Crystalline polymers
&
Vibrational spectroscopy of
polymers
Crystalline: Polymer molecules show some degree of
ordering. Depending on molecular symmetry (tacticity),
molecular weight (kinetics) and branching, etc.
Lamellar growth
direction ~10 µm
Lamella thickness
~100 – 200 Å
Glassy: molecules in a random coil conformation.
For example fully amorphous PMMA and PPO
10 mm x 10 mm
Microscopy image of a
crystal of high density
poly(ethylene) - viewed
while “looking down” at the
lamella.
Lamella grows
outwards
Polymers with some
symmetry are usually
polycrystalline. They are
usually never completely
crystalline but have
some amorphous
regions and “packing
defects”.
Several crystals of isotactic poly propylene
G. Ellis*, M. A. Gómez and C. Marco
Why is the lamellar crystal a basic unit?
competition between polymer chain stretching and
coiling on one hand and on reduction in free energy
for crystal formation on the other hand determines
lamellar thickness.
  S 

melt  crystal rate   exp 
 kB 
-1
 TS  g 

crystal  melt rate   exp  
k BT 

-1
1 is a microscopic frequency, g is negative by definition
Calculating the maximum net rate for a crystal of thickness l gives an estimate of
the optimal thickness (fastest growing).
Lamellar thickness of PE grown from a melt
 melt crystallization
 annealing
Lamellar Thickness:
2Tm0
Lc 
H v (Tm0  Tc )

Tm0
Surface energy
Equilibrium melting
Temperature
H v Enthalpy of fusion per
unit volume
T Crystallization temperature
c
Micellar Structures
When diblock copolymes are asymmetric, lamellar
structures are not favoured.
Instead the shorter block segregates into small
spherical phases known as “micelles”.
Interfacial “energy
cost”: g(4pr2)
Reduced stretching
energy for shorter
block
Density within phases
is maintained close to
bulk value.
Exotic Morphologies
Molecular vibrations – vibrational
spectroscopy
m1
m1
X1
m2
equilibrium
m2
X2
Restoring force (the bond): F=k(X2+X1)
d2 x
a 2
dt
F  ma  kx
d2 x
m 2  kx
dt

d2 x
k


x
2
m
dt
x(t)  A cos2  t 

k
k

m
m
Quantum Vibrational Motion
• molecular motion is quantized; vibrational quantum levels (quantum number “v”)
1
1
Ev  v     v  h 
 2 
 2 

h
2p
  2p 

1
2p
k
m
• energy absorbed is energy difference between two levels; for SHO, spacing is
same between ALL adjacent levels.
Evv1    h  h
1
2p
k
m
Anharmonic Oscillator
• real molecules, vibrations “close to being”
harmonic.
• relaxes the selection rules (overtones and
combination bands)
• distorts the intensities of the transitions
• changes energy levels so that they come
closer together as you go up the vibrational
ladder.
• bond can “break”; not so with SHO.
Types of Vibrations
• molecular dipole moment must change during a vibration to be IR active.
• this oscillating dipole interacts with the oscillating E-M field of the photon,
leading to absorption.
Stretching Vibrations
symmetric
anti-symmetric
Changes in bond length
Bending Vibrations
+
–
rocking
scissoring
In-Plane
+
+
–
twisting wagging
Out-of-Plane
Changes in bond angle
Vibrational spectroscopy
Raman scattering
Virtual
states
Infrared
absorption
Excited state
Ground state
E
Stokes
antiStokes
Rayleigh
2850
-3500
400
0
514
3500 Raman shift (cm-1)
630 wavelength (nm)
3500
22900
19400
15900 wavenumber (cm-1)
Infrared is Rovibrational Spectroscopy
• Wavelengths between 0.8 µm to 1 mm.
• Associated with changes in nuclear motion (vibrations and rotations).
• In gas phase, rotational transitions are resolved; in liquid phase, they are
broadened. Usually only focus on vibrational character.
• Energy is usually reported in wavenumbers (cm-1); also proportional to
frequency
1
 
  c

most
commonly
studied
Near IR
0.8 - 2.5 µm
12800 - 4000 cm1
Mid-IR
2.5 - 50 µm
4000 - 200 cm-1
Far IR
50 - 1000 µm
200 - 10 cm-1
The Raman Spectrum
A complete Raman spectrum
consists of:
• a Rayleigh scattered peak
(high intensity, same
wavelength as excitation)
• a series of Stokes-shifted
peaks (low intensity, longer
wavelength)
• a series of anti-Stokes shifted
peaks (still lower intensity,
shorter wavelength)
• spectrum independent of
excitation wavelength (488,
632.8, or 1064 nm)
Spectrum of CCl4, using an Ar+ laser at 488 nm.
Origin of Raman Effect - Classical
E  E0 cos ex t 
The oscillating electric field of the excitation light.
minduced  E  E0 cosex t 
The induced dipole moment from this oscillating field.
d
   0  r  req
dr
r  req  rmax cos vib t 


The molecular polarizability changes with bond length.
The bond length oscillates at vibrational frequency.
d
Hence the polarizability oscillates at same frequency.
   0   rmax cos vib t 
 dr 
d

minduced  
 0   rmax cos vib tE 0 cos ex t    0 E 0 cosex t  

 dr 

Substitute.
d
E0 rmax  cosex t cos vib t 
 dr 
cos x cosy 
1
cosx  y   cosx  y
2
Remember trig identity.
 m induced   0 E0 cos ex t 
E0 rmax d 
cos ex   vib t  cos ex   vib t  Induced dipole has Rayleigh,


2
dr
Stokes, and anti-Stokes


Components.
Raman vs. IR
Infrared Spectroscopy
Raman Spectroscopy
Interaction
Absorption
Scattering
Excitation
Polychromatic
Monochromatic
Frequency
Absolute
measurement
Activity
Relative
Dipole moment change Polarizability change
m/Q0
Band intensity (m/Q
/Q0
/Q)
Compare IR and Raman
Spectra of PETN explosive. From D.N. Batchelder, Univ. of Leeds
Group frequencies
For large molecules vibrations of some
functional groups acts
like independent
oscillators i.e. always
found at ~ same
frequencies
Group
cm-1
- C-H
2900-3000
- C=O
1700
- C-F
1100
- O-H
3600
- C-C -
900
Factors affecting group
frequencies
• Center of Symmetry (i):determine IR
active or Raman active.
• For IR active vibration an oscillating
electric dipole must be generated.
• For Raman active vibration a change in
polarizability of the molecule is produced,
which gives rise to induced dipole.
Symmetry factor
• A molecule having a center of symmetry (i) has
no permanent dipole moment, so a vibration
symmetric to i (sym. mode) does not generate
oscillating dipole and therefore it is an IR
inactive vibration.
• But vibration anti-symmetric to i (anti-sym. mode)
generates transient oscillating dipole, so it will
be IR active vibration and show up in the
spectrum.
Mutual exclusion rule
• Symmetric mode vibration usually gives rise
to Raman scattering which causes changes
in polarizability of molecule, and it is a
Raman active vibration, showing up in the
Raman spectrum.
• Mutual exclusion rule : For IR and Raman
spectra, some lines missing in one would
show up in the other, due to different
symmetry requirement for each spectra.
Thus, the information from IR data is
complementary to that obtained from Raman.
General rule of symmetry
• Symmetry in molecule reduces the normal
modes of vibrations and simplifies
spectrum.
• CO2 : sym. stret.
= 1340 cm-1 , IR
inactive, but Raman active.
assym. stret.
= 2349 cm-1 , IR active.
IR vs. Raman : mutual exclusive.
Symmetry : IR shows only assym. stret.
Symmetry simplify spectra
Mechanical coupling
• Interaction between two vibrational modes
through common atom or common bond:
Such two identical groups are linked (or
fused) by a common atom or a common
bond.
• Induce mixing and redistribution of energy
states, yielding new energy levels, one
being higher and one lower in frequency.
Degrees of freedom
Always 3 N degrees of
freedom (N = number of
atoms in molecule) with
3N-6 (-5) vibrational
degrees of freedom.
For polymers in practice we
have 3n-6 modes
(n=number of atoms in
repeat unit) instead of
3N-6
Quick IR Analysis Algorithm
Infrared spectra: It is important to remember that the absence of an absorption band can often provide more information
about the structure of a compound than the presence of a band. Be careful to avoid focusing on selected absorption bands
and overlooking others. Use the examples linked to the table to see the profile and intensity of bands. Remember that the
absence of a band may provide more information than the presence of an absorption band.
Look for absorption bands in decreasing order of importance:
1. the C-H absorption(s) between 3100 and 2850 cm-1. An absorption above 3000 cm-1 indicates C=C, either alkene or
aromatic. Confirm the aromatic ring by finding peaks at 1600 and 1500 cm-1 and C-H out-of-plane bending to give
substitution patterns below 900 cm-1. Confirm alkenes with an absorption at 1640-1680 cm-1. C-H absorption between
3000 and 2850 cm-1 is due to aliphatic hydrogens.
2. the carbonyl (C=O) absorption between 1690-1760cm-1; this strong band indicates either an aldehyde, ketone,
carboxylic acid, ester, amide, anhydride or acyl halide. The an aldehyde may be confirmed with C-H absorption from
2840 to 2720 cm-1.
3. the O-H or N-H absorption between 3200 and 3600 cm-1. This indicates either an alcohol, N-H containing amine or
amide, or carboxylic acid. For -NH2 a doublet will be observed.
4. the C-O absorption between 1080 and 1300 cm-1. These peaks are normally rounded like the O-H and N-H peak in 3.
and are prominent. Carboxylic acids, esters, ethers, alcohols and anhydrides all containing this peak.
5. the CC and CN triple bond absorptions at 2100-2260 cm-1 are small but exposed.
6. a methyl group may be identified with C-H absorption at 1380 cm-1. This band is split into a doublet for
isopropyl(gem-dimethyl) groups.
7. structure of aromatic compounds may also be confirmed from the pattern of the weak overtone and combination tone
bands found from 2000 to 1600 cm-1.
This is a little recipe from Stanislau State University (California).
Some Raman Advantages
Here are some reasons why someone would prefer to use Raman Spectroscopy.
• Non-destructive to samples (minimal sample prep)
• Higher temperature studies possible (don’t care about IR radiation)
• Easily examine low wavenumber region: 100 cm-1 readily achieved.
• Better microscopy; using visible light so can focus more tightly.
• Easy sample prep: water is an excellent solvent for Raman. Can probe sample
through transparent containers (glass or plastic bag).
A Raman disadvantage Fluorescence
Spectrum of anthracene. A:
using Ar+ laser at 514.5 nm.
B: using Nd:YAG laser at
1064 nm.
Want to use short
wavelength because
scattering depends on 4th
power of frequency.
…BUT…
Want to use long
wavelength to minimize
chance of inducing
fluorescence.
What is it good for?
• Composition
• Co-ordination
• Conformation
Endgroups - example
CH2 and CH3 stretching and bending modes in
saturated hydrocarbons. With increasing chain
length the absorption from CH2 groups increases.
Introduction to Mol. Spect. Academic press 1970
.
Molecules in motion. A presentation
created by Dr Alexander Brodin