toluene
chlorobenzene / toluene
chlorobenzene / toluene
7
8
9
p-chlorotoluene/p-dichlorobenzene
p-chlorotoluene/p-dichlorobenzene
p-chlorotoluene/p-dichlorobenzene
ZLI 1132
55 wt% ZLI 1132/EBBA
EBBA
ZLI 1132
55 wt% ZLI 1132/EBBA
EBBA
10
11
12
p-xylene / p-dichlorobenzene
p-xylene/p-dichlorobenzene
p-xylene/p-dichlorobenzene
ZLI 1132
55 wt% ZLI 1132/EBBA
EBBA
13
14
15
o-chlorotoluene / o-dichlorobenzene
o-chlorotoluene/ o-dichlorobenzene
o-chlorotoluene / o-dichlorobenzene
ZLI 1132
55 wt% ZLI 1132/EBBA
EBBA
16
17
18
o-xylene/o-dichlorobenzene
o-xylene/o-dichlorobenzene
o-xylene/o-dichlorobenzene
ZLI 1132
55 wt% ZLI 1132/EBBA
EBBA
19
20
21
m-chlorotoluene/m-dichlorobenzene
m-chlorotoluene / m-dichlorobenzene
m-chlorotoluene /m-dichlorobenzene
ZLI 1132
55 wt% ZLI 1132/EBBA
EBBA
22
23
24
m-xylene/m-dichlorobenzene
m-xylene /m-dichlorobenzene
m-xylene /m-dichlorobenzene
ZLI 1132
55 wt% ZLI 1132/EBBA
EBBA
25
o-xylene / o-chlorotoluene / o-dichlorobenzene
ZLI 1132
6
c
d
Total solute concentration is « 10 mol%.
The orientational standard 1,3,5-trichlorobenzene was also co-dissolved in each sample.
See Ref. [37] for chemical composition.
EBBA refers to N-(p-ethoxybenzylidene)-p'-n-butylaniline.
Chapter 2. NMR and Molecular Structure
27
using a Lorentzian line broadening of 1.0 Hz. Half height line widths were typically
2-3 Hz. Typical spectra (obtained from Samples #1 and #11) are presented in Figs. 2.3
and 2.4 (pages 30 and 32). An expansion region of Fig. 2.4 is presented in Fig. 2.6
(page 35). For samples which contained p-xylene, two-dimensional selective 7Q and 8Q
spectra were acquired whereas for samples which contained m- and o-xylene, only 8Q
spectra were acquired using the pulse sequence [33,34]
(2.13)
with 1000-1500 increments in t\ and for each ti increment 1024 points were collected in t ;
2
a one dimensional MQ spectrum was produced by zero filling to 2048 in ti, 2D magnitude
Fourier transforming and performing a summed projection onto the Fi axis. To selectively
detect specific M-quantum coherences, the pulse sequence 2.13 is applied M*2 times for
each ti increment with the collected FID's alternately added and subtracted; the phase
<j> of the first and second pulse is incremented by (M*2)/360 degrees relative to the third
pulse (and receiver) for each application of the pulse sequence[33,34]. For example to
selectively detect 8-quantum coherences, the pulse sequence is applied 16 times for each
ti increment and the phase of the first and second pulse is incremented by 22.5° after
each application of the pulse sequence 2.13. While in principal this pulse sequence also
permits detection of ±k * 7-quantum or ±k * 8-quantum spectra, where k = 2,3,...,
this was not a problem since for a n-spin-| system, n is the highest attainable MQ order;
28
Chapter 2. NMR and Molecular Structure
for the MQ spectra which were recorded, only the xylenes possessed > 7 or 8 spins.
The intensity of MQ lines is highly dependent on the r value and therefore at least two
MQ spectra with two different r values between 10-21 milliseconds were acquired in an
attempt to detect all 7- or 8-quantum transitions. The recycling time was 4 seconds.
The 7-quantum spectrum obtained from Sample #11 is presented in Fig. 2.5 (page 34).
2.3
Spectral Analysis and Strategy
The proton NMR spectrum of orientationally ordered molecules is dependent on the
flexibility and symmetry of the molecules and on the number and type of nuclear spins;
for example, compare the complexity of the spectra for acetonitrile, propyne, p-dichlorobenzene, p-xylene and the liquid crystal (Fig. 2.3, page 30 and Fig. 2.4, page 32). Spectral
parameters of small solutes can be determined accurately by analyzing the experimental
spectrum using the spin Hamiltonian (which is equivalent to the Hamiltonian presented
in Eqs. 1.6-1.10, pages 13-14)
f
= - _ > t f + E E [( «+w*) ? !
J
i
where I ,I
Z
+
and Jij and
i
1
1
+
\ v «
-
Dv)&*7+int)]
( 2
1
4
)
j>i
and I~ are the spin operators, Ui is the resonance frequency of nucleus i,
are the indirect and dipolar coupling constants between nuclei i and j
on the same molecule.
To analyze experimental spectra, initial estimates of spectral parameters U{,
and
Chapter 2. NMR and Molecular Structure
29
Dij, either from previous studies or a "best guess," are required. The best guess may
be from the D^'s of similar molecules dissolved in the same liquid crystal. From the
estimates of the spectral parameters, a trial spectrum is calculated using Eq. 2.14 and
the appropriate selection rules for high-resolution or MQ spectra. Experimental and calculated spectra are compared and spectral parameters are manually adjusted until the
overall structure of the calculated spectrum is similar to the experimental. The calculated frequencies are then assigned to the experimental ones and spectral parameters are
adjusted by a least-squaresfittingroutine. Frequencies are repeatedly assigned and/or
unassigned and parameters adjusted until a reasonable fit to the experimental spectrum
is obtained; this is the most time consuming portion of spectral analysis. Assignment
of calculated to experimental frequencies was performed with the aid of a macro driven
graphical interface program SM . The macro was designed so that experimental frequen1
cies could be matched to calculated frequencies using cursor controls. Care was taken to
avoid assignment of overlapping or unresolvable lines and experimental frequencies were
determined from a five point weighted average about the maximum intensity point. In
all cases the frequencies were no more than 0.2 Hz different from a standard Bruker peak
picking routine for lines with half height line width < 3 Hz.
High-resolution spectra for samples which contained propyne, acetonitrile and 1,3,5trichlorobenzene (Fig. 2.3) were relatively easy to analyze. The spectrum of 1,3,5-trichlorobenzene
The back-end graphical interface program SM (Edition 2.2.0. Jan. 1992) is a configurable plotting
program written by Robert Lupton (Princeton University) and Patricia Monger (McMaster University).
1
30
Chapter 2. NMR and Molecular Structure
VJJL-^
ttjj
o o
CH -C=N
©
o © o o
©
i L-
3
©
LiUL
3
CH -C=C-H
©
li
Jul
5000
-5000
10
4
Frequency
Figure 2.3: The experimental high-resolution spectrum (top) is of Sample #1. The main
triplet from acetonitrile has been truncated. The calculated spectra of acetonitrile and
propyne (values from Table B.6) are in the middle and on the bottom. The two sets of
doublets from the coupling to the two C nuclei are visible in the experimental and calculated (indicated with a o) spectra of acetonitrile and are required in order to determine
the absolute sign of DHH- Resonances marked with an * are from 1,3,5-trichlorobenzene
and resonances marked with a J and the many low intensity resonances around the center
of the spectrum are from unknown impurities. In the experimental spectrum, the rolling
base line which is approximately 50 kHz wide is from the liquid crystal molecules.
13
31
Chapter 2. NMR and Molecular Structure
is a triplet with a splitting of 3 x DHH- Thus, the DHH could be determined without
the aid of a least-squares fitting routine. For the spectrum of acetonitrile, there is a
triplet with a splitting of 3 x DHH and there are two sets of doublets centered around
each of the lines of the triplet which are due to the two H - C
1
are (2 x
DHC
13
+
JHC ),
13
and the H - C
1
13
13
couplings. The splittings
couplings were required in order to determine
the absolute sign of DHH- The spectrum of propyne is slightly more complex and thus,
DHH were determined using the least-squares routine. However, it is still quite trivial
to analyze and only the proton-proton dipolar couplings were required; the absolute sign
of the D H were defined by setting the initial value of the J coupling to the isotropic
H
value of —3.551 [55] (see Fig. A.22, page 107 for the structure and atom numbering of the
solutes and Table B.6, page 109 for the spectral parameters determined from the spectral
analysis).
Determining spectral parameters from the high-resolution spectra of p-xylene is very
difficult; p-xylene has two resonance frequencies and seven independent dipolar couplings.
Without accurate estimates of such parameters, it may require months to analyze the
high-resolution spectrum (see Fig. 2.4). For a typical spectral analysis method of such
complicated spectra, the MQ spectrum is analyzedfirstto obtain estimates of spectral
parameters which are used as initial parameters in the analysis of the high-resolution
spectra; accurate spectral parameters are then obtained from the high-resolution spectrum. Within the least-squares routine, the non-equivalent D^s are adjusted independently. For p-xylene seven independent D^'s and two resonance frequencies were
Chapter 2. NMR and Molecular Structure
i
i
i
-lxlO
i
4
i
'
'
i
-5000
i
i
i
i
I
32
i
i
0
Frequency /Hz
i
i
I
5000
i
i
i
i
I
1
1
10*
Figure 2.4: The experimental high-resolution spectrum C is of Sample #11, partially
oriented p-xylene, p-dichlorobenzene and 1,3,5-trichlorobenzene (TCB) in 55 wt% ZLI
1132/EBBA at 299 K. Spectrum B is the calculated spectrum of p-xylene from the fit
to spectrum C. Spectrum A is a subtraction of the calculated from the experimental
spectrum. Since experimental lines had a broad base, the subtraction was performed
using a calculated spectrum in which the lineshape is the addition of two Lorentzians
with line broadenings of 1 and 4 Hz. Note that resonances corresponding to the external
lock signal (acetone-d in a capillary tube), TCB and p-dichlorobenzene are clearly visible
in the top spectrum. Lines from the 1,3,5-trichlorobenzene (TCB) triplet have been
truncated.
6
Chapter 2. NMR and Molecular Structure
33
determined from about 45 lines from the 7Q (Fig. 2.5 and Table B.6, page 109) and
8Q spectra; it must be remembered that intensities in the calculated MQ spectrum are
meaningless. There is a chance that the spectral parameters determined from analysis of
the MQ spectra are incorrectly determined. However, for p-xylene this was not the case;
the agreement between experimental and calculated spectral line positions is excellent.
Spectral parameters obtained from the fit to the MQ spectrum were then used to
calculate the high-resolution NMR spectrum, and a section of the spectrum from Sample #11 is shown in Fig. 2.6D. Most peaks can be assigned immediately to lines in the
experimental spectrum (compare Figs. 2.6C and 2.6D). As has been found for several
other complicated spin systems[44,45,52], a correct fit to the MQ spectrum can give a
prediction of the high-resolution spectrum that is amazingly close to the experimental
spectrum. In the current case, the fit to the high-resolution spectrum is complicated
by the presence of lines from the extra two solutes. Once spectral parameters for the
MQ spectra were determined, the high-resolution spectra were analyzed within hours
and the spectral parameters obtained are given in Table B.6, page 109. The spectrum
calculated from the parameters in Table B.6 for Sample #11 is presented in Figs. 2.4B
and 2.6B. The excellent quality of the fit to the high-resolution spectrum of p-xylene is
demonstrated by subtracting the calculated (Figs. 2.4B and 2.6B) from the experimental
(Figs. 2.4C and 2.6C) spectrum, the result being presented as Figs. 2.4A and 2.6A. The
experimental p-dichlorobenzene and 1,3,5-trichlorobenzene spectra are readily observed
34
Chapter 2. NMR and Molecular Structure
J
0
10
4
I
I
L
2xl0
J
4
I
I
_
3xl0
Frequency /Hz
_l
4
I
I
L_
_L
4xl0
_i
4
i
i
i_
J
5xl0
4
Figure 2.5: The experimental +7-quantum spectrum A is of Sample #11. Only resonances from p-xylene are observed; for an n-spin-| system, n is the highest attainable
MQ order. Spectrum B is the calculated +7-quantum spectrum of p-xylene. Note the
line width in the experimental spectrum is approximately 50 Hz and the intensities of
the calculated spectrum do not correspond with those of the experimental.
35
Chapter 2. NMR and Molecular Structure
LLJ
J
1000
I
I
L
1500
J
I
l_
Frequency/Hz
J_
2000
J
l_
D
J
2500
Figure 2.6: The top three spectra A, B and C are an expansion of Fig. 2.4. Spectrum
D is an expansion of the spectrum predicted from the "fit" to the 7-quantum spectrum.
Note the line positions and intensities between the 7-quantum prediction and the experimental spectra are in sufficiently good agreement that only minor adjustments to
spectral parameters were required in order to "fit" the experimental spectrum. In the
experimental spectrum, the average line width at half maximum height is 2-3 Hz. The
intensities of the calculated spectrum closely correspond with those of the experimental
one. In spectrum A, resonances indicated with an * are from p-dichlorobenzene.
36
Chapter 2. NMR and Molecular Structure
and were easily analyzed. For each sample which contained p-xylene, the complete determination of the spectral parameters obtained by starting from the MQ spectra and
then analyzing the high-resolution spectrum required only a month.
Unfortunately, for o- and m-xylene, the sparsity of lines in the MQ spectra and the
number of adjustable spectral parameters caused problems when attempting to fit the
£>ij's independently; this is not uncommon when analyzing MQ and some simple highresolution spectra. Spectral parameters may be meaningless even though the spectrum
appears to be "fit". The problem can be overcome by realizing that Dy's can be related
to molecular orientational order parameters and structural parameters (eg. Eq. 1.5,
page 12). The number of adjustable parameters required to analyze the spectrum can be
significantly reduced which will greatly simplify the analysis; for example, o-xylene has
ten independent A / s but only two independent S^'s and a couple of crucial structural
parameters. It should be noted that the calculated frequencies are very sensitive to minor
changes in structural parameters and thus reasonably good estimates of proton positions
are required for this method to succeed.
For the essentially inflexible molecules in this study the D 's can be calculated from
y
Eq. 1.5 (page 12). The least-squares routine was modified so that 5 j's, structural
Q/
parameters and/or D^-'s for an arbitrary molecule can be adjusted independently; within
thefittingroutine Di/s (which are still required for the calculation of the spectrum from
Eq. 2.14, page 28) are calculated from 5 g's and structural parameters. However, if a Dij
Q/
is to be adjusted independently, it is not calculated from S ps and structural parameters,
a
37
Chapter 2. NMR and Molecular Structure
but allowed to freely vary. Thus, the dependence of the A / s on 5 g's is removed; this
a/
is useful, for example, if the molecule has internal rotations where the potential barrier
is uncertain or if specific structural parameters are not well known. Derivatives of the
line positions with respect to the Dj/s are calculated analytically. The derivatives of the
line positions with respect to the S^'s and structural parameters are calculated using
finite difference and structural data obtained from other studies. This is similar to a
fitting method presented in Refs. [45] and [52]; however thefittingroutine described in
Refs. [45] and [52] was designed for a specific molecule and only allowed for adjustment
of S
zz
and S
xx
Syy.
Analysis of the very complicated spectra from o- and m-xylene is exemplified with
Sample #25 (o-xylene/o-chlorotoluene/o-dichlorobenzene/1,3,5-trichlorobenzene in ZLI
1132). The 8Q spectrum was analyzed first using the modified version of the fitting
program. 5 j's and resonance frequencies were adjusted until a reasonable fit to the 8Q
a/
spectrum was obtained. Then using the original version of the MQ analysis program
the .Dy's and resonance frequencies were more accurately determined (Fig. 2.7). The
values obtained for Sample #25 are presented in square brackets in Table B.6 and in
Table B.7 (pages 109 and 122) for the other solute molecules. As was the case for pxylene, the predicted high-resolution spectrum of o-xylene (Fig. 2.8B) is very similar to
the experimental (Fig. 2.8A) and in most cases only minor adjustments to the spectral
parameters were required to fit the high-resolution spectrum (Fig. 2.8C).
After analysis of the high-resolution spectrum the resultantfittedspectrum of either
38
Chapter 2. NMR and Molecular Structure
i
0
i
i
i
I
5000
i
i
i
i
I
10
4
i
i
i
i
I
i
1.5xl0
Frequency
4
i
i
i
I
2xl0
i — i — i — 1 _
4
2.5xl0
4
Figure 2.7: The experimental +8-quantum spectrum (top) is of Sample #25. The calculated +8-quantum spectrum of o-xylene (from values in square brackets from Table B.7,
page 122) is on the bottom.
Chapter 2. NMR and Molecular Structure
39
-
a
,LlMi I J l l i J i l i l ^
Exp
^
(predicted from
8Q analysis)
H 3
, ig.uJa,,i\i.liliiiLii il ilJiiLJ llilllkJkli JLJLU B
C H i
C^CH
L
JAL 11L1IJkllbll,,iii C
3 ..i^L.,
A- C
0
A
I
JUUi.I j.Mlil|,^.|,yMll>Mi|Wi
JlD
/CH3
(calc.)
Nilml
^Cl
D- E
• *4
Llii.L i llill E
<tt
CI
||
(calc.)
CI
* *1
ll 1 ill 11 ill, 1,
LL
1
1
1
i i
-5000
1
11
c
1
*
*
* t
j
O
F- G
1
t
i
i
i
1i
ii i 1
i
0
5000
-3000
-2000
-1000
Frequency
Frequency
Figure 2.8: The caption to thisfigureis on the next page.
i
H
i 1
1
i
Chapter 2. NMR and Molecular Structure
40
Figure 2.8: Spectral analysis strategy: Full spectra are displayed on the left and expansions are displayed on the right. A is the experimental spectrum of Sample #25. B
is the predicted o-xylene spectrum from the parameters determined by analysis of the
8Q spectrum (Fig. 2.7). Spectrum C is calculated from the fit to the high-resolution
spectrum of o-xylene. Note that there are only minor differences between spectra B and
C. Spectrum D is the difference between A and C. The negative residuals in Spectrum D
are due to slight differences between the line shapes of the calculated and experimental
spectra. The calculated spectrum of o-chlorotoluene is E and F is the difference between D and E. Spectrum G is the calculated o-dichlorobenzene spectrum and H is the
difference between F and G. Note that when calculated spectra are subtracted from experimental, resonances from the.other molecules are readily visible. Resonances marked
with an * are from 1,3,5-trichlorobenzene. Resonances indicated with a $ are impurities
and the resonance indicated with a o is from the partially protonated acetone used for a
field/frequency lock. The calculated spectrum of 1,3,5-trichlorobenzene is not displayed.
For high-resolution spectra intensities of the calculated spectrum closely correspond with
those of the experimental spectrum.
o- or m-xylene was subtracted from the experimental one and resonances from the other
solutes could be identified (see Fig. 2.8D). For samples which did not contain o, m- or pxylene (or acetonitrile and propyne) analysis of the high-resolution spectrum begins with
this step in the strategy. The initial dipolar couplings for the o-, m- or p-chlorotoluenes
were estimated from the order parameters of o-, m- or p-xylene in the same liquid crystal.
The initial estimates for chlorobenzene and toluene were taken from previous studies. For
the spectrum of toluene, and o- m- and p-chlorotoluene, there is a group of resonances up
frequency ( « +4000Hz) from the main portion of the spectrum (for o-chlorotoluene see
Figs. 2.8D and E). Thefinestructure is due to the A / s between methyl and ring protons,
and by assigning some of these resonances certain A?'s could be roughly determined
which aided with the identification of resonances in the main portion of the spectrum.
Chapter 2. NMR and Molecular Structure
41
Once a few resonances within the main portion of the spectrum were correctly assigned
the spectrum was analyzed quickly.
Again after the high-resolution spectrum of toluene or chlorotoluene wasfittedand
subtracted from the experimental spectrum, resonances from chlorobenzene or dichlorobenzene were easily identified (eg. Figs. 2.8F and G). In Fig. 2.8H only a few resonances
remain after thefittedo-xylene, o-chlorotoluene and o-dichlorobenzene spectra are subtracted from the experimental one. The remaining resonances correspond to 1,3,5trichlorobenzene, acetone-d (from lock) and an unknown impurity. The complete anal5
ysis of the very complex 8Q and high-resolution spectra of o- and m-xylene was reduced
to less than a week.
It should be emphasized that one of the objectives of this study is to determine
accurate S^'s and structural parameters and thus precise Aj's are required. Due to the
poor resolution (line-width « 50Hz), to the possible correlations between some A / s , and
to the sparsity of lines in the MQ spectra, D 's from analysis of the MQ spectra are rather
y
imprecise. Thus it is prudent to analyze the complex high-resolution spectra. Some of
the Aj's from the MQ analysis differ significantly from those determined from the highresolution spectra (refer to Table 2.2 which contains a subset of the data presented in
Table B.6). These discrepancies would have a significant effect on the calculated S ps
a
and structural parameters.
Chapter 2. NMR and Molecular Structure
42
Table 2.2: Selected Dipolar Couplings" from Table B.6
Sample #
10
16
16
17
17
17
23
23
23
Solute
p-xylene
o-xylene
o-xylene
o-xylene
oxylene
o-xylene
m-xylene
m-xylene
m-xylene
c
d
d
d
d
d
d
d
d
Value of Du from
Dij high-resolution multiple quantum
-2733.9
-2670.51.
Di,
-1083.9
-1157.11
D
1425.5
1508.17
-240.7
-140.23
A,3
-505.4
-588.10
£>2,3
13.4
-69.81
D ,5
-1139.4
-1080.34
A,2
-744.2
-697.73
D ,5
1510.8
1426.23
D,
c
2
lt2
2
4
5 e
For atom numbering refer to Fig. 2.9 (page 44). There are significant differences between the Di/s determined from analysis of the high-resolution and MQ spectra. This
will cause large inaccuracies in the calculated molecular parameters.
Dipolar couplings are in Hz.
Values determined from the analysis of the 7-quantum specturm.
Values determined from the analysis of the 8-quantum specturm.
a
6
c
d
2.4
2.4.1
Molecular Structure and Order Parameters
Calculations
Except for o-chlorotoluene, relative positions of the nuclei (Tables C.8, C.9, C.10,
C.ll and C.12; pages 125-133) and 5 's (Tables D.13, and D.14; pages 137 and 141)
Qj3
were calculated from a simultaneous fit to the Z) 's determined for the solute in all
y
three liquid crystals. Since the spectrum of o-chlorotoluene in EBBA (Sample #15)
was of poor quality, molecular parameters for o-chlorotoluene were calculated using A / s
43
Chapter 2. NMR and Molecular Structure
from o-chlorotoluene dissolved in ZLI 1132 and 55 wt% ZLI 1132/EBBA. The 5 's
Q/3
of o-chlorotoluene in EBBA were calculated using the structure determined from the
other liquid crystals. Calculations were performed using Eq. 1.5 (page 12), a priori
estimates[56] and a least-squares minimization routine NL2SNO[57] which minimizes
the square of the difference between experimental and calculated D^s. The a priori
estimates are values of structural parameters (taken from other studies) that have an
associated error and are adjusted in the least-squares routine; large deviations from the
a priori estimates are discouraged by the least-squares criteria.
Dipolar couplings within the methyl group and between methyl and ring protons are
an average over the methyl rotation; -D^'s were calculated for each 15 degree rotation of
the methyl group. For o-xylene, the Case II rotational potential and potential parameters
reported by Burnell and Diehl[58] was used; the potential was expanded as a Fourier series
about the rotation angles OL\ and a.2 of the two methyl groups
V — V^l—cos3a+ cos3a_)+\4 cos6a++V^ cos6a_+V (l—cos6a+ cos 6a_)+... (2.15)
r
6
where a
+
= |(ai + 0:2), a_ = \{ai - a ), and V
2
3
=
8.4,14
= 1-21, V = 1.55,
g
and 14 = O.OkJ/mol. For o-xylene, the potential minimum (at ai = 0 and a = 0)
2
is where protons 5 and 10 of the methyl groups are in the plane of the benzene ring
and adjacent to protons 4 and 1 (see Fig. 2.9 for atom numbering). For o-chlorotoluene
only the three fold potential is used; a , V , V and V arefixedat zero, V is fixed at
2
a
g
&
3
Chapter 2. NMR and Molecular Structure
44
6 kJ/mol[59,60] and the potential minimum (at cei = 0) is where proton 5 is in the plane
of the benzene ring and adjacent to proton 4. For toluene, m- and p-chlorotoluene, and
m- and p-xylene, each methyl group was independently modeled with a six fold potential V = VQ(1 — cos6o:)/2 where V is fixed at 0.060 kJ/mol[59] and the minimum in
E
the potential is where one proton of the methyl group is perpendicular to the benzene
ring. In the approximation that a P (cos0) bond additive interactional] describes the
2
orientational potential, and that the methyl group retains C 3 symmetry upon rotation,
the orientational potential is invariant to the methyl rotation.
45
Chapter 2. NMR and Molecular Structure
Since the D^s are related to < r
- 3
>, molecular vibrations will affect the experimen-
tal observations. The effect of vibrations on the experimental data will be different for
different experimental techniques. Therefore, to compare data determined from various
experimental methods results should be "vibrationally corrected" . The effect on the
2
dipolar couplings from normal mode vibrations is calculated using a Taylor expansion of
Dij about the equilibrium position
6
S
where Dfj is the dipolar coupling at equilibrium, 8 is the x', y',and z' internuclear axes,
(AS) is the average vibrational amplitude (anharmonic) in the 6 direction and (A5 ) is
2
the corresponding mean-square amplitude (harmonic). The average structure determined
by subtracting the contributions from harmonic vibrations, the r structure, has been
Q
established as a suitable physical basis for comparing results [66-69]. The average r
a
structures determined from different techniques are usually in good agreement with each
other. A calculation of the r structural parameters and S p s (Tables C.8, C.9, C.10,
:
a
a
C.ll and C.12 and Tables D.13 and D.14; ) was performed using a version of the leastsquares routine that was modified to include the subroutine VICO[55,70] which corrects
In this study molecules axe in an anisotropic condensed phase; the anisotropy of the phase affects
vibrational motions (orientational-vibrational correlations). Corrections have been calculated for simple
molecules such as CH462], acetylene[25], benzene[63], chlorobenzene[63], and CH3F[64]. For molecules
with a large Sap's, the orientational-vibrational correlations will have a very small effect ( « 0.2%) on
the observed Djj's[63,65]. Normal mode bond vibrations have a larger effect ( « 2.0%) on the observed
.Djj's[65] and thus only corrections for these effects have been attempted.
2
46
Chapter 2. NMR and Molecular Structure
for the non-negligible effects of normal mode molecular vibrations using Eq.2.16. Mean
square amplitudes (Ao~) were calculated using the program MSAV[71] from normal mode
2
vibrational analysis using force constants from Refs. [72], [73], [74] and [75].
2.4.2
Molecular Structure
One of the goals of this study is to report accurate S ps which in turn could be utilized
a
when examining statistical theories. Since D^s are products of order and geometric
parameters, it is essential when determining accurate S^'s to carefully consider the
molecular structure. Thus, geometric parameters have been determined using a priori
estimates and vibrationally and non-vibrationally corrected Z? -'s. The relative values of
y
the proton coordinates reported in Tables C.8, C.9, C.10, C . l l and C.12 (pages 125133) are from simultaneous fits to the D^'s obtained in three different liquid crystals
for each molecule except for o-chlorotoluene. The use of more than one liquid crystal
provides extra independent equations for the fitting procedure.
In order to determine the complete molecular structure, it is necessary to fit the
proton geometry to the carbon skeleton. The error associated with the resulting structure
is difficult to determine. Bond angles are probably not accurate to better than 0.2
of a degree, and CH bond distances to O.OlA. Thus the statistical uncertainties (68%
confidence level) for the values reported in Tables C.8, C.9, C.10, C . l l and C.12 are
optimistic.
47
Chapter 2. NMR and Molecular Structure
Unfortunately r structural data for toluene, o- and m-chlorotoluene and o- and mQ
xylene could not be found in the literature. Even-though the a priori estimates for
these molecules were obtained from a combination of data from various other studies,
it is noteworthy that most of the calculated structural values (vibrationally and nonvibrationally corrected) do not differ greatly from these a priori estimates. However,
there are some exceptions and it is difficult to ascertain the nature of the discrepancies
but it is most likely due to the inaccuracies of the a priori estimates.
For the other molecules, the calculated structural values are very similar to those
previously determined r values from electron diffraction studies. However, it is well
a
known that proton coordinates are difficult to determine by electron diffraction and the
new NMR values for chlorobenzene, p-, o- and m-dichlorobenzene, p-chlorotoluene and
p-xylene are taken to be more reliable.
2.4.3
Order Parameters
It is generally accepted that anisotropic short-range repulsive forces are primarily responsible for the orientational ordering of liquid crystals [9-13,76]. Controversy has arisen over
the importance of anisotropic long-range interactions[6,14,16,18]. The spectra in this
study have been recorded in such a manner so that the 5 a's obtained can be used to exQ|
plore various models for the anisotropic potential. A detailed quantitative analysis of the
anisotropic intermolecular potential using the vibrationally corrected S ps is presented
a
in Chapter 3.
48
Chapter 2. NMR and Molecular Structure
2.5
Summary
In this study spectral, orientational order, and structural parameters (including vibrationally corrected molecular parameters) for p-, o and m-disubstituted benzenes,
chlorobenzene, toluene, propyne and acetonitrile co-dissolved in various liquid crystals
were determined. Resonance frequencies and dipolar couplings for p-xylene were estimated by analyzing the 7 and 8Q spectra and adjusting the resonance frequencies and
dipolar couplings independently whereas for. o and m-xylene the resonance frequencies
and Saps were estimated by analyzing the 8Q spectra using a modified version of the
least-squares fitting routine which could adjust S ps, structural parameters, and/or Di/s
a
independently. With this modified version of the program, the time required for analysis
was greatly reduced. More accurate resonance frequencies and D^s were then determined
with the original MQ program and used as initial estimates when accurately determining
spectral parameters from the high-resolution spectra. After the high-resolution spectra
were fitted, the calculated spectrum was subtracted from the experimental one and resonances from the other molecules were identifiable. The spectra of the other molecules
were then analyzed one by one and subtracted from the experimental spectrum. This
is one of very few studies where many solutes were co-dissolved in a liquid crystal solvent and where MQ spectroscopy and analysis of the MQ spectra by adjusting 5 g's was
Q|
utilized in a successful attempt to simplify the analysis of high-resolution spectra.
Chapter 3
Dipole-Induced Ordering in Nematic Liquid Crystals:
The Elusive Holy Grail
The material presented in this chapter has been submitted for publication in Ref. [19].
Analysis of non-vibrationally corrected order parameters of toluene, chlorobenzene, pdichlorobenzene, p-chlorotoluene and p-xylene have been published in Ref. [18].
3.1
Introduction
Nematic liquid crystals are fluid phases which are characterized by long-range orientational correlations but no long-range positional correlations of the component molecules.
The orientational ordering of molecules within liquid-crystal phases mainly arises from
size and shape dependent anisotropic short-range interactions[8-14] and to a lesser extent from anisotropic long-range interactions [6,15-17] such as interactions that involve
molecular dipoles, quadrupoles and polarizabilities. An important objective when studying liquid crystals is to gain a detailed understanding of the effects of the intermolecular
potential on the structure of the phase[6,8,14,16,39,76-79]. The roles of the various
49
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
50
contributions to the intermolecular potential have been investigated by choosing, for example, solutes with particular properties, or by choosing a liquid crystal solvent that may
have special properties [8].
One such liquid crystal with special properties is a mixture of 55 wt% ZLI 1132 (see
Ref. [37] for chemical composition) in EBBA (see Fig. 1.1, page 3); from deuterium NMR
studies of D and HD, it was determined that for this particular mixture there is no con2
tribution to the orientational potential from anisotropic long-range quadrupole interactions^]. From other NMR studies, the orientational order parameters of a wide collection
of solutes dissolved in this mixture were very well predicted by various mean-field models
that only incorporate the details of the molecular size and shape anisotropy[8]; it was
concluded that all solutes experience roughly the same environment, and that size and
shape dependent short-range repulsive interactions were the principal factor responsible for the solute orientational ordering. More recently, a computer simulation study
of hard ellipsoids [13], undertaken to compliment this experimental work, confirmed the
connection between these model potentials and the short-range forces, and provided further convincing evidence that short-range forces dominate the orientational behavior of
molecules in nematic solvents.
The choice of probe molecules permits another means of disentangling the many factors that influence the behavior of liquid crystalline systems. Evidence for a solute molecular quadrupole-liquid crystal electric field gradient ({EFG)) interaction was obtained
from several studies employing D and HD as a solute in nematic liquid crystals[20-23,80].
2
51
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
In other studies acetylene, like D , was found to have a negative order parameter in the
2
nematic solvent EBBA [24, 25]; EBBA is a solvent which was determined from the D and
2
HD studies to have a negative (EFG). The counter-intuitive negative order parameter
is the predicted result for a positive quadrupole/negative (EFG) interaction. Similarly,
the behavior of the order parameters for benzene and hexafluorobenzene, molecules with
very similar shapes but with quadrupole moments of opposite signs, follows the pattern predicted from the quadrupole moment/{EFG) mechanism [26]. These experiments
demonstrated that interactions involving molecular quadrupoles provide an important
orientational mechanism. For a particular liquid crystal, the (EFGYs determined from
the dissolved solutes are the same sign and same order of magnitude. Therefore, it was
concluded [8] that within a particular liquid crystal all solutes experience roughly the
same average environment regardless of the size, shape or electrostatic properties of the
solute.
The concept of a solute-independent mean-field has been criticized by Photinos et
al. [6,17,27]; this type of model was inconsistent with their theoretical calculations. They
predicted that short- and long-range interactions were approximately equal in magnitude, that long-range interactions were mainly from quadrupoles and dipoles and that
the long-range interactions were sensitive to the magnitude, position and orientation of
the multipole. Emsley, Luckhurst and coworkers have also discussed the significance of
the solute-independent (EFG) using a theory for orientational ordering which is closely
related to the Maier-Saupe theory of nematics[16,28,81]. In the context of this theory,
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
52
it was shown that the nematogen quadrupole was the lowest order multipole that contributed to a non-vanishing (EFG).
In an experimental study to compliment the theory,
it was concluded that the (EFGYs were strongly dependent on both solvent and solute
molecular properties.
From recent computer simulations [39] which employed a point quadrupole electrostatic model, the sign and magnitude of the (EFG)'s sampled by solutes were also found
to be highly sensitive to the shape and electrostatic properties of the solutes. This is
in contrast to most experimentally determined (EFGYs; for a particular liquid crystal,
solutes experience (EFGYs which are at least the same sign. From the computer simulation studies it was also concluded that the origin of the discrepancy was most likely the
inadequacy of using point quadrupoles for dense systems and an improved description
of molecular electrostatic interactions will likely be essential in order to generate solute
orientational behavior consistent with that observed experimentally. Nevertheless, these
computer simulations can be used to test the accuracy and reliability of theories; the
simulations represent an exact system for the theories of Emsley et al. [16,28,81] and
Photinos et al.[6,17,27]. The orientational ordering predicted by the Emsley theory was
found to be qualitatively consistent with the computer simulations. However, due to
the mathematical approximations and the inadequacy of the electrostatic potential, predictions of the long-range contributions to the orientational ordering were not accurate.
For the Photinos theory, the orientational ordering predicted for the hard-body computer
simulations were drastically underestimated by the theory. Due to the inadequacy of the
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
53
short-range potential, the long-range electrostatic contributions were not evaluated.
Regardless of the inadequacies of the short-range potential with the Photinos et al.
theory, they suggested that molecular dipoles are an important orientating mechanism,
especially if the dipole is not located at the geometrical centre of the molecule[17,27]. In
the context of the Emsley and Luckhurst mean-field theory, for apolar nematic phases the
average electric field is necessarily zero and thus the contributions to the orientational
potential for dipoles should vanish.
An understanding of intermolecular forces within liquid crystals is not complete.
There are discrepancies among results from theory, experiment and computer simulations. Nevertheless, there is an agreement that short-range repulsive interactions which
are based on the size and shape of the molecules are an important ordering mechanism,
and that molecular quadrupoles are significant for the long-range contributions; the form
of the quadrupole intermolecular potential is still in much debate[6,18]. From theory and
computer simulations the sign and magnitude of the (EFG) is found to be dependent
on the solute properties whereas from experiments it is observed that at least the sign of
the (EFG) is the same for all solutes in a particular liquid-crystal solvent[8,24-26]. The
importance of dipoles to the intermolecular potential is still uncertain.
The objective of this study is to determine the effects of permanent quadrupoles,
dipoles, and molecular polarizabilities on solute ordering. The reasoning for the choice
of probe solutes is outlined in Chapter 1, Section 5.
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
3.2
54
Experiments and Results
A major concern when comparing experimental with theoretical or computer simulation
results is the lack of consistent experimental data. Typically, solutes are dissolved in
different sample tubes and then results are scaled to account for the variation in the
solvent orientational ordering that results from different sample conditions. In an effort
to alleviate the ambiguity with the scaling of S p, molecules were co-dissolved in the
a
same sample tube. However, due to overlap of spectral lines all solutes could not be
dissolved in the same tube and thus a method of scaling was still required for different
samples. However, 5 g's for solutes within the same sample can be directly compared.
Qj
Sap's were scaled using the equation
'scaled
'TCB
(3.17)
where S p and STCB are the order parameters of the solute and 1,3,5-trichlorobenzene
a
(TCB) in the same sample tube and
S'
T C B
is the order parameter of TCB in the p-
dichlorobenzene/p-xylene mixture of the same liquid crystal. The p-dichlorobenzene/pxylene mixture was arbitrarily chosen as the standard for comparison. Values obtained for
scaled, vibrationally corrected order parameters S ^
L E D
are given in Table E.15, page 143.
In previous studies (see Refs. [8], [14], [17] and [82]) other scaling methods have been
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
55
utilized; for example, spectra were recorded at the same reduced temperature (the ratio of the sample temperature to the nematic-isotropic transition temperature) or the
orientational potential could be scaled to the ratio of the 1,3,5-trichlorobenzene dipolar
couplings. The concerns with scaling of S p's is part of an ongoing investigation[83]. Neva
ertheless, differences between scaled order parameters for dichlorobenzene in the same
liquid crystal but different sample tubes are < 1.7% (see Table E.15, page 143) using this
simple method.
3.3 Mean-Field Models
For a mean-field orientational potential C/(fi), where fi denotes the Eulerian angles,
solute molecular order parameters S^jjj are calculated (by taking the appropriate Boltz0
mann averages as the molecule is rotated through all possible orientations) using the
equation (which is identical to Eq. 1.3, page 6)
ocalc
°a/3 —
/(3cosfl
aZ
cosflflz - Sap) exp(-J7(fi)/fcT)dfi
2fexp(-U(Q)/kT)d£l
(3.18)
where 6 z and 8pz are the angles between the molecular a and (3 axes (molecular axis
a
are defined in Fig. 3.10) and the nematic director Z (which for the liquid crystals used
in this study lies along the magnetic field direction). i7(fi) can be represented as a sum
of two terms U(Q)SR and t/(fi)£s; U(Q,)SR accounts for the short-range repulsive interactions and U(Q)ES describes the long-range electrostatic interactions. In the context of
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
56
Figure 3.10: Coordinate System for Solutes. R i refers to either a CH or a Cl constituent.
When R i is a CH , R can either be a CH or a Cl constituent. However when Ri is a
Cl, R is also a Cl.
3
3
2
2
3
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
57
this mean-field model, the potentials can be represented by interactions between solute
properties (eg. dipoles, quadrupoles, shape anisotropy) and an average field "felt" by
the solute due to the solvent[8,18]. This average field is assumed to be a property of
the nematic solvent alone, and not significantly influenced by the solute. Due to the
presence of various ordering mechanisms, it is difficult to test directly the concept of a
solute independent mean-field. However, by utilizing sets of molecules with similar size
and shape, it is either assumed that the short-range orientational potential is the same
for each set, or that a model for the potential can be used in order to account for the
slight differences in molecular size and shape within each set. In both cases, differences
among the ordering within each set of molecules should be dominated by the long-range
interactions.
The short-range potential U(£1)SR is expressed in one of two forms. In thefirstform
the potential t7(ft)|^ is written as an expansion in spherical harmonics and is truncated
at the first non-zero term [18]. The mean orientational potential is then
U(n) % = -^
s
s
( a^)(3cos^
M
QZ
cos^ -M
z
(3.19)
a,0=x,y,z
where M is a traceless second rank tensor related to the size and shape of the molecule,
and kzz is a parameter that depends only on the liquid-crystal solvent. The shape
anisotropy of each set of similar size and shape molecules is represented by oneM tensor.
The kzz parameter is related to the degree of orientational ordering of the nematogen.
58
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
The second short-range potential U(Q)g is a phenomenological model based on the
R
CI model [8] of Burnell and co-workers where
(3.20)
and kzz is the solvent parameter, C(ft) is the circumference of the projection of the solute
at orientation ft onto the plane perpendicular to the director, k and k are constants,
s
and Z is the position along the nematic director bounded by the minimum, Z , and
min
maximum, Z , points of the orientation-dependent projection of the solute along this
max
axis. C(Z, ft) is the circumference traced out by the solute at position Z along the
director. Thus, C(Z,Q)dZ is the area of an infinitesimally thin ribbon that traces out
this circumference, and the integral is the area of the full projection of the surface of the
solute parallel to the nematic director. For thefirstterm k(C(Q)) , the liquid crystal can
2
be thought of as an elastic continuum and the solute as a distortion on the liquid crystal
solvent. The second term can be thought of as an anisotropic interaction between solute
surface elements and the liquid-crystal average field[8].
For the long-range electrostatic potential U(£1)ES, the most important contributions
are suspected to arise from molecular quadrupoles, dipoles and polarizabilities. The
contribution to the potential of a solute quadrupole with an (EFG) felt by the solute is
a,P=x,y,z
(3.21)
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
59
where €Q is the permittivity constant, F z is the ZZ component of the (EFG) tensor
Z
parallel to the nematic director and Q p is the a.0 component of the solute molecular
a
quadrupole tensor. The (EFG) is a traceless, second-rank tensor and for a nematic
phase has only one independent term.
The interaction of a molecular dipole Jl with an averaged electric field (E) is — fl- (E).
However, due to the apolar nature of nematic phases, the average laboratory frame (E)
"felt" by the solute must be zero. Thus, if the above approach for short-range and
quadrupole effects is used (where the solute is assumed to "see", on average, a field
that is constant in the laboratory frame), the dipole interaction is zero. Nevertheless, a
permanent dipole can affect the orientational order of a molecule through the field that
the solute dipole induces in the surrounding medium. This induced or reactionfieldin
turn interacts with the instigating dipole. The magnitude of the reactionfielddepends
on the solute dipole
(*> = \ E
E
T=X,Y,Z
Yl A*cos0
Qr
(3.22)
a-x,y,z
where fj, is the a component of the solute dipole, A and T are the laboratoryfixedX, Y
a
or Z direction, R^r is the AT component of the reaction tensor, and (E\) is the reaction
field in the A laboratory fixed direction. The potential is then
U(n)™f
e
= -(47rc ) ^
^(Rzz-Rxx)^coae cos0p -6af3)
_1
0
aZ
a,/3=x,y,z
Z
(3.23)
60
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
where Ryy = Rxx
off diagonal elements of the reactionfieldtensor are zero.
a n a >
Within the liquid-crystal phase there arefluctuatingelectric fields which can distort
the electronic structure of molecules. The distortion of the electronic structures coupled
with these electric fields can effect the orientation of the molecules. The potential for
such an interaction is
^Marizability
where
QL $
a
=
_
(
4
?
r
e
o
)
- l l
£
a (W -El)(3
a0
z
CO 9
S
aZ
(3.24)
COS 9pZ - 5a0).
is the af3 component of the molecular polarizability tensor and
(E — E\)
z
is the difference in the average electric field squared between the Z and X laboratory
fixed directions. E\ is equal to E\ and off diagonal elements of this tensor are zero for
nematic phases.
Molecular dipoles, quadrupoles and polarizabilities were calculated with respect to
1
the centre of mass using Gaussian 98[84] with RHFS/6-311+-l-G** (theory/basis set).
The values obtained (Table 3.3, page 63) are in accordance with other calculations and
experiments [85-87].
Geometry optimized molecular coordinates and electrostatic properties were also calculated using
G98[84]. These properties varied by no more than 5% between non-optimized and optimized calculations.
1
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
3.4
61
Analysis and Discussion
Intermolecular potential parameters were determined by a series of non-linear least
squares minimizations to S^ s using Eq. 3.18 and the /i , Q p and OL p values deled,
Q
a
a
termined from G98. The values of the intermolecular potential parameters from several
"fits" are presented in Tables 3.3 and 3.4. When analyzing short-range interactions with
the minimization routine, either Eq. 3.19 or Eq. 3.20 was utilized. For the short-range
interaction described with Eq. 3.19, M g's and kzz were adjusted, whereas with Eq. 3.20,
Q|
k z was adjusted keeping k and kfixedat 48.0 x 10~ Jm~ and 2.04 x 10~ J m . The
9
Z
2
9
-2
s
k and k values were taken from a previous NMR study of 46 solutes dissolved in the
s
liquid crystal mixture of 55 wt% ZLI 1132/EBBA for which D and HD experience a
2
zero (EFG) [8].
From examination of the RMS errors reported in Table 3.4, the short-range models
U(£l)gR (Fit #1) and 11(0,)^ (Fit #2) are approximately equivalent and account for
most of the orientational ordering. This is consistent with previous experiments[8,14,18,
88] and computer simulation results[39,76-79,89,90]. As expected, thefitsto the longrange interactions alone U(Q)^
ole
(Fit #3) and [/(fi)^^
016
(Fit #4) are significantly
poorer.
The RMS from the f/(fi)^
arizabili1y
(Fit #5) model is the same order of magnitude
as the RMS of the short-range models. However, when the long-range (7(fi)^5
arizablhty
interaction is coupled with a short-range potential, the RMS is virtually the same as
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
62
for the short-range potential alone, and the potential parameters for the short-range
interaction are rendered meaningless (eg. Fit #6): the k
zz
parameter for EBBA is 0.18
and for ZLI 1132 is 1.81. In the context of the model presented the degree of orientational
ordering within EBBA would be 10 times smaller than the degree of ordering within ZLI
1132 for short-range effects alone; this discrepancy is unreasonable. Thus, with the
molecules chosen for this study it is difficult to separate the effects of short-range size
and shape from long-range polarizability interactions; this is not surprising since to a
large extent the anisotropy in the polarizability tensor is related to the anisotropy in
the molecular dimensions. From previous studies[88,91] it has also been noted that the
effects of size and shape and polarizability could not be separated. Since polarizabilities
are expected to make a small contribution to the anisotropic intermolecular potential[6]
and since short-range interactions are thought to be very significant, the polarizability
interactions will not be utilized further.
Short-range interactions which are related to the size and shape of the molecule are an
important ordering mechanism; the longer-range interactions are more subtle. From examination of the S%p s of acetonitrile and propyne, and of the mono and p-substituted
led,
benzenes (Figs. 3.11 and 3.12), dipoles that are collinear with the symmetry axis of the
molecule have little or no influence on the orientational ordering of the molecules. The
value of
U(Q)SR
is similar for each set of molecules and for all liquid crystals; thus if
U(CI)ES
is dominated by a solute dipole interacting with a reactionfieldthere should be
a correlation between the solute dipole moments and the S^ s for a particular set of
led,
63
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
©
co
CO
LO
Tf
LO
o
t~
co,
o
co
co
co
Tf
CD
co
00
CO
LO
©
LO
^s
-a
8.32
9.04
CO
CM
03
s,
o
OO
CO
CO
LO
CO
CM
co
CM
LO
CM
co
co
CM
3.80
4.39
o
CM
oo
co
LO
co
co
LO
00
co
Tf
05
"o
l-H
o
oo
co
©
oo
co
o
a
o
Tf
L6
LO
CO
i—i
T—1
Oi
LO
Tf
©
T—1
i—i
©
i—i
©
LO LO
CO CO
i
i
Oi
T—I
1—1
CM
1
CO
i—i
7—1 T—1
CM CM
©
T—1
©
co CM
CM CM CM
od I>
©
i—1
CM
l-H
Tf
CO
Tf
Tf
t -
T—J
1
i—l
co
CM CM
i
OO CO ©
CO ©
co i - J ©
o
CO
CM
Tf
Tf
10.22
9.29
9.98
10.81
oo
LO ©
© ©
©
©
LO
T-H
1—1 i—i
l-H
CM t—5 ©
CM
CM CM
CO
©
f~
oq
©
CM
LO
t—i
LO
o
CM
CM
l-H
©
©
©
Tf
LO
l>-
©
I>
co
od
CM
LO
CM
oo
co
Tf
i
Tf
co
Tf
i-H
co
CM CM CM
i
i-H
CM
i
i-H
T-H
T-H
T-H
Tf
LO
Tf
00 CO LO
1—5 CM CM
t
i
co
l-H
1—J
T-H
o
CM
©
T-H
i-H
CM
o
I> CO
i-H
l-H
i-H
i-H
oo
LO
1©
CM
i—1
cd
CM
t~
Oi
o
1
©
Tf
l-H
©
LO
CM
O
Tf
CM
i-H
i-H
©
O
Tf
©
o
i—'
o
o
o
o
o
o
o
O o
©
©
o
o
o
©
O
CM
CO ©
o
o
o
©
©
o
©
o
©
C3 co o
o
co ©
o
13.72
3.22
fl
a
co ©
Oi
Or
Q
i—i
Tf
CO
Oi
i> LO
o
co
T—1
O 1—'
1 O i—i
i-H
©
o
0.00
IC?
00
CO
LO
-5.20
-1.95
1.59
O
<—i
©
co
-7.82
-3.14
2.36
Cu
3
co
-5.56
1.49
SH
©
0.00
7.16
0.00
.2 c
o
9.27
10.05
10.67
CH
9.23
10.03
10.82
>H
cu
el
cu
cu
SI
a
>>
"o
CD
o
SH
OH
el
cu
, o
o
SH
o
3
co
03
S
s i <13
CU
O
Xi
Q
QJ
-§1
O
o
o
Xi
-ai oi xi
2§
O
S)
el
S%
el
cu
cu
cu
<U
•a 3 >>
• i i
o o o
cu
s§
-Q
° Os
3
O
tH
o
o o
Xi
•a
3
<13
i
i
+^
I
LO^
CO"
©
o o
o
• ^H
i-l
£ SS
•
©
o
CO
4J
Cl
03
+3
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
SH
O •
SH
LO
T f
LO
fa
CO
CN
CO
GO
4 J
o
CD
CD
Si
fa tf
cr
&^
tf
CD
TJ
00
*<-.
o oo
O
ST
1
O
o oo
odd
O
o oo
odd
o oo
o oo
to
co
to
co
T f
LO
co co cd
t>M
CN
0
CO
rl
CN
3
i >
1
ffi
^
T f
52
^
9
2
^ co "
o co co
"OJ
64
>—I i—I
•^ G
eco
S-i
CD
o
CD
fa tf
*H
CD
CD
r>5
SH
CD
>
CD
a
tf
PH
"tf
4 J
CO
SH
o
3
cr
T f
bO ^
£ "O
o
bO
tf
It,
O
O
©
o oo
odd
s
1
CD
o oo
odd
o oo
^3
•—
fa
IN!
(S)
Oi
LO
td N
C71 N
O)
w
^
s
CO
CO
LO
CM
i—I
T—I
O
O
co oi co
co co o
odd
^ co co
o oo
odd
o oo
odd
|
O
O
odd
LO
o oo
odd
^ ^
o oo
odd
o © ©
odd
•*-. •*-.
o oo
odd
CO
N
—
t>
CO
•CD
(-1
CD
«8
CD
3 -«
t-i
I
<tf
S-l
TF
O
LO
CN
CO
Oi
CO
CM
1
—
5
d
i—1 d
©
fa
e
o
" co"
o © ©
T f
O
cn
O^ O
d
d
u
• i-H
cr
CN
CO
CD
SH
4 J
X
fa
d
d
o
d
Oi
CO
Oi
O
d
o
O
d
d
O
d
o
o o o
d
d
d
H
CO
T
—
5 CO
<
m
CM
CO
CN
CN
CO
CN
CO
pq
fa
pq
fa
co
3
LO
m
CS!
LO
fa
CN
& pq
L O CQ
LO
d
<
pq
pq
fa
co
<
pq
Tf
fa fa J L O CQ X
N io H fa
<
NI
LO
LO
<
pq
fa
pq
pq
fa
CN
CO
CN
CO
i—I
1 — 1
s^ <
d
1—H
<
pq
vo
LO
T f
cn
O
O
d
<
PQ
i-H
SH
T f
<
m
m
CO
"LO"
pq
pq fa
a
CN
CO
vo
3 ^
3
M
N
i—l
CM
1 — 1
<
£ CQ
LO
LO
m
fa
CO
co
r _ l
S ^
<
& CQ
J L O CQ
fa
CS] L O fa
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
SH
o
Tf
CO
LO
00
3
o3
-O
cu
CG
• -iH
o
o
o o
d d
*->
**->
0 0 0
o d d
0 0 0
o d d
3
13
03
• -iH
HHJ
SH
o
3
a
CU
HH5
O
3
a
co
cu
--a
coco
•*-. •<-.
o o o
o d d
00" 00 o T
d d d
oT oT oT
d^ d_ d
LO
d
S
co 0
d 06
LO
CO
CO
T-H
T^
CU
xi
00
CJ
=tt=
co
3
1
3
LO
-o
o
CM
«3
SH
OH
I>
CU
HJ
co"
o;
d
o
N
d d
o oq
W CN
0 0 0
o d d
cu
0 0 0
o d d
*
T-T
1
CO
+3
-O
• I—1
SH
. "0
a£
.
O
CO
CN
O)
.
O O
O
T-H
CO
<=> ~
.
O
QO
O i
O
Tf
CM
CM CM CM
CM
o
o
OS
O
o
O
r-H
T-H
~—'
0
o
O i
<
PQ
PQ
fa
CM
CM
CO
a d 1
Xi
O i
fa
fa
CM
CO
T-H
CO
HH5
PQ
PQ
PQ
^ CM
is
LO ffl •S
2
LO fa fa
KH
N
O i
T — l
^
is
LO
<J
PQ
H
2
_
13
N
b<
is CQ
m
LO H
LO
CO
SH
03 LO
SH T - H
a
CU
HO
2 -03
is EH
O
d
<
co
co
cu
•-!
co ,,.
J
SH
Oltlsg
CXcoO O
O
«<
CQ
CQ
fa
CM
s
o3
1
o
H
CO
CM 01
d
CO
O
CO
3 co >—
o
CJ
Tf
2
D
X X
fa
LO
3
S3
ic ^
cu ^ —
CU
SH
«3
w
G § 'a
S
o
CO
8 8
o
2 «
rr-
fa
? >
—
.I
o
T-H
-a
-H
o
T-H
o
tin
•
cu
22 3 -O
3
-5"
s3
°C H Cl
9
SH
+i
a
X
is
£
CO
^
03 LO
LO
.2SH2
O
SH
SH
CU
o o
co co
o
i-H -i-H
CO
S
3
SH
cu
H
>
- H-=
<+H <+H
."tin
< .t3 D
a
a
•p -p
O '6
o
b CD g
3
IM
cu
iS
SH
CU
CU
a
03
03
Cti fa
CD
H3
4 3
CU
3
cu
CO
cu
SH
OH
CU
SH
03
CO
CU
d
3
s
H-H
>
U
Co
66
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
molecules. However, the S^ s
led,
of p-chlorotoluene (dipole moment of 7.17 x 1 0
- 3 0
Cm)
are intermediate between those of p-xylene and p-dichlorobenzene (dipole moment = 0)
(Fig. 3.11). Chlorobenzene and toluene have very similar order parameters (Fig. 3.11)
but very different molecular dipole moments (Table 3.3). The 5 f ' ' s of propyne, a
s
ed
z
molecule with a small dipole, decreases significantly between ZLI 1132 and E B B A whereas
the S^ s
of acetonitrile, a molecule with a large dipole, remains virtually unchanged
led,
(Fig. 3.12; Table 3.3). If dipoles were important then it would be expected that the
gscaiedi
0
s
f
t o n i t r i l e would change significantly and the S^ s
led:
ace
of propyne would
remain virtually unchanged.
For the molecules with dipoles along a symmetry axis there is no correlation between order parameters and dipoles. This simple observation is also evident for the
sets of molecules which have dipoles along the molecular z and x axes. The m- and
o-chlorotoluenes have dipole components along the z and x axis directions. The m- and
odichlorobenzenes and xylenes have dipole components along the z axis direction only.
If dipoles were important to the orientational potential, the S ^
s
the S*
led
values (particularly
s of the chlorotoluenes) should be substantially different from those of the
c aled,
x
dichlorobenzenes and xylenes. However, as is the case for the p-disubstituted molecules,
the diagonal order parameters of the chlorotoluenes are intermediate (except for the
^scaled
Q
f o-chlorotoluene in E B B A ) to those of the dichlorobenzenes and the xylenes
(Figs. 3.13 and 3.14; Table 3.3). The conclusion that dipoles have little or no effect on
the orientation of solutes is also evident by examination of Table 3.4; the R M S error
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
67
Figure 3.11: S^ s (values taken from Table E.15, page 143) for p- and mono substituted benzenes are represented by A and correspond with the axis labeling in Fig. 3.10.
led,
68
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
-0.1
p
•0.15
T
I
I
I
I
J
— trichlorobenzene
1
1 1
1 1
1
1 1 1
i
1 1 1
i
i
i
i
i i
i
| i i i | i i i J 0.25
acetonitrile :
- 0.2
-0.2 "r
•0.25 fc\
-0.3
-0.35
_L
20
i
40
60
wt% EBBA
80
100
i
20
i i
40
60
wt% EBBA
_L
80
1o8
Figure 3.12: Experimental order parameters for 1,3,5-trichlorobenzene in samples containing p-dichlorobenzene and p-xylene, and S^ s (values taken from Table E.15,
page 143) for acetonitrile and propyne are represented by • and correspond with the
axis labeling in Fig. 3.10.
led,
of Fit #7, which includes the U(Q)1% and [/(Q)^|
includes only
t/(£2)f|[,
ole
interactions, and Fit #1, which
are identical. The (Rzz — Rxx) is zero within the calculated
errors. Thus, within the context of this theory, dipoles are of minimal importance in the
anisotropic part of the electrostatic potential and have no influence on solute ordering.
When the V (STj££
r
adrupole
interaction is included with one of the short-range potentials
the RMS significantly decreases compared to the RMS of the short-range interactions
alone (in Fig. 3.15 compare A l , 2 and 3 to B l , 2 and 3 and in Table 3.4 compare Fits #8
and #9 to #1 and #2). This is not surprising since quadrupole interactions are known
to be important to the orientational potential. The S%p values for Fits #8 and #9 are
c
presented in Table E.15, page 143.
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
69
Figure 3.13: S^f s (values taken from Table E.15, page 143) for o- and nvdisubstituted
benzenes are represented by A and correspond with the axis labeling in Fig. 3.10.
led,
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
0.1
I
1
I
I
I' ' I
m— dichlorobenzene
m— chlorotoluene
m —xylene
1 1 1
0.05
1 1 1
1
1 1 1
1 1 1
I
70
I
I 'J0.1
o—dichlorobenzene
o—chlorotoluene
0.05
o-xylene
1 1 1
1 1 1
1 1
to
-0.05
±
20
40
60
wt% EBBA
_L
•
100
80
•
•
•
_L
I i i iI
40
60
80
wt% EBBA
•
20
•
•
-0.05
100
•
Figure 3.14: S£f 's (values taken from Table E.15, page 143) for o- and m-disubstituted
benzenes are represented by A and correspond with the axis labeling in Fig. 3.10.
icd
The calculated Fzz& change sign between ZLI 1132 and EBBA. This is most evident from the S^ s
of the p- and m-disubstituted benzenes, and propyne and ace-
led,
tonitrile (Figs. 3.11, 3.12 and 3.13). For the ^-substituted benzenes in ZLI 1132 the
trend of S ^
led
zz
is: S (xylene) > S (chlorotoluene) > S (dichlorobenzene). For the
zz
zz
m-disubstituted benzenes the trend of the S
zz
aled
zz
is: S (xylene) < S (chlorotoluene)
zz
zz
< Szz(dichlorobenzene), and for propyne and acetonitrile the trend of the S
aled
zz
is:
S (propyne) > S (acetonitrile). However, in EBBA these trends are reversed. Since
zz
zz
U(Q)SR is similar for the individual sets of molecules there must be a change in sign of
C/(ft)^
adrupole
between ZLI 1132 and EBBA. The 55 wt% ZLI 1132/EBBA mixture is
where [/(ft)^adrupole happens to be » 0. The change in sign of f/(n)g^ drupole is due to
Fzz changing sign. The trend in the observed order parameters is most evident with
these molecules because there is a relatively large difference among their Q values. The
ZZ
71
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
ZLI1132/EBBA
i i i I i i i I i i i I i i i I i.
ZLI 1132
_i
TT' |
1
0.1
' I'
1
A1
I
I -
-
o
CO
1
I!
CO
r_
-
4
0
a ft -
—
- i
llh
3.75;
D Q D >
1
1 | 1
co
6
4
-- 1
8
1
*
- RHS: • = 1.82; A s 1.39
h
1 1
I
1 1
• 1 •,•1
' I
1 1 1
I
I I I
I
I I I
I '
1
1
I
I I I
RHS: • - 3 .32; A - 3.54
I
I
i i i I i i i I i i i I i i i I i-
I'
H
IT ri j i
I I I
- B3
—
^A
A*
CO
1
I I
B2
•
i
•I
1 | 1 1 1 |
0.1 h
• •1
BUS: • - 0.58; A - 0.91
A - 2.76
i I i i i i i i i I i-
I .
- B1
0.1
dh
&
A
—
.1 1 1
-0.1
I I I |
U A3
*
6—r
B
I I |
-
_
-0.1
1
-m
A
A
A
A2
EBBA
I I | I II| I
i
:
A
s
_
-
-
•J :• 1
I'
C1
u
a
RHS: Q = 0.54; A s 031
1
1
iiI ii iI t i i I i i i
1 1
I
1 11
C2
I
1 11
-
I
RMS: •
-1 1 1
I
= 2.10; A H 2.69
1
I
C3
1 11
i
1
1
I
i i i 1 i i i 1 i-
I I
I I
I
CO
•
A
CO
-0.1
(- RHS: • - 1JS8; A - 0.91
i iI ii iI ii iI iiiIi
-0.4 -0.2 0 0.2 0.4
gsealed
h RUB: • - 138; A - 2.23
RHS: • - 0.48; A - 0.82
• • • I • • • I • • • I • • • I •-!
-0.4 -0.2
0 0.2
Cj scaled
0.4
ii
I . . .I
-0.4 -0.2
ii
. I . . .I
0 0.2
gsealed
0.4
Figure 3.15: S s minus S ^ ' s results (values are taken from Table E.15, page 143) are
plotted against S s. The principal (largest absolute diagonal value) order parameter
element is represented. Note that the vertical scale is expanded by three compared to
the horizontal scale. Series A is the results from Fit #1 (•) and Fit #2 (A) and series
B is the results from Fit #8 (•) and Fit #9 (A). Series C is the results from the fits
where by the parameters of Fit #8 (•) and Fit #9 (A) were fixed and the origin of the
quadrupole tensor was allowed to vary. RMS errors ( x l O ) between S s and 5 ' 's
are reported within the graphs.
scaled,
scaled,
-2
scaled,
ca
c
72
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
difference among Q 's for the ortho and mono substituted benzenes is smaller and thus
22
the trend is not as evident. In all cases (including the S
s c aled
z z
of o-chlorotoluene in EBBA)
the trends are consistent with the signs of the molecular quadrupoles.
For the 55 wt% ZLI 1132/EBBA mixture, the F 's
zz
determined from D and HD
2
studies were « 0. Within the reported error of our calculated values, the Fzz's in
the 55 wt% ZLI 1132/EBBA mixture is also « 0 (Table 3.4). The value of the F z
Z
can be rationalized by examining the 5^ ' 's; since the molecules of similar size and
a ed
shape, have similar S af
s
ed
in the 55 wt% ZLI 1132/EBBA mixture (Figs. 3.11, 3.12, 3.13
and 3.14), all long-range electrostatic contributions (not only the F z) to the potential
Z
are essentially zero. Only short-range interactions are important in the 55 wt% ZLI
1132/EBBA mixture.
The Fzz's determined from D and HD studies were «s 6.11, « 0.0 and « -6.41 x 10
11
2
esu (18.44, 0.0 and -19.16 x 10 volt-m- )[20] for ZLI 1132, 55 wt% ZLI 1132/EBBA
17
2
and EBBA. In this study the calculated F ' s are « 7.0, « 0.8, and -7.7x 10 volt-m~ .
17
2
z z
The discrepancy between the calculated Fzz's of D /HD and the much larger molecules
2
in this study may have several causes, including: the approximations involved with the
G98 calculations of molecular quadrupole tensors; the differences in sample conditions
between the D /HD and the present experiments; or the assumption that the (EFG) is
2
a property of only the liquid crystal.
Our calculated Fzz's presented above are from a global fit to all the molecules. In
an attempt to minimize the inadequacies of the short-range potentials, to minimize the
73
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
ambiguities with the scaling of the experimental S p, and to test the concept of a solutea
independent Fzz, individual F z values were determined for each set of similar size and
Z
shape molecules (Fig. 3.16). Regardless of the size, shape or electrostatic properties of
these solutes, all calculated Fzz's for a specific liquid crystal have the same sign and
have approximately the same magnitude. The calculated values of the Fzz* in ZLI 1132
and EBBA are the same sign but smaller in magnitude than the F z's determined from
Z
the D 2 / H D experiments. Both theory[16] and computer simulations[39] predict that the
Fzz's
are very sensitive to solute molecular properties. In fact, from computer simula-
tions, the F z for a particular liquid crystal changes sign depending on the size, shape
Z
and quadrupole moment of the solute particle (see Chapter 4). While the experimental
Fzz*
do depend on solute molecular properties, this discrepancy is far less than that
predicted by either computer simulations or the theory. The rationalization of these
different dependencies represents an interesting problem to both theory and computer
simulations.
In the case of the m-chlorotoluene, the trend in the S™ s
lc,
is incorrectly predicted
(Table E.15, page 143). Also, from examination of Fig. 3.15, A l , 2 and 3, and Bl, 2 and
3, the inclusion of the [/(ft)^™ ™
1
16
interaction decreases the difference among
S
s
scaled,
and S ' 's for the liquid crystal ZLI 1132 more than for EBBA. Also the difference is
ca
c
much smaller for the 55 wt% ZLI 1132/EBBA mixture then for the component liquid
crystals. It is interesting to ask: to what extent are the disparities due to inaccuracies
with the calculation of the quadrupole tensor? For molecules that possess a molecular
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
74
Figure 3.16: Graph (A) is the individually and globally determinedfieldgradients for the
molecules in this study from least-squaresfitsusing Eq. 3.20 coupled with Eq. 3.21. Graph
(B) is the field gradients from least-squares fits using Eq. 3.19 coupled with Eq. 3.21.
Regardless of the size, shape or electrostatic properties of the solute, all calculated field
gradients (units of 10 volt m ) for the same liquid crystal are the same sign and
roughly similar in magnitude.
17
-2
75
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
dipole, one simple method to help compensate for these inaccuracies is to adjust the
origin at which the quadrupole is calculated (the value of the first non-zero multipole is
origin independent). The center of mass has been chosen as the origin but this may not
be an appropriate choice. The origin dependence of the new quadrupole component Q'
a/3
for a neutral molecule is
Q'a = Qap
0
+ 3/2(/i A + Hf)& ) - (/xA)5
a
/J
a
(3.25)
Q/3
where Q ? is the original quadrupole component, ft is the dipole and A is the difference
Q/
in distance between the original origin and the new origin. Another series of least-squares
minimizations was performed whereby the short-range parameters and the Fzz& were
fixed to the values determined from Fit #8 and the origin of the quadrupole was adjusted
in the z direction (Table 3.5 and Figure 3.15 C l , 2 and 3). The adjustments in the
z direction reported in Table 3.5 seem unreasonably large. However, the quadrupole
tensor components of the molecules are still within reasonable values; the magnitudes
and not the signs of most of the quadrupole components were altered. The Q values of
zz
acetonitrile and p-chlorotoluene, and the Q
xz
value of m-chlorotoluene, did change sign.
Since acetonitrile has a large dipole moment, the choice of origin is particularly important, and only a slight shift of the origin is required to change the sign of the quadrupole
component. With the origin shift, the difference between the S
s
aled,
zz
and S 's is
lc
zz
smaller. However, the difference between the quadrupole components is not significant
76
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
Table 3.5: Adjusted Molecular Parameters"
Quadrupole
Component
acetonitrile
propyne
0.356
3.727
-0.178 -0.178
-1.863 -1.863
0.000
0.000
Adjustment in z
axis origin
A
0.41 (0.13)
2.74 (0.59)
chlorobenzene
toluene
0.719
0.709
1.979
1.503
-2.698
-2.212
0.000
0.000
-0.24 (0.31)
-2.52 (1.18)
p-dichlorobenzene
p-chlorotoluene
p-xylene
-2.301
-1.013
1.826
3.681 -1.379
2.662 -1.649
0.792 -2.619
0.000
0.000
0.000
0.0
-1.01 (0.25)
0.0
o-dichlorobenzene
o-chlorotoluene
o-xylene
0.736
0.957
0.547
1.372
1.376
1.459
-2.108 0.000
-2.333 -1.196
-2.006 0.000
0.59 (0.22)
0.18 (0.4.3)
-1.45 (0.74)
m-dichlorobenzene
m-chlorotoluene
m-xylene
2.335
2.209
2.130
-0.819 -1.516
0.480 -2.689
0.967 -3.097
0.000
0.588
0.000
0.61 (0.36)
-1.70 (0.38)
3.45 (1.21)
1,3,5-trichlorobenzene
0.492
0.492
-0.974
0.000
0.0
Solute
0
6
Qzz
Qxx
Qyy
Qxz
2
d
d
d
For axis definitions see Fig. A.22. Fit performed byfixingthe parameters from Fit #8
and adjusting the origin of the quadrupole in the z direction. RMS error is 1.23 x 10 .
Units of IO coulomb-m .
Units of A.
Quadrupole components are origin independent.
a
-2
6
c
c
-39
2
77
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
enough to suggest an inconsistency with the current theory or to suggest a poor G98
calculation.
For p-chlorotoluene it is expected that the value of Q be between the value of the
zz
Q
zz
components of p-dichlorobenzene and p-xylene. The original Q value, as well as
zz
the Q' value, is in-between the Q values of p-dichlorobenzene and p-xylene. Thus it is
zz
zz
difficult to discount the sign change in the adjusted Q . It could be due to the difficulty
zz
in calculating the electronic charge density around a chlorine constituent.
With a positive Q' for m-chlorotoluene, the trend in S^.f is correctly predicted.
c
xz
However, since there is a large negative charge distribution around the chlorine, the
Q
xz
is expected to be negative (as was calculated by G98). It is difficult to suggest,
within the context of the current mean-field model, an interaction which could account
for the trend in Sl
c led
z
of m-chlorotoluene and correctly predict the trend for all other
order parameters. It is noted that the values of the S
s
aled,
xz
are small and, even with
the somewhat crude mean-field model, the trends with all other order parameters are
correctly predicted.
For the fit in EBBA the difference between the S
s
scaled,
and S s
calc,
slightly decreases.
However, the fit is still somewhat poorer than the fit in ZLI 1132. For the 55 wt%
mixture all long-range interactions are minimal and the F'zz's are almost zero; thus
the adjustment of the quadrupole tensor has a small effect on the RMS error. For the
component liquid crystals, there may be other interactions (other than dipole, quadrupole
or polarizability) which are important. It is also possible that this mean-field model is
78
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
too crude and that i n d i v i d u a l molecules (not just individual sets) experience slightly
different average environments. Nevertheless, the quadrupole interactions are important
for the long-range potential.
3.5
Conclusions
Short-range interactions account for most of the solute orientational ordering i n liquid
crystalline solvents. T h e relative importance of various electrostatic interactions on order parameters is demonstrated by using solute molecules of similar sizes and shapes.
W i t h i n the reported errors the reaction field anisotropy (Rzz
— Rxx)
is zero and thus
for these molecules interactions involving the solute dipole moment have little influence
on ordering. In addition, the effects between polarizability anisotropy and short-range i n teractions cannot be distinguished. However, it is expected that polarizability anisotropy
interactions are minor.
Trends among experimental order parameters (except for the very small
' ' s of
ed
m-chlorotoluene) are consistent w i t h a short-range interaction coupled w i t h a quadrupole/ (EFG)
interaction. T h e trend for the S
s
aled
xz
of m-chlorotoluene is correctly pre-
dicted when the origin of the quadrupole is shifted which may suggest that for a dense
system the center of mass is not an appropriate choice for the origin. T h e sign of Fzz$
in a l l liquid crystals is i n accordance w i t h previous results from D and H D experiments.
2
However, since values of Fzz
small solute D
2
change by approximately a factor of two between the very
and the larger benzene derivatives, the assumption that a l l solutes feel
Chapter 3. Dipole-Induced Ordering in Nematic Liquid Crystals
79
essentially the same average environment may not be completely valid. Nevertheless,
the signs and relative magnitudes of all the Fzz's calculated for the larger molecules are
consistent among the various sets of similar size and shape molecules; at least the larger
molecules seem to experience similar average environments.
This study presents the analysis of a self consistent set of order parameters and is one
of a small number of studies that provide an estimate of the sign and magnitude of the
(EFG).
It has been demonstrated that the average electricfieldgradient (EFGYs felt
by solutes in the 55 wt% ZLI 1132/EBBA mixture are « 0. Not only are the
(EFG)-
quadrupole interactions « 0 in this special mixture, but other long-range interactions
appear to be negligible as well.
Chapter 4
Intermolecular Potentials in Liquid Crystals:
Comparison Between Simulations and N M R Experiments
The material presented in this chapter has been published in Ref. [76].
4.1 Introduction
Current thinking is that short-range interactions dominate the anisotropic intermolecular potential which is responsible for the partial orientational order in liquid crystalline
phases. However, it is recognized that longer-range electrostatic interactions are also
important. These long-range interactions are often expressed in terms of molecular electrostatic multipoles and polarizabilities.
An important means of learning about the intermolecular potential is to compare
results obtained from real experiments with those predicted by theories, models or simulations. In this chapter second-rank orientational order parameters obtained by NMR
experiments on small probe molecules dissolved in nematic liquid crystalline phases are
compared with those obtained from Monte Carlo (MC) simulations. Results for two
particular sets of experiments are utilized.
80
Chapter 4. Comparative Study Between MC and NMR Experiments
81
The first set of experiments involves published work on a series of 46 solutes which
was studied in a special mixture of nematic liquid crystals for which the nuclei of the solute dihydrogen are known to experience a zero average electricfieldgradient {EFG)[8\.
In this special mixture experimental results for other solutes such as methane [92] and
substituted aromatics[18,19,40,41] (Chapter 3) have been interpreted to mean that these
molecules also experience a zero (EFG); the orientational ordering is purported to arise
mainly from short-range repulsive forces[8, 26,46]. The NMR results are compared with
MC simulations of hard ellipsoids. The comparison is performed with the aid of phenomenological models for short-range interactions.
The second set of NMR experiments (results taken from Chapter 3) was designed
to probe long-range electrostatic interactions by using molecules of essentially the same
size and shape but different electrostatic multipole moments as solutes in several different
nematic liquid crystal solvents. It was concluded that permanent molecular dipoles have a
negligible effect on solute orientational order, while order parameters obtained for solutes
in the various liquid crystal solvents are consistent with an anisotropic interaction that
involves the solute molecular quadrupole. In order to make comparisons, MC simulations
with point quadrupoles placed at the centre of hard ellipsoids are employed (results taken
from Ref. [39]).
82
Chapter 4. Comparative Study Between MC and NMR Experiments
4.2
Experiments for which short-range interactions are thought to dominate
the intermolecular potential
Dideuterium experiences a zero (EFG) in the nematic liquid crystal mixture of 55 wt%
ZLI 1132/EBBA. This has been taken as evidence that long-range electrostatic interactions can be neglected in this special mixture [8]. The second-rank orientational order
parameters S p obtained from NMR measurements for a series of 46 solutes dissolved
Q
in this mixture have been fit previously to several phenomenological models for a shortrange interaction[46]. In one of these, model C[26], the solute exerts an elastic distortion
on the liquid crystal solvent,
U(Q) =
(4.26)
\k(C(Q))
2
where C(Q) is the circumference of the projection of the solute at orientation Q, (which
refers to the polar angles 9,4>) onto the plane perpendicular to the director, and k is a
(Hooke's law) constant.
Model I [46] is one of several basically equivalent [88] models which assume that the
anisotropic intermolecular potential can be written in terms of an anisotropic interaction
between solute surface elements and the liquid crystal average field [46,47]. The potential
used for model I is
(4.27)
where Z is the position along the nematic director bounded by the minimum, Z , and
min
83
Chapter 4. Comparative Study Between MC and NMR Experiments
maximum, Z , points of the orientation-dependent projection of the solute along this
max
axis. C(Z, Q) is the circumference traced out by the solute at this position along the
director. Thus, C(Z, Vt)dZ is the area of an infinitesimally thin ribbon that traces out
this circumference, and the integral is the area of the full projection of the surface of the
solute parallel to the nematic director.
A third model, model CI (described in Chapter 3, Eq. 3.20, page 58), is a twoparameter model formed by combining Eqs. 4.26 and 4.27. The reasonable fits obtained
for these three models (see below) were taken as an indication that in this special liquidcrystal mixture the anisotropic intermolecular potential is dominated by short-range
repulsive terms that depend on the solute size and shape.
The same models C, I and CI are used to fit order parameters from MC simulations of
hard cylindrically symmetric ellipsoidal solutes of various dimensions and aspect ratios in
a collection of 95 or 239 hard cylindrically symmetric ellipsoidal solvent particles of aspect
ratio 5:1 (Fig. 4.17). The simulations for single prolate solutes in 95 solvent particles have
been presented previously[13], while the simulations for oblate ellipsoids in 239 solvent
particles are new for this study; the simulation program that was utilized for this study
is described in Ref. [13]. Constant-volume simulations were performed using a reduced
density p*=Ni> /V=0.488, where N is the number of particles confined to the cell, v is
0
0
the volume of a solvent ellipsoid, and V is the volume of the cell. Particles were randomly
chosen for an attempted repositioning, which consisted of a simultaneous translation and
rotation, the maximum magnitudes of which were chosen so that the translation and
84
Chapter 4. Comparative Study Between MC and NMR Experiments
rotation would contribute about equally to the likelihood that the new position would be
rejected. Solute orientational order was monitored by measuring the second-rank order
parameter S
zz
— (P2(cos6)), where 6 is angle between the solute symmetry axis and the
nematic director.
Models C and I both involve a single adjustable parameter, and both fit the MC
results reasonably well (short dash (C) and dotted (I) curves in Fig. 4.17). However,
the difference between fit and simulation is consistently in opposite directions for the
two models. Thus, it is not surprising that the two-parameter CI model provides a
particularly good fit (solid curves in Fig. 4.17). The value 38.1 obtained for the ratio of
the two parameters ^ compares with the value 23.5 realized fromfittingexperimental S p
a
from NMR experiments[46]. More important, when this ratio is fixed to the NMR value
of 23.5, the agreement between model and simulation (long dashed curves in Fig. 4.17) is
essentially equivalent to that found when the two parameters are adjusted independently
(solid curves in Fig. 4.17).
In order to investigate to what extent the same phenomenological models rationalize
both NMR and MC results, we compare in Fig. 4.18 the difference between S pS recalcuQ
lated from the fits to the three models and the experimental values. Circles are used for
principal (largest absolute value) solute Sap's determined by NMR measurements, and
filled squares are used for the MC values.
The fits of the models to both the NMR and MC results show quite similar trends.
Model C (Fig. 4.18a) tends to overestimate the orientational order of more asymmetric
Chapter 4. Comparative Study Between MC and NMR Experiments
85
i—i—i—i—i—i—i—I—i—r
~i—i—i—i—i—i—i—i—i—r
7
w=0.5
0.5 h
co
Oh
.
-0.5
J
.
I
o
I
0
I
I
oO
o 0
U V
I
I
i
J
I
i_
J
I
L
J
L
i—i—i—i—i—i—i—i—i—r
7
w=1.0
CO
-I
h
- o O O O
J
-|—i—i—i—|—i—i—i—|—i—r
w=1.25
CO
oh
h
-0.5 h
0
I
L
1
I
L
1
J
I
L
2
4
length
Model C
Model I
- C o m b i n e d CI
loooO
J
0
J
L
1
2
4
length
— C o m b i n e d CI
with k / k
fixed
Figure 4.17: Solute order parameters S's versus solute length from MC simulations (•)
for various width (w, indicated within the graph) and length particles. Solute shapes
are represented at the bottom of the graph; they are not directly in line with their
corresponding points. The liquid-crystal is represented by the shaded particle. The
model used for each fitted curve is indicated at the bottom right.
Chapter 4. Comparative Study Between MC and NMR Experiments
86
~l—I—I—I—I—I—I—I—I—I—I—I—I—rq
r(b)
• •
t_l
I
I
I
I
I
_
I
I
I
••
I
I
I
I l_
~\—i—I—i—i—i—r
04(c)
m
0.1
I
3
0
-0.1
-o.2 r-
t_i
i
i
i
-0.5
i
i i
0
i
• i .
0.5
S
Figure 4.18: The 5 's from fits to various models minus S's from NMR[46] (O) or MC
(•) results are plotted against S's. The principal (largest absolute diagonal value) S p
element is used for the NMR results. Note that the vertical scale is expanded by three
compared to the horizontal scale. Graph (a) is a fit from Model C, graph (b) from Model
I, graph (c) from the combination CI model adjusting both k and k , and graph (d) is a
fit where the ratio of y for the MC results is fixed to the value 23.5 obtained from the
fit to the NMR data.
calc
a
s
Chapter 4. Comparative Study Between MC and NMR Experiments
87
solutes (i.e. those with the most positive or most negative S p), while model I (Fig. 4.18b)
a
tends to do the opposite. Combining both potentials in a two-parameterfitting(model
CI, Figs. 4.18c and d) produces an excellent fit to both NMR and MC results. As was
the case with Fig. 4.17, the two-parameter fit of the MC simulation results (Fig. 4.18c)
is only marginally better than the one-parameter fit (Fig. 4.18d) with the ratio y fixed
to the NMR value 23.5.
The similar trends found for fits to both NMR and MC results is an indication that
the same anisotropic intermolecular potential applies in both cases. This is further evidence that in the special 55 wt% ZLI 1132/EBBA liquid-crystal mixture the anisotropic
intermolecular potential is dominated by short-range forces that depend on molecular
size and shape.
While the C and I models were developed with specific physical interactions in mind
(an elastic distortion of the nematic solvent and an anisotropic surface interaction), they
are also phenomenological descriptions of the anisotropic potential. The C and I models
were based on an elastic continuum model. As the molecule reorients the continuum
exerts an elastic restoring force on the molecule. The MC calculations involve only
excluded volume effects, and hence the intuitive picture of the C and I models do not
necessarily apply in this case. Nevertheless, the fact that the combination CI model
does such and excellent job in fitting both NMR data for solutes in the special liquid
crystal mixture and MC simulations of hard ellipsoidal particles is strong evidence that in
both cases the anisotropic intermolecular potential is dominated by short-range repulsive
Chapter 4.
Comparative Study Between MC and NMR Experiments
88
forces.
It must be noted that attempts to generalize this notion to arbitrary nematic phases
are fraught with difficulty. A most dramatic example is the negative S^'s found for
both acetylene[24,25] and hydrogen[93] in EBBA. To emphasize the difficulty, we plot in
Fig. 4.19 the relative difference between experimental and fitted S^ s for least squares
c,
fits to the CI model. Fig. 4.19a gives the results presented before in Fig. 4.18d (for the
55 wt% ZLI 1132/EBBA mixture and the MC hard ellipsoids). Most relative differences
are less than 20%. Fig. 4.19b gives the fit obtained for a collection of solutes in EBBA[91].
Huge relative differences (the largest being -225% for acetylene, 127% for iodomethane
and 88% for propyne) are noted, especially for solutes with small S^'s (such solutes do
not in general have a large shape anisotropy). These results are completely contrary to
the notion that short-range repulsive interactions alone determine the solute orientational
behavior.
4.3
Experiments for which long-range electrostatic interactions are thought
to contribute significantly to orientational ordering
The previous section focused on the effects of short-range interactions on solute ordering.
The MC simulations only incorporated hard-body interactions and the experimental
solute S 3's were determined using a liquid crystal for which all long-range interactions
Q/
seem to be minimized. However, for most liquid crystals long-range interactions are not
negligible.
Chapter 4. Comparative Study Between MC and NMR Experiments
89
1 -0.5
Figure 4.19: Relative difference between calculated and experimental solute principal
S g's; AS = S —S. (a) is a different representation of the results presented in Fig. 4.18d.
(b) is a fit of the two-parameter CI model to S ^s from NMR experiments of solutes in
the nematic liquid crystal EBBA[91]; the fitting parameters obtained are k — 2.4 ± 1.0
dyne c m and ^ = 11 ± 9.
calc
a/
a
-1
Chapter 4. Comparative Study Between MC and NMR Experiments
90
Quadrupole interactions are commonly utilized in the description of the orientational
potential[8]. From the NMR experiments of D and HD, the value of the (EFG) in ZLI
2
1132 was determined to be positive whereas in EBBA it was negative. If as assumed
in the previous section all solutes experience essentially the same average environment,
the negative S 's found for acetylene and dihydrogen dissolved in EBBA can be easily
zz
rationalized by the interaction between the positive solute quadrupole and the negative
(EFG) in EBBA[20]. However, Emsley et al. have developed a theoretical model for
describing the orientational ordering of solutes in a uniaxial nematic solvent and concluded that the (EFG) should in fact be dependent on the solvent as well as the solute
quadrupole [7] (discussed in Chapters 1 and 3).
In this section we compare (EFGYs determined from previous MC simulations[39] and
NMR experiments (from Chapters 2 and 3) to test the assumption that all solutes experience the same average environment. The MC simulations[39] employed hard-body interactions together with point quadrupoles at the center of the particles. Only quadrupoles
were used because the quadrupole moment is the lowest order electrostatic multipole
moment that the theory by Emsley et al. predicts to contribute to a non-vanishing FzzNematogens were modeled as axially symmetric hard ellipsoids with an aspect ratio of
5:1 and with a fixed value of the reduced quadrupole moment Q*
^ = — \/2T5. Solutes
nem
zz
were modeled as axially symmetric hard ellipsoids with varying lengths and quadrupole
moments. The (EFGYs were determined at the center of the solute using
91
Chapter 4. Comparative Study Between MC and NMR Experiments
Fr A
= V £
R
=
-g [
A
= -V V </>
R
- 2 C #
A
A
+
2^
10<
3TA
r
rr +
T=x,y,z
+ £
Qrr
10
r
r
rr
A
r=x.y,z
5QS ^r*o- -
35QS ^r r r ],
m)
£
m)
rA
$
r
(4.28)
A
where f is a unit vector describing the orientation of the displacement between the
quadrupole pair, and QrvT™^ is the solvent quadrupole moment in the laboratory frame.
The dimensionless F* is then defined as
zz
\Qzz I
From the NMR experiments, the Fzz's were determined from a combination of the
potentials presented in Eqs. 3.20 (page 58) and 3.21 (page 58) (Fig. 4.20; the F z's for
Z
acetonitrile and propyne are not displayed); k and k (the ratio of ^f- was fixed to the
s
value from previous studies [46]) and Fzz$ were determined by a least-squares fit to the
non-vibrationally corrected S^s presented in Table D.13, page 137. Note, Fig. 3.16
(page 74) presents results from fits to the vibrationally corrected S /j's. In Fig. 4.20a
Q
the T 's
zz
Fzz§
calculated from the fits to Eqs. 3.20 (page 58) and 3.21 (page 58), and the
determined from D experiments[21], are shown. The signs of the calculated
2
Fzz's are the same as those determined from the deuterium experiments. However, the
magnitudes in ZLI 1132 and EBBA are approximately 1/3 the magnitudes determined
from D . Nevertheless, the approximately zero value for Fzz$ in the special 55 wt% ZLI
2
1132/EBBA mixture is predicted by both the D and the substituted benzene results.
2
The size, shape and electrostatic properties of the solute seem to have a small effect on
Chapter 4. Comparative Study Between MC and NMR Experiments
92
the magnitude, but have no effect on the sign of the F zz's
In Fig. 4.20b we show the F s
,
zz
determined from the MC simulations. The F
s
zz
for a given solute ellipsoid is very dependent on its quadrupole moment and also on its
size and shape. Thus, in agreement with Emsley et al.[7], the solutes in MC simulations
do not seem to experience the same average environment.
In the case of non-spherical solutes, the (EFG) experiences a concomitant change in
sign with the solute quadrupole moment. This result is in sharp contradiction with the
experimental NMR results for which it was found that the S%jj s of several molecules
c,
conform to the mean-field model where the solutes interact with an (EFG) which, at
the very least, has the same sign. To emphasize this point the relative differences between calculated and experimental NMR or MC order parameters are shown in Fig. 4.21.
Most of the predicted S%p s from the NMR studies are within 20% of the experimentally
c,
determined 5 g's whereas most of the predicted order parameters from the MC simuQ|
lations are > 20%. The origin of the discrepancy between NMR experiments and MC
simulations is very likely the inadequacy of using point quadrupoles for dense systems for
which the convergence of the multipole expansion at short distances becomes an important consideration. Thus, an improved description of molecular electrostatic interactions
will likely be essential in order to generate solute orientational behavior consistent with
that observed experimentally. It is most likely that small, almost spherical solutes are
the best choice for investigating long-range interactions since the influence of size and
shape on their S ps is Lilliputian.
a
93
Chapter 4. Comparative Study Between MC and NMR Experiments
Figure 4.20: Graph (a) is field gradients F ' s (in units of 10 volt m ) for dideuterium[20] and for the substituted benzenes from least-squares fits to S pS obtained
from NMR experiments. Regardless of the size, shape or electrostatic properties of the
solute, all determined Fzz§ for the same liquid crystal are the same sign and roughly
similar in magnitude. Graph (b) is F s taken from MC simulations for various shape
solute particles with various point quadrupole moments [39]. The solute ellipsoid dimensions are: A 0.65:1; • 1:1; and • 2:1. The quadrupole of the nematogen Q z i ^ was
fixed at — \/2T5. Note that this graph represents one liquid crystal mixture and thus all
the points in thisfigurecan be compared with the points in (a) for either 0% or 100%
EBBA. For these MC simulations, the F is not a solute independent property, which
is contrary to the experimental NMR results of graph (a).
17
-2
z z
Q
zz
n
zz
e
m
94
Chapter 4. Comparative Study Between MC and NMR Experiments
1 1 |
1
1 1 1 |
1 1 1 1 |
0.5
11
•
•
•
—
CO
CO
<
0
—
-
-0.5
•
•
1 1
1I
-0.5
•
l
l
l
—
1I
0
I
I
I
1I
l
0.5
Figure 4.21: Relative difference between calculated and NMR (A = solutes in ZLI 1132
and • = solutes in EBBA) or MC (•) order parameters; AS = S - S. S$ 's for both
the NMR and MC results are calculated from a global fit to all solutes in a particular
liquid crystal using the CI model (Eq. 3.20, page 58; with the ratio of ^ fixed to 23.5)
coupled with Eq. 3.21, page 58.
calc
c
Chapter 4. Comparative Study Between MC and NMR Experiments
4.4
95
Conclusions
Figs. 4.18 and 4.19a demonstrate that 5 g's from both NMR experiments in special liquid
Qj
crystal mixtures (such as 55 wt% ZLI 1132/EBBA) for which dideuterium experiences
zero (EFG) and MC simulations can be rationalized in equivalent ways. This is strong
evidence that the anisotropic intermolecular potential is dominated by short-range interactions in such liquid crystals. Fig. 4.19b demonstrates that results for arbitrary liquid
crystals such as EBBA cannot be rationalized in a similar manner. In such cases longrange electrostatic interactions must be considered. MC simulations of hard ellipsoids
containing point quadrupoles at their centres yield average electric-field gradients that
depend on solute size, shape and quadrupole moment. This result agrees with theory[7],
but is not consistent with NMR experimental results (Fig. 4.20a) which indicate that,
solutes experience at least the same sign Fzz-
Chapter 5
Summary and Future Considerations
Accurate spectral parameters for orientationally ordered p-, o- and m-disubstituted benzenes, chlorobenzene, toluene, propyne and acetonitrile co-dissolved in various liquid
crystals were determined from analysis of high-resolution NMR spectra. For the more
complex molecules, initial estimates of the spectral parameters were determined by analysis of MQ spectra. For o- and m-xylene, resonance frequencies and 5 a's were estiQj
mated by analyzing the 8Q spectra using a modified version of the least-squares fitting
routine which could adjust 5 g's, structural parameters, and/or Di/s independently;
Q|
once a reasonable fit to the MQ spectrum was obtained, the original version of the MQ
analysis program was used to determine the Aj's and resonance frequencies. The estimates of spectral parameters from the MQ analysis were used as initial parameters
when analyzing the high-resolution spectra. After the high-resolution spectrum was fitted, it was subtracted from the experimental one and resonances from the other solutes
could be easily identified and spectral parameters for those molecules were determined.
After spectral parameters from the high-resolution spectra were determined, S^/j's and
molecular structural parameters were calculated from vibrationally and non-vibrationally
96
Chapter 5. Summary and Future Considerations
97
corrected D^s.
From analysis of the experimental SQ^'S, it was determined that short-range interactions account for most of the solute orientational ordering in liquid crystalline solvents. It
has been demonstrated that the (EFGYs felt by solutes in the 55 wt% ZLI 1132/EBBA
mixture are « 0. Not only are the (E'FG)-quadrupole interactions « 0 in this special
mixture, but all other long-range interactions appear to be negligible as well. This was
supported by Monte Carlo computer simulation results. Models for short-range interactions which best fit the NMR experimental solute order parameters also best fit the
simulation results.
For the molecules in this study, interactions involving the solute dipole have little
influence on ordering. In addition, the effects of polarizability could not be separated
from short-range interactions. However, it is expected that polarizability interactions
are minor.
Trends among experimental order parameters are consistent with (a model for) a
short-range interaction coupled with a quadrupole/(EFG) interaction. The sign of
Fs
zz
in all liquid crystals is in accordance with previous results from D and HD experiments.
2
However, values of F
zz
change by approximately a factor of three between the very small
solute D and the larger benzene derivatives; the assumption that all solutes feel essen2
tially the same average environment may not be completely valid. Nevertheless, the signs
and relative magnitudes of all the F s
,
zz
are consistent among different sets of similar
size and shape molecules. MC simulations of hard ellipsoids containing point quadrupoles
Chapter 5. Summary and Future Considerations
98
at their centres yield average electric-field gradients that depend on solute size, shape
and quadrupole moment. The correct prediction of the NMR results could constitute
an interesting challenge for computer simulation studies. At close distances, the point
quadrupole is a very poor approximation of the charge distribution of a molecule. An
atomistic type calculation which includes a more realistic charge distribution and possibly the flexibility of liquid crystal molecules may be required in order to rationalize
orientationaL ordering that is consistent with experiments.
It has been demonstrated that effects from long-range interactions are relatively small.
Therefore, it is important to determined a self-consistent set of order parameters either by
co-dissolving many solutes in the same sample tube, or by scaling order parameters among
different samples. The effects of relative solute concentration and temperature on the
orientational ordering of solutes is an important question which requires investigation[83].
Effects from long-range interactions should be more prevalent with small, almost
spherical solutes. One such study would involve trichloroethane, 2,2-dichloropropane
and 2-chloro-2-methylpropane. These three solutes have a small shape anisotropy and
very different electrostatic properties and it would be interesting to investigate the orientational ordering of these almost spherical solutes[94,95].
Bibliography
[1 Reinitzer, F., 1888, Monatsh., 9, 421.
[2; Lehmann, 0., 1889, Z. Phys. Chem., 4.
[3 de Gennes, P. and Prost, J., 1993, The Physics of Liquid Crystals, Clarendon Press,
Oxford, 2 edition.
nd
[4 Kohli, M., Otness, K., Pynn, R., and Riste, T., 1976, Z. Phys., 24B, 147.
[5 de Gennes, P., 1972, C. R. Acad. Sci. (Paris), B 274, 142.
[6 Terzis, A. and Photinos, D., 1994, Mol. Phys., 83, 847.
[7 Emsley, J., Hashim, R., Luckhurst, G., Rumbles, G., and Viloria, F., 1983, Mol.
Phys., 49, 1321.
[s;
Burnell, E. and de Lange, C , 1998, Chem. Rev., 98, 2359.
[9 Gelbart, W., 1982, J. Phys. Chem., 86, 4289.
[10; Frenkel, D., 1989, Liq. Crystals, 5, 929.
[11 Vertogen, G. and de Jeu, W., 1989, Thermotropic Liquid Crystals, Fundamentals
Springer, Heidelberg, 2 edition.
nd
[12; Vroege, G. and Lekkerkerker, H., 1992, Rep. Prog. Phys., 55, 1241.
[13 Poison, J. and Burnell, E., 1996, Mol. Phys., 88, 767.
[14 Terzis, A., Poon, C , Samulski, E., Luz, Z., Poupko, R., Zimmermann, H., Muller,
K., Toriumi, H., and Photinos, D., 1996, J. Am. Chem. Soc., 118, 2226.
[is:
Photinos, D., Samulski, E., and Toriumi, H., 1990, J. Phys. Chem., 94, 4694.
[16 Emsley, J., Palke, W., and Shilstone, G., 1991, Liquid Crystals, 9, 643.
[17; Photinos, D., Poon, C , Samulski, E., and Toriumi, H., 1992, J. Phys. Chem., 96,
8176.
[18] Syvitski, R. and Burnell, E., 1997, Chem. Phys. Letters, 281, 199.
99
Bibliography
100
[19] Syvitski, R. and Burnell, E., submitted, J. Chem. Phys.
[20] Patey, G., Burnell, E., Snijders, J., and de Lange, C., 1983, Chem. Phys. Letters,
99, 271.
[21] van der Est, A., Burnell, E., and Lounila, J., 1988, J. Chem. Soc, Faraday Trans.
2, 84, 1095.
[22] Barker, P., van der Est, A., Burnell, E., Patey, G., de Lange, C., and Snijders, J.,
1984, Chem. Phys. Letters, 107, 426.
[23] Burnell, E., van der Est, A., Patey, G., de Lange, C., and Snijders, J., 1987, Bull.
Magn. Reson., 9, 4.
[24] Diehl, P., Sykora, S., Niederberger, W., and Burnell, E., 1974, J. Mag. Reson., 14,
260.
[25] van der Est, A., Burnell, E., Barnhoorn, J., de Lange, C., and Snijders, J., 1988,
J. Chem. Phys., 89, 4657.
[26] van der Est, A., Kok, M., and Burnell, E., 1987, Mol. Phys., 60, 397.
[27] Photinos, D. and Samulski, E., 1993, J. Chem. Phys., 98, 10009.
[28] Emsley, J., Heeks, S., Home, T., Howells, M., Moon, A., Palke, W., Patel, S.,
Shilstone, G., and Smith, A., 1991, Liquid Crystals, 9, 649.
[29] Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. M., and Teller,
E., 1953, J. Chem. Phys., 21, 1087.
[30] Drobny, G., Pines, A., Sinton, S. W., Weitekamp, D. P., and Wemmer, D., 1979,
Faraday Symp. Chem. Soc, 13, 33.
[31] Sinton, S. and Pines, A., 1980, Chem. Phys. Let, 76, 263.
[32] Warren, W. S. and Pines, A., 1981, J. Am. Chem. Soc., 103, 1613.
[33] Wokaun, A. and Ernst, R., 1977, Chem. Phys. Lett, 52, 407.
[34] Warren, W., Weitekamp, D., and Pines, A., 1980, J. Chem. Phys., 73, 2084.
[35] Pierens, G. K., Carpenter, T. A., Colebrook, L. D., Field, L. D., and Hall, L. D.,
1992, J. Mag. Res., 99, 398.
[36] Barker, P. and Freeman, R., 1985, J. Mag. Res., 64, 344.
[37] Lounila, J. and Jokisaari, J., 1982, Prog. NMR Spectrosc, 15, 249.
101
Bibliography
[38] March, J., 1992, Advanced Organic Chemistry: Reactions, Mechanisms and S
ture, Wiley-Interscience, New York, 4 edition.
rd
[39] Poison, J. and Burnell, E., 1997, Phys. Rev. E, 55, 4321.
[40] Syvitski, R. and Burnell, E., 1999, Can. J. Chem., 77, 1761.
[41] Syvitski, R. and Burnell, E., in press, J. Mag. Res.
[42] Diehl, P. and Khetrapal, C , 1969, p 1, NMR Basic Principles and Progress, volume 1, Springer-Verlag, Berlin.
[43] Emsley, J. W. and Lindon, J., 1975, NMR Spectroscopy using Liquid Crystal Solvents, Pergamon Press, Oxford.
[44] Poison, J. and Burnell, E., 1995, J. Chem. Phys., 103, 6891.
[45] Chandrakumar, T., Poison, J., and Burnell, E., 1996, J. Magn. Reson., A 118,
264.
[46] Zimmerman, D. S. and Burnell, E., 1993, Mol. Phys., 78, 687.
[47] Ferrarini, A., Moro, G., Nordio, P., and Luckhurst, G., 1992, Mol. Phys., 77, 1.
[48] Yim, C. and Gilson, D., 1990, Can. J. Chem., 68, 875.
[49] Barnhoorn, J., de Lange, C., and Burnell, E., 1993, Liquid Crystals, 13, 319.
[50] Bodenhausen, G., 1981, Prog. NMR Spectrosc, 14, 137.
[51] Slichter, C. P., 1990, Principles of Magnetic Resonance, Springer-Verlag, New York,
3 edition.
rd
[52] Poison, J. and Burnell, E., 1994, J. Magn. Reson., A 106, 223.
[53] Rendell, J. and Burnell, E., 1995, J. Magn. Reson., A 112, 1.
[54] Keller, P. and Liebert, L., 1978, Solid State Phys. Supplemental, 14, 19.
[55] Sykora, S., J. Vogt, H. B., and Diehl, P., 1979, J. Mag. Res., 36, 53.
[56] Wong, T. and Burnell, E., 1976, J. Magn. Reson., 22, 227.
[57] Dennis, J. E., Gay, D. M., and Welsch, R. E., 1981, ACM Trans. Math. Software,
7, 3.
[58] Burnell, E. and Diehl, P., 1972, Mol. Phys., 24, 489.
102
Bibliography
[59] Lister, D., MacDonald, J., and Owen, N., 1978, Internal Rotation and Inversion,
Academic Press, London.
[60 Diehl, P., Kellerhals, H. P., and Niederberger, W., 1971, J. Mag. Res., 4, 352.
[61 Long, D. A., 1953, Proc. R. Soc. A, 217, 203.
[62 Snijders, J., de Lange, C , and Burnell, E., 1983, Israel J. Chem., 23, 269.
[63 Wasser, R., Kellerhals, M., and Diehl, P., 1989, Mag. Res. in Chem., 27, 335.
[64 Barnhoorn, J. and de Lange, C , 1996, Mol. Phys., 88, 1.
[65 Kaski, J., Vaara, J., and Jokisaari, J., 1996, J. Am. Chem. Soc, 118, 8879.
[66 Kuchitsu, K. and Cyvin, S., 1972, Molecular Structure and Vibrations, Elsiver,
Amsterdam.
[67; Robiette, A., 1973, Specialist Periodical Reports, Molecular Structure by Diffra
Methods, Chem. Soc, London, 1 edition.
st
[68; Lucas, N., 1971, Mol. Phys., 22, 147.
[69 Emsley, J. and Lindon, J., 1975, Mol. Phys., 29, 531 (and references therein).
[70;
Diehl,.P. and Niederberger, W., 1973, J. Mag. Res., 9, 495.
[71 Program written by R. L. Hilderbrandt utilizing the methods developed by R. L.
Hilderbrandt and J. D. Wieser, J. Chem. Phys. 55, 4648 (1971); M. Toyama, T.
. Oka and Y. Morino, J. Mol. spectrosc. 13, 193 (1964); Y. Morino and E. Hirota, J.
Chem. Phys. 23, 737 (1955).
[72 Scherer, J. R., 1964, Spectrochim. Acta, 20, 345.
[73; Draeger, J. A., 1985, Spectrochim. Acta, 41A, 697.
[74 Duncan, J., 1964, Spectrochim. Acta, 20, 1197.
[75; Duncan, J., McKean, D., and Nivellini, G., 1976, J. Mol. Struct, 32, 255.
[76 Syvitski, R., Poison, J., and Burnell, E., 1999, Int. J. Mod. Phys. C, 10, 403.
[77; Frenkel, D., Mulder, B. M., and McTague, J. P., 1984, Phys. Rev. Letters, 52, 287.
[78; Frenkel, D., 1987, Mol. Phys., 60, 1.
[79; Samborski, A., Evans, G. T., Mason, C. P., and Allen, M. P., 1994, Mol. Phys.,
81, 263.
Bibliography
103
[80] Barnhoorn, J. and de Lange, C , 1994, Mol. Phys., 82, 651.
[81] Emsley, J., Luckhurst, G., and Sachdev, H., 1989, Mol. Phys., 67, 151.
[82] Celebre, G., De Luca, G., Longeri, M., and Ferrarini, A., 1994, Mol. Phys., 83,
309.
[83] M. Pau and R.T. Syvitski and E.E. Burnell, study currently in progress.
[84] Gaussian 98, Revision A.6, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E.
Scuseria, M. A: Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery, Jr.,
R. E. Stratmann, J. C. Burant, S. Dapprich, J. M. Millam, A. D. Daniels, K. N.
Kudin, M. C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B.
Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G. A. Petersson, P. Y.
Ayala, Q. Cui, K. Morokuma, D. K. Malick, A. D. Rabuck, K. Raghavachari, J.
B. Foresman, J. Cioslowski, J. V. Ortiz, B. B. Stefanov, G. Liu, A. Liashenko, P.
Piskorz, I. Komaromi, R. Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A. AlLaham, C. Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P. M. W. Gill,
B. Johnson, W. Chen, M. W. Wong, J. L. Andres, C. Gonzalez, M. Head-Gordon,
E. S. Replogle, and J. A. Pople, Gaussian, Inc., Pittsburgh PA, 1998.
[85] Flygare, W. and Benson, R., 1971, Mol. Phys., 20, 225.
[86] Gierke, T., Tigelaar, H , and Flygare, W., 1972, J. Am. Chem. Soc., 94, 330.
[87] Hernandez-Trujillo, J. and Vela, A., 1996, J. Phys. Chem., 100, 6524.
[88] Celebre, G., De Luca, G., and Ferrarini, A., 1997, Mol. Phys., 92, 1039.
[89] Allen, M. P., Evans, G. T., Frenkel, D., and Mulder, B. M., 1993, Adv. Chem.
Phys., 136, 1.
[90] Frenkel, D. and Mulder, B. M., 1985, Mol. Phys., 55, 1171.
[91] Kok, M., van der Est, A., and Burnell, E., 1988, Liquid Crystals, 3, 485.
[92] van der Est, A., Barker, P., Burnell, E., de Lange, C , and Snijders, J., 1985, Mol.
Phys., 56, 161.
[93] Burnell, E., de Lange, C , and Snijders, J., 1982, Phys. Rev., A25, 2339.
[94] K. Cheng and R.T. Syvitski and E.E. Burnell, study currently in progress.
[95] Cheng, K. W. Y. A., 1999, In Search of Dipole Ordering in Nematic Liquid Cryst
Honour's thesis, University of British Columbia.
Bibliography
104
[96] Diehl, P., Jokisaari, J., and Amrein, J., 1982, J. Mag. Res., 48, 495.
[97] Cradock, S., Liescheski, P. B., and Rankin, D. W. H., 1991, J. Mag. Res., 91, 316.
[98] Diehl, P. and Moia, F., 1981, Organ. Mag. Res., 15, 326.
[99] Diehl, P. and Bosiger, H., 1977, J. Mol. Struct, 42, 103.
100] Diehl, P., Heinrichs, P., and Niederberger, W., 1971, Mol. Phys., 20, 139.
101] Diehl, P. and Bosiger, H., 1977, Org. Magn. Reson., 9, 98.
102] Yamamota, O., Hayamiza, K., Sekine, K., and Funahira, S., 1972, Anal. Chem.,
44, 1974.
103] Almenningen, A. and Hargittai, I., 1984, J. Mol. Struct, 116, 119.
104] Chen, P. C. and Wu, C. W., 1995, J. Phys. Chem., 99, 15023.
105] Domenicano, A., Schultz, G., Kolonits, M., and Hargittai, I., 1979, J. Mol. Struct,
53, 197.
106] Richard, E., Walker, R., and Weisshaar, J., 1996, J. Chem. Phys., 104, 4451.
107] Gough, K., Henry, B., and Wildman, T., 1985, J. Mol. Struct, 124, 71.
108] Anderson, D., Cradock, S., Liescheski, P., and Rankin, D., 1990, J. Mol. Struct,
216, 181.
[109] Lu, K., Weinhold, F., and Weisshaar, J., 1995, J. Chem. Phys., 102, 6787.
Appendixes
105
Appendix A
Solutes
106
Appendix A. Solutes
107
Appendix B
Dipolar Couplings
108
109
Appendix B. Dipolar Couplings
Table B.6: Fitting Parameters and RMS Errors from
Analysis of High-Resolution and MQ NMR Spectra
0
Solute
ZLI 1132
Sample #1
Liquid Crystal
55 wt% 1132/EBBA
#2
EBBA
#3
1342.01(15)
915.69(61)
-269.16(61)
135.7
-9.94
1859.34(38)
1.28
1206.45(14)
836.29(70)
-240.92(57)
135.7
-9.94
2350.32(38)
1.17
1077.56(27)
777.6(10)
-214.9(11)
135.7
-9.94
1904.00(66)
2.08
15
13
15
2200.24(30)
-310.03(40)
-2.848(74)
1820.88(63)
1460.8(10)
1.83
1475.25(09)
-207.58(11)
-2.28(21)
2318.98(18)
2091.79(29)
0.54
602.91(12)
-84.02(15)
-2.36(28)
1878.27(26)
1811.65(45)
0.73
15
15
13
190.85(08)
2748.95(19)
0.20
166.25(08)
3251.12(19)
0.20
144.93(12)
2808.05(31)
0.31
Parameter
6
acetonitrile
DHC(methyl)
Dc
H
{JHC'{methyl))
0
(JHCY
M
RMS Error
Number of lines
assigned
d
propyne
DH (methyl) H (methyl)
DHH(methyl)
JHH(methyl)
{vH(methyl))
d
RMS Error
Number of lines
assigned
1,3,5-trichlorobenzene
e
M
RMS Error
Number of lines
assigned
d
110
Appendix B. Dipolar Couplings
Sample #4
#5
#6
-1862.92(07)
-280.89(16)
-80.45(06)
-43.01(24)
-624.69(18)
-42.53(21)
7.608
1.451
0.864
1.781
7.280
1.301
-3851.15(02)
-3870.82(02)
-4019.38(01)
0.298
-1282.57(06)
-187.54(21)
-45.04(06)
-9.12(36)
-352.96(24)
-8.57(33)
7.608
1.451
0.864
1.781
7.280
1.301
-3976.17(03)
-3973.60(03)
-4071.38(01)
0.330
-1506.95(06)
-199.17(46)
-12.39(05)
72.60(64)
-99.53(40)
71.44(67)
7.608
1.451
0.864
1.781
7.280
1.301
-2895.17(07)
-2880.10(07)
-3011.00(01)
0.289
39
39
35
-1870.33(08)
-279.68(13)
-81.16(07)
-46.31(13)
-617.57(05)
-635.73(13)
-46.37(14)
-176.35(06)
-133.58(13)
2464.93(03)
8.00
0.92
0.94(16)
-1262.18(02)
-186.31(03)
-50.01(01)
-21.90(03)
-407.24(01)
-394.32(03)
-21.76(03)
-118.11(02)
-90.26(03)
1662.25(01)
8.00
0.92
0.49(44)
-1491.20(10)
-206.09(18)
-32.58(09)
28.07(22)
-426.78(09)
-262.45(25)
27.67(22)
-134.67(11)
-106.39(22)
1963.05(04)
8.00
0.92
0.37(25)
chlorobenzene
01,2
01,3
01,4
^1,5
02,3
02,4
(W
(J*AY
RMS Error
Number of
assigned lines
toluene
01,2
01,3
01,4
01,5
01,6
02,3
02,4
02,6
03,6
06,7
(*,2)
«A,4
h
111
Appendix B. Dipolar Couplings
«A,6
^2,3
(J2 )
h
A
^2,6
^3,6
(^l)
fl
(^)
9
K)
S
RMS Error
Number of
assigned lines
chlorobenzene
1.86
-0.72(08)
7.28(20)
1.11
0.57(09)
-1.28(27)
-3813.17(01)
-3869.13(01)
-3971.21(02)
-1669.00(01)
0.510
1.86
-0.69(02)
7.46(05)
1.11
0.34(03)
-0.56(08)
-3912.96(01)
-3969.34(01)
-4025.51(01)
-1681.38(01)
0.110
1.86
-0.58(13)
7.27(48)
1.11
0.36(17)
-0.54(43)
-2782.23(02)
-2840.32(02)
-2927.76(02)
-562.88(01)
0.660
171
151
149
213.59(08)
-3707.32(02)
0.199
147.67(06)
-3816.21(01)
0.136
151.55(04)
-2689.23(01)
0.109
3
3
3
Sample #7
#8
#9
-2411.29(07)
-49.89(08)
56.36(08)
8.55
0.39
2.57
-2621.48(09)
0.186
-2255.46(17)
-24.02(19)
99.98(19)
8.55
0.39
2.57
-2699.33(25)
0.620
-3035.20(15)
27.68(16)
254.98(15)
8.55
0.39
2.57
-3058.53(22)
0.531
8
10
10
e
D
HH
(VH)
9
RMS Error
Number of
assigned lines
p-dichlorobenzene
01,2
01,3
01,4
(»i)
RMS Error
Number of
assigned lines
9
Appendix B. Dipolar Couplings
112
p-chlorotoluene
01,2
01,3
01,4
A,5
02,3
02,5
05,6
Jl,2
^2,5
(^)
s
RMS Error
Number of
assigned lines
1,3,5-tr ichlor obenzene
-2596.80(06)
-41.16(06)
83.51(16)
-707.50(07)
83.30(17)
-231.75(06)
3424.82(04)
8.52 (22)
0.39
2.58
-0.64(08)
2.58
0.28(09)
-2537.69(17)
-2605.87(18)
-482.12(07)
0.563
-2323.54(07)
-23.24(08)
102.78(20)
-605.32(09)
102.21(21)
-204.91(09)
3063.94(04)
8.42(66)
0.39
2.58
-0.58(12)
2.58
0.36(13)
-2606.36(21)
-2688.29(24)
-502.43(09)
0.612
-2901.55(09)
11.83(08)
211.14(23)
-673.78(11)
210.49(23)
-248.26(10)
3828.14(05)
8.49(41)
0.39
2.58
-0.64(13)
2.58
0.45(13)
-2934.16(26)
-3045.33(26)
-849.59(09)
0.688
132
100
111
203.29(01)
-2580.31(02)
0.024
165.53(10)
-2664.43(25)
0.245
156.51(01)
-3058.21(01)
0.013
3
3
3
6
D
HH
RMS Error
Number of
assigned lines
113
Appendix B. Dipolar Couplings
Sample #10
#11
#12
-2403.92(05)
-49.35(06)
57.21(06)
8.55
0.39
2.57
-837.52(07)
0.196
-2189.81(15)
-22.61(16)
97.13(16)
8.55
0.39
2.57
-908.56(22)
0.531
-2702.88(14)
23.80(16)
225.83(16)
8.55
0.39
2.57
-2755.40(21)
0.521
12
10
10
-2670.51(04)
[-2733.9]
-39.60(05)
[-39.8]
87.97(05)
[92.6]
-714.82(03)
[-727.1]
-235.24(03)
[-241.4]
3472.13(04)
[3495.2]
-121.38(25)
[-124.2]
7.93(14)
0.40(15)
2.04(19)
-0.61(06)
0.36(07)
0.56(05)
-756.80(05)
-2229.24(08)
[-2269.0]
-27.47(08)
[-28.0]
85.13(09)
[91.2]
-585.03(06)
[-593.3]
-195.37(07)
[-201.7]
2896.91(10)
[2908.2]
-101.24(05)
[-102.9]
8.16(47)
0.85(39)
1.57(45)
-0.68(12)
0.42(13)
0.57(10)
-826.20(10)
-2369.51(04)
[-2386.7]
-8.58(04)
[-4.6]
131.66(04)
[134.55]
-580.35(03)
[-582.6]
-203.74(04)
[-204.0]
3076.68(02)
[3088.7]
-107.58(02)
[-109.9]
7.59(20)
0.64(18)
1.49(21)
-0.79(06)
0.36(07)
0.60(05)
-2662.65(05)
p-dichlorobenzene
01,2
01,3
01,4
(Jl*Y
RMS Error
Number of
assigned lines
p-xylene
fc
01,2
01,3
01,4
01,5
01,8
05,6
05,8
Jlfi
J\A
J\,b
Jl,8
(»i)
9
114
Appendix B. Dipolar Couplings
RMS Error
Number of
assigned lines
[-756.7]
1307.29(06)
[1299.3]
0.485
[5.113]
[-826.1]
1293.08(13)
[1291.9]
0.780
[4.303]
[-2662.6]
-537.47(05)
[-538.07]
0.522
[9.636]
210
[44]
172
[34]
275
[30]
202.66(01)
-795.85(01)
0.008
160.76(15)
-873.33(38)
0.385
139.70(01)
-2745.15(03)
0.033
3
3
3
Sample #13
#14
#15
-1182.09(05)
-161.98(06)
-84.41(11)
-643.54(12)
8.06
1.52
0.35
7.45
-2160.66(15)
-2245.63(14)
0.230
-887.83(02)
-113.68(03)
-55.62(06)
-427.11(06)
8.06
1.52
0.35
7.45
-2334.90(08)
-2373.25(08)
0.125
-791.22(03)
-68.16(03)
-16.93(18)
-135.99(18)
8.06
1.52
0.35
7.45
-2436.27(23)
-2476.69(23)
0.103
19
20
14
-1124.97(05)
-166.82(09)
-92.91(07)
-910.64(05)
-122.84(10)
-59.00(09)
-950.84(05)
-91.58(28)
-20.37(28)
1,3,5-trichlorobenzene
e
DHH
M
RMS Error
Number of
assigned lines
9
o-dichlorobenzene
01,2
01,3
01,4
02,3
(»i)
9
RMS Error
Number of lines
assigned
o-chlorotoluene
;
01,2
01,3
01,4
115
Appendix B. Dipolar Couplings
A,5
02,3
02,4
02,5
03,4
03,5
04,5
05,6
Jl,2
(Ji,s)
m
(Ji,s)
m
<7,4
2
(^2,5)
TO
•^3,4
(^3, )
m
5
[v y
x
RMS Error
Number of lines
assigned
chlorobenzene
-100.78(04)
-712.98(06)
-168.91(10)
-82.72(04)
-1159.40(06)
-142.29(03)
-705.83(03)
1510.26(02)
8.24(08)
1.64
0.29
0.40
7.54
1.62(11)
-0.60
7.58(07)
0.40
-0.83(05)
-2139.28(09)
-2206.71(09)
-2234.88(06)
-2157.64(06)
-19.02(03)
0.309
-68.02(05)
-452.76(07)
-110.81(10)
-61.45(05)
-866.88(06)
-113.15(03)
-573.11(03)
1121.67(02)
7.86(10)
1.64
0.29
0.40
7.54
1.32(12)
-0.60
7.55(09)
0.40
-0.97(06)
-2301.41(12)
-2333.93(12)
-2365.16(06)
-2289.40(07)
-106.06(04)
0.337
-44.95(27)
-153.44(27)
-60.99(29)
-56.53(27)
-810.02(06)
-120.61(28)
-628.72(04)
1031.86(02)
8.15(31)
1.64
0.29
0.40
7.54
2.04(20)
-0.60
7.54(11)
0.40
-0.77(07)
-2371.73(70)
-2420.63(69)
-2457.61(08)
-2339.36(08)
-193.17(04)
0.379
220
200
156
195.81(04)
-2084.23(09)
0.091
148.90(05)
-2232.41(13)
0.131
131.33(01)
-2317.31(01)
0.002
3
3
3
6
DH
H
M
RMS Error
Number of lines
assigned
9
Appendix B. Dipolar Couplings
Sample #16
#17
#18
-1208.43(03)
-165.02(04)
-85.64(07)
-655.06(07)
8.06
1.52
0.35
7.45
-2562.42(09)
-2651.38(09)
0.154
-987.27(06)
-124.94(07)
-60.29(15)
-464.04(16)
8.06
1.52
0.35
7.45
-3495.31(19)
-3552.21(19)
0.246
-877.21(08)
-74.47(09)
-18.97(55)
-143.58(54)
8.06
1.52
0.35
7.45
-3682.95(68)
-3744.86(68)
0.248
20
17
12
-1157.11(03)
[-1083.9]
-177.32(04)
[-177.0]
-102.07(05)
[-90.8]
-103.89(03)
[-79.6]
-716.87(02)
[-696.6]
-780.36(05)
[-705.7]
-82.70(03)
[-58.6]
-141.16(03)
[-156.3]
1508.17(01)
[1425.5]
-979.16(03)
[-987.9]
-140.23(04)
[-240.7]
-76.60(06)
[-53.0]
-83.42(04)
[-90.5]
-619.37(03)
[-616.0]
-588.10(06)
[-505.4]
-69.81(04)
[13.4]
-121.96(04)
[-189.6]
1271.18(01)
[1284.2]
-968.23(03)
[-967.2]
-116.66(04)
[-115.2]
-54.33(07)
[-62.2]
-72.64(04)
[-69.8]
-641.37(03)
[-638.2]
-419.47(05)
[-419.8]
-68.71(04)
[-76.4]
-125.94(04)
[-118.4]
1247.47(01)
[1245.3]
o-dichlorobenzene
01,2
01,3
01,4
02,3
(W
(W
RMS Error
Number of lines
assigned
o-xylene
n
01,2
01,3
01,4
01,5
01,8
02,3
02,5
02,8
05,6
117
Appendix B. Dipolar Couplings
£>
-252.05(01)
[-237.4]
7.50(06)
1.50(06)
0.54(09)
0.44(05)
-0.69(04)
7.39(09)
-0.86(06)
0.37(06)
0.42(02)
-2534.15(05)
[-2533.7]
-2603.67(05)
[-2592.6]
-377.71(02)
[-369.7]
0.377
[9.18]
-184.40(01)
[-183.0]
7.77(07)
1.41(07)
0.57(11)
0.43(06)
-0.73(05)
7.50(10)
-0.69(07)
0.37(07)
0.40(03)
-3429.84(05)
[-3429.7]
-3500.48(05)
[-3507.6]
-1236.73(03)
[-1232.8]
0.413
[14.88]
-117.93(01)
[-119.5]
7.44(08)
1.37(07)
0.27(11)
0.61(08)
-0.74(05)
7.46(10)
-0.56(09)
0.26(08)
0.44(03)
-3557.98(06)
[-3556.7]
-3649.12(05)
[-3641.0]
-1376.92(03)
[-1373.6]
0.403
[3.02]
501
[22]
427
[22]
374
[24]
1,3,5-trichlorobenzene
D
(p y
RMS Error
Number of lines
200.07(07)
-2486.79(17)
0.174
164.55(01)
-3396.67(01)
0.011
145.88(02)
-3566.11(04)
0.038
assigned
3
3
3
Sample #19
#20
#21
-1342.52(05)
-318.61(11)
-144.36(07)
-1122.42(05).
-275.317(11)
-99.39(07)
-1095.21(05)
-296.046(12)
-37.55(07)
5j8
Ji,
Ji,
J
Ji,
Ji,
J
J
J,
J
(v y
2
3
M
5
8
2)3
2l5
2
8
5)8
x
(v y
2
(i/ )»
8
RMS Error
Number of lines
assigned
e
HH
H
m-dichlorobenzene
D
£>i
Di,
1|2
>3
4
118
Appendix B. Dipolar Couplings
02,4
UM)
0
(J2,4)°
(1/4)'
RMS Error
Number of lines
assigned
Dtoluene
01,2
01,3
01,4
01,5
02,3
02,4
02,5
03,4
03,5
04,5
05,6
Ul,2)
P
(JIAY
(J2,*y
( W
^2,5
(^3,4)
^3,5
^4,5
P
-56.33(09)
8.10
2.00
1.80
0.40
-2339.57(08)
-2240.18(14)
-2022.961(10)
0.265
-26.31(10)
8.10
2.00
1.80
0.40
-2435.74(08)
-2328.10(14)
32.63(10)
8.10
2.00
1.80
0.40
-3850.49(09)
-3677.43(14)
-2137.61(11)
0.262
-3453.63(11)
0.270
28
26
26
-1559.065(23)
-339.72(10)
-103.68(10)
-90.38(06)
-1249.99(30)
-44.05(07)
-72.88(07)
-168.14(09)
-177.47(10)
-919.22(03)
1655.06(02)
8.09
1.10
2.71
-1247.31(56)
-287.14(14)
-80.27(18)
-77.53(10)
-1079.54(68)
-22.98(09)
-59.46(10)
-116.83(18)
-118.44(12)
-1144.35(36)
-303.61(12)
-54.05(11)
-83.24(07)
-1157.04(35)
19.81(08)
-50.72(14)
-54.63(12)
-12.42(12)
-798.88(04)
0.00
0.00
0.00
7.53
0.39
-0.05(14)
1.65
-1.10(20)
-0.84(06)
-2277.75(13)
7.53
0.39
-0.02(20)
1.65
-0.75(27)
-0.42(09)
-2375.82(22)
7.53
0.39
0.57(27)
1.56
-0.50(27)
-0.47(08)
-3775.89(19)
-770.59(18)
1426.57(10)
8.09
1.10
2.71
1531.65(03)
8.09
1.10
2.71
119
Appendix B. Dipolar Couplings
0.350
-2290.13(14)
-2377.84(23)
-2106.64(09)
-91.77(06)
0.426
-3620.80(12)
-3715.48(20)
-3397.48(08)
-1401.47(06)
0.409
159
134
146
205.51(02)
-2137.15(05)
0.046
165.28(06)
-2234.33(14)
0.148
142.13(06)
-3586.12(15)
0.158
3
3
3
Sample #22
#23
#24
-1288.85(03)
-305.41(07)
-139.17(04)
-54.49(07)
8.10
2.00
1.80
0.40
-3057.83(06)
-2962.75(09)
-2757.10(07)
-1029.43(02)
-252.94(05)
-90.88(03)
-23.63(04)
8.10
2.00
1.80
0.40
-3684.85(04)
0.198
0.127
-1151.31(05)
-311.24(11)
-39.17(06)
34.71(09)
8.10
2.00
1.80
0.40
-3842.65(08)
-3661.69(13)
-3419.55(10)
0.240
31
28
26
-1382.31(04)
[-1372.0]
-334.82(27)
-1080.34(03)
[-1139.49]
-263.28(21)
-1211.96(07)
[-1204.28]
-308.63(53)
-2198.39(10)
-2322.36(12)
-2005.36(07)
-54.42(04)
(i/ )»
4
RMS Error
Number of lines
assigned
l,3,5-trichlorobenzene
e
DHH
RMS Error
Number of lines
assigned
m-dichlorobenzene
01,3
01,4
02,4
(Jl,2)°
VIA)
0
(J2A)°
(»l)
9
RMS Error
Number of lines
assigned
m-xylene
-3583.56(06)
-3417.19(04)
n
01,2
01,3
Appendix B. Dipolar Couplings
01,4
01,5
01,8
02,4
02,5
04,5
05,6
05,8
•A ,2
JlA
Jl,5
Jl,&
J2A
^2,5
^4,5
•^5,8
M
d
(^Y
{vsY
[-323.3]
-128.69(04)
[-120.4]
-99.84(04)
[-118.4]
-225.32(03)
[-198.9]
-38.93(07)
[-44.4]
-89.22(04)
[-97.9]
-884.83(01)
[-885.2]
1827.38(01)
[1825.2]
-127.65(01)
[-126.7]
7.69(20)
1.03(12)
1.70(08)
-0.55(08)
-0.70(06)
0.53(13)
0.30(06)
-0.77(02)
-0.22(02)
-2975.53(03)
[-2975.4]
-2907.24(07)
[-2917.5]
-2711.86(04)
[-2708.1]
-767.40(02)
[-770.8]
120
[-284.55]
-95.53(03)
[-96.28]
-78.03(03)
[-82.87]
-159.57(04)
[-155.71]
-25.50(06)
[-21.86]
-67.51(03)
[-68.98]
-697.73(01)
[-744.20]
1426.23(01)
[1510.85]
-100.66(01)
[-107.32]
7.24(17)
0.87(08)
1.87(07)
-0.48(07)
-0.70(08)
0.46(11)
0.32(05)
-0.71(02)
-0.22(01)
-3571.06(03)
[-3571.1]
-3536.71(05)
[-3561.6]
-3353.38(04)
[-3352.1]
-1336.21(02)
[-1358.2]
[-313.64]
-77.29(06)
[-76.55]
-87.66(11)
[-87.67]
-80.20(10)
[-79.16]
0.45(09)
[1.31]
-62.34(04)
[-61.60]
-821.09(01)
[-820.94]
1596.53(01)
[1597.69]
-118.42(01)
[-118.43]
7.06(40)
0.72(99)
1.76(11)
-0.20(22)
-0.97(24)
0.63(17)
0.31(08)
-0.73(02)
-0.30(02)
-3647.19(06)
[-3647.2]
-3571.89(07)
[-3579.3]
-3352.63(05)
[-3361.7]
-1395.72(02)
[-1400.0]
121
Appendix B. Dipolar Couplings
RMS Error
Number of lines
assigned
0.304
[5.85]
0.305
[10.01]
0.384
[11.48]
402
[24]
501
[25]
440
[22]
197.80(04)
-2860.41(11)
0.119
151.74(05)
-3497.34(13)
0.132
149.66(07)
-3565.45(18)
0.186
3
3
3
1,3,5-trichlorobenzene
6
DHH
M
RMS Error
Number of lines
assigned
9
For atom numbering refer to Fig. A.22. Numbers in round brackets are errors (68%
confidence) in the last two reported digits of varied parameters.
Dipolar couplings, J couplings, chemical shifts and RMS Errors are in Hz. Unless
otherwise specified, dipolar couplings, J couplings and chemical shifts are for protons.
Parameters not varied during analysis of spectrum. Values taken from Ref. [96].
Frequency is referenced to an arbitrary zero and is increasing to high field. Spectra
were acquired at 200.05 MHz.
1,3,5-trichlorobenzene is an internal orientational standard.
f Parameters not varied during analysis of spectrum. Values were determined from a
separate analysis of chlorobenzene dissolved in the nematic phase of ZLI 1132.
Frequency is referenced to an arbitrary zero and is increasing to high field. Spectra
were acquired at 500.13 MHz.
Parameters not varied during fitting of spectrum. Values taken from Ref. [60]
Parameters not varied duringfittingof spectrum. Values taken from Ref. [97]
Parameters not varied duringfittingof spectrum. Values taken from Ref. [98]
Values in square brackets are from analysis of the 7-quantum spectrum. J couplings
were set to zero for the MQ analysis.
' Parameters not varied during analysis of spectrum. Values taken from Ref. [99].
Parameters not varied during analysis of spectrum. Values taken from Ref. [100].
Values in square brackets are from the analysis of the 8-quantum spectrum. J couplings
were set to zero for the MQ analysis.
Parameters not varied during analysis of spectrum. Values taken from Ref. [101].
Parameters not varied during analysis of spectrum. Values taken from Ref. [102].
Q
6
c
d
e
9
h
1
J
k
m
n
0
p
122
Appendix B. Dipolar Couplings
Table B.7: Fitting Parameters and RMS Errors from
Analysis of High-Resolution and MQ NMR Spectra of
Sample #25°
Parameter
o-dichlorobenzene
o-chlorotoluene
o-xylene
-1200.30(09)
-1145.14(06)
-1147.51(03) [-1157.53]
L>i,
-163.97(11)
-169.31(10)
-175.93(04) [-169.98]
Di
-84.76(21)
-94.01(07)
-101.17(06) [-101.20]
-102.17(04)
-103.08(02) [-108.11]
6
Di
>2
3
|4
£>i
c
|5
d
Di
-710.74(02) [-711.40]
fi
L>2,
3
-649.78(21)
-720.68(06)
2
-83.95(04)
2)5
D,
-82.10(03) [-80.59]
-139.95(03) [-144.10]
2 8
£>
-774.72(05) [-789.86 ]
-170.79(11)
£> ,4
D
e
-1177.36(06)
3i4
L>3,
-144.66(03)
£4,5
-718.62(03)
L> ,
1533.32(01)
1495.65(01) [1507.09]
5
5 6
Ji,
2
8.06
7.93(09)
7.52(07)
Ji,
3
1.52
1.64
1.29(08)
J
1>4
0.35
0.29
0.55(10)
J
1)5
0.40
0.47(05)
J
1;8
J
2>3
J ,4
J,
2
2
J,
2
J
5
7.45
7.54
7.20(10)
- - -
1-47(11)
-0.60
-0.57(06)
0.27(06)
8
3)4
J ,5
3
J
-0.66(04)
4)5
7.57(09)
0.40
-0.82(05)
123
Appendix B. Dipolar Couplings
J,
5
0.48(02)
8
{u y
-2392.96(27)
-2371.91(09)
-2363.55(05) [-2363.6]
(v y
-2480.69(29)
-2441.83(09)
-2432.16(06) [-2432.2]
x
2
(u y
-2470.72(06)
(u )
-2391.22(06)
- - -
258.00(03)
-204.36(02) [-207.5]
0.421
0.301
0.419 [7.79]
18
188
437 [23]
3
f
4
(v )
f
5
RMS Error
Number of lines
assigned
For atom numbering refer to Fig. A.22. Numbers in round brackets are errors (68%
confidence) in the last two reported digits of varied parameters.
Dipolar couplings, J couplings, chemical shifts and RMS Errors are in Hz. Dipolar
couplings, J couplings and chemical shifts are for protons.
J couplings are not varied during analysis of spectrum. Values taken from Ref. [99].
Some J couplings are not varied during analysis of spectrum. Values taken from
Ref. [100].
Values in square brackets are from the analysis of the 8-quantum spectrum. J couplings
were set to zero for the MQ analysis.
•f Frequency is referenced to an arbitrary zero and is increasing to high field. Spectra
were acquired at 500.13 MHz.
Resonance frequency, dipolar coupling and RMS error for 1,3,5-trichlorobenzene was
determined to be -2317.02(02), 198.59(01) and 0.028 Hz.
a
6
c
d
e
9
Appendix C
Structural Parameters
124
125
Appendix C. Structural Parameters
Table C.8: Molecular Parameters" from Fits to Vibrationally Corrected Dipolar Couplings
Solute
acetonitrile
Propyne"
Molecular
Parameter
r(C-H(methyl)){
r (C-C (methyl)){
r(N=C or C=C){
r(C-H){
<(C-C-H (methyl))/
6
0
fitted
a priori*
fitted
a priorf
1.0994(71)
1.1044(15)
1.4634(91)
1.4596(15)
fitted
1.1627
a priorf
fitted
a priori
6
fitted
a priorf
RMS'
110.025(22)
109.994(150)
3.74
1.1030(05)
1.1010(10)
1.4703(06)
1.4710(10)
1.2066(06)
1.2073(10)
1.0593(06)
1.0600(10)
109.977(42)
110.251(100)
0.25
Numbers in round brackets are standard deviations in the last reported digits of varied
parameters. Bond distances (r) in A and bond angles (<) in degrees. In the least squares
a
fit to experimental dipolar couplings the weight given to each dipolar coupling is ^ error )
where the errors are reported in Table B.6.
For axis definitions see Fig. A.22
a priori estimates were taken from the r structure reported in Ref. [74]
a priori estimates were taken from the r structure reported in Ref. [75]
a priori estimates[56] are values of structural parameters (taken from other studies) that
have an associated error and are adjusted in the least-squares routine; large deviations of
the a priori estimates are discouraged by the least-squares criteria. For the least squares
6
c
a
d
a
e
fitting routine the weight associated with the a priori estimates is (
) where the
errors are reported in brackets.
RMS error in Hz between vibrationally corrected and calculated dipolar couplings.
errx>r
1
Appendix C. Structural Parameters
Table C.9: Structural Parameters from Fits to Dipolar Couplings for chlorobenzene, toluene and 1,3,5trichlorobenzene
a
Parameter
n
r(C2-Hl) {
V
n
r(C3-H2) |
V
n
r(C4-H3) {
V
1.0812(04)
1.0819(02)
1.0838(15)
1.0831(15)
1.0803(05)
1.0791(02)
1.0824(14)
1.0792(14)
1.0803(04)
1.0808(02)
1.0742(17)
1.0778(17)
V
n
Z(C4C3H2) {
V
121.53(08)
121.30(04)
120.11(09)
120.27(09)
121.04(07)
120.66(03)
120.53(10)
120.41(10)
V
n
Z(C2C1C7) {
0.3098
0.1601
6
121.0
120.85
120.85
V
d
1.094
110.49(17)
111.42(17)
n
Z(C2C1H6) {
1.094
1.4896(51)
1.5044(46)
n
n
1,3,5-trichlorobenzene
1.0983(10) )
1.0929(11) )
V
Z(C3C2H1) {
r(C2-Hl)
r(C3-H2)
r(C4-H3)
r(C7-H6)
r(Cl-C7)
Z(C3C2H1)
toluene
V
r(Cl-C7) {
a priori estimates
chlorobenzene
n
r(C7-H6) {
R M S Error
R M S Error
6
0.3150
0.3111
h
1
1.0823(02)
1.0787(02)
1.0808(02)
120.89(05)
1.077(02)
1.076(02)
1.076(02)
1.113(02)
1.516(05)
119.70(05)
c
1.094
1.094
.121.0
c
127
Appendix C. Structural Parameters
Z(C4C3H2)
Z(C1C7H6)
Z(C2ClC7)
120.56(05)
i
—
Fixed Parameters
r(Cl-C2)
r(C2-C3)
r(C3-C4)
r(Cl-Cl)
Z(C1C2C3)
Z(C2C3C4)
Z(C3C4C5)
Z(C3C4H3)
Z(C2C1C1)
—
9
1.389
1.394
1.393
1.739
119.04
120.06
120.23
119.89
119.27
120.10(05)
110.00(05)
120.70(-)
h
1.388
1.388
1.383
120.90
120.20
119.50
120.30
—
—
—
c
1.3908
1.3908
1.3908
1.7326
118.0
122.0
118.0
121.0
119.0
Refer to Fig. A.22 for structure and atom numbering of molecules. Bond distances
r in A and bond angles Z in degrees. In the least squares fit to experimental dipolar
a
couplings the weight given to each dipolar coupling is ^ error j where the errors are from
Table B.6. Numbers in round brackets are statistical errors (68% confidence) in the last
two reported digits of varied parameters.
Parameters which are indicated with "n" are calculated with no vibrational corrections to dipolar couplings whereas parameters indicated with "v" are calculated with
vibrational corrections and are the r structural parameters.
Structural parameters not adjusted. From Ref. [103]. 1,3,5-trichlorobenzene is an
internal orientational standard.
RMS Error in Hz between calculated and experimental dipolar couplings.
RMS Error in Hz between vibrationally corrected and experimental dipolar couplings.
' a priori estimates are from Ref. [63] and [104] and the weight associated with the
6
Q
c
d
e
estimates is (error)
the errors are reported in brackets.
r structure determined from liquid-crystal NMR data which has been corrected for
normal mode vibrations and orientational-vibrational correlations [63].
From molecular orbital calculations using Gaussian 92 and HF/6-31G* theory/basis
set [104].
no error is associated with this parameter. This is adjusted so the C1-C7 (and C4-C8)
bond directions are collinear with the z axis of the molecule.
w n e r e
9
h
1
a
Appendix C. Structural Parameters
Table C.10: Structural Parameters from Fits to Dipolar
Couplings for p-disubstituted benzenes"
Parameter
p-dichlorobenzene
p-chlorotoluene
p-xylene
n
1.0760(04)
1.0760(03)
1.0792(53)
1.0806(04)
1.0914(11)
1.0890(14)
1.0760(04)
1.0760(03)
1.0737(63)
1.0749(05)
1.0914(11)
1.0890(14)
1.1032(04)
1.0986(04)
1.1038(08)
1.0988(11)
1.4898(06)
1.4892(05)
1.5066(16)
1.5109(22)
120.58(01)
120.58(01)
118.84(05)
119.31(04)
119.67(01)
119.78(01)
(119.99)
(119.95)
120.27(07)
120.41(05)
(118.93)
(118.82)
110.12(05)
111.50(04)
109.84(08)
111.12(11)
120.90
120.88
121.4
121.4
0.3121
0.2195
0.2949
0.2335
0.3867
0.4795
9
1.076(02)
1.076(02)
h
1.0811(02)
1.0745(02)
1.0989(02)
1.4891(02)
118.90(05)
120.40(05)
111.17(05)
120.91(-)
1.076(02)
1.076(02)
1.113(02)
1.512(02)
120.80(05)
(117.8)
110.30(05)
121.4(-)
6
r(C2-Hl) {
r(C3-H2) {
r(C7-H5) |
r(Cl-C7) {
Z(C3C2H1) {
Z(C4C3H2) {
Z(C1C7H5) {
Z(C2C1C7) {
RMS Error
RMS Error
d
e
a priori estimates ^
r(C2-Hl)
r(C3-H2)
r(C7-H5)
r(Cl-C7)
Z(C3C2H1)
Z(C4C3H2)
Z(C1C7H5)
Z(C2C1C7)J
V
n
V
n
V
n
V
n
V
n
V
c
c
n
V
n
V
120.05(05)
(120.48)
c
c
c
c
129
Appendix C. Structural Parameters
Fixed Parameters
r(Cl-C2)
r(C2-C3)
r(C3-C4)
r(C4-Cl)
Z(C1C2C3)
Z(C2C3C4)
Z(C3C4C5)
Z(C3C4C1)
9
1.395
1.391
1.395
1.729
119.47
119.47
121.06
119.47
h
i
1.406
1.404
1.400
1.72
121.52
118.64
121.48
119.26
1.405
1.392
1.405
121.40
121.40
117.10
Refer to Fig. A.22 for structure and atom numbering of molecules. Bond distances
r in A and bond angles Z in degrees. In the least squares fit to experimental dipolar
a
couplings the weight given to each dipolar coupling is (
) where the errors are from
Table B.6. Numbers in round brackets are statistical errors (68% confidence) in the last
two reported digits of varied parameters.
Parameters which are indicated with "n" are calculated with no vibrational corrections to dipolar couplings whereas parameters indicated with "v" are calculated with
vibrational corrections and are the r structural parameters.
Parameters are calculated from Z(C1C2C3) and Z(C3C2H1).
RMS Error in Hz between calculated and experimental dipolar couplings.
RMS Error in Hz between vibrationally corrected and experimental dipolar couplings.
* a priori estimates are from Ref. [97], [98] and [105] and the weight associated with the
e r r o r
6
a
c
d
e
estimates is (
r) h
the errors are reported in brackets.
r structure from a joint analysis of liquid-crystal NMR, electron diffraction and rotational spectroscopy data [97].
r structure from liquid-crystal NMR data which has been corrected for normal mode
vibrations [98].
r structure from electron diffraction data [105].
no error is associated with this parameter. This is adjusted so the C1-C7 (and C4-C8)
bond directions are collinear with the z axis of the molecule.
w
e r r 0
9
a
h
a
1
a
J
e r e
Appendix C. Structural Parameters
Table C.ll: Structural Parameters from Fits to Dipolar
Couplings for o-disubstituted benzenes"
Parameter
6
r(Cl-C2) {
r(C2-C3) |
r(C3-C4) {
r(C4-C5) {
r(C5-C6) {
r(C6-Cl) {
r(Cl-Hl) {
r(C2-X) {
r(C3-H3) {
r(C4-X) {
r(C5-X) {
r(C6-X) {
r(C7-H5) {
<(C1C2C3) {
n
V
n
V
n
V
n
V
n
V
n
V
n
V
n
V
n
V
n
V
n
V
n
V
o-dichlorobenzene
o-chlorotoluene
o-xylene
1.3799(15)
1.3793(13)
1.3849(30)
1.3839(34)
1.3751(59)
1.3764(62)
1.4025(15)
1.4001(13)
1.3982(23)
1.3938(26)
1.3820
1.3820
1.3799(15)
1.3793(13)
1.3890(30)
1.3909(33)
1.3751(59)
1.3764(62)
1.3822(16)
1.3826(14)
1.3840(30)
1.3836(34)
1.3771(58)
1.3764(62)
(1.4050)
(1.4054)
(1.3850)
(1.3839)
(1.3880)
(1.3924)
1.3822(16)
1.3826(14)
1.385
1.385
1.3771(58)
1.3764(62)
1.0819(15)
1.0826(13)
1.0754(30)
1.0753(33)
1.0732(18)
1.0726(19)
1.0890(15)
1.0883(13)
1.0830(36)
1.0842(39)
1.0912(59)
1.0944(60)
1.0890(15)
1.0883(13)
1.0909(35)
1.0909(39)
1.0912(59)
1.0944(60)
1.0819(15)
1.0826(13)
1.0733(19)
1.0726(21)
1.0732(18)
1.0726(19)
1.733
1.733
1.5202(48)
1.5250(53)
1.5288(20)
1.5294(21)
1.733
1.733
1.751
1.751
1.5288(20)
1.5294(21)
1.1051(18)
1.1037(20)
1.1054(20)
1.1045(18)
119.10(26)
118.69(34)
118.97(13)
118.97(14)
d
d
c
c
c
c
n
V
n
V
119.54(07)
119.65(06)
d
d
c
c
c
c
c
c
d
d
131
Appendix C. Structural Parameters
<(C2C3C4) {
<(C3C4C5) {
<(C4C5C6) {
<(C5C6C1) {
<(C6C1C2) {
<(C2C1H1) {
<(C3C2X) {
<(C2C3H3) {
<(C3C4X) {
<(C4C5X) {
<(C1C6X) {
<(CXC7H5) {
n
V
n
V
n
119.54(07)
119.65(06)
118.94(19)
119.57(30)
118.97(13)
118.97(14)
121.01(12)
120.86(10)
122.00
122.00
122.24(15)
122.35(16)
(119.43)
(119.48)
117.50
117.50
(118.78)
(118.67)
(119.43)
(119.48)
121.40
121.40
(118.78)
(118.67)
121.01(12)
120.86(10)
(121.04)
(120.83)
122.24(15)
122.35(16)
121.10(14)
120.99(12)
121.86(48)
121.50(54)
120.00(48)
120.36(50)
120.46(12)
120.33(10)
119.96(33)
119.72(43)
118.82(19)
118.85(20)
120.46(12)
120.33(10)
119.65(24)
118.71(36)
118.82(19)
118.85(20)
121.10(14)
120.99(12)
119.64(12)
119.69(13)
120.00(48)
120.36(50)
118.99
118.99
118.88(14)
118.65(16)
119.94(24)
119.03(25)
118.99
118.99
116.90
116.90
119.94(24)
119.03(25)
110.48(23)
111.73(26)
110.21(23)
111.53(24)
0.5148
0.5667
0.7022
0.7337
d
d
V
n
d
d
V
n
V
n
V
n
V
n
V
n
V
n
c
c
V
n
6
6
V
n
V
RMS Error
RMS Error'
0.5630
0.4914
6
a priori estimates
r(Cl-C2)
r(C2-C3)
r(C3-C4)
r(C4-C5)
r(C5-C6)
r(C6-Cl)
r(Cl-Hl)
r(C2-X)
r(C3-H3)
9
c
6
d
6
c
d
6
d
d
6
d
d
c
6
h
1.3760(02) 1.38200(025)
1.3960(02) 1.38500(025)
1.3760(02) 1.38300(025)
1.3850(02) 1.39300(025)
1.4078(02)'' 1.38990(025)
1.385
1.3850(02)
1.0870(02) 1.08000(025)
1.0800(03)
1.0840(02)
1.0800(03)
1.0840(02)
d
c
3
1.38700(015)
1.3820
1.38700(015)
1.38800(015)
1.3978(03)
1.38800(015)
1.0820(01.)
1.0820(01)
1.0820(01)
c
d
132
Appendix C. Structural Parameters
r(C4-X)
r(C5-X)
r(C6-X)
r(C7-H5)
<(C1C2C3)
<(C2C3C4)
<(C3C4C5)
<(C4C5C6)
<(C5C6C1)
<(C6C1C2)
<(C2C1H1)
<(C3C2X)
<(C2C3H3)
<(C3C4X)
<(C4C5X)
<(C1C6X)
<(CXC7H5)
1.0870(02)
1.7330
1.7330
c
c
120.30(05)
120.30(05)
119.90(02)
119.80(05)"
119.80(05)
119.90(02)
120.28(02)
120.10(05)
120.10(05)
120.28(02)
118.99
118.99
d
c
c
1.08000(016)
1.5100(04)
1.751
1.09600(025)
119.65(05)
119.75(05)
122.0
117.50
121.40
119.70(05)
120.15(05)
120.18(05)
120.13(05)
119.40(01)
119.90(05)
116.90
111.00(04)
c
C
c
c
d
c
1.0820(02)
1.5260(015)
1.5260(015)
1.0960(01)
119.60(05)
119.60(05)
121.20(01)
120.00(05)
120.00(05)
121.20(01)
119.50(03)
120.40(05)
120.40(05)
119.50(03)
120.00(05)
120.00(05)
110.90(02)
d
d
Refer to Fig. A.22 for structure and atom numbering of molecules. Bond distances (r)
in A and bond angles (<) in degrees. In the least squares fit to experimental dipolar
a
couplings the weight given to each dipolar coupling is ^error) where the errors are
reported in Tables B.6 and B.7.
Parameters which are indicated with "n" are calculated with no vibrational corrections
to dipolar couplings and parameters indicated with "v" are calculated with vibrational
corrections.
Parameter not adjusted during fit.
Dependent parameter is calculated from the bond angles and lengths of the carbon
skeleton.
RMS Error in Hz between calculated and experimental dipolar couplings.
f RMS Error in Hz between vibrationally corrected and experimental dipolar couplings.
For the least squares fitting routine the weight associated with the a priori estimates
6
c
d
e
9
is ^ r ) where the errors are reported in brackets.
er
0r
r structure from Ref. [99].
* Structure from Ref. [100] and [106].
Structure from Ref. [58] and [107].
h
a
j
Appendix C. Structural Parameters
133
Table C.12: Structural Parameters from Fits to Dipolar
Couplings for m-disubstituted benzenes
0
Parameter
6
r(Cl-C2) {
r(C2-C3) {
r(C3-C4) {
r(C4-C5) {
r(C5-C6) {
r(C6-Cl) {
r(Cl-Hl) {
r(C2-X) {
r(C3-H3) {
r(C4-X) {
r(C5-X) {
r(C6-X) {
r(C7-H5) {
<(C1C2C3) {
n
V
n
V
n
V
n
V
n
V
n
V
n
V
n
V
n
V
n
V
n
V
n
V
m-dichlorobenzene
m-chlorotoluene
m-xylene
1.4039(05)
1.4041(06)
1.3846(12)
1.3857(14)
1.3991(42)
1.4013(34)
1.4039(05)
1.4041(06)
1.3818(12)
1.3830(14)
1.3991(42)
1.4013(34)
1.3921(06)
1.3920(06)
1.3880(12)
1.3889(15)
1.3884(23)
1.3896(22)
(1.3872)
(1.3872)
1.3901(12)
1.3904(15)
(1.3941)
(1.3930)
(1.3872)
(1.3872)
(1.3860)
(1.3870)
(1.3941)
(1.3930)
1.3921(06)
1.3920(06)
1.382
1.382"
1.3884(23)
1.3896(22)
1.0846(05)
1.0847(06)
1.0860(12)
1.0886(14)
1.0793(41)
1.0776(33)
1.0913(06)
1.0912(06)
1.0898(12)
1.0899(14)
1.0898(44)
1.0916(36)
1.0846(05)
1.0847(06)
1.0838(12)
1.0845(14)
1.0793(41)
1.0776(33)
1.7355"
1.7355*
1.5096(22)
1.5140(26)
1.5139(20)
1.5193(20)
1.0911(06)
1.0910(06)
1.0860(12)
1.0915(15)
1.0913(22)
1.0883(21)
1.7355
1.7355
1.746
1.746
1.5139(20)
1.5193(20)
1.1014(07)
1.0942(09)
1.1083(09)
1.1006(09)
120.77(10)
120.85(12)
(121.02)
(120.84)
c
c
c
c
d
d
d
V
V
c
d
d
n
n
c
(120.59)
(120.65)
c
c
c
c
c
c
c
c
Appendix C. Structural Parameters
<(C2C3C4) j *
118.40(06)
118.37(06)
119.63(13)
119.84(15)
118.75(28)
119.17(23)
<(C3C4C5) { J
122.40(11)
122.34(11)
119.67(19)
119.55(22)
121.34(26)
120.19(22)
<(C4C5C6) { *
(117.80)
(117.89)
(118.72)
(119.06)
(118.78)
(120.42)
122.40(11)
122.34(11)
121.50
121.50
121.34(26)
120.19(22)
<(C6C1C2) { J
118.40(06)
118.37(06)
119.69(16)
119.16(19)
118.75(28)
119.17(23)
<(C2C1H1) { J
120.67(06)
120.83(07)
120.33(17)
120.61(22)
120.43(80)
120.32(62)
<(C3C2X) { *
119.70(03)
119.67(03)
118.78(11)
118.61(12)
119.48(45)
119.57(35)
<(C2C3H3) { J
120.67(06)
120.83(07)
121.30(11)
121.29(13)
120.43(80)
120.32(62)
<(C3C4X) { *
118.75
118.75
120.34(13)
120.55(15)
119.50(27)
119.96(21)
<(C4C5X) { J
(121.09)
(121.05)
120.43(19)
120.09(22)
(120.60)
(119.78)
118.75
118.75
119.30
119.30
119.50(27)
119.96(21)
110.67(09)
111.78(11)
110.98(12)
111.73(15)
0.2989
0.3466
0.2204
0.2281
c
c
<(C5C6C1) {
1
d
d
6
c
a priori estimates
r(Cl-C2)
r(C2-C3)
r(C3-C4)
r(C4-C5)
r(C5-C6)
r(C6-Cl)
r(Cl-Hl)
r(C2-X)
r(C3-H3)
c
d
d
<(CXC7H5) { J
6
c
d
d
RMS Error
RMS Error'
c
d
d
• <(C1C6X) { J
6
6
c
0.2372
0.2385
h
1.4040(02)
1.4040(02)
1.3920(02)
1.3873(02)
1.3873(02)
1.3920(02)
1.0850(02)
1.0910(02)
1.0850(02)
c
c
1.38500(025)
1.38300(025)
1.39000(025)
1.39000(025)
1.38510(025)
1.3820
1.08500(025)
1.0910(02)
1.08500(025)
c
d
j
1.40400(015)
1.40400(015)
1.39200(015)
1.3873(02)
1.3873(02)
1.39200(015)
1.08500(015)
1.0910(01)
1.08500(015)
c
c
135
Appendix C. Structural Parameters
r(C4-X)
r(C5-X)
r(C6-X)
r(C7-H5)
<(C1C2C3)
<(C2C3C4)
<(C3C4C5)
<(C4C5C6)
<(C5C6C1)
<(C6C1C2)
<(C2C1H1)
<(C3C2X)
<(C2C3H3)
<(C3C4X)
<(C4C5X)
<(C1C6X)
<(CXC7H5)
1.7355
1.0910(02)
1.7355
d
121.10(05)
118.10(05)
122.30(05)
118.10(05)
122.30(05)
118.10(05)
120.70(05)
119.45(05)
120.70(05)
118.75
120.95(05)
118.75
c
c
d
c
d
1.51200(045)
1.09100(025)
1.7460
1.09880(025)
121.100(055)
119.000(055)
119.000(055)
118.570(055)
121.50
120.23(04)
120.700(055)
119.450(055)
120.700(055)
121.100(055)
120.950(055)
119.30
111.120(025)
d
c
d
d
1.51200(025)
1.0910(01)
1.51200(025)
1.09880(015)
121.100(025)
118.100(025)
122.300(025)
118.100(025)
122.300(025)
118.100(025)
120.700(025)
119.450(025)
120.700(025)
121.100(025)
120.950(025)
121.100(025)
111.12(01)
c
c
c
Refer to Fig. A.22 for structure and atom numbering of molecules. Bond distances (r)
in A and bond angles (<) in degrees. In the least squares fit to experimental dipolar
a
couplings the weight given to each dipolar coupling is (error) where the errors are
reported in Table B.6.
Parameters which are indicated with "n" are calculated with no vibrational corrections
to dipolar couplings and parameters indicated with "v" are calculated with vibrational
corrections.
Dependent parameter is calculated from the bond angles and lengths of the carbon
skeleton.
Parameter not adjusted during fit.
RMS Error in Hz between calculated and experimental dipolar couplings.
' RMS Error in Hz between vibrationally corrected and experimental dipolar couplings.
For the least squares fitting routine the weight associated with the a priori estimates
6
c
d
e
9
is (error)
h
J
the errors are reported in brackets.
r structure from Ref. [108].
Structure taken from Ref. [109] and m-dichlorobenzene[108].
Structure taken from ra-dichlorobenzene[108].
a
1
w n e r e
Appendix D
Order Parameters
136
137
Appendix D. Order Parameters
Table D.13: Order Parameters from Fits to Dipolar
Couplings
0
Order
Parameter b
Solute
ZLI 1132
Sample #1
Liquid Crystal
55 wt% 1132/EBBA
#2
EBBA
#3
acetonitrile
V
0.1305(24)
. 0.1174(22)
0.1049(19)
S
V
0.2162(01)
0.1449(01)
0.0592(01)
S
n
-0.2576
-0.2244
-0.1956
Sample #4
#5
#6
0.23724(26)
0.23921(14)
0.29192(15)
0.29559(08)
0.16334(18)
0.16469(09)
0.17442(10)
0.17661(06)
0.19191(21)
0.19355(11)
0.09667(13)
0.09767(07)
V
0.23233(35)
0.23539(35)
0.29035(20)
0.29427(20)
0.15668(23)
0.15874(23)
0.18412(12)
0.18652(12)
0.18503(28)
0.18747(28)
-0.14883(23)
-0.15017(24)
n
-0.28838
-0.19938
-0.20462
Sample #7
#8
#9
0.30854(20)
0.31062(13)
0.23495(07)
0.23654(04)
0.28860(19)
0.29055(12)
0.15805(17)
0.15915(10)
0.38838(25)
0.39099(16)
0.05427(16)
0.05469(10)
0.32950(20)
0.33489(16)
0.21944(13)
0.22247(10)
0.29479(13)
0.29961(14)
0.16033(13)
0.16259(10)
0.36830(22)
0.37432(18)
0.09268(18)
0.09416(14)
propyne
zz
1,3,5-trichlorobenzene
zz
chlorobenzene
<? /
&zzS
q
'-'xx
Q )
^yy
1
n
V
n
V
toluene
n
V
C
&xx
C
J
^yy |
n
1,3,5-trichlorobenzene
Sz
Z
p-dichlorobenzene
<? /
C
>Jxx
Q )
^yy
\
n
V
n
V
p-chlorotoluene
<7 /
c
iJxx
c /
^yy
|
n
V
n
V
138
Appendix D. Order Parameters
1,3,5-trichlorobenzene
S
zz
-0.27447
-0.22350
-0.21132
Sample #10
#11
#12
0.30761(12)
0.30967(12)
0.23307(04)
0.23465(04)
0.28021(11)
0.28209(11)
0.15293(11)
0.15399(11)
0.34586(14)
0.34818(14)
0.05006(09)
0.05044(09)
V
0.33637(43)
0.34157(59)
0.21971(14)
0.22495(19)
0.28066(36)
0.28500(49)
0.16824(15)
0.17226(21)
0.29811(38)
0.30272(52)
0.12447(15)
0.12756(21)
n
-0.27362
-0.21705
-0.18862
Sample #13
#14
#15
0.17132(67)
0.17232(59)
0.34056(38)
0.34343(33)
0.13099(50)
0.13180(44)
0.24319(25)
0.24525(22)
0.12676(45)
0.12773(39)
0.16231(12)
0.16369(11)
0.16600(56)
0.16984(64)
0.34678(39)
0.35486(64)
0.13327(45)
0.13654(51)
0.24827(27)
0.25419(31)
0.14387(50)
0.14767(56)
0.18577(39)
0.19101(44)
V
-0.00037(16)
-0.00125(67)
0.00468(15)
0.00363(59)
0.01128(25)
0.00949(78)
n
-0.26436
-0.20103
-0.17730
Sample #16
#17
#18
0.17527(69)
0.17630(60)
0.34743(38)
0.35038(33)
0.14611(56)
0.14702(49)
0.26802(30)
0.27028(26)
0.14081(50)
0.14189(44)
0.17843(14)
0.17995(12)
n
p-dichlorobenzene
<7 /
q
" i i
Q )
^yy I
n
V
n
V
p-xylene
q
^II
<7
°zzS
1
n
q
j
n
^yy
|
1,3,5-trichlorobenzene
S
zz
V
o-dichlorobenzene
<7 /
^ZZ]
C
&xx
J
C
^yy I
n
V
n
V
o-chlorotoluene
<? /
os
q /
]
zz
q
^II
<
? /
xzS
n
V
n
V
n
J
1,3,5-trichlorobenzene
o-dichlorobenzene
<7 1/
'-'zz
C
&xx
C
^yy
/
|
n
V
n
V
139
Appendix D. Order Parameters
o-xylene
c
^xx
V
0.16646(71)
0.16956(76)
0.35394(46)
0.35912(49)
0.14369(61)
0.14637(65)
0.28468(34)
0.28877(36)
0.14859(61)
0.15138(66)
0.24869(22)
0.25212(24)
n
-0.27012
-0.22217
-0.19696
Sample #19
#20
#21
0.05755(18)
0.05809(18)
0.48431(25)
0.48777(25)
0.02678(16)
0.02702(17)
0.39784(22)
0.40067(22)
-0.03363(16)
-0.03399(16)
0.36841(22)
0.37099(23)
0.04365(20)
0.04561(25)
0.48878(33)
0.49674(40)
0.02255(17)
0.02374(21)
0.40026(28)
0.40663(33)
-0.01916(17)
-0.01930(20)
0.38199(29)
0.38766(34)
V
0.02617(30)
0.02632(35)
0.01539(28)
0.01583(32)
0.00259(35)
0.00369(41)
n
-0.27747
-0.22314
-0.19190
Sample #22
#23
#24
0.05581(14)
0.05633(15)
0.46513(24)
0.46846(24)
0.02422(10)
0.02444(10)
0.36476(19)
0.36740(20)
-0.03567(15)
-0.03605(15)
0.38717(23)
0.38989(24)
V
0.03912(46)
0.03921(37)
0.48225(64)
0.49831(55)
0.02550(35)
0.02557(28)
0.37482(51)
0.38034(44)
-0.00036(34)
-0.00047(28)
0.41029(61)
0.41663(52)
n
-0.26706
-0.20488
-0.20207
{
n
c /
n
<?
zz
J
1
^yy I
V
1,3,5-trichlorobenzene
m-dichlorobenzene
<? 1/
'-'ZZ
C
^II
C
/
^yy \
n
V
n
V
m-chlorotoluene
<? 7
c
L^XX
n
^zz|
V
c J
n
2/2/1
<?
/
'-'xz'l
V
n
1,3,5-trichlorobenzene
m-dichlorobenzene
n
>->zz1
C
*^£x
C
/
*^2/2/ 1
V
n
V
m-xylene
n
«->zzl
C
C /
'-'yy |
V
n
1,3,5-trichlorobenzene
S
zz
Appendix D. Order Parameters
140
For axis definitions see Fig. A.22. For corresponding structural parameters refer to
Tables C.8, C.9, CIO, C . l l and C.12. Numbers in round brackets are standard
deviations in the last two reported digits of varied parameters.
Order parameters which are indicated with "n" are calculated with no vibrational
corrections to dipolar couplings and parameters indicated with "v" are calculated with
vibrational corrections.
a
6
141
Appendix D. Order Parameters
Table D.14: Order Parameters for solutes in Sample #25
from Fits to Dipolar Couplings"
Order
Parameter
o-dichlorobenzene
o-chlorotoluene
o-xylene
1,3,5-trichlorobenzene
<? J
n 0.17412(69)
V 0.17514(60)
0.16894(57)
0.17286(65)
0.16503(71)
0.16811(76)
-0.26812
c J
n 0.34494(42)
V 0.34785(37)
0.35172(40)
0.35990(65)
0.35116(46)
0.35628(49)
n
-0.00017(16)
-0.00108(69)
6
c
'-'xx
^yy |
<? /
V
For axis definitions see Fig. A. 22. For corresponding structural parameters refer to
Table C.ll. Numbers in round brackets are standard deviations in the last two reported
digits of varied parameters.
Order parameters which are indicated with "n" are calculated with no vibrational
corrections to dipolar couplings and parameters indicated with "v" are calculated with
vibrational corrections.
0
6
Appendix E
Scaled and Calculated Order Parameters
142
143
Appendix E. Scaled and Calculated Order Parameters
Table E.15: Scaled and Calculated Order Parameters
ZLI 1132
Liquid Crystal
55 wt%1132/EBBA
Oscaled I1 cca,lc\b It Qcalc\c
qscaled 11 ccalc\b It ccalc\c
d0
a
/{°a0 ) A a / 3 )
D
acetonitrile
S
0.1386/0.1371/0.1258
22
propyne
S
0.2296/0.1861/0.1983
22
a0
D
I Wa0 ) I \°a0 )
EBBA
cscaled 11 qcalc\b 11 qcalc\c
°aQ
I \ a0 ) I \ a0 )
D
J
0.1135/0.1187/0.1087
0.1012/0.1419/0.1305
0.1402/0.1233/0.1308
0.0571/0.0827/0.0895
chlorobenzene
0.1792/0.1769/0.1812
0.1783/0.1839/0.1879
S
0.2269/0.2136/0.2195
-0.1857/-0.1865/-0.1930 -0.1341/-0.1586/-0.1655
-0.2537/-0.2376/-0.2452
yy
0.0064/0.0095/0.0118 -0.0441/-0.0252/-0.0223
0.0267/0.0239/0.0257
22
}
toluene
0.1728/0.1789/0.1699
0.1728/0.1593/0.1495
0.2233/0.2351/0.2255
S
-0.2512/-0.2392/-0.2398 -0.1879/-0.1866/-0.1863 -0.1556/-0.1561/-0.1552
0.0151/0.0077/0.0163
-0.0171/-0.0032/0.0056
0.0279/0.0040/0.0143
22
p-dichlorobenzene (with p-chlorotoluene)
S
0.3096/
/
0.2821/S
-0.2727/
/
-0.2183/-0.0638/-0.0369/
/d
22
ro
7-
0.3489/
-0.1989/
-0.1500/
///-
p-dichlorobenzene (with p-xylene)
0.2820/0.2836/0.2817
0.3481/0.3592/0.3539
S
0.3096/0.3011/0.3007
-0.2721/-0.2651/-0.2649 -0.2180/-0.2246/-0.2234 -0.1993/-0.2268/-0.2240
yy
-0.0375/-0.0359/-0.0357 -0.0640/-0.0589/-0.0582 -0.1488/-0.1324/-0.1298
22
p-chlorotoluene
0.3340/0.2987/0.2836
0.2909/0.2884/0.2758
S
0.3338/0.3518/0.3391
S
-0.2777/-0.2760/-0.2715 -0.2244/-0.2259/-0.2202 -0.2090/-0.2074/-0.2000
S
-0.0560/-0.0757/-0.0676 -0.0665/-0.0625/-0.0556 -0.1250/-0.0912/-0.0835
22
w
xx
p-xylene
0.3027/0.2664/0.2417
0.2850/0.2910/0.2689
S
0.3415/0.3777/0.3549
S
-0.2832/-0.2803/-0.2713 -0.2286/-0.2264/-0.2160 -0.2151/-0.2005/-0.1879
S
-0.0583/-0.0974/-0.0836 -0.0563/-0.0645/-0.0528 -0.0875/-0.0659/-0.0538
Z2
yy
xx
Appendix E. Scaled and Calculated Order Parameters
o-dichlorobenzene (with o-chlorotoluene)
S
0.1783/
/
0.1423/S
-0.2669/
/
-0.2035/0.0612/
0.0885/
/-
144
d
22
yy
-/-/-
/-
0.1358/
-0.1550/
0.0191/
///-
o-dichlorobenzene (with o-xylene)
0.1358/0.1224/0.1351
S
0.1785/0.1919/0.2078
0.1436/0.1458/0.1582
S
-0.2667/-0.2601/-0.2701 0.2038/-0.2089/-0.2186 -0.1541/-0.1820/-0.1928
0.0182/0.0595/0.0577
0.0602/0.0630/0.0604
S
0.0881/0.0682/0.0623
22
yy
xx
o-chlorotoluene
0.1474/0.1447/0.1474
0.1570/0.1365/0.1393
S
0.1757/0.1799/0.1830
-0.1801/-0.1846/-0.1897
-0.2109/-0.2087/-0.2135
-0.2715/-0.2588/-0.2638
yy
0.0230/0.0480/0.0503
0.0635/0.0640/0.0660
S
0.0957/0.0789/0.0808
0.0101/0.0268/0.0353
S
-0.0013/-0.0237/-0.0132 0.0039/-0.0021/0.0063
Z2
xx
xz
o-xylene
0.1449/0.1320/0.1253
0.1429/0.1450/0.1386
S
0.1717/0.1838/0.1755
S
-0.2677/-0.2583/-0.2584 -0.2125/-0.2087/-0.2084 -0.1932/-0.1850/-0.1843
S
0.0960/0.0744/0.0828
0.0482/0.0529/0.0590
0.0695/0.0636/0.0698
22
w
xx
m-dichlorobenzene (with m-chlorotoluene)
S
0.0572/
/
0.0262/-0.2691/- 7"
-0.2080/yy
0.1817/0.2118/- 7 d
22
}
7-
-0.0334/
-0.1656/
0.1990/
///-
m-dichlorobenzene (with m-xylene)
S
0.0577/0.0637/0.0595
0.0258/0.0265/0.0240 -0.0336/-0.0342/-0.0367
Syy -0.2688/-0.2543/-0.2649 -0.2075/-0.2092/-0.2190 -0.1651/-0.1970/-0.2071
0.1988/0.2312/0.2438
S
0.2111/0.1906/0.2054
0.1816/0.1827/0.1949
22
xx
m-chlorotoluene
S
0.0449/0.0299/0.0237
0.0230/0.0235/0.0201
S
-0.2674/-0.2597/-0.2649 -0.2093/-0.2099/-0.2142
S
0.2224/0.2297/0.2411
0.1862/0.1863/0.1941
S
0.0259/-0.0222/-0.0064 0.0154/-0.0020/0.0104
zz
yy
xx
I2
-0.0189/0.0021/-0.0004
-0.1810/-0.1873/-0.1919
0.2000/0.1852/0.1924
0.0036/0.0251/0.0376
Appendix E. Scaled and Calculated Order Parameters
145
m-xylene
S
0.0401/0.0178/0.0176
0.0270/0.0225/0.0232
-0.0004/0.0152/0.0163
S y -0.2707/-0.2616/-0.2617 -0.2150/-0.2101/-0.2090 -0.1942/-0.1837/-0.1819
S
0.2305/0.2438/0.2441
0.1879/0.1876/0.1858
0.1946/0.1685/0.1655
Z2
y
IX
1,3,5-trichlorobenzene
S
-0.2736/-0.2550/-0.2818 -0.2170/-0.2143/-0.2403 -0.1886/-0.2087/-0.2353
w
For axis definitions see Fig. A.22.
Sffi values are predicted using potential parameters from Fit #8 (see Table 3.3 and 3.4).
° Softf
predicted using potential parameters from Fit #9 (see Table 3.4).
Order parameters were not used when determining potential parameters and thus S^
are not reported. The S^
are shown for comparison.
a
6
v a m e s
a r e
d
c
led