CHAPTER 1. INTRODUCTION AND APPROACH
“It is the theory that decides what can be observed.”-Albert Einstein
1.1 INTRODUCTION
Control over opacity and luminosity of particles and fillers extend the efficiency and
benefits of the particle characteristics while increasing the abilities and advantages of the
final material. Current polymer composite technology relies on the dispersion of microand nanosized filler particles into uniform polymer matrices in order to tailor the
materials’ optical, thermo-mechanical, or transport properties.[1-3] Nanoscale filler
materials have attracted particular attention as additives because of the unique properties
such as UV absorption (e.g. ZnO nanocrystals), luminescence (semiconductor quantum
dots), supra-paramagnetism (magnetic nanocrystals) or extraordinary mechanical strength
(e.g. carbon nanotubes) that result as a consequence of the spatial confinement and the
particular bonding situation in nanomaterials.[4] Additional motivation to use nanoscale
particle (NP) additives derives from the reduced scattering strength of particles that are
smaller than the wavelength of light thus facilitating property enhancements without
sacrificing e.g. optical clarity.[5]
In this work, we demonstrate that the scattering of filler particles can efficiently be
suppressed (or ultimately tuned) by grafting of polymers of appropriate composition,
molecular weight, and grafting density to the particles’ surface such as to match the
effective dielectric constant of the resulting core-shell particle to the dielectric constant of
1
the embedding medium. Key to the presented approach is the observation that for coreshell particles with a size less than the wavelength of light, optical properties are equal to
those of a homogeneous particle with an effective dielectric constant which can be simply
derived from the known optical properties and volume fractions of the respective
constituents.
Applying the Effective Medium Theory (EMT), particle additives formerly known to
produce scatter and opacity are altered to a low, quasi-transparent material. Prediction of
materials that satisfy the ‘null scattering condition’ is introduced utilizing Maxwell
Garnett theory[6] equations. To test this hypothesis, developing well-characterized,
monodisperse additives that fit the model is imperative due to added complexity to scatter
with every inhomogeneity. Because the particle growth depends on the details of the
nucleation and growth process, the stabilization of the particle surface by the surrounding
matrix, the homogeneity of the precursor distribution, as well as the change of transport
properties during the course of the reaction the in-situ approach often results in broad
particle distributions. The limited possibilities to control the surface chemistry and
architecture (such as core-shell structures) of the embedded nanocrystals are further
drawbacks of the in-situ approach. Therefore, novel techniques based on atom transfer
radical polymerization (ATRP) were applied to modify pre-synthesized nanoparticles and
applied ex-situ resulting in model systems with well-defined architecture, composition,
and optical properties.[7] Chapter II presents a detailed discussion of the synthetic
approach as well as the characterization of the resulting particle additions.
2
Chapter III focuses on the theoretical background of light scattering in reference to
particle species. The results and discussion of the optical properties of a series of model
particle systems (evaluated using static light scattering) will be provided in Chapter IV.
The final chapter (V) of this thesis discusses some of the opportunities for the technique,
such as its application to a wider array of commercially relevant polymer systems as well
as address directions in future research.
1. 2 THEORETICAL BACKGROUND
The particular properties of nano-sized inorganic materials are of central importance to
the design of modern composite materials such as polymer composites or cosmetic
products where particle additives are used in order to improve mechanical, thermal,
transport, or optical properties.[2-4, 8-10] However, in many instances the improvement of
some performance characteristic is compromised by a loss in transparency that results
from the scattering of visible light by the embedded particle inclusions – a consequence
of the significantly different refractive index of most inorganic materials and the organic
embedding medium. For applications that capitalize on optical transparency the
pronounced scattering of particle inclusions presents severe limitations to the maximum
concentration of filler particles as well as the design possibilities of the organic-matrix
composites.
1.2.1. Refractive Index and Scattering Theory
The index of refraction or refractive index (n) of a material is a quantity that describes
how much the speed of a wave (usually light) is reduced inside the medium. In absorbing
3
materials the term (n) represents a complex quantity (n`= n + ik) where k is the imaginary
part. However, k=0 for non-absorbing materials (e.g. silica) so only the real part (n) will
be relevant for our purposes.[11, 12] Explicitly defined, refractive index is the ratio of the
phase velocity of a wave in a reference medium (air in a vacuum) to the phase velocity in
the medium itself. Therefore, the higher the refractive index of a medium, the slower the
propagation of the wave through it.[13] Changes in phase velocity are often observed by
the human eye when looking at objects from above that go beneath a water line can be
described by Snell’s law[14] outlined in Figure 1.1.
n1
n2
θ1
θ2
Figure 1.1. Bending of light caused by changes in refractive index at the interface of two
materials. Velocity of the beams slows at it moves into a medium with a higher refractive
index (n2 in this case), reducing the angle of refraction, relative to the incident angle, at
the interface. The relationship is described by Snell’s law: n1sinθ1 = n2sinθ2.
The optical properties of nanocrystal composites were investigated experimentally by
Bockstaller et al. in the context of block copolymer (BCP)-based photonic crystal
materials.[15, 16] The key idea in these experiments was to increase the refractive index
contrast between adjacent polymer domains of a BCP by selective sequestration of high-
4
refractive index nanocrystals into one of the polymer domains (preferably the domain
with the higher refractive index) and thereby to increase the materials efficiency to reject
light. When particles much smaller than the wavelength of light are randomly dispersed
in polymer matrices, the optical properties of the resulting composite materials can be
approximated by means of weighted volume averages of the properties of its constituents
(Figure 1.2). This was the first experimental study aimed at extension of the application
of effective medium concepts to microstructured particle composites.[11, 17-19] While
providing a proof of concept, the experiments of Bockstaller et al. also point to subtle
considerations that need to be taken into account when designing BCP/NP composites for
optical applications e.g. exponential impact for regions of the nanoscale.[5, 11, 12]
Figure 1.2. Illustration of the effective medium theory. Properties of the individual
constituents (such as conductivity, and dielectric constant) of a composite for which the
volume of each is known can be mathematically combined in order to approximate values
for entire medium.
1. 2. 2 Effective Medium Theory
Refractive indexes of materials also relate the permeability and permittivity of materials
to that of the travel of light in a vacuum by the equation:
5

n 

(1.1)
where μ and ε are the relative permeability and permittivity, respectively. Permeability
(μ) describes the magnetization of a material that responds linearly to an applied
magnetic field. The relative static permittivity (ε), sometimes called dielectric constant,
describes a materials ability to transmit an electric field. Therefore, for non-magnetic and
non-absorbing materials, permittivity is simply the square of the refractive index of a
material (εn).
The measure of scattering strength is contained in the term for the scattering cross section
of a material. For optically isotropic particles with linear dimensions significantly less
than the wavelength of light the particle scattering cross-section is given by:
 k4
Csca = V2 
 6

 

2
 n 
and k   2 2 


V=volume
(1.2)
where nis the surrounding material’s refractive index. For a binary system, this can be
approximated as ~ V2(2 with V denoting the particle volume and  the
polarizability difference between the particle and the embedding medium.[20] Equation
1.3 describes the polarizability of a sphere embedded in a matrix material;
  4r 3
 p m
 p  2 m
(1.3)
where α is the polarizability for a sphere of radius (r) with a dielectric constant (εp)
embedded in a medium with a dielectric constant (εm). Because the scattering is
6
proportional to ()2 significant scattering can arise even for small particle sizes when
the refractive indices of the matrix and the filler particles are significantly different. This
is the origin for the strong scattering of most inorganic/organic material composition.
Due to the dependence on a value for scattering will therefore be suppressed if the
effective dielectric constant of the core-shell particle equals the dielectric constant of the
embedding medium as illustrated in Figure 1.3.[21]
m
m
p
p
Figure 1.3. Illustration of the concept of transparent nanocomposites. Scattering is
produced by differences (left) in dielectric constants of the matrix (m) and the particle
(p) and are absent when the dielectric constants of the medium and particle match (right).
The key idea of the present work is to use effective medium theory to “design” the
effective polarizability of core-shell particles such that the net polarizability of the
particle when embedded within a target medium vanishes. As illustrated in Figure 1.4,
these findings can be applied for the development of optically transparent composites
when the hybrid’s effective dielectric constant is tuned to match that of the embedding
medium.
7
εp
εg
εm
εm ≈ εeff
Figure 1.4. Conceptualization of the effective medium theory. For an incident beam, the
effective dielectric constant (εeff) of a non-magnetic material (μ = 0) is a function of the
dielectric constants of both the particle (εp) and the matrix (εm). Likewise in the case of
hybrids, the dielectric constant of the polymer graft(s) (εg) contributes to the εeff for the
composites material. Maxwell-Garnett theory predicts the theoretical compositions from
the effective permittivity and vice versa.
The most widely encountered expression in effective medium theory is that derived by
Maxwell-Garnett. Developed to explain and predict the permittivity of glasses containing
spherical particles the model considers a single spherical dielectric inclusion in a uniform
electric field. Assuming the absence of free charges in or around the core, the solution of
Laplace’s equation in spherical coordinates gave the relationship between the fields
within the inclusion and outside the host material.[22] The derived relationship can be
used to calculate an effective permittivity for a composite using the volume averaged
electric flux density and field strength (this latter term being divided into contributions
from within the inclusion and outside them in the host material).
8
If Vf is the volume fraction of the inclusions, the effective permittivity of the binary
composite derived by Maxwell-Garnett can be summarized in the form:[17, 22]

 core   shell
  core 1  V f   2 shell 1  V f
 eff   shell  3V f  shell 


 
In particular, for a core-shell particle at wavelengths larger than the particle dimension
the particles’ effective dielectric constant is given by Maxwell-Garnett theory as:

 eff   shell1  3


x 

1   x 
(1.4)

Here, x  1  core   shell   core  1  core   shell  , core and shell represent the dielectric
3
3
constant of the particle-core and shell, respectively, and  = Vcore/(Vcore + Vshell) is the
relative particle-core volume.[6, 17, 19, 23, 24] Equation 1.4 thus provides a design criterion
for the synthesis of quasi-transparent particle additives, i.e. by grafting a shell with a
dielectric constant greater than (less than) the one of the embedding media to a particle
core that has a dielectric constant less than (greater than) the embedding media, such that
eff = m.[25] The ‘effective index-matching’ method to suppress scattering contributions is
particularly attractive if the shell is comprised by a polymer grafted to the particle surface.
This is because polymer-grafting techniques are ubiquitously being used in order to
facilitate the dispersion of particle additives in organic matrices and thus no additional
synthetic processing steps – other than control of the grafting density and molecular
weight of the surface-bound polymer – are necessary.
Small et al.[21] modeled and tested various variables of these equations in terms of core
shell particles such as shell radius and volume fraction effects, and our experiments were
9
designed to validate or disprove their findings. The system in our study consists of
polystyrene (PS)-functionalized silica nanoparticles (PS@SiO2; average particle-core
diameter d = 20 nm) solubilized in toluene. The choice of a liquid embedding medium
is motivated by experimental convenience, i.e. straightforward experimental verification
of the dispersion state of the particle inclusions by dynamic light scattering, however,
analogous conclusions pertain to solid embedding media such as polymers or gels (see
Chapter IV for literature support regarding this concept). Figure 1.5 depicts the calculated
effective refractive index (neff) of a core-shell particle consisting of a low refractive index
silica core and a high refractive index poly(styrene) (PS) shell. This illustration defines
property characteristics of the PS@SiO2/toluene system as well as the dependence of the
particles’ effective refractive index on the core-shell composition. According to Equation
1.4, a weight fraction of m(PS)/m(silica)  0.19 the core-shell particle is effectively
index-matched to the solvent toluene (shown as a dotted line) thus resulting in a nonscattering configuration.
10
Figure 1.5. Calculated effective refractive index neff of a silica-core/PS-shell composite
nanoparticle (see equation 1.4). For the composition m(PS)/m(silica) ~ 0.2 the core-shell
particle is isorefractive with toluene (black dotted line). The refractive index of silica and
PS are assumed to be nSiO2 = 1.458 and nPS = 1.550.
In order to verify this prediction, a series of PS-coated silica nanocrystals were
synthesized using various ATRP methods including the recently developed ‘activator regenerated by electron transfer atom-transfer radical polymerization’ (ARGET-ATRP)
technique. The synthetic procedure (represented in Scheme 1.1) is fully described in
Chapter II. The principal advantage of this technique is that the addition of a sacrificial
reducing agent during the ATRP reaction facilitates both, high molecular weight and low
polydispersity of the resulting polymer through reduction of the necessary amounts of the
catalytic agent Cu(I). [26-28]
11
Scheme 1.1. Synthesis of poly(styrene)-functionalized silica nanoparticles of varying
grafting density and degree of polymerization.
To validate or oppose Small’s conclusion[21] that volume and not shell radius was the
relevant factor in the effective medium approach, a sample with the same polymer length
was prepared (DP = 150) but with a density  ~ 0.85 chains/nm2 that placed the sample
far outside of the 20% vol. target. Finally, a large polymer shell (DP = 760) was grown
from a high-density initiated silica to exhibit particle size boundaries on the formula. The
corresponding mass ratios m(PS)/m(SiO2) of the particle samples were calculated to be
0.12 (DP10), 0.22 (DP140), 2.5 (DP150) and 7.5 (DP760), respectively.
The implications of particle additives on the properties of the composite material depend
on the particle size, shape, and composition as well as the particular morphology of the
particle distribution.[5] The properties of composites are determined by the interplay
between the characteristic lengthscales of the constituents, the particle-polymer
interactions as well as the size and density of the grafted ligands. This thesis provides an
experimentally validated route to control the composite opacity that holds the promise of
higher efficiency and access to transparent composite materials.
12
CHAPTER 2. MATERIALS
“First, have a definite, clear practical ideal; a goal, an objective. Second, have the
necessary means to achieve your ends; wisdom, money, materials, and methods. Third,
adjust all your means to that end.”- Aristotle
2. 1 SYNTHETIC INTRODUCTION
Design and synthesis of novel materials is often an approach aimed at solving materials
related problems. The aim of this work is to create novel composite materials by
controlling architecture with an end application in mind. Specifically, the development of
optically transparent polymer composites as for particle fillers is being targeted here.
Thus it is crucial to understand how to achieve well-defined materials as well as how to
achieve physical transparency. The first chapter outlined the theoretical method utilized
to achieve transparency as a function of the final product. In this chapter, synthetic
pathways that will yield the target compositions and structures are described and detailed.
The development of well-defined materials will always be a function of the degree of
control a scientist has over the system further compositional and structural control is
particularly important in the area of nanoparticle composites. Development of
monodisperse inorganic particles has been the subject of literally thousands of papers[29,
30]
with well-accepted successes including gold,[31, 32] silica,[33, 34] and magnetic
particles.[35, 36] Additional features can be introduced into these systems via particle
modification-usually via surface modification. Achievement of advanced materials
properties, such as increased dispersion and complex functionality,[37] has been the result
13
of fastidious planning and control over their synthesis.[38, 39] However, the various
organic/polymeric materials coupled to monodisperse particle suspensions can introduce
infinite degrees of polydispersity, yielding materials of varying stability and having
various properties.[40-44] To achieve the well-defined particle systems desired herein, the
synthetic processes for developing monodisperse hybrid particles must be fully
understood.
2. 1. 1 Uncontrolled/Free Radical Polymerization
For most bulk synthetic polymeric applications free radical, chain, and step
polymerization methods can typically provide the desired materials. Chain length and
functionality are not issues in the development of the majority of paints and plastics,
however, the future of novel materials capable of complex activity in some system is
fundamentally based on the ability of the scientist to control the very concatenation of the
material. Highly tuned, well-defined composite materials are uncommon in nature;
therefore, their syntheses are original, methodical processes.[5, 45, 46]
Free radical or uncontrolled polymerizations of vinyl monomers are significant because
they can be easily performed and easily processed. Initiated either by itself or a small
molecule that can decompose with heat (or ultraviolet light) and form molecules
containing an unpaired electron, or radical, free radical processes start easily, proceed
quickly, and generally cease on their own. For a free radical polymerization to proceed,
once initiated, the active radical generally must have sufficient monomer access. Hence,
the rate of propagation is usually determined simply by the concentration of the monomer.
14
Termination occurs when the free radical on the growing chain end couples or
disproportionates with another free radical, participates in a radical scavenging reaction,
or transfers (chain transfer or inhibition/retardation) to an inactive species. In reactions
where radicals are scavenged or transferred to a notable degree, the propagation rate will
vary, yielding a system that obeys non-linear kinetics. Scheme 2.1 shows the general
processes of initiation, propagation, and termination in free radical polymerization.[47]
Initiation:
Δ
I
Δ/h
2R
kd
or
M
Δ
R
+M
M
ki
M
ki
Propagation:
M
+
P
P
(or M)
n+ 1
kp
+M
Termination:
k ct
Pn
+
Pm
Pn +m
k dt
Pn
+
Pm
Pn + Pm
Scheme 2.1: Initiation, propagation and termination reactions for free radical
polymerization. Rate constants of dissociation (kd), initiation (ki), propagation(kp),
coupling (kct), and disproportionation (kdt) termination as well as reaction components
catalyst/initiator (I), radical (R°), and Monomer(M) are given in shorthand. Monomer and
Polymer(P) are interchangeable.
15
Drawbacks of materials made with uncontrolled polymerizations have typically included
high polydispersity of chain lengths and loss or lack of functionality. However,
Advincula et al. recently described free radical polymerization from clay nanocomposites
that resulted in low polymer polydispersity for the composites compared to the bulk.[48]
Their group designed a set of experiments involving the same AIBN-functionalized
intercalated clay nanoparticle platelets conducted in solution, suspension, and bulk
polymerization conditions. As seen in Table 2.1, their results showed that although the
polymerization yields unattached polymer free in solution with the nanoparticles with the
characteristic high molecular weight (MW) and high polydispersity (PDI) of an
uncontrolled free radical polymerization reaction, the polymer removed from the
composites displayed polymer chains in which the polydispersities were significantly
lower. All three techniques resulted in grafted polymers with polydispersities less than
1.5.
Table 2.1. MWs and MW Distributions of the Polymers from Different Nanocomposites
initiator/monomer weight
Mn (g/mol)/PDIa
Mn (g/mol)/PDI
Sample
ratio
(free)
(bound)
PMMA0
N/Ab
585K/2.35
N/A
SoluPMMA1
0.0024
292K/2.88
102K/1.46
SuspPMMA1
0.0024
1744Kc/2.58
196K/1.28
BulkPMMA1
0.0024
1629Kc/2.67
310K/1.25
a
Number-average MW (Mn) in grams per mole/polydispersity index (PDI).b To obtain
comparable MW, the molar ratio of AIBN/MMA was kept the same as that of the three
SIPs.c The absolute value may not be accurate, as their MWs have exceeded the
maximum MW of PMMA standards for GPC.
16
X-ray diffraction (XRD) and Transmission Electron Microscopy (TEM) were utilized to
determine the level of system aggregation. XRD diffractograms for the nanocomposites
are given in Figure 2.1. A peak indicating aggregation is present in nanocomposite
samples synthesized in the suspension free radical polymerization. TEM images of each
sample dispersed in the polymer matrix supported these findings, by displaying bundles
of electron dense nanocomposites.[48]
Figure 2.1: X-Ray diffraction diffractograms of three nanocomposite samples. The peak
from the suspension-prepared clay composites (a) indicates the presence of aggregates.
It is unusual that the suspension-synthesized nanocomposites are similar to those made in
solution and bulk conditions by their comparable low polydispersity yet aggregated (a
condition generally associated with high polydispersity) and the results suggest a possible
error in these results and a need for further experimentation.
17
More importantly, the results show that there was no relation between the grafted
polymer and the material in bulk which is incredibly problematic when trying to design
and reproduce specialty materials. In conclusion, the random nature of free radical
polymerization significantly limits the ability to synthesize materials that require a high
level of precision.
2.1.2 Controlled Radical Polymerization
Development of monodisperse materials has been the topic of study for numerous
research groups.[5, 41, 48] Designed to be more certain than radical polymerization
processes, controlled radical polymerization (CRP) is the method of choice in any system
requiring precise composition, architecture, and/or functionality.[49, 50] Accurate control
over the size of each segment permits the formation of materials that display selforganized, nanostructured morphologies with properties suitable for use in a variety of
sensing or biomedical applications[51] and as reinforcing organic polymers.[52] Materials
synthesized by controlled radical polymerizations have therefore been dominating
literature since their discovery in the early nineties.[49, 53] Controlled radical
polymerizations are free radical polymerizations that have been adapted to control the
undesirable reactions that would normally lead to uncontrolled, unpredictable growth and
termination; and result in dramatically affecting key properties of the final material (See
Figure 2.2).
18
Figure 2.2. Diagram illustrating the necessity of control over growth of a polymer chain
in colloidal system. Randomness of free radical processes lead to inefficient initiation,
and particle instability.
The characteristic benefits of any homogeneous controlled or ‘living’ radical
polymerization are a steady concentration of long-living radical species (obeying linear
kinetics), a foreseeable degree of polymerization determined by the linear relationship
between monomer conversion and number average molecular weight(Mn), and narrow
molecular weight distribution.[54, 55] To ensure these ‘characteristic’ qualities, the system
must be designed with a competitive rate of initiation versus the rate of propagation,
sufficiently fast exchange (i.e. faster than propagation) between species of variable
reactivity, limited chain transfer and/or termination, and a depropagation rate
substantially lower than the rate of propagation.[56-58] For all CRP systems, this is easily
attainable with minor calculations, followed by experimental adjustments.
19
The three main methods of controlled polymerizations that exist today for the most
common vinyl monomers are Atom Transfer Radical Polymerization (ATRP), NitroxideMediated Polymerization (NMP), and Reversible Addition Fragmentation chain Transfer
(RAFT) Polymerization.[49] RAFT processes achieve the ‘living’ character of CRP via
degenerative transfer. Generally, a thiocarbonyl chain transfer agent is designed for each
monomer(s)/polymer(s) target to form stabilized radical intermediates unlikely to
terminate. The reaction proceeds as the chain transfer agent stabilizes the radical long
enough to propagate (add to) the C=S bond until the radical fragments and transfers
(transfer is to be highly preferred over termination) to another chain transfer agent.[59, 60]
NMP is initiated by heat in the presence of a radical scavenger or ‘trap’. It proceeds with
an ongoing, reversible deactivation process of growing chain end via coupling (and
decoupling) to the species capable of stabilization of the free radical.[61, 62]
kact
Pn-X + Mtn-Y/L
Pn
kdeact
kp
+ Monomer
+
X-Mtn+1-Y/L
2kt
Pm
Pn+m/Pn+Pm
Scheme 2.2. ATRP. The activation and deactivation steps proceed with the rate constant
kact and kdeact. Generated free radicals (Pn·) propagate and terminate (including
combination and disproportionation) with rate constants kp and kt.
ATRP is a free radical process that occurs in a symbiotic relationship with an ongoing
oxidation- reduction (redox) process involving the reaction’s catalyst. The scheme for
ATRP is described in Scheme 2.2. Monomer, solvent (if required), and a metal
20
solubilized by a ligand are added to a reaction vessel. An alkyl halide acts as the initiation
species when the metal-ligand catalyst in a lower oxidation state accepts the halide
(shifting to the higher oxidation state) and generates a radical in its place. Utilizing the
natural drive to equilibrium of a redox process, the catalyst in the lower oxidation state
will generate radicals only until there is an excess of the species in the higher oxidative
state, at which point it will lose the halide (terminate) to the growing chain end. This
process is synonymous with the persistent radical effect. As the reaction continues, the
active polymer-radical continues to propagate and deactivate to the polymer-halide to
balance/equilibrate the redox process.[63] The reversibility and transfer of the radical
termination, without a significant decrease in radical concentration defines its ‘living’
character.
[56]
The rate law for ATRP is given in equation 2.1. In ATRP, catalyst concentration can
simply be tuned to contend with fast rates of propagation. The polymerization process
will end when all of the monomer is consumed or the radicals are terminated either by
chain transfer to monomer, radical scavenger, or radical-radical termination.[63]
 [Cu I ] 

Rp = k p [ M ][ P]  k p [ M ]K eq [ I ]0 
II 
[
X

Cu
]


Equation 2.1: The rate law for ATRP. [M], [I], and [P*] are concentrations of monomer,
initiator, and propagating chain, respectively. Ratio of activator [CuI] and deactivator [XCuII] concentrations determine overall rate.
21
Termination is suppressed when radical concentration is low, chain transfer is unlikely,
and/or the scavenging of radicals is avoided. By examining the rate law, it is easy to
understand that the rate of ATRP depends on CuI/CuII concentration.[64] This is due to
the drive towards equilibrium in any redox process.
Because the ATRP mechanism depends on a redox reaction, several interesting
phenomena can be observed and manipulated. Firstly, the equilibrium reaction responds
independent of the approach, allowing for the initiation via a high concentration of
radical (reverse ATRP),[65, 66] conventional radical initiators (Simultaneous reverse and
initiation ATRP),[67, 68] and transition metal complexes in higher oxidation states. Further,
advantageous oxygen can slow, or essentially deactivate the polymerization, by oxidizing
the catalyst species. In this way, the addition of antioxidants can increase the reaction
rate by reducing the deactivating species, if a sufficient amount is present.[69] And finally,
the most important development in ATRP methodology to date has been the development
of AGET and ARGET ATRP, which manipulate the ratio of activator to deactivator with
electron transfer, or reducing agents.[69, 70]
2.1.3 Specific ATRP Techniques & Limitations of Normal ATRP in Colloidal Systems
CRP, and specifically ATRP, is rapidly becoming the paramount synthetic method used
for producing novel materials; this is because it allows for the mass control of fine
structure.[41, 59, 71] Designer polymers with brush, star, and comb-like structures have been
22
synthesized and characterized in numerous papers by various groups.[49, 72] Surface
modification of colloidal particles from a normal ATRP system has already been shown
to yield well-defined materials.[73-75] But there are caveats to the utilization of a method
dependent on a metal-containing redox process for composite synthesis: 1) crosslinking
occurs at low conversions (>15%)[73, 76, 77] and 2) catalyst contamination can occur,
making it difficult to produce pure composites.[78, 79]
To illustrate the problem arising from cross-linking reactions and/or macroscopic
gelation for multifunctional initiators (MIs), a bulk ATRP of n-butyl acrylate(BA) was
carried out using functionalized silica particles. The MIs were prepared, as previously
reported, by reacting 1-(chlorodimethylsilyl)propyl 2-bromoisobutyrate with the hydroxyl
groups on the silica particle surface (silica particle diameter D =20 nm). On the basis of
elementary analysis it was determined that each functionalized silica particle had ~1600
initiating sites. Solvent-free normal ATRP was conducted with the silica MIs in a series
of reactions. The reaction conditions are listed in Table 2.2, entries 1-5 (Specific
experimental details are given in Section 2.2.2.2).
23
Table 2.2. ATRP of BA from Functionalized Silica Particles in Bulk and Miniemulsion*
No
Media
[BA]:[Initiating Site]:
Time
Conv
Mn, theo
Mn, exp
[Cu]:[L]:[Reducing Agent]
(h)
%
(g/mol)
(g/mol)
Initiation
Mw/Mn
1
Bulk
Normal
200: 1: 0.4: 0.4: 0
8.5
35.9
9190
12660
1.17
2
Bulk
Normal
200: 1: 0.4: 0.4: 0
12.5
62.5
16000
18500
1.16
3
Bulk
Normal
200: 1: 0.4: 0.4: 0
15.5
78.8
20170
23170
1.13
4
Bulk
Normal
200: 1: 0.4: 0.4: 0
19.7
91.4
23400
27500
1.13
5
Bulk
Normal
200: 1: 0.4: 0.4: 0
51.5
99.9
25570
38600
1.60
6
Miniemulsion
AGET
200: 1: 0.4: 0.4: 0.18
6
51.0
13050
17500
1.27
7
Miniemulsion
AGET
200: 1: 0.4: 0.4: 0.18
6
57.0
14600
19000
1.25
8
Miniemulsion
AGET
200: 1: 0.4: 0.4: 0.18
20
71.4
18280
24600
1.16
9
Miniemulsion
AGET
200: 1: 0.2: 0.2: 0.08
13
80.0
20480
27900
1.30
* Temp = 80 °C. Ligand: bis(2-pyridylmethyl)octadecylamine (BPMODA). In all normal
ATRP systems CuBr was used. In all AGET ATRP systems, CuBr2 was used together
with ascorbic acid as a reducing agent. Miniemulsion conditions: [Brij 98]:[hexadecane]
= 2.3/3.6 wt % based on monomer; solids content = 20 wt % (based on 100% conversion).
In experiment no. 9, the silica MI had ~1100 initiating sites per particle. Polymers were
analyzed by GPC after etching silica with hydrofluoric acid (HF).
The viscosity of the bulk reaction system quickly increased and the stirring bar stopped
moving at 25% monomer conversion and at 35% ( ~ 8.5 h) the reaction mixture could not
form a solution on further dilution, indicating macroscopic gel formation. Since sampling
the reaction mixture was not possible after macroscopic gelation, multiple parallel
polymerizations were carried out in order to measure the monomer conversions before
and after gelation (Table 2.2, entries 1-5). As seen from the kinetic plot (Figure 2.3A), the
24
monomer conversion continued to increase even after gelation, demonstrating the
“living” character of the systems. Polymerization accelerated after gelation, plausibly due
to a slower deactivation at higher viscosity and increased steric hindrance about the
initiating sites involved in crosslinking or coupling reactions.
4x10
1.0
A
8
ln([M]0/[M])
4
0.10
0.05
0.2
4
2x10
4
2.2
1.9
Mn
Conversion
0.15
1
2
3
4
5
3x10
1.6
1x10
2
Mw/Mn
0.4
6
Entry
Entry
Entry
Entry
Entry
0.20
ln([M]0/[M])
Gel
Point
2.5
Experimental
Theoretical
B
0.8
0.6
4
4
1.3
0.00
0
1
2
3
4
5
Time (h)
0.0
0
10
20
30
6
0
0.0
0
40
50
60
1.0
0.2
0.4
0.6
0.8
1.0
Conversion
Time (h)
1.0 h
2.2 h
3.0 h
5.0 h
8.5 h
12.5 h
15.5 h
19.7 h
51.4 h
C
3
10
4
5
10
10
Mn
Figure 2.3. (A) The first-order kinetic plot of ATRP of BA from silica MIs in bulk. Inset:
the first-order kinetic plots during the first 6 hours. (B) Evolution of molecular weight of
polyBA of hybrid particles versus monomer conversion and (C) GPC traces of polyBA
from bulk ATRP of BA from silica particle MIs. Polymerization conditions: Table 2.2,
entry 1-5.
On the basis of Flory’s gelation theory for multifunctional systems, a critical gel point
should occur when (on average) every multifunctional species is connected to more than
two neighbors. Since the average number of initiating sites (functionalities) per silica
particle was ~1600, the macroscopic gel point should occur when 2/1600 = 0.125% of the
chains terminate in an inter-particle fashion. The amount of terminated chains (including
25
inter- and intra-particle terminations) can be estimated from the radical concentration and
the termination coefficient, i.e., Δ[Pt] = ∫ kt[P ·] 2 dt. The radical concentration [P · ] was
calculated from the kinetic plot (Figure 2.3A) to be 3.8 × 10 -10 M (kp = 4.82 × 10 4 M -1 s
-1 ).[64] Thus, the total number of terminated chains during 8.5 h should be 10 8 M -1 s -1
× (3.8 × 10 -10 M)2 × 8.5 × 3600 s ) = 4.42 × 10 -7 M (using an averaged constant value of
kt ~10 8 M -1 s -1 , although it is recognized that kt is not only chain length dependent but
also affected by the surrounding of the growing radicals).[80] Since the total concentration
of initiating sites was 1.75 × 10 -4 M, 0.25% of the chains would have terminated at ~35%
conversion ( ~8.5 h). This is beyond the calculated gel point, indicating concurrent intraparticle and inter-particle termination reactions.
When the monomer conversion exceeded 35%, the product was partially insoluble in
THF due to macroscopic gelation. The fraction of insoluble gel in the reaction flask
visibly increased as the reaction progressed, indicating a continuation of the macroscopic
gelation process. After the silica particles were etched using hydrofluoric acid (HF), the
bound polymer was separated and analyzed by GPC as reported in other studies.[81] The
molecular weights increased linearly with conversion, displaying a narrow molecular
weight distribution (Mw/Mn), which is evidence of a controlled polymerization, as seen
in Figure 2.3B. It is important to stress that the fraction of chains terminated by coupling
(inter- or intra-particle) among all generated polymers was initially not high enough to be
detected by GPC (the estimated fraction of the coupled chains was only 0.24% at 8.5 h).
However, after ~50 h the conversion was essentially complete and the GPC trace of the
grafted polymer showed a significant shoulder with molecular weight twice that of the
26
major peak (2.3C). This shoulder peak (ca. 20% of all polymers) can be ascribed to
radical coupling.[51, 82]
In order to suppress the impact of this inevitable macroscopic gelation, “grafting from”
reactions are typically conducted under a high dilution condition,[42, 83] over long reaction
time,[41, 73] and/or are stopped at low monomer conversion.[73, 77, 84]
2.2 SYSTEMS
2.2.1 DILUTION SYSTEM ACHIEVEMENTS: Polyacrylonitrile-Silica Composites as
Templates for Nanoporous Carbons
A novel strategy was developed for the synthesis of various thin (sublayer, monolayer,
and multilayer) film-based nanoporous carbon using a hairy-like polyacrylonitrile (PAN)grafted silica hybrid as a carbon source and template through pyrolysis of grafted
polymers and removal of silica template by HF as illustrated in Scheme 2.3. Well-defined
hybrids were prepared by ATRP using the “grafting from” approach in heavy dilution.
The grafting reaction of PAN was carried out in diluted DMF solution in order to prevent
the crosslinking reaction between colloidal particles. The crosslinking reactions and
subsequent particulate aggregation can be further minimized by limiting polymerization
conversion by increasing the deactivation rate. The addition of a small proportion of CuII
(compared to CuI) increased the deactivation rate and provided better control of the
polymerization. The soluble PAN-grafted silica nanoparticles can be easily processed
27
into thin or thick films of silica-carbon source composites by simple manipulation of
solution concentration in dimethylformamide (DMF). Following carbonization of PAN
and removal of silica, replicated nanoporous carbon films were prepared. The prepared
nanoporous carbon ultimately exhibited reasonably high adsorption capacity.
I I I
I
I
I
I
I
I = initiator
ATRP
= PAN
1) Carbonization
2) Etching
Scheme 2.3. Nanoporous carbon sheets templated from solution-processable PAN-grafted
silica nanoparticle (SiO2-g-PAN) prepared by ATRP.
Because of their high surface area, large pore volume, and narrow pore size distribution
(PSD), nanoporous carbon materials have been successfully developed for use in
chromatography packing, electrodes, molecular sieves, gas separation, and catalyst
supports.[85-89] Recently, various groups have directed their research at the synthesis of
nanoporous carbons using nanostructured silica materials as templates.[85, 87, 90, 91] The
structural characteristics (e.g., pore size, pore volume, surface area, PSD and textual
structure) of the materials synthesized in this way can be finely tuned by selecting
28
appropriate templates. The circumvention of the disadvantages of these template methods
is their difficulty to be processed in the form of thin or even thick films, preventing their
use in the development of numerous thin film-based devices with nanoporous carbon
components lies in the design novel appropriately-grafted silica-based precursors, which
should render thin-film processable properties. The synthesis of nanoporous carbons from
PAN-grafted silica hybrids has opened a new, convenient way to fabricate nanoporous
carbons in thin films. Film-based nanoporous carbons prepared in this way are promising
as new candidates for a number of emergent applications, including membranes and
photovoltaic cells.
Grafted PAN recovered from the nanoparticles had narrow molecular weight distribution
with a unimodal peak. Two well-defined PAN polymers with different lengths were
prepared using this “grafting from” technique: hybrid-1 (DPAN = 120, PDI = 1.1)) and
hybrid-2 (DPAN = 200, PDI = 1.3)). Discrete nano-objects of PAN-grafted silica hybrids
observed with the aid of tapping mode atomic force microscopy (AFM) displayed welldefined round protrusions surrounded by hairy-like corona comprised of PAN polymers.
TEM images of these individual nanoparticles revealed that after the grafting reaction,
particles with hairy-like structures surrounding the silica cores did not exhibit
aggregations. Compared with the functional colloidal silica particles, aggregation
between particles was greatly reduced due to the repulsion force between inter-particle
grafted chains.
29
TGA characterization of the composites was carried out under inert atmosphere (N2) and
oxidative conditions (air) (Figure 2.4). The composite from hybrid-1 had a fraction of
54.4 wt.% carbon while hybrid-2 yielded 43 wt.% carbon after thermal treatment at
800 °C in N2.
o
Carbonized at 800 C
Carbon 43%
Silica 57%
in N2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
in N2
in N2
Hybrid - 1, DPAN = 120
Silica Initiator in N2
Si-g-PAN in N2
Si-g-PAN in Air
0
200 400 600 800
o
Temperature ( C)
in Air
1000
Weight
Weight
o
Carbonized at 800 C
Carbon 54.4%
Silica 45.6%
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
in N2
Hybrid - 2: DPAN = 200
SiO2 initiator in N2
SiO2-g-PAN in N2
SiO2-g-PAN in Air
0
in Air
200 400 600 800
o
Temperature ( C)
1000
Figure 2.4. Thermogravimetric analysis of SiO2 initiator and SiO2-g-PAN in N2 or air
atmosphere: a) hybrid-1; b) hybrid-2.
Thin films of the organic/inorganic hybrids were prepared by solution-casting the PANgrafted silica hybrids in DMF onto cleaned silicon wafer substrates that possessed a
native oxide layer. Typical film thickness ranged from tens of nanometers to a few
micrometers, yielding films having structures ranging from sub-monolayer, monolayer to
multilayer. These organic/inorganic composite films were subjected to thermal
stabilization at 280 °C under air and subsequent carbonization at 800 °C under nitrogen
that subsequently converted the film into silica and carbon inorganic/inorganic composite
material. The carbonized composites were then immersed into HF (50% vol.) solution to
etch away the silica templates, yielding a nanoporous carbon film. TEM images (Figure
2.5) of multilayer carbon films prepared from hybrid-1 show a well-defined nanoporous
30
array in a carbon matrix. The average pore size is about 16 nm, which agrees well with
the size of silica colloidal nanoparticle templates. A sublayer carbon film from hybrid -1
with a network of nanopores was clearly observed by TEM. The TEM image (Figure 2.6)
of carbon films from hybrid-2 also revealed nanoporous structures with an average pore
diameter of 16 nm. The TEM studies indicate that these nanoporous thin films exhibited
good stability during carbonization and the HF etching process.
Figure 2.5. TEM images of nanoporous carbon prepared from hybrid-1: a) thin film; b)
sublayer film.
Nitrogen adsorption measurements were conducted on the nanoporous carbon film from
hybrid-2 in order to characterize the pores. Thick films (> 1um) were cast to provide
enough nanoporous carbon material for analysis. The TEM image of the film exhibited
porous structures after etching the silica template away from silica/carbon composites
(Figure 2.6b).
31
Figure 2.6. TEM images of nanoporous carbon prepared from hybrid-2: a) thin film; b)
thick film.
Figure 2.7 showed nitrogen adsorption isotherms at -196°C for the carbons derived from
hybrid-2. The isotherms featured capillary condensation steps at relatively high pressures
(p/p0=0.8–0.9); hysteresis loops characteristic of mesoporous materials, consistent with
the above TEM images, showed mesoporous structures in these carbons. The BET
specific surface areas of the nanoporous carbons were around 450 m2 g-1 with pore
volume of 0.72 cm3 g-1, which are reasonably high from the point of view of film-based
nanoporous materials. These pores exhibited narrow pore size distribution, which is in
good agreement with TEM studies. The pore size distributions (PSDs), however, showed
the presence of mesopores with average pore diameter of 15 nm--somewhat smaller than
one obtained from thin-film materials. This may be attributed to the relatively lower
efficiency of the HF etching process for thick film samples. It is expected that the
adsorption capacity of these carbons can be improved through the adjustment of the
grafted PAN carbon precursors and colloidal silica nanoparticles. Moreover, the
32
adsorption capacity currently achieved is sufficient for many prospective applications,
including those where thin-film or thick-film morphology, which can be readily achieved
in the present case, is of primary importance. Although a novel method and a success, the
technique required to synthesize the carbon precursor of these materials is limited by its
low conversion characteristic of high dilution of normal ATRP required to decrease
crosslinking reactions when grafting from macroinitiators.
Figure 2.7. a) Nitrogen adsorption isotherms and b) pore side distribution of thick film of
nanoporous carbon prepared from hybrid-2.
Another method for preparing nanoparticle composites, based on concurrent
polymerization from an unbound “sacrificial” initiator, also efficiently limits interparticle coupling. This plausibly works by “diluting” the particles with the free polymer
chains with a single functionality (side-stepping the factor that increases the Flory
prediction for gelation given before) which could lead to non-gel forming termination
reactions.[42, 84] Molecular weights of free and bound polymer are essentially the same,
33
but composite materials are produced with free polymer impurities, which are nearly
impossible to fully remove.[39, 84] In all of these systems gelation has been successfully
avoided, producing particles with a uniform polymeric corona. These approaches
therefore minimize inter-particle termination; however, high dilution and low monomer
conversion result in solvent and monomer waste and increased cost. The method based on
using sacrificial initiator requires the separation of free polymer, which is challenging,
especially for very small particles.
2.2.2 Experimental Detail for Polyacrylonitrile-Silica Composites
Experiments and Characterization
Materials.
Acrylonitrile (99.9 %, Acros) was purified by filtration through a short
alumina column to remove the stabilizer directly before use. The preparation of 1(chlorodimethylsilyl)propyl 2-bromoisobutyrate and the subsequent functionalization of
the silica (30% wt. Silica in methyl isobutyl ketone, effective diameter = 10~15 nm,
MIBK-ST, Nissan) was adopted according to published procedure.[92] Copper (I) chloride
(99.999%, Aldrich) was purified via several slurries in acetic acid followed by filtration,
and stored over nitrogen before use. Copper (II) chloride (99.999%, Aldrich), 2,2’bipyridyl (99%, Aldrich), Aliquat 336 (Aldrich), toluene (Fisher), dimethylformamide
(Fisher) and hydrofluoric acid (50 vol. % HF, Acros) were used as received.
ATRP of PAN from functional silica colloidal nanoparticles
CuCl2 (0.0214 g, 1.6 ×
10-4 mol), 2,2’-bipyridyl (0.736 g; 4.72 × 10-3 mol), and DMF (140 mL) were mixed in a
250 mL Schlenk flask and purged with nitrogen. Acrylonitrile (60 mL) was purged for
30 min with nitrogen and then added to the above mixture. Silica nanoparticles (0.36g,
34
1.12 × 10-4 mol Br), and CuCl (0.2256 g; 2.28 × 10-3) were added and purged with
nitrogen before being placed in a 55C oil bath. The reaction ran for ~330 hrs. The
reaction product was then precipitated in methanol, and purified via additional methanol
washes and drying in vacuo to yield final PAN-grafted hybrids.
Characterization. Molecular weight distribution and evolution of molecular weight
over time were measured on a SEC system consisting of a Waters 510 HPLC pump, three
Waters Ultrastyragel columns (500, 103, and 105Å), and a Waters 410 DRI detector, with
a DMF flow rate of 1.0 ml/min, linear polystyrenes were used as standards. Note that
SEC is not a very reliable tool for the determination of molecular weight of PAN, since
calibration standard polystyrenes have a limited solubility in DMF solvent. Despite this
weakness, SEC can be still used to qualitatively follow progress of the polymerization
reaction and provide useful information about the shape of molecular weight distribution
curves. Relatively precise molecular weight was further calibrated by using several PAN
homopolymers with known molecular weight (from proton NMR measurements) as
standards. Thermal characterization of bulk samples (6-14 mg) was carried out with the
aid of Seiko TGA/DTA 300 instruments (Seiko Instruments, Inc.) operated at the heating
rate 10 oC/min under controlled atmosphere (air, N2, O2; flow rate 30-90 mL/min).
Sublayer, monolayer or multilayer films of PAN-grafted hybrids were prepared by
solution-casting in DMF onto mica or silicon wafer substrates. The morphology of these
films was studied with tapping mode atomic force microscopy (TMAFM). TMAFM
studies were carried out with the aid of a NanoScope III-M system (Digital Instruments,
Santa Barbara, CA), equipped with a J-type vertical engage scanner. The AFM
observations were performed at room temperature under air using silicon cantilevers with
35
nominal spring constant of 40 N/m and nominal resonance frequency of 300 kHz
(standard silicon TESP probes). Thin and thick films of nanoporous carbon were
prepared through (1) stabilization in air and carbonization in N2 of PAN-grafted silica
hybrids and (2) HF etching (immersion in 25 vol. % HF). These films were studied with
the aid of transmission electron microscopy (TEM) (Hitachi H-7100 electron microscope
operating at 70 KV). Nitrogen adsorption isotherms were measured at -196°C on a
Micrometritics ASAP 2010 volumetric gas adsorption analyzer. X-ray diffraction (XRD)
patterns were recorded on a Rigaku Geigerflex equipped with a theta/theta goniometer.
The Raman spectra were collected on a Jobin Yvon T64000 triple Raman system (ISA,
Edison, NJ) in subtractive mode with microprobe sampling optics. The excitation was at
514.5 nm (Ar+ laser, Model 95, Lexel Laser, Fremont, CA).
2.2.2 MINIEMULSION SYSTEMS ACHIEVEMENTS
2.2.2.1 AGET ATRP of Poly(n-butyl acrylate)-Silica Composites
An alternative method to suppress inter-particle coupling and macroscopic gelation
would be to create boundaries and force polymerization to occur inside very small
compartmentalized cells. This “boundary effect” is naturally present in colloidal
systems, such as miniemulsion, in which polymerization occurs in separate droplets and
multifunctional species cannot react with each other when isolated in different droplets
(Scheme 2.4).[93, 94] Although microscopic cross-linking/gelation can occur inside the
droplet, macroscopic gelation can be efficiently avoided.
36
Therefore, the “grafting-from” polymerization attains higher monomer conversion in a
miniemulsion process without macroscopic gelation. Reported below is an approach for
the synthesis of pure (without sacrificial initiator) well-defined hybrid materials: via
ATRP of n-butyl acrylate (BA) from silica particle MIs in an aqueous miniemulsion
system.
water
Scheme 2.4. Illustration of ATRP of BA grafting from silica particles in bulk (left) and
miniemulsion (right).
The initiation technique has to be carefully selected in order to conduct a successful
miniemulsion ATRP. A normal ATRP, starting from alkyl halide initiators and Cu(I)
activators, is difficult to conduct in a miniemulsion system since either the initiator or
catalyst have to diffuse to the dispersed monomer droplets.[95, 96] It is even more
challenging in the presence of solid particles, such as silica MIs, which cannot penetrate
the droplet, particularly since MIs cannot be added at the same time as the Cu(I)
activators. Because initiator and catalyst could not be added at the same time, distribution
of initiator and catalyst was uneven. Even after a further sonication process, the silica
MIs cannot be uniformly dispersed throughout the reaction medium. When a series of
normal miniemulsion ATRPs were conducted it was found that the polymerization rates
varied, suggesting irreproducible concentrations of radicals, plausibly caused by the
uncontrolled distribution of silica MIs.
37
AGET vs. SR & NI ATRP
-Miniemulsion Heterogeneous ConditionsX-Mtn+1/L
(A)AGETReducing Agent
Pn-X
+
I* + I*
(B)SR & NI
∆
kact
Pn*
n
Mt /L
kdeact
+
X-Mtn+1/L
kp
Monomer
Scheme 2.5: AGET (A) and Simultaneous Reverse and Normal Initiation (B)
modifications to the general ATRP scheme. In this case, the initiator (I) was
Azobisisobutyronitrile (AIBN) and the reducing agent was ascorbic acid.
In order to solve the problem of silica particle distribution, a recently developed
technique, activators generated by electron transfer (AGET),[28, 97] was used for an ATRP
miniemulsion polymerization from silica MIs. AGET ATRP allows for the acceleration
of traditional ATRP on colloidal surfaces in water-based emulsions.[96, 98, 99] In this
procedure, catalyst is introduced in its oxidatively stable state and is subsequently
activated by non-radical forming redox reaction with a reducing agent. After activation,
the polymerization system is essentially the same as a normal ATRP, and is directly
compared to SR & NI ATRP in Scheme 2.5. Because the catalyst is added in a higher
oxidation state and converted in-situ to the activator, it can be added together with the
macroinitiators and easily survive the sonication procedure (Modeled in Scheme 2.6).
38
Particle Synthesis
Macroinitiator Synthesis
Attachment of ATRP Initiator
Br
Si
O
Cl
ATRP
O
Monomer Droplet
Functionalized Macroinitiator particle
CuII/L
CuI/L
CuI/LCuII/L
Activator/Deactivator Complexes
C18H37
N
CuI/L
CuI/L
L
L
Ligand
N
N
BPMODA
Co-Stablilizer
H3C
CH 2
CH 3
14
CuII/L
Surfactant
WATER
HO
CH2
CH2
O
n
Brij 98
CH2
8
CH
CH
CH2
7
CH3
n~20
Scheme 2.6: Route to ATRP from particle surfaces in miniemulsion system.
AGET ATRP has been successfully carried out under various heterogeneous
conditions.[96, 100-102] In the present study, AGET ATRP was applied to the preparation of
hybrid particles in miniemulsion (Table 2.2, entries 6-9). The reducing agent, ascorbic
acid, was added to the system at a sub-stoichiometric amount. The particle size of the
miniemulsion was 220 ± 10 nm. In each particle, there were ~75 silica particles and
~120,000 growing chain ends (active and dormant).
39
4
A
0.8
Experimental
Theoretical
B
Entry 6
Entry 7
Entry 8
4
2.0
4
1.5
2x10
0.6
Mn
Mw/Mn
ln([M]0/[M]t)
2.5
3x10
1.0
0.4
1x10
0.2
0.0
0
0
1
2
3
4
5
Time (h)
6
0.0
1.0
0.2
0.4
0.6
0.8
1.0
Conversion
C
1.5 h
2h
3.33 h
6h
20 h
10000
100000
Molar Mass (g/mol)
Figure 2.8. (A) The first-order kinetic plots for AGET ATRP of BA from silica particle
MIs in miniemulsion. (B) Evolution of molecular weight of polyBA of hybrid particles
versus monomer conversion and (C) GPC traces of polyBA from ATRP of BA from
silica particle MIs in miniemulsion. Polymerization conditions: Table 2.2, entries 6-9.
Compared to the bulk reaction, ATRP in miniemulsion exhibited a higher reaction rate
(Figure 2. 8A), most likely due to diffusion of some Cu(II) deactivator species out of the
miniemulsion droplets.[95, 96, 101] According to the kinetic plot, [P · ] can be calculated as
9.6 × 10 -10 M and the concentration of terminated chains in 6 h were estimated to be
~[Pt] = ∫ kt[P · ] 2 dt = 10 8 M -1 s -1 × (9.6 × 10 -10 M)2 × 6 h × 3600 s = 2.0 ×10 -6 M.
Since the concentration of total initiating sites was 1.75 × 10 -4 M, ~ 1.1% of the chains
would participate in termination reactions. As discussed before, the system should form a
40
macroscopic gel when 0.125% of the propagating chains terminate via an inter-particle
process. Therefore, in miniemulsion the gelation should have occurred before 6 h.
However, in a miniemulsion polymerization inter-particle termination reactions are
confined to single droplets and macroscopic gelation is suppressed. In addition, based on
the volume of miniemulsion droplet (5.57 × 10 6 nm 3), the average number of
propagating chains per droplet was only 5.4 × 10 -3. This means, on average
0.54% of droplets were “active” and 99.46% of the droplets were “inactive” with all alkyl
halides at the dormant stage. Since the possibility of two radicals existing simultaneously
in one droplet was very small, the probability of termination (including intramolecular
and intermolecular processes) in one droplet should be further decreased.
The miniemulsion remained stable during the entire polymerization. AGET ATRP in
miniemulsion reached 70% monomer conversion after 20 h. The molecular weight
evolution plot (Figure 2.8B) shows that high initiation efficiency, (76%), was achieved,
comparable to the bulk system. Therefore, miniemulsion media facilitated a faster
polymerization and avoided macroscopic gelation.
Figure 2.9. Tapping mode AFM micrographs of core-shell hybrid particles from SR&NI
ATRP (a) and AGET ATRP (b) in miniemulsion.
41
The miniemulsion AGET ATRP for the hybrid silica particles first shown resulted in
monomer droplets of ~ 220 nm diameter forming polymer particles, and each of them
contained ~75 silica-polyBA hybrid particles (each with ~ 1600 chains). After drying the
miniemulsion samples, these hybrid particles were individually dispersed in THF and
were subject to AFM characterizations. Direct visualization of the core-shell hybrid
particles (Figure 2.9b) provides additional evidence for a gel-free system and a controlled
miniemulsion ATRP. Random imaging of the other regions on the same substrate surface
also indicated a small fraction of particle aggregates in the entire sample. The soft
polyBA chains formed a shell with uniform size and can be clearly distinguished from
rigid silica cores by AFM. The presence of some free polymer chains (ca. 1%) can result
from a small contribution of transfer reactions, chain shear in processing, or residual free
initiators remaining after the functionalization of the silica particles. As a comparison for
composite purity, SiO2-pnBA materials formed by SR & NI ATRP in miniemulsion are
given in Figure 2.9A. Due to the necessity of a small percent (~12.5%) free radical
initiator, such as AIBN, there is a significant increase in the amount of free polymer
chains in the product.
42
2.2.2.2 Experimental Detail for Poly(n-BA)-Silica Miniemulsion Systems
Reactions from Silica particles in Miniemulsion and Bulk (Including those listed in
Table 2.2.)
Materials. n-Butyl acrylate (BA, Acros, 99%) was purified by filtration through a basic
alumina column to remove the inhibitors, and stored at -5 oC. The procedure for the
preparation of 1-(chlorodimethylsilyl)propyl 2-bromoisobutyrate and the subsequent
functionalization of the silica (30% wt. silica in methyl isobutyl ketone, effective
diameter D = 20 nm, MIBK-ST, Nissan) was derived from the previously described
procedure.[73] According to the elementary analysis, the Br content of the modified silica
particles was ~ 0.322 mmol∙g -1, which corresponds to ~1600 Br initiating sites tethered
to the surface of each silica particle (using the density of silica d = 2.0 g∙cm-3). CuBr
(Aldrich, 99 %) was purified via several slurries in acetic acid followed by filtration, and
stored over nitrogen before use. Bis(2-pyridylmethyl)octadecylamine (BPMODA) was
synthesized according to the procedures previously published.[103] CuBr2 (Aldrich,
99.999%), ethyl 2-bromoisobutyrate (EBiB, Aldrich), polyoxyethylene (20) oleyl ether
(Brij 98, Aldrich), hexadecane (Aldrich), L-ascorbic acid (Aldrich, 99%) and
hydrofluoric acid (50 vol.% HF, Acros) were used as received.
Normal ATRP of BA from functional silica particles in bulk.
Silica macroinitator powder, CuBr, and BPMODA were added into 25 mL Schlek flask.
The flask was evacuated for 1 h, and then backfilled with nitrogen, evacuated again for 5
min, followed by additional backfiling with nitrogen. The evacuation/backfilling cycle
was repeated twice, and then BA (bubbled for 40 min with nitrogen before use) was
43
added to the flask. The reaction mixture was homogenized by agitation on a vortex mixer
for 5 min. After that, the flask was placed in a 80 oC oil bath.
Normal ATRP of BA from functional silica particles in miniemulsion. 4.47 g BA (35
mmol), 31.5 mg BPMODA (0.070 mmol), and 0.18 g hexadecane were added to a 50 mL
Schlenk flask. After dissolving, the solution was deoxygenated by bubbling nitrogen for
30 min. 10.0 mg CuBr (0.070 mmol) was added to the solvent under the nitrogen flow
and a yellow solution was formed thereby. Deoxygenated Brij 98 solution (20 mL,
5mmol/L) was added to the organic phase and sonication (Heat Systems Ultrasonics W385 sonicator; output control set at 8 and duty cycle at 70% for 1 min) was carried out
under strong nitrogen flow. After sonication the flask was sealed and immersed in an oil
bath preheated at 80 oC. A deoxygenated anisole solution of silica particle macroinitiators
(0.434 g, 0.175 mmol initiating sites) was injected to the flask to initiate the
polymerization. (Alternatively, in order to force an improved distribution of silica
macroinitiators in miniemulsion droplets, a sonication process under nitrogen flow was
carried out after adding silica macroinitiators for 1 min.) Aliquots were taken at intervals
to monitor the conversion by gravimetry. The polymerization was stopped by exposing
the polymer to air and THF. Products were precipitated and washed with methanol.
Activators generated by electron transfer (AGET) ATRP of BA from functionalized
silica particles in miniemulsion. 4.47 g BA (35 mmol), 0.434 g silica particle
macroinitiators (0.175 mmol initiating sites), 15.6 mg CuBr2 (0.070 mmol) and 31.5 mg
BPMODA (0.070 mmol) were added to a 10 mL Schlenk flask and allowed to stir at 60
C for ~40 minutes to form the CuII complexes. Hexadecane (0.18 g) and aqueous Brij 98
solution (20 mL, 5 mmol/L) were added to the complexes solution and the miniemulsion
44
was formed with the aid of sonication. The miniemulsion was deoxygenated by bubbling
nitrogen for 30 minutes, and immersed in an oil bath preheated at 80 oC. A deoxygenated
aqueous solution (0.5 mL) of ascorbic acid (5.5 mg,
0.031 mmol) was added to initiate
the polymerization. Aliquots were taken at intervals to monitor the conversion
gravimetrically. The polymerization was stopped by expose the polymer to air and THF.
Products were precipitated and washed with methanol.
Measurements
and
Characterization.
Conversion
was
determined
either
gravimetrically (in the case of miniemulsion polymerization) or by GC (in the case of
bulk polymerization) using a Shimadzu GC-14A gas chromatograph, equipped with a
J&W Scientific 30 m DB-WAX column with a Shimadzu CR51 Chromatapac. Molecular
weight and molecular weight distribution (Mw/Mn) were determined by GPC equipped
with an autosampler (Waters, 717 plus), HPLC pump with THF as eluate at 1 mL/min
(Waters, 515), and four columns (guard, 105 Å, 103 Å, and 100 Å; Polymer Standards
Services) in series. Toluene was used as an internal standard. A calibration curve based
on linear polystyrene standards was used in conjunction with a differential refractometer
(Waters, 2410). Elemental analysis for initiator content (Bromine-based) was conducted
by Midwest MicroLab, IN.
Tapping-mode atomic force microscopy (AFM) analysis was carried out using the
Nanoscope-III Multimode System (Digital Instruments, Santa Barbara, CA). The images
were acquired in air with standard silicon TESP probes (nominal spring constant and
resonance frequency respectively 50 N/m and 300 kHz). Deformable polymer layers on
silica were contrasted well from the procedure described previously.[73]
45
2.2.2.3 AGET ATRP of Poly(n-butyl acrylate)-Quantum Dot Composites
The synthesis of Quantum Dot (QD)/ polymer nanocomposites was also recently
achieved using ATRP in miniemulsion to graft controlled polymer chains from the QD
surface (Scheme 2.7). The QDs were initially functionalized with a trialkylphosphine
oxide modified with a chlorine-based ATRP initiator and subsequent polymerization was
carried out from the functionalized surface of the QDs. This polymerization involves the
recently developed AGET catalytic system, thus avoiding the use of conventional radical
initiators that can degrade the QDs and initiate free polymer chains. Through this
approach, polymerization from the QD surface occurred with a high degree of control,
yielding polymer encapsulated QDs.
Scheme 2.7: Synthetic strategy for the preparation of QDs/polymer nanocomposites by
AGET ATRP in miniemulsion.
In a first attempt, ligands modified with the bromide initiator (2-bromoisobutyryl
bromide) were used. However, the QDs were extensively degraded over time or during
the ligand exchange process. In fact, several experiments have shown a complete
degradation of the CdS QDs after several hours. This degradation became visible by
the change of color from bright yellow to brown, until a colorless solution was finally
46
obtained. This degradation was further confirmed by recording the visible absorption
spectra of such reacting solutions. Although this effect could be attenuated by reducing
the concentration of the bromide modified ligands, modifying the temperature and
adjusting the time of the exchange reaction, extensive degradation of the QDs could only
be minimized, not avoided.
Scheme 2.8: Ligands exchange at the surface of the QDs: TOPO= tris(octyl)phosphine
oxide;Py=Pyridine;THP=tris(hydroxypropyl)phosphine;THP-Cl=tris(hydroxypropyl)
phosphine oxide macroinitiator.
In order to minimize QD degradation via oxidation mechanisms a chloride-based
initiator (2-chloropropionyl chloride) was used to prepare the ATRP macroinitiator. This
initiator was considered a better candidate due to the lower reactivity of a chloride
species. TOPO molecules at the dot surface were first exchanged with pyridine and
subsequently with the THP-Cl ligand (Scheme 2.8). Tris(3-hydroxypropyl)phosphine
(THP) was first modified with 2-chloropropionyl chloride to obtain the macroinitiator
47
ligand (THP-Cl). The esterification reaction was carried out at room temperature using an
excess of macroinitiator in the presence of triethylamine to ensure complete esterification.
Unbound ligands were removed by successive dissolution/centrifugation cycles until a
clear supernatant was obtained. The final product was purified through alumina columns
and the product was characterized by FTIR spectroscopy, 31 P NMR and EA (expected
43.6% C and 6.1%H, obtained 40.8% C, 5.7% H).
FTIR spectroscopy (Figure 2.10) displayed the disappearance of the broad absorption
band at ~3400 cm-1 attributed to the νO-H vibration of the hydroxyl groups of the THP and
the presence of a sharp, strong absorption band attributed to the νC=O vibration at 1744
cm-1, confirming the successful esterification of the phosphine ligand.
Figure 2.10. FTIR spectra of THP and THP-Cl.
The exchange process was monitored by visible absorption spectroscopy (Figure 2.11). A
blue shift of the absorption bandgap compared to the initial CdS-TOPO samples was
48
registered upon the ligands’ exchange with pyridine and THPO-Cl macroinitiator,
indicating a significant reduction in QD size. The visible spectrum for the TOPO-capped
CdS QDs is typical of CdS nanoparticles prepared by the single source approach.
Quantum confinement effects are evidenced by a blue shift at the onset of absorption of
the CdS-TOPO QDs (489 nm), in comparison to the absorption of the bulk CdS (517 nm).
Figure 2.11: Visible absorption spectra of the samples: a) CdS-TOPO, b) CdS-Py, c)
CdS-THP-Cl, and d) CdS-THP-Cl/Pn-BA. Samples a) and b) were recorded in toluene; c)
and d) in THF. The corresponding solvents were used as references.
According to this shift in the absorption wavelengths, there was a decrease in the
CdS particle size from 6.6 nm (CdS-TOPO) to 3.4 nm (CdS-THP-Cl) in diameter
(estimated using Brus equation and the effective mass approximation).[104] The size
reduction observed clearly indicates that the last exchange step was responsible for the
most relevant shift, probably due to the removal of some atoms from the QD
surface.
49
The chloride-functionalized QDs were dispersed in the monomers (n-butyl acrylate or tbutyl acrylate) and a miniemulsion with 20% solids (based on 100% conversion) was
prepared using Brij 98 as surfactant and hexadecane as hydrophobe. AGET ATRP was
conducted using ascorbic acid (Asc. Acid) as reducing agent to activate the catalyst
complex via reduction of the Cu(II) species in situ. The optimal ratio of reagents required
to grow polymer chains with an average degree of polymerization of 200 from the surface
of the QDs was found to be: [M]0: [QDs-THPO-Cl]0: [Cu(II)]0: [Asc. Acid]0= 200:1: 0.7:
0.25. Monomer conversion was followed by gravimetric analysis. The final latex was
stable and without aggregated particles.
The composite materials were precipitated from miniemulsion and dissolved in
THF. In Figure 2.11 the visible absorption spectrum of the composite CdS-THP-Cl/
Poly(n-butyl acrylate) (CdS-THP-Cl/Pn-BA) is presented. The optical spectrum for the
final nanocomposite is quite similar to the surface exchanged CdS-THP-Cl QDs. From
these results, it is clear that the polymerization process itself has a negligible effect on the
CdS QD degradation.
The atomic force microscope (AFM) phase image (Figure 2.12) of the nanocomposite
CdS/Pn-BA shows a very homogenous nanocomposite material evidencing two distinct
phases: the semiconductor (white spots) surrounded by a uniform polymer layer.
Attempts to accurately determine the CdS QD diameter of the composite particles by
TEM failed to afford good quality micrographs due to the low glass transition
temperature of the polymer matrix. An accurate estimated value of QD diameter in the
50
composite nanoparticles could not be obtained due to experimental limitations from the
tip used (15-20 nm size), which did not allow the detection of such small individual
particles. However, as discussed above, we did not find evidence of QD aggregation in
the final nanocomposites relative to that observed for the original TOPO capped QDs
deposited on a glass slide.
Figure 2.12. Tapping mode AFM phase micrograph (2.5x2.5µm) of core-shell hybrid
CdS-THP-Cl/ Pn-BA nanocomposite prepared by AGET ATRP in miniemulsion.
Determination of the MW and PDI of the polymer chains grown from the surface of the
QDs required that the polymers be detached by treatment with hexylphosphonic acid.
GPC traces of detached polymers are shown in Figure 2.13. The values of Mn and PDI
(28,000 g/mol and PDI= 1.23 for n-PBA; and 17, 000 g/mol and PDI=1.24 for t-PBA,
respectively) indicate a controlled polymerization and good agreement with the
theoretical Mn indicating efficient initiation.
51
Figure 2.13: GPC trace of Pn-BA prepared by AGET ATRP after detachment from CdSTHP-Cl nanoparticles.
The above results show that the use of AGET ATRP to graft polymers from
functionalized QDs is an efficient strategy to obtain this type of nanocomposite with
good control over the polymer matrix structure. Since the polymers present in the
nanocomposites were grown from the QD surface, the final materials show a high
homogeneity at the molecular level. Although the exchange reactions, prior to
polymerization, led to a reduction of CdS particle size, the final nanocomposites
consist of CdS QDs evenly dispersed in the polymer. Although the work focuses on the
use of CdS QDs, this method can be implemented to other functionalized nanoparticles.
Highlighted is the possibility of preparing block copolymers and tuning the
functionalization of the polymer chain ends based on the chemical strategy initiated with
52
this work. QD/polymer nanocomposites with controlled functionalities can be chemically
bound to diverse systems and used for molecular recognition.
In conclusion, the efficient synthesis of hybrid organic/inorganic nanoparticles using a
silica particle model study followed by results with CdS QDs with surface tethered
initiators using an AGET ATRP miniemulsion process was reported. In comparison to
bulk polymerization, using the same stoichiometry, miniemulsion allowed the preparation
of hybrid materials with a higher yield, i.e., higher monomer conversion, and a higher
polymerization rate without macroscopic gelation. Direct visualization by AFM provided
additional evidence for the formation of well-controlled hybrids. This approach can be
applied to the synthesis of various well-defined polymers with complex architectures
based on multifunctional initiators.
A drawback to AGET ATRP exists in the fine tuning of the balance of the reducing agent
to catalyst species. Because the reducing agent in AGET ATRP has the potential to
reduce all of the catalyst to the activation state (causing the polymerization to be out of
control), adjusting the amount of reducing agent used for each reaction is crucial. This
reduction allows the polymerization to continue in a controlled manner.[69, 105] However,
this process can be tedious when synthesizing multiple polymerizations.
In another ATRP process, namely Activators ReGenerated by Electron Transfer
(ARGET) ATRP, a method of regeneration of catalyst increases purity and precision
control and to the AGET approach, at the sacrifice of accelerated reaction times. The
experimental design in ARGET ATRP requires less premeditation due to its flexibility in
53
required concentration of reducing agent.[69] It is therefore excellent for producing welldefined hybrids.
2.2.2.4 Experimental Detail for Quantum Dot Miniemulsion Systems
Quantum Dot Materials and Instrumentation
2-Chloropropionyl chloride (Aldrich, 97%), tris(hydroxypropyl)phosphine (THP, Strem
Chemicals 80 %); EA: 49.2%C and 9.9%H (expected 51.9% C and 10.2% H). n-Butyl
acrylate (n-BA Aldrich, 99%) was purified by passing through a column filled with
aluminum oxide ( Merck, 70-230 mesh) to remove the inhibitor and stored at -4ºC.
BPMODA [N,N-bis(2-pyridylmethyl)octadecylamine] was synthesized according to
procedures described in literature.[56, 106] CuCl2 (Aldrich, 97%), Brij98
(polyoxyethylene(20)oleyl ether, Aldrich, Mn=1150) and hexadecane (Aldrich, 99%)
were used without purification.
Visible absorption spectra were recorded on a Jasco V560 spectrometer. For each
spectrum, the wavelength relative to the optical bandgap was roughly estimated by
intercepting the band edge and the wavelength axis. 31 P NMR spectra were recorded
using a Bruker Advance 300 NMR spectrometer in methyl sulfoxide-D (99.9%) using
phosphoric acid as standard.
Synthesis of the ATRP chloride macroinitiator (THP-Cl)
2-Chloropropionyl chloride (6g/0.0473 mol) was added drop wise to a solution of
tris(hydroxypropyl)phosphine (THP) (3g/0.0144 mol) in dry tetrahydrofuran (THF, 50
mL) in the presence of triethylamine (4.8g/ 0.0473 mol). The reaction was kept at room
temperature cooling with an ice bath. A white precipitate was formed during the
54
addition. The mixture was stirred at room temperature for approximately 12 h after
which the solid was filtered and discarded. The supernatant was dried under reduced
pressure. The resulting material was purified through alumina columns (2x) and eluted
with ethyl acetate/diethyl ether mixture (2:3). Evaporation under reduced pressure
yielded a viscous and colorless product which was thoroughly dried under high vacuum
to remove residual solvents.
Synthesis and functionalization of CdS QDs with THP-Cl macroinitiator
TOPO capped CdS QDs were prepared following a method described in literature based
on the thermal decomposition of the single molecule precursor
Cd[S2CN(CH2CH3)2]2.[107] The as prepared QDs were precipitated with methanol and
centrifuged (3500 rpm; 10 min.) to remove the excess of TOPO until a clear supernatant
was obtained. The CdS QDs were dispersed in pyridine (Py) (~15mL) and the solution
was stirred for ~12 h, at 50 ºC under N2 atmosphere. Upon this the QDs were precipitated
from Py with n-hexane and centrifuged (3500 rpm; 10 min.). Successive
dissolution/centrifugation cycles were repeated until a clear supernatant was obtained.
The solid collected was dispersed in acidic (5% HCl) THF (30 mL) and THP-Cl (~300
mg) was added.
The mixture was stirred at room temperature for 12 h. After this period the solution was
still colored indicating the integrity of the QDs. The solid, CdS-THP-Cl, was
precipitated with n-hexane, collected by centrifugation (3500 rpm; 10 min.) and left to
dry at room temperature under vacuum.
55
Synthesis and characterization of CdS-THP-Cl/Polymer nanocomposites
A round bottom flask was charged with CuCl2 (1.33x10 -4 mol), BPMODA (N,N-bis(2pyridylmethyl)octadecylamine) (1.33x10 -4 mol ) and the monomer (0.0379 mol ). The
mixture was stirred vigorously at 70 ºC until complete dissolution of the solids. A small
amount of the monomer was kept apart to dissolve the CdS-THP-Cl nanoparticles,
which were added after all the solids were dissolved. The mixture was cooled with an
ice bath and the hydrophobe, hexadecane (7.14x10 -4 mol) was added. A 20 mM aqueous
solution of Brij 98 (2.3 wt% relative to the monomer) was added and the mixture was
sonicated for approximately one minute (amplitude 80%, 20 W power, Sonics-Vibracel
Sonifier). The flask was sealed and purged with N2 for ~1 h. Separately, an ascorbic
acid aqueous solution was also deoxygenated with N2 (5.32x10 -5 mol in 1 g H2O). The
reaction was started by immersion of the flask in an oil bath at 80 °C. The ascorbic acid
solution was added sequentially (during the 10 minutes immediately after immersion in
the oil) to the reaction vessel through a N2 purged syringe. The polymerizations were
typically carried out for 24 hours under continuous stirring. The polymerizations were
stopped by exposure to air. In order to determine the molar mass of the polymer chains
formed a sample of the final product was dissolved in THF and precipitated with
methanol. A moderately dark yellow viscous sample was collected which was later
treated with acid as described below.
For AFM analysis the precipitated samples CdS-THP-Cl/PnBA were dissolved in
chloroform at a standard concentration (1 mg/mL) and spun-coated onto freshly cleaved
mica surfaces before imaging. Tapping-mode AFM was carried out using the
56
Nanoscope-III Multimode System (Digital Instruments, Santa Barbara, CA). A new tip
with a 15-20nm radius was used.
For GPC analysis the dark yellow viscous QDs-THP-Cl/Pn-BA samples were dissolved
in a solution of hexylphosphonic acid in THF and stirred overnight at 50°C to detach the
polymers. [22] GPC was performed using THF as the mobile phase at 35 °C, a Waters 510
pump set to a flow rate of 1 mL/ min, three Styragel columns (Polymer Standard
Service, pore sizes 105, 103 , and 102 ) and a Waters 2410 refractive index detector.
Molecular weights were determined using the PSS software with a calibration based on
linear polystyrene standards (range 1k-2000k, PDI<1.07).
2. 3 ARGET ATRP FOR COMPOSITE SYNTHESIS
2.3.1
ARGET ATRP method description
The reaction scheme representing ARGET ATRP is given in Scheme 2.9. The concept
for ARGET ATRP is essentially the same as for AGET ATRP; but to avoid AGET’s
need to quantify reducing agent concentrations (to ensure a controlled process) the
ARGET process significantly decreases the amount of catalyst (generally ppm).[69] This
can yield good control even if all the species is reduced because the number of growing
chains is so small that expected loss/deactivation of radical due to transfer or
advantageous oxygen provides enough deactivation of the few propagating chains.[69, 105]
ARGET ATRP also has the benefit of being able to be re-started after exposure to air,
since oxygen is a necessary part of the system.[105] This advantage also guarantees that
57
(unlike normal ATRP) reactions from colloids, run in heavy dilution with long reaction
times, will not be terminated over extended periods by the always-prevalent system air
entry. The added bonus of designing experiments via this method is low catalyst
contamination,[69] which is necessary for precision measurements involving the final
material. For all of these reasons, some of the materials synthesized in this study were
better formed with ARGET ATRP.
Monomer
kact
Pn-X
+
kp
Pn* + X-Mtn+1/L
Mtn/L
kdeact
k
t
Pn-Pn + X-Mtn+1/L
Oxidized Agent
Reducing Agent
Pn-X
+
Mtn/L
Scheme 2.9: ARGET modifications to the general ATRP scheme. In this case, the
reducing agent was Sn(II) (specifically tin(II) 2-ethylhexanoate (Sn(EH)2).
To test this hypothesis, the method was selected based on the best available approaches.
ARGET ATRP would be ideal for these materials due to its purity alone, but because the
control of ARGET ATRP is sensitive at low conversions it was not feasible for all
samples.[105] Samples of high initiator density and very low chain length (i.e. DP10)
required a very slow reaction, so that the target molecular weight was not overshot.
58
Therefore, traditional or normal ATRP was best suited for its synthesis. Normally, the
reaction would be highly diluted (which slows the rate when above ~40% solvent) and
contain a reasonable amount of deactivator species at the onset, further guaranteeing a
slow reaction rate. However, because purity of the samples was a major factor in their
measurements, additional metals in the catalyst (activator or deactivator) species was
highly undesirable and the reaction was only diluted (at 50% volume) to slow the rate and
to maintain a low conversion that would yield a low probability of crosslinking reactions.
To account for the fact that crosslinking in colloidal particle polymerization at
conversions >15% is currently only avoidable in a miniemulsion (AGET) ATRP, and the
reaction conditions for AGET ATRP had not been sufficiently tested, going to conversion
above 15% was not an option in the other syntheses. However, heavy dilution of the
reaction would be neither ideal nor necessary in the case of DP140 and DP150. This is
because the target is 15 times that of DP10. Simply stopping at low conversion would
thus make crosslinking unlikely. However, due to the normal amount of catalyst species,
the hybrids had to be purified via dialysis for several days to remove the contaminating
metals.
Very high molecular weight hybrids have never been prepared by CRP in large quantities.
High conversion has always yielded crosslinked materials, and the length of time
required for a very large molecular weight to be achieved in heavy dilution has always
been greater than the reaction’s sensitivity to oxygen. However, because ARGET ATRP
is able to continue to polymerize in the presence of oxygen, it was ideal of the DP760
59
sample. Additionally the low catalyst concentration (ppm) required, allowed for limited
purification of the final material.
All experimental details are given in the experimental section (Appendix A). Dynamic
light scattering (DLS) and TEM of the commercial colloidal nanoparticles after
functionalization with initiating sites (from MIBK-ST, Nissan) confirmed that these
particles have average diameters of 20 nm (DLS, z-average) and 16 ± 4.5 nm (TEM,
number average). TEM images show that colloidal nanoparticles in the above size range
have relatively broad distribution, which contrasts with other nearly mono-disperse
commercially available colloidal particles with larger size (> 50 nm). Samples of the
materials from each of the experiments were etched to measure the attached polymers via
GPC and imaged via TEM (both given and discussed with results in Chapter IV). GPC
curves exhibited control of all the detached chains, and TEM spacing was generally
indicative of controlled spacing. An issue with the ARGET-generated sample (DP760)
arose when particles apparently free of polymer growth were found in some of the TEM
micrographs (see supplemental information in Appendix C). Although still under
discussion, it is most likely that ARGET is too sensitive to low conversions. At the
conversion of the reaction that produced DP760 samples (~6%), some chains had not had
sufficient time to be initiated and therefore had particles free of growth. It is important to
note that this is only an issue in the polymerization of macroinitiators, since non-initiated
chains with molecularly-sized initiators will simply be removed in the filtration process.
60
2.3.2
Experimental Detail for Quasi-Transparent Polystyrene-Silica Composites
Materials. All chemicals were purchased from Sigma-Aldrich Co., USA, unless
otherwise specified.
Inhibitor from the styrene monomer was removed by passage
through a column filled with basic alumina. Copper (I) bromide was purified by washing
several times with glacial acetic acid and stored (dry) under a blanket of nitrogen. Silica
was obtained from Nissan Chemicals (MIBK-ST) and functionalized with the alkyl
halide initiator 1-chlorodimethylsilylpropyl 2-bromoisobutyrate according to the
procedure described previously.[73] Elemental analysis, conducted by Midwest Microlab
(IN) provided bromine content for the functionalized particles. Copper (II) bromide,
anisole, hydrofluoric acid (concentration 36%, Acros), and 2,2-bipyridine were used as
received. Toluene (ACS, 99.5%) was purchased from Fisher Scientific and purified
through a distillation apparatus and filtration through a 0.2 µm filter before being added
to samples. Styrene was purified by passing through a column filled with basic alumina.
Tris(2-(dimethylamino)ethyl)amine (Me6TREN), Copper (I) bromide was purified as
described
elsewhere.[108]
Ethyl
Pentamethyldiethylenetriamine
2-bromoisobutyrate
(PMDETA),
(EBiB),
N,N,N’,N”,N”-
4,4-dinonyl-2,2-bipirydyne
(dNbpy),
copper(II) bromide, copper(II) chloride, tin(II) 2-ethylhexanoate (Sn(EH)2), anisole were
used as received.
Normal ATRP of St from 2-Bromoisobutyrate Functional Colloids with DP = 10.
A Schlenk flask was charged with PMDETA ligand (21.9 μL, 0.105 mmol), initiatormodified silica particles (1.4837 g, 0.524 mmol), anisole (12.0 mL) and styrene (6.0 mL,
61
52.4 mmol). After three freeze-pump-thaw cycles, the flask was filled with nitrogen, then
while the mixture was immersed in liquid nitrogen, 15.0 mg (0.105 mmol) of CuBr was
added. The flask was sealed with a glass stopper, evacuated, and back-filled four times
with nitrogen. After melting the reaction mixture and warming to the room temperature,
the initial sample was taken and the sealed flask was placed in thermostated oil bath at 90
o
C. The reaction was stopped by opening the flask and exposing the catalyst to air after 5
h. Hybrid particles were isolated and purified by precipitation into an excess of methanol
and recovered by filtration for three times. The cleavage of polymer brushes from silica
particles was conducted as reported.3 SEC of the cleaved polystyrene was conducted to
determine the molar mass of the tethered polymer (Mn = 1 020 g/mol and Mw/Mn =1.08).
The monomer conversion was about 2.5%, as determined from gravimetric analysis.
Normal ATRP of St from 2-Bromoisobutyrate Functional Colloids with DP = 150.
A Schlenk flask was charged with dNbpy ligand (0.635 g, 1.55 mmol), initiator-modified
silica particles (0.50 g, 0.177 mmol), copper (II) bromide (15.8 mg, 0.071 mmol) and
styrene (20.2 mL, 177 mmol). After three freeze-pump-thaw cycles, the flask was filled
with nitrogen, then while the mixture was immersed in liquid nitrogen, 101.3 mg (0.706
mmol) of CuBr was added. The flask was sealed with a glass stopper, evacuated, and
back-filled four times with nitrogen. After melting the reaction mixture and warming to
the room temperature, the initial sample was taken and the sealed flask was placed in
thermostated oil bath at 90 oC. The reaction was stopped by opening the flask and
exposing the catalyst to air after 22.5 h. Hybrid particles were isolated and purified by
precipitation into an excess of methanol and recovered by filtration for three times. The
cleavage of polymer brushes from silica particles was conducted as reported. SEC of the
62
cleaved polystyrene was conducted to determine the molar mass of the tethered polymer
(Mn = 15 500 g/mol and Mw/Mn =1.21). The monomer conversion was about 11.0%, as
determined from gravimetric analysis.
ARGET ATRP of St from 2-Bromoisobutyrate Functional Colloids with Targeting
DP = 770.
Styrene (40.5 mL, 0.353 mol), and anisole (38.2 mL) were added to a dry Schlenk flask.
Then, silica particle initiator (0.20 g, 0.0706 mmol) and a solution of CuCl2 complex
(0.475 mg, 3.53 μmol)/Me6TREN (0.932 μL, 3.53 μmol) in anisole (1.70 mL) were added.
The resulting mixture was degassed by four freeze-pump-thaw cycles. After melting the
mixture, a solution of Sn(EH)2 (2.29 μL, 7.06 μmol) and Me6TREN (1.86 μL, 7.06 μmol)
in anisole (0.54 mL) was added. An initial sample was taken and the sealed flask was
placed in thermostated oil bath at 90 oC. The polymerization was stopped by opening the
flask and exposing the catalyst to air after 23.5h. Hybrid particles were isolated and
purified by precipitation into an excess of methanol and recovered by filtration for three
times. The cleavage of polymer brushes from silica particles was conducted as reported.
SEC of the cleaved polystyrene was conducted to determine the molar mass of the
tethered polymer (Mn = 80 400 g/mol and Mw/Mn =1.32). The monomer conversion was
about 5.9%, as determined from gravimetric analysis.
Analyses. Molecular weight and molecular weight distribution were determined by GPC,
conducted with a Waters 515 pump and Waters 2414 differential refractometer using PSS
columns (Styrogel 105, 103, 102 Å) in THF as an eluent (35 oC, flow rate of 1 mL/min).
Linear polystyrene standards were used for calibration.
63
Static and dynamic light scattering. Measurements were performed using a
Brookhaven Instruments Corporation BI-200SM goniometer and a green diode laser light
source (λ = 532 nm). Samples were filtered using PTFE Millipore syringe filter with 0.25
m pore size diameter and equilibrated for 48 h before measurement. The total intensity
R(q) was determined using the relation R(q) = (I(q) - I(q)toluene) R(90)toluene
(I(q)toluene)-1 sin with R(90)toluene = 2.52 × 10-5 cm-1 denoting the Rayleigh ratio of
toluene at 2 = 90 degree for vertical polarized incident light.[109]
Transmission Electron Microscopy. Particle imaging was conducted using a JEOL
2000 FX electron microscope operated at 200 kV. TEM samples of nanoparticles and
hybrid nanoparticles were prepared by the casting the colloid solution diluted to 0.1
mg/mL in tetrahydrofuran (THF) onto a carbon-coated copper grid.
64
CHAPTER 3. METHOD BACKGROUND
“As far as the laws of mathematics refer to reality, they are not certain; as far as they are
certain, they do not refer to reality.”— Albert Einstein
To achieve a better understanding of complex hybrid particles in solution considerable
effort has been made over the past decade on the static and dynamic behaviors both from
theoretical and experimental points of view. This chapter develops the necessary
background for the interpretation of the scattering properties of polymer-coated particle
systems that will be relevant in the characterization of the hybrid particle samples.
A significant amount of theoretical background is needed to extract information from the
measured scattered intensity (Is) to understand properties of colloidal hybrid materials.
Concepts in static light scattering (SLS) intensity are of particular importance, therefore
theoretical background information related to the specific interference that can be found
in this system, namely form and structure factor effects are detailed within this chapter.
Dynamic light scattering (DLS) will be used to determine and confirm the dispersion
state of the particles in solution – an assumption that is implicit in the application of
effective medium theory. Therefore, theoretical background on the interpretation of
relaxation time spectra and autocorrelation functions will also be presented.
3.1 LIGHT SCATTERING
Light scattering has been successfully used for the measurement of nano-sized objects for
more than thirty years, however the availability of laser light sources and computers for
65
detailed calculations has increased scientific interest recently.[110] In this section, the
fundamentals of laser light scattering will be explained in detail. The discussion will
leave out the general description of scattering phenomena by solution of the respective
Maxwell’s equations, the reader should refer to Bohren and Huffman [20] for further detail.
Sample Cell
Laser Source
Distance to particle (rd)
Incident Beam
(Io)
Scattered beam
(Is)
Angular Measurement
(θ)
Detector
(a)
Composite Particles
Rh
(ki)
(θ/2)
Ri
R
(q)
(ks)
(b)
(c)
( ri - rj )
Figure 3.1. Light Scattering experimental setup (a) and definitions for Incident (Io) and
scattered (Is) beam intensities, detector distance (rd), and angle of measurement (θ). The
representations for scattering vector (q) and angle (θ /2) and wave vectors (ki and ks) are
given in b. Composite factors of importance (utilized mainly in the structure factor
calculations), namely particle radius (R), inner/core radius (Ri), radius of gyration (Rh)
and particle to particle distance (ri-rj), are defined in (c).
66
Linearly polarized light with wavevector ki is incident on a sample (scattering center) that
gives rise to scattering of light with wavevector ks. A schematic illustration of the
experimental set-up given in Figure 3.1 where
ki 
2
0
eˆi and k s 
2
0
eˆ s
(3.1)
and êi is the unit vector in the direction of propagation of the incident ( ês for scattering)
beam. For convenience, the scattering vector q is introduced that describes the
momentum transfer associated with the scattering process. Note that the modulus of q is
given as
q  ks  ki 
4  n p
0
sin  2
(3.2)
The Rayleigh ratio R(q) is introduced as a measure for the absolute excess scattering of
the solution with respect to the solvent and is defined as:
 I r2
R(q) =  s
 Io

 or more traditionally:

 I
n

( )  I solvent ( )   abs
 I 90 toluene solvent  sin 
R(q)   solution

I toluene (90 )
 ntoluene 


2
(3.3)
The units of R(q) are cm-1 since it describes the scattering per path length through the
sample.
Both, the absolute values as well as angle dependence of the Rayleigh ratio can be
evaluated to yield information about the structure and solutions state of solutes. In order
67
to simplify the analysis, all experimental constants as well as the particle polarizability
are condensed in the optical constant, K (K= 4π2no2(dn/dc)2/(Naλ4)). In the following the
relevant relationships between the experimental R(q) and the size of colloidal solutes are
established. Before introducing the general relations a brief comment should be made
about the evaluation of R(q) for macromolecular solution. Zimm demonstrated that for
macromolecular solutions R(q) can be related to the molecular weight (M) or the second
virial coefficient (A2) via[111]:

Kc 
R(q)  
1  2 A2 c 
 M

(3.4)
This relation can be regarded as an approximation to the more general relation (discussed
below) that is valid for most polymers in solution.
3.1.1 Static Light Scattering
Static light scattering (SLS) probes the equilibrium form and static structure factors of
solution systems by measuring the scattered light intensity (Is) that can be related to the
Rayleigh ratio R(q). In general the experimental R(q) will be given as the product of three
terms, i.e. Rayleigh scattering factor (Rsca), form factor (P(q)) effects, and the system’s
structure factor (S(q)) for all particles:
Is(q)= Rsca  P(q)  S (q)
(3.5)
The three terms take in to account the scattering strength of the scattering center (Rsca) as
well as intramolecular (P(q)), and intermolecular (S(q)) interference effects of the
material.
68
3.1.1.1 Rayleigh Scattering
The theory of light scattering was first put forth by Lord Rayleigh[112] in a series of papers
in which he discussed the case of gas particles with a small size when compared to the
wavelength of the incident light. The Rayleigh scattering for a point scattering particle
is[20]:
 I o Nk i 4 2
Rsca = 
rd2


 and k i   2 n 

 

(3.6)
where Io is the intensity of the light, N is the number of particles, ki is the wave vector, α
is the polarizability (defined in Chapter I), np is the refractive index of the particle, and rd
is a detector distance. Further, it should be noted that for macromolecules the
polarizability introduces the refractive index increment ((dn/dc)2), that is a measure for
the change in refractive index n with varying concentration.
3.1.1.2 Form Factor
The form factor P(q) is a measure for the intramolecular interference effects that occur
when scattering particles are sufficient in size (typically greater than about 5 nm) such
that the coherent scattering from distinct scattering centers within the same particle give
rise to interference effects that render the measured R(q) angle dependent.
69
The general formula for a form factor can be expressed as the Van de Hulst’s integral[113]:
P(q) =
1



0
exp if q d
(3.7)
where the shape parameter (Φ) might represent a length or radius of gyration. Many form
factors (e.g. rigid rods, ellipsoids, etc.) have been derived but the most simple form factor,
due to its symmetry of scatter in all directions, is that of a sphere (radius, R):
 3sin qR  qR cos qR  

 and qR   2kR sin 
P(q)sphere = 
3

2
qR 



2
(3.8)
where k (defined in Eq.1.2). These vectors depend on the direction of the scattered
wave; however, because the scattering is symmetric, the phase (qR) is a constant. Further,
because of the geometric nature of the equation, the form factor can be eliminated for all
angles such that:[20]
tan qR  qR  0
(3.9)
70
The graph of equation 3.8 for all angles, is shown in Figure 3.2 for validation.
1.05
1.04
1.03
1.02
P(qR)
1.01
1
0.99
0.98
0.97
0.96
0.95
0
20
40
60
80
100
Angle (degrees)
120
140
160
180
Figure 3.2: Graph of the form factor P(qR) for a sphere, given in equation 3.8.
Calculations utilized λ = 532 nm, np = 1.55, and R = 10 nm. For angles less than 15° the
value of P(qR) is very close to 1.
In Chapter IV, comparisons of the sphere (effective sphere in our case) versus a coreshell form factor will be made. For those purposes, the form factor for a core-shell
particle is also given:[114]
P(qR)core-shell =
 3sin qR  sin( qR( Ri / R))  qR cos( qR)  (( Ri / R)qR) cos(( Ri / R)qR) 2


qR 3 1  ( Ri / R) 


 (3.10)


where the known sample inner radius (Ri) and total radius (R) will be inserted and
calculated in order to be compared to data over all angles. Note that the above relation is
valid for particles with a small phase shift (i.e., 2πd ‫( ׀‬neff/nm)-1 ‫ ׀‬λ<<1).
71
3.2.1.3 Structure Factor
With increasing concentrations of particle solutions, coherent scattering contributions that
arise due to the interaction of the solute particles become increasingly important. These
intermolecular interference effects are summarized in the structure factor (S(q))[20, 115]
that is defined as:
S(q) = 2  1  (G (r )  1) exp iqr dr and G(r )  N 1
 r  r 
i
j
(3.11)
i, j
The pair distribution function, (G(r)), generally describes the microstructure of the
solutes as it is a measure for the probability of finding one particle at a given distance (r)
from another particle located at the origin. Generally, intermolecular interference effects
complicate the interpretation of R(q), however, S(q) can be neglected if the
measurements are performed in the dilute regime since G(r) 0.[20]
From the former discussion, it can be concluded that for spherical particles in the dilute
solution and at small scattering angles (q ~ 0), only Rayleigh scattering has an effect at
small angles (since P(q) ≈ 1). Thus, forward scattering (i.e. scattering at zero angle)
provides a quantitative measure for the scattering strength or polarizability of a species.
3.2.2 Dynamic Light Scattering
Dynamic light scattering (DLS) is a tool for the classification and derivation of a particle
system’s dispersion state that can be concluded from measuring the particles diffusion
coefficient (Dc) that can be henceforth related to the particle’s size by utilizing Brownian
72
motion equations describing the motion of particles in solution. The Brownian motion of
the solute particles gives rise to spatial and temporal fluctuations of the scattering
intensity.[116] In DLS these fluctuations are measured and quantified using an
autocorrelator that determines the intensity autocorrelation function. The characteristic
time scale of the fluctuations can then be related to the diffusivity of the dispersed species
and (via the Stokes-Einstein relation) to their characteristic hydrodynamic radius.
3.2.2.1 Autocorrelation Function and Relaxation Time Spectra
The dynamic information about the particles can be derived from an autocorrelation of
the intensity trace recorded during the experiment. At scattering vector q, dynamic light
scattering experiments provide a measure of the normalized intensity autocorrelation
function of the scattered electric field (g2(q,t)):[20, 116]
g 2 (q, t )  I (t 0 )  I (t   )
I (t 0 )
2
(3.12)
where t is the delay time. From g2(q,t) the field autocorrelation function g1(q,t) is
computed via: [20, 116]
g 2 (q, t )  1  f coh g1 (q, t )
2
(3.13)
where fcoh is an instrumental coherence factor, determined by a standard and g1 (q, t ) is
defined as:
g1 (q, t )  E (t 0 )  E * (t   )
E (t 0 )
2
(3.14)
73
For ideal monodisperse solutions, g1 (q, t ) can be shown to be related to the diffusion
coefficient of the dissolved species:[20]
g1 (t )  exp( t ) with   Dq 2
(3.15)
Here, D is the translational diffusion coefficient that is related to the size of the
(spherical) diffusing species via the Stokes-Einstein relation (strictly valid only for
infinite diluted solutions):[115]
D=
k BT
6 s Rh
(3.16)
where kb is Boltzmann’s constant, T is absolute temperature,  s is the solvent viscosity,
and Rh is the hydrodynamic radius.
In the more realistic case of real (polydisperse) solute solutions, g1 (q, t ) is given as the
sum of the individual contribution of diffusing species(A):
g1 poly (t )   Ai exp(  Di q 2 t )
(3.17)
i
or in continuum representation (Laplace transform):
g1 poly (t )   P() exp( t ) d
(3.18)
Where P(Г) is the probability of an occurrence of particles with the diffusion coefficient,
Г/q2. P(Г) is also called the relaxation time spectra and is of major interest as it describes
the size distribution of dissolved particles. It can be obtained from g1 (q, t ) via an inverse
Laplace transform implemented in the constrained regularization method (CONTIN)
74
developed by Steven Provencher.[117] This numerical routine is part of the DLS analysis
software.
3.2.2.2 The Diffusion Coefficient
The autocorrelation function’s exponential decay is then related to the motion of the
particles, specifically, the diffusion coefficient. At small values of q, g(t) can be
approximated by the exponential function:

g1 (q, t )  exp  Dc q 2  t

(3.19)
where Dc is the cooperative diffusion coefficient given by:[115, 116]
Dc = 1   
2
M
Nf
  


 C 
(3.20)
in which is the volume fraction of the polymer/particle, (∂π/∂C) the osmotic
compressibility, and f, or friction coefficient predict the movement of a material through
a solvent. The inverse osmotic compressibility is inversely proportional to the apparent
molar mass, so we can write:[116, 118]
Dc = 1   
2
k BT
f
 M 


M 
 app 
(3.21)
The friction coefficient, f, should not be confused with the friction coefficient of an
individual particle moving with respect to solution, which determines the self-diffusion of
a polymer. Only in cases of infinite dilution (where the structure factor is eliminated) are
75
the two friction coefficients the same.[115] In this case, the term f = 6πsRh and equation
3.21 can be reduced to the well-known Stokes-Einstein relationship:
Dc =
k BT
6 s Rh
(3.22)
The Stokes-Einstein equation defines the relation between diffusion coefficient and
material size (variables previously defined in 3.16). Therefore, in the dilute regime, DLS
data can provide information regarding sample size.[116]
From the term Г = Dq2, it is clear that the autocorrelation function and relaxation spectra
can be used to determine both size and width of the particle distribution (polydispersity).
3.2 PRACTICAL CONSIDERATIONS
For weakly scattering systems with low signal-to-noise ratio, the autocorrelation process
occurs over long time scales in order to improve the statistical relevance of the result.
Under these conditions impurities (such as dust) dominate the signal. The presence of
impurities presents a formidable problem in the analysis of g1 (q, t ) since the standard
CONTIN routine cannot be applied. In samples where the signals were extremely low
and dust had a significant contribution, an alternative mathematical approximation was
used to analyze the correlation function.
76
First, the relaxation time interval [τmin, τmax] relevant to the sample diffusion was
extracted. Second, g1 (q, t ) with t = [τ1, τ2] was analyzed using a stretched exponential
function:
g1 poly (q, t ) ~ exp  (t ) 
(3.23)
(also called Kohlrausch-Williams-Watts). While this approach has no direct physical
relation to the solute diffusion it has been shown to be a valid mathematical
approximation to an exponential correlation function. The stretching exponent β indicates
the breadth of the distribution (i.e. sample’s polydispersity). Typically β ≈ 1 is considered
narrow disperse.[119, 120]
In conclusion, the theoretical background presented in this chapter serves to explain all
data presented in the forthcoming results and discussion (Chapter IV). More advanced
discussion of scattering theory based on shape (e.g. form factors presented above) and
exact solutions to equations based on available form factors will also be presented and
applied in that chapter.
77
CHAPTER 4. CHARACTERIZATION AND EXPERIMENTAL RESULTS
“The true delight is finding out rather than knowing.”— Isaac Asimov
4.1 SYNOPSIS
While Chapter III focused on the theory regarding the scattering of light, this chapter
presents a detailed discussion of the characterization of molecular and optical properties
of the PS@SiO2 particle systems in toluene solution and in particular, validates the
hypothesis that effective medium theory facilitates the prediction of null-scattering
conditions. The choice of a liquid embedding medium is motivated by experimental
convenience, i.e. straightforward experimental verification of the dispersion state of the
particle inclusions by dynamic light scattering.
Figure 4.1 illustrates the property characteristics of the PS@SiO2 /toluene system as well
as the dependence of the particles’ effective refractive index on the core-shell
composition calculated using Maxwell-Garnett theory (equation 1.4).Assuming a
refractive index for toluene of ntol = 1.4969 it is found that particles with mass
composition of m(PS)/m(SiO2)  0.19 are index-matched to toluene and thus nullscattering of the particle solutions is expected.
78
Figure 4.1. Illustration of the optical characteristics of PS@SiO2 core-shell particle
system. The dotted gray line indicates the dielectric constant of the embedding medium
toluene.
In order to verify this prediction, a series of PS-coated silica nanocrystals were
synthesized using the recently developed ‘activator re-generated by electron transfer
atom-transfer radical polymerization’ (ARGET-ATRP) technique described in Chapter II.
The principal advantage of this technique is that the addition of a sacrificial reducing
agent during the ATRP reaction facilitates both, high molecular weight and low
polydispersity of the resulting polymer through reduction of the necessary amounts of the
catalytic agent Cu(I).[105]
79
4.2 CHARACTERIZATION OF PARTICLE ARCHITECTURE AND SOLUTION
PROPERTIES
Particles were characterized with respect to the molecular weight and grafting density of
surface-bound polymers, the dispersion state of the particles in solution as well as the
effective (hydrodynamic) size in solution.
4.2.1 Molecular weight and grafting density
Characterization of molecular weight and grafting density of the surface-bound polymer
chains for all particle samples was performed using size exclusion or gel permeation
chromatography (GPC) of detached chains and thermal gravimetric analysis (TGA) of the
dry, solid samples. Figure 4.2a displays the GPC curves for all four of the samples.
Comparison to polystyrene standards insured accuracy of resulting molecular weights for
the samples. Sample identification and corresponding chain molecular weights are as
follows: DP10 = 1020 g/mol, DP140 = 14200 g/mol, DP150 = 15550 g/mol and DP760 =
80400 g/mol. Narrow molecular weight distributions (<1.25) were achieved for DP10,
DP140, and DP150. Slightly higher polydispersity (1.32) was observed in polymerization
target DP760, evident by the widening of the GPC trace and increased M n. Increases in
polydispersity are often observed in the ATRP of high molecular weight polystyrene
generally attributed to thermal polymerization over long reaction times.[28]
80
DP10
DP150
DP140_LD
DP760
2
10
3
10
4
10
5
10
Mn
Figure 4.2a. Size exclusion chromatography traces of polystyrene chains after
detachment from core-shell samples, measured against polystyrene standards. From left :
DP10 (black), DP140 (red), DP150 (blue), and DP760 (green).
ATRP was applied to polymerize styrene with varying degree of polymerization yielding
samples in the range of the proposed 20% vol. composition for sample DP140.
Elemental analysis of the bromine content of the initiator-functionalized silicas gave a
measured initiator density which was applied in the calculation of desired chain length.
TGA of the PS@SiO2 samples provided the actual volume composition (when combined
with the GPC data) and is given in Table 4.1.
Table 4.1. SiO2-PS samples prepared by ARGET ATRP for transparent target material
and studies.
From the discussion above it follows that the effective medium prediction for null
scattering conditions prediction (m(PS)/m(SiO2) = 0.19) was approximately satisfied by
81
sample DP = 140 (m(PS)/m(SiO2) = 0.22, grafting density  ~ 0.09 chains/nm2). While
sample DP =10 ( ~ 0.7) differed in density from the targeted material, it was still
proximate to the predicted composition (DP =10; m(PS)/m(SiO2) =0.12). Sample DP =
150 differed (effectively) from DP140 only in density ( ~ 0.7 chains/nm2) and DP = 760
was provided an example of a material unlike the targeted material in volume
composition and chain DP. The corresponding mass ratios m(PS)/m(SiO2) of the particle
samples were calculated to be 0.12 (DP10), 0.22 (DP140), 2.5 (DP150) and 7.5 (DP760),
respectively.
4.2.2 Transmission Electron Microscopy
Transmission electron microscopy (TEM) of particles confirmed the dispersion and
regularity of the samples and provided agreement with GPC and TGA results. Previous
research has demonstrated that the interparticle distance is dependent of two parameters –
the molecular weight as well as the grafting density of the surface-bound polymers. In
particular the decrease of polymer graft density on particles has been shown to result in
decreasing particle-to-particle distances as the conformation of a lower density graft is
capable of an entropically-favored coiled state while higher density grafts are forced into
stretch conformations.[121] Figure 4.2b-d depicts electron micrographs of the respective
particle monolayers deposited on carbon film revealing the close-packed hexagonal
arrangement of the particle samples with high polymer grafting density indicative of
hard-sphere type repulsive particle interactions.
82
Analysis of the micrographs yields the estimated radius of the grafted polymer shell for
particles: rDP10  1.25 nm, rDP140  2.5 nm rDP150  21.5 nm rDP760  28.5 nm.
Prediction of PS@SiO2 sizes are summarized in Table 4.2.
Sample
Calc. Size (nm)*
Size via TEM (nm)
% Agreement
DP10
21.8
22.5
96.7
DP140
23.2
25
92.6
DP150
51.5
63
81.7
DP760
115
77
67.0
Table 4.2. PS@SiO2 calculated and measured size agreements. *Calculated size
determined assuming a stretched conformation of the attached chains (0.25 nm per
monomer unit) and densities provided from TGA data.
Calculation from GPC and TGA data show less than 8% error for samples DP10 and
DP140, while DP150 shows a slightly larger discrepancy (<20%) which could rationalize
a lower chain density and therefore, slightly more compact architecture than predicted
with the fully stretched model. The large discrepancy in size correlation for DP760 is
most likely due to some free polystyrene that may have formed thermally during the
reaction (and indicated by the higher polydispersity observed in the GPC trace).
83
Figure 4.2. Panels b-e depict bright-field electron micrographs of the respective particle
samples prepared in Table 4.1. Panel b: DP10 (grafting density σ = 0.71 chains/nm2).
Panel c: DP140 (grafting density σ = 0.09 chains/nm2). Panel d: DP150 (grafting density
σ= 0.5 chains/nm2). Panel e: DP760 (grafting density σ = 0.5 chains/nm2). Scale bar is
100 nm.
The results confirm a stretched conformation of PS chains for DP10 and extended-coil
conformation for DP150. For low grafting densities (DP140) repulsive entropic
interactions are reduced and a more condensed particle arrangement is observed. These
results are in agreement with previous studies on the dependence of hydrodynamic radius
of PS-coated silica colloids on polymer molecular weight and grafting density.[81] With
respect to the conclusions drawn from the experimental data these values provide an
84
appropriate estimate since deviations (e.g. arising from the finite disparity of particle
sizes) will affect all samples similarly.
4.2.3 Dynamic Light Scattering
After surface modification all particle samples were soluble in toluene. Dynamic light
scattering experiments were performed in order to evaluate the dispersion state as well as
the hydrodynamic radius of the particles in solution. It was found that only the scattering
intensity for particle samples DP150 and DP760 was sufficient for data analysis. A fine
particle distribution is assumed for the effective medium theory and therefore is critical
for the success. For particle samples DP10 and DP140 the scattering intensity was found
to be too low for quantitative measurements and is discussed in more detail below.
Specifically, the problems associated with low-scattering samples are related to the long
measurement times that increase the likelihood of dust contamination. Since counting
times of about 30 minutes were found to be necessary to obtain reasonably good data
statistics the removal of dust to appropriately low concentrations was found to be
impractical.
Figure 4.3 shows the measured autocorrelation functions as well as corresponding
relaxation functions that were determined using CONTIN for DP10 and DP150 at 30 and
150 degree, respectively. For all measurements of sample DP150, a single peak was
observed from which an average relaxation time could be determined (see Figure 4.3a).
The diffusion coefficient calculated from the relaxation spectra (using equation 3.16) was
found to be angle independent thus providing evidence for the diffusive origin of the
relaxation process (necessary prerequisite for well dispersed particles in solution).
85
For the weaker scattering sample DP10, measurements resolved a single relaxation peak
shifted toward either the earlier or later times depending on angle and peak intensity
(Figure 4.3b and c, respectively).
0.03
0.035
100
100
0.030
80
80
60
60
0.020
C(t)
Intensity
C(t)
150 Degree
0.015
40
40
0.01
Intensity
0.025
0.02
30 Degree
0.010
20
0.00
0.1
1
10
100
1000
10000
100000
0
1000000
20
0.005
0.000
0.1
s
a)
1
10
100
1000
10000
100000
0
1000000
s
b)
0.010
100
1.0
100
80
0.8
80
0.008
150 Degree
0.004
0.6
60
DP10
Bare SiO2
DP150
0.4
40
0.002
0.2
20
0.0
0
20
0.000
0.1
1
10
100
1000
10000
100000 1000000
0
1E7
0.1
1
s
c)
40
d)
10
100
1000
10000
100000
1000000
s
Figure 4.3. Computer-extrapolated (via CONTIN) relaxation time spectra from sample
angles of overlaid with the corresponding correlation functions given in Figure 4.7. a)
DP150 at 150 degrees b) DP10 at 30 degrees c)DP10 at 150 degrees d) Correlation
functions and resulting relaxation times (returned by CONTIN analysis) for bare silica,
DP10, and DP150 at 30 degrees.
86
Intensity
C(t)
60
Intensity
C(t)
0.006
The apparent q-dependence of the diffusion coefficient of particle sample DP10 can be
attributed as a consequence of the failing of the algorithm to resolve the two coexisting
peaks (particle diffusion and dust sedimentation). Correlation functions for bare silica and
DP10 were identical at 30 degrees, yet, the resulting relaxation time spectra (returned by
CONTIN analysis) differed greatly (Figure 4.3d) further elucidating the limitations of
the algorithm. The diffusion coefficient determined from the relaxation time spectra
exhibited similar accuracy problems for the DP10 sample. Due to this error, the samples
appear to grow in size from the 16.62 nm measurement at 30 degrees to ~80-300 nm over
the full angle range (Figure 4.4). The diffusion coefficient and radius of gyration for
DP150 could be averaged over all angles for a size return of 56.21 nm, similar to the
predicted values given in Table 4.2. We attribute the deviations of the DLS results of
DP10 from the TEM results to the contribution of dust to the autocorrelation function.
Figure 4.3b clearly reveals a second slow relaxation process corresponding to  ~ 0.1
seconds. Since the motion of dust particles is not random but directed (sedimentation) the
exponential decay is steeper than single-exponential. In this case CONTIN fails to
provide an adequate description of the autocorrelation function.
87
-11
4.0x10
DP10
DP150
Linear Fit of DP10
Linear Fit of DP150
-11
3.5x10
-11
3.0x10
-11
2
D (m /s)
2.5x10
-11
2.0x10
-11
1.5x10
-11
1.0x10
-12
5.0x10
0.0
0.0
6
5.0x10
7
1.0x10
7
1.5x10
7
2.0x10
q (m)
7
2.5x10
7
3.0x10
7
3.5x10
-1
Figure 4.4. Calculated D vs. q for all angles, and average D shown with lines of similar
color. DP10 display contrary results to TEM in relation to size. Particle diameters derived
from this data were 56.21 nm for DP150 and 127.67 nm for DP10.
For samples with significant dust impurities, a modified data analysis procedure was
applied as described in the following: First the appropriate range of the field
autocorrelation function g1(q, t) was separated from the raw data file. Subsequently the
relaxation process was analyzed using the Kohlrausch-Williams-Watts (stretched
exponential) approach (see equation 3.23).
88
0.04
0.04
0.03
g1()
g1()
 = 131 s
 = 0.99
 = 64.7 s
 = 0.97
0.02
0.02
0.01
DP760
DP150
0.00
0.1
1
10
100
1000
10000
0.00
0.1
1
10
100
1000
10000
-6
 /10 s
-6
 /10 s
Figure 4.5. Field autocorrelation function g1(q, t) at q = 2.75  107 m-1 of particle
samples DP150 (left) and DP760 (right) with the fits to stretched exponential function
(Kohlrausch-Williams-Watts). Stretching parameter is  = 0.97 and 0.99 for DP150(a)
and DP760(b), respectively, indicating single-dispersed particles of uniform size in
solution. The hydrodynamic radius follows from Stokes–Einstein relation as rH, DP150 = 19
nm and rH, DP760 = 35 nm, respectively. For particle samples DP10 and DP140 the
scattering intensity was too small to facilitate resolution of the correlation functions
without dust interference (See Figure 4.6).
Using this approach narrow size dispersity for the silica particle samples could be
verified (via a stretching parameter  ~ 1) for all signal-producing samples. The results
are given in Figure 4.5. Extracted values for τ were 64.7 μs for DP150 and 131 μs for
DP760. The hydrodynamic radius follows from Stokes –Einstein relation (equation 3.18)
as Rh, DP150 = 19 nm and Rh, DP760 = 35 nm.
Discrepancies between these
measurements and the results presented in Table 4.2 are due to high variability of τ when
curve fitting over logarithmic scales and proved this technique not as accurate for the
single distribution samples as the CONTIN algorithm results.
89
-3
DP10
DP760
DP140
-2
C()
-1
0
1
2
3
1000
10000
100000

Figure 4.6. Sample correlation functions for various samples. The break in the curve
observed in DP140 is attributed to sudden interference from dust.
Neither the CONTIN algorithm (Figure 4.3) or the stretched-exponential fit (Figure 4.5)
was capable of deriving consistent and reliable sizes for DP140 or DP10 due the
discontinuity (displayed in Figure 4.6) or bimodality of the correlation functions (induced
by the presence of dust particles in the solution). Because of the very low signal-to-noise
ratio in the measurement of these samples, correlation times were too long such that
sufficient dust removal was found to be impractical. Therefore TEM, TGA, and GPC data
was considered sufficient for size determination of particle samples DP10 and DP140.
90
4.3 CHARACTERIZATION OF OPTICAL PROPERTIES
4.3.1 Refractive Index Increment
The variation of refractive index with concentration is commonly called the refractive
index increment (dn/dc) and is a measure for the polarizability of the particles embedded
in a solvent medium. The (dn/dc) value is necessary for the quantitative analysis of static
light scatting data (see equation 3.6) but also provides a measurable that allows to verify
the null-scattering condition ((dn/dc) = 0) that is predicted by effective medium theory.
The refractive index increment was measured at wavelengths (633 nm or 532 nm) for 3
suspensions in toluene using an laser inferometer technique developed at the Max-Planck
Institute for Polymer Research.[122, 123] Sample DP760 and DP150 registered a (dn/dc) of
9.61  10-8 m3/g and 3.8  10-8 m3/g while DP10 registered a negative (dn/dc) of -9.8 
10-9 m3/g (Figure 4.7 and 4.8, respectively).
Figure 4.7. Refractive Index Increment measurement for sample DP10.
91
Figure 4.8. Refractive Index Increment measurement for sample DP760.
DP140 was not available to be measured available, however the data acquired was used
to extrapolate a line (shown in Figure 4.9) indicating the refractive-index matching
((dn/dc) = 0) is expected for a composition m(PS)/m(SiO2) ~ 0.2, thus confirming the
effective medium prediction.
92
Figure 4.9. The refractive index increment for particle samples DP10, DP150, and
DP760 confirming that index-matching (i.e. (dn/dc) = 0) is expected for particle
compositions m(PS)/m(SiO2) ≈ 0.2, close to the theoretical value.
4.4.1 Static Light Scattering
Static light scattering experiments were performed in order to infer the implications of
particle architecture on the scattering cross-section. Raw scattering intensity at all angles
for all samples is given in Figures 4.10-4.14 for all samples. Figure 4.15 accentuates the
dependence on the Maxwell-Garnett prediction rather than molecular weight. The two
particle samples with similar chain molecular weights, but different chain densities
(DP140 and DP150) display marked differences in scattering intensities consistent with
their difference in composition (0.22 for DP140, 2.2 for DP150). Note that blocking a
larger fraction of the incoming beam intensity was necessary (filter was 10% as opposed
to 50 %) when comparing these two samples on the same graph.
93
1.2 [mg/mL]
0.8 [mg/mL]
0.3 [mg/mL]
0.8 [mg/mL]
0.5 [mg/mL]
0.3 [mg/mL]
0.17[mg/mL]
1.0 [mg/mL]
0.8 [mg/mL]
0.3 [mg/mL]
Toluene
6
2.5x10
6
2.0x10
6
I(q )
1.5x10
6
1.0x10
5
5.0x10
0.0
0.0
6
5.0x10
7
1.0x10
7
1.5x10
7
2.0x10
7
2.5x10
7
3.0x10
7
3.5x10
q = 4n/ Sin(/2)
Figure 4.10. Scattering intensity I(q) vs. q of PS-coated Silica DP10(red), 150 (blue), &
760 (black, except toluene) for all measured concentrations. Note that equal mass
concentration of all particle samples implies an even stronger scattering contribution per
particle for DP760 since its number concentration is only about one third of DP150.
5
1.2x10
1.0 [mg/mL]
0.8 [mg/mL]
0.3 [mg/mL]
5
1.0x10
4
I(q)
8.0x10
4
6.0x10
4
4.0x10
4
2.0x10
0.0
6
5.0x10
7
1.0x10
7
1.5x10
7
2.0x10
7
2.5x10
7
3.0x10
7
3.5x10
q = 4n/ Sin(/2)
Figure 4.11. Intensity (q) vs. q of PS-coated Silica DP10 at various concentrations.
94
5
0.8 [mg/mL]
0.5 [mg/mL]
0.3 [mg/mL]
0.17 [mg/mL]
3.5x10
5
3.0x10
5
I(q)
2.5x10
5
2.0x10
5
1.5x10
5
1.0x10
4
5.0x10
0.0
6
5.0x10
7
1.0x10
7
1.5x10
7
2.0x10
7
2.5x10
7
3.0x10
7
3.5x10
q = 4n/ Sin(/2)
Figure 4.12. Intensity (q) vs. q of PS-coated Silica DP150 at various concentrations.
1.2 [mg/mL]
0.8 [mg/mL]
0.3 [mg/mL]
6
2.6x10
6
2.4x10
6
2.2x10
6
2.0x10
6
1.8x10
6
I(q)
1.6x10
6
1.4x10
6
1.2x10
6
1.0x10
5
8.0x10
5
6.0x10
5
4.0x10
5
2.0x10
0.0
6
5.0x10
7
1.0x10
7
1.5x10
7
2.0x10
7
2.5x10
7
3.0x10
7
3.5x10
q = 4n/ Sin(/2)
Figure 4.13. Intensity (q) vs. q of PS-coated Silica DP760 at various concentrations.
95
5
1x10
Toluene
0.5 [mg/mL] DP=140
0.3 [mg/mL] DP=140
5
1x10
5
1x10
4
9x10
4
8x10
4
I(q)
7x10
4
6x10
4
5x10
4
4x10
4
3x10
4
2x10
4
1x10
6
5.0x10
7
1.0x10
7
1.5x10
7
2.0x10
7
2.5x10
7
3.0x10
7
3.5x10
q = 4n/ Sin(/2)
Figure 4.14. Intensity (q) vs. q of PS-coated Silica DP140 at various concentrations.
Measurement taken at a 50% filter setting.
Toluene
0.5 [mg/mL] DP=140
0.3 [mg/mL] DP=140
0.017 [mg/mL] DP=150
5
1x10
5
1x10
5
1x10
4
9x10
4
8x10
4
I(q)
7x10
4
6x10
4
5x10
4
4x10
4
3x10
4
2x10
4
1x10
6
5.0x10
7
1.0x10
7
1.5x10
7
2.0x10
7
2.5x10
7
3.0x10
7
3.5x10
q = 4n/ Sin(/2)
Figure 4.15. Intensity (q) vs. q of PS-coated Silica DP140 and DP150. Measurement
taken at a 10% filter setting.
96
sample is calculated[11] assuming uniform
The molecular weight of each PS@SiO2
particle diameter d = 20 nm with chain molecular weights and grafting densities as
presented in Table 4.1.
Therefore, directly comparable dilute solutions with equal
number density of particles (i.e. constant c/M, with c denoting the mass concentration and
M the molecular weight of the core-shell particle) can be presented in the following
discussion. Scattering intensities for comparable sample densities is given in Figure 4.16.
In agreement with the larger deviation from the predicted null scattering condition of
sample DP10, a higher scattering intensity is observed.
DP760
DP150
DP10
DP140; 0.5 [mg/mL]
DP140; 0.3 [mg/mL]
6
2.5x10
6
2.0x10
6
I(q)
1.5x10
6
1.0x10
5
5.0x10
0.0
0.0
6
5.0x10
7
1.0x10
7
1.5x10
7
2.0x10
7
2.5x10
7
3.0x10
7
3.5x10
q = 4n/ Sin(/2)
Figure 4.16. Absolute values for Intensity (q) vs. q of PS-coated Silica DP10, 140, 150, &
760 for comparable volumes at filter setting of 10% versus toluene standard. Equivalent
volumes were 10.0 (DP10), 0.5(DP150), and 0.3 (DP140) mg/mL, respectively. The
curve of 0.5 mg/mL for DP140 is shown (overlapping) to accentuate minimal scatter in
this sample for higher concentrations.
Figure 4.17 depicts the angular dependence of the absolute scattered intensities given in
terms of the Rayleigh ratio R(q) of samples DP10, DP140 and DP150. Whereas the
97
scattered intensity of sample DP150 (and similarly DP760, see Figure 4.13) exhibits
pronounced q-dependence the scattering curves of DP10 and DP140 are found to be
approximately angle-independent with the scattering intensity of DP140 approximately
equal to the solvent scattering.
Figure 4.17. Total scattered intensity R(q) for particle samples DP10 (diamonds), DP140
(circles) and DP150 (squares) revealing the reduced angular dependence of the scattering
intensity for particle samples DP10 and DP140 indicating a decrease in optical phase
shift.
In order to test the null-scattering hypothesis and to quantitatively compare the scattering
strength of the respective particle samples, measurements of the absolute scattering
intensity of dilute solutions of particles with equal number density were performed at
small scattering angles (here the form factor P(q)~1 does not significantly contribute to
scattering intensity as discussed in Chapter III). In general, the angular dependence of the
scattered light for a dilute solution of particles with small phase shift (i.e. 2d|(neff/nm) –
1|/ << 1) is given by the Rayleigh-Gans-Debye approximation as I(q) = I(0)P(q)[20].
98
I(0) is the forward scattered intensity that provides a measure for the overall scattering
strength of the particles and can be determined by extrapolation of I(q) to q = 0.[25] Since
established form factor relations are only limited applicable to core-shell particles close
to the index-matching condition, I(0) will be approximated by experimental values at
small scattering angles. Figure 4.18 depicts the scattered intensity at q* = 9.16  106 m-1
(corresponding to a scattering angle of 30 degree) for all particle samples revealing a
decrease in the scattering strength for sample DP140 by four orders of magnitude as
compared to DP760 and a decrease by 300% as compared to DP10.
Figure 4.18. Scattering characteristics of PS@SiO2 particle systems at equal particle
number density c/M. Plot of the total scattering intensity R(q) at q = 9.16  106 m-1 as
function of the particle composition m(PS)/m(SiO2) for all particle samples. The
reduction of forward scattering of sample DP140 confirms the approximate indexmatching condition. Arrow indicates theoretical null-scattering composition
m(PS)/m(SiO2) ≈ 0.19.
Note that the mass composition of sample DP140 m(PS)/m(SiO2) = 0.22 is close to the
theoretical index-matching condition m(PS)/m(SiO2) ≈ 0.19.
99
This result is supported by measurements of the refractive index increment (dn/dc) of the
respective particles in solution that confirm index-matching conditions (i.e. (dn/dc) = 0)
for a composition close to m(PS)/m(SiO2) = 0.2.
To further illustrate the dependence on refractive index matching on the reduction of light
scattering, the samples were dispersed in carbon disulfide (n = 1.63). The chi parameter
for polystyrene in carbon disulfide varies in many studies greatly with the molecular
weight, polydispersity, and temperature of the solution.[124] Therefore, polystyrene of
high molecular weight and low polydispersity (411,000 g/mol; Mw/Mn= 1.06) was first
confirmed to completely dissolve in carbon disulfide (0.5 M) at room temperature to
predict the solubility behavior of the functionalized nanoparticles. Figure 4.19 displays
the visual phenomenon of transparency for larger samples (DP150) relative to smaller
ones (DP10) of the same particle densities due to the refractive index condition being
close to satisfied for DP150 in the higher refractive index liquid. Note that the reduced
scattering intensity of larger particles (DP150 as apposed to DP10) is a direct
consequence of the particle architecture.
Figure 4.19. Digital photograph of equivalent volume density of samples used in this
study dispersed in carbon disulfide in front of a black background. From left: DP10,
DP150, and DP760.
100
In conclusion, the presented results demonstrate that the scattering cross-section of
nanoparticle inclusions within an embedding medium can be dramatically reduced by
appropriate surface modification such as to match the effective refractive index of the
resulting core-shell particle to the refractive index of the embedding medium (quasitransparency condition) and that classical effective medium theory provides a viable
means to predict null-scattering conditions. While synthetic methodologies to achieve
appropriate architectures are a challenge, the further development of polymerization
techniques such as ATRP, nitroxide mediated polymerization (NMP), and reversible
addition fragmentation transfer (RAFT) that facilitate the control of both, grafting density
and molecular weight of the surface-bound polymer holds the promise to realize the
potential of quasi-transparent filler additives for a wide array of filler and polymer
compositions.
4.4 FURTHER ANALYSIS AND DISCUSSION
Few studies have successfully resulted in such well-characterized hybrid particles as
these, especially those formed from a controlled polymerization method. Exhaustive
analysis of the dynamic and static light scattering data found good agreement with the
TEM, TGA, and GPC predictions for sample DP150. In the following section, this
sample is explored as an accurate core-shell model sample in terms of angular
dependence and agreement with form factor model equations given in Chapter III. This
section presents a more detailed discussion of the effect of particle architecture on the
101
angular dependence of the scattered light as well as the interaction between the particles
in solution. A fundamental problem in the interpretation of the static light scattering data
is that they not amendable to approximations that are typically used to determine the
particle radius of gyration and the second virial coefficient (a measure for the interaction
between the particles in solution) via the classical Zimm analysis. Thus, in a first step, the
angular dependence will be compared to existing analytical form factor expressions to
identify the appropriate data extrapolation. Second, the respective second virial
coefficient will be determined for dilute particle solutions. The purpose of this
quantitative comparison of the measured angular dependent scattering intensity with the
theoretical models is to evaluate the applicability of existing models to describe the
scattering properties of polymer-coated nanoparticles as well as to validate the
assumptions made in the effective medium approach.
4.4.1 Characterization of Angular Dependence
As detailed in Chapter III (Section 3.1.1.2) form factor P(q) expressions were derived to
describe the internal configuration of the scattering material.[111]
The equation for a
sphere was given in Equation 3.8, and can be expanded to describe a core-shell particle as
an ‘effective sphere’ with the core and shell combined to give a single effective radius,
Reff. In comparison, the core-shell form factor expression (given in Equation 3.10) treats
the core and shell separately in terms of physical properties and individual radii.
Evaluation of the form factor expression was done in MATLAB. The effective sphere
model simply calls for the effective refractive index. For DP150, the TGA data was
utilized in conjunction with the Maxwell-Garnett formula to calculate an effective
102
refractive index of 1.569. A program has been developed to evaluate the form factor
expressions and to determine the best fit by minimizing the root mean squared error of
the residuals. For the core-shell model, the same procedure was utilized in determining
the best fit (a routine error minimization algorithm) as above, however the input required
was either a core or shell radius (not an effective refractive index). Because the core and
shell refractive indexes and core size (via TEM of the bare silica) were known, these
numbers were held constant allowing the program to produce the radius of the shell
deemed from the best fit.
5
5
x 10
5
5
I(q) /a.u.
I(q) /a.u.
5.5
4.5
4
4.5
4
3.5
0
0.5
1
1.5
2
2.5
3
3.5
 /m
4
1
1.5
2
2.5
3
3.5
4
7
x 10
4
x 10
1
x 10
0.5
res
res
0.5
 /m
x 10
4
2
0
-0.5
0
-2
0
7
4
6
x 10
-1
0
0.5
1
1.5
2
 /m
2.5
3
3.5
4
7
x 10
0
0.5
1
1.5
2
2.5
3
 /m
3.5
4
7
x 10
Figure 4.20. Top: Form factor model fits to the raw intensity (I(q))data for the DP150
sample (concentration = 0.97 mg/mL). Effective sphere (left) and core-shell (right) best
fits shown by the blue lines. (Note: Best fits determined via the sum of the RMS residual
errors squared.) Bottom: Error for the above fit for each curve in terms of the residual.
Sample best fits for the two form factor models to the raw intensity (I(q))data for the
DP150 sample are shown in Figure 4.20. The effective sphere model was found to
produce larger RMS errors (2.22  103) than the core shell (1.15  103) and displayed an
obvious skew from the actual data. In addition to the smaller calculated error for the
103
core-shell model, the residual curve is random to ensure there is not a systematic error in
the fit. Neither expression deviated much from the TEM size prediction of 31.5 nm with
the effective sphere model calculation yielding a total radius of 27.2 nm and the coreshell giving a total radius of 26.5 nm. Due to the better fit of all the curves/concentrations
for DP150, the core-shell model was determined to be more effective at the prediction of
angular dependence of a hybrid particle.
5
5.5
x 10
I(q) /a.u.
5
4.5
4
3.5
0
0.5
1
1.5
2
2.5
3
3.5
 /m
4
7
x 10
4
4
x 10
res
2
0
-2
0
0.5
1
1.5
2
 /m
2.5
3
3.5
4
7
x 10
Figure 4.21. Top: Form factor model fits to the raw intensity (I(q))data for the DP150
sample (concentration = 0.97 mg/mL) for the effective sphere after rejecting the first four
data points (left).
To determine if a better fit was possible, points (up to 5) were removed from the data set
and subjected to the effective sphere model fit. The best obtained fit is shown (Figure
4.21) but has a higher error (1.43X103) than the core shell model for the same data set. In
this case, the effective sphere model calculated a total particle radius of 29.8 nm. Similar
particle sizes were calculated for all DP150 data sets for both models (Figure 4.22).
104
However, the better fit of all the curves/concentrations for DP150, the core-shell model
was determined to be more effective at the prediction of angular dependence of a hybrid
particle.
5
4
x 10
10
x 10
9
1.4
I(q) /a.u.
I(q) /a.u.
1.6
1.2
8
7
1
0
0.5
1
1.5
2
2.5
3
3.5
6
4
0.5
1
1.5
4000
2000
2000
0
2
2.5
3
3.5
 /m
4000
4
7
x 10
0
-2000
-2000
-4000
0
7
x 10
res
res
 /m
-4000
0
0.5
1
1.5
2
 /m
2.5
3
3.5
4
7
x 10
0
0.5
1
1.5
2
 /m
2.5
3
3.5
4
7
x 10
Figure 4.22. Top: Core shell form factor model fits to the raw intensity (I(q))data for the
DP150 sample for concentrations 0.3 mg/mL(left) and 0.17 mg/mL (right). Particle radii
determined to be 29.1 and 30.5 nm, respectively. Bottom: Error for the above fit for each
curve in terms of the residual.
4.4.2
Interaction of Particles in Solution
Light scattering data is typically used to calculate molecular weight, radius of gyration
and, second virial coefficient in macromolecules using a Zimm Plot (described in Chapter
III). The validity of the Zimm plot depends largely on the validity of the underlying
Guinier approximation: I(q) ~ exp[-1/3q2RG2]  1 + 1/3 q2RG2 for systems with
q*RG<<1.[20] In our system, the Zimm method is not expected to be valid because the
size of the particles are too large (qRG~1) for the Guinier approximation to hold. In
Figure 4.23, Guinier approximation best fits deviate most strongly from the data as
expected for this system, rejecting the possibility of using a standard Zimm method.
105
-4
-4
x 10
4.5
2.5
R(q)[1/cm]
R(q)[1/cm]
3
2
1.5
0
0.5
1
1.5
2
2.5
3
3.5
 /m
4
3.5
3
0
4
0.5
1
1.5
2
2.5
3
3.5
 /m
7
x 10
4
7
x 10
-5
-5
10
x 10
x 10
15
x 10
10
res
res
5
0
-5
5
0
0
0.5
1
1.5
2
 /m
2.5
3
3.5
7
x 10
-5
0
0.5
1
1.5
2
 /m
2.5
3
3.5
7
x 10
Figure 4.23. Best fit curve comparison for Guinier approximation (black) versus effective
sphere (left, red) and core shell (right, red) form factors. Top: Core shell form factor
model fits to calculated (R(q))data for the DP150 sample for concentrations 0.17 mg/mL
(left) and 0.3 mg/mL (right) after rejecting first two points due to a poor background
calibration at those angles). Bottom: Error for the above fit for each curve in terms of the
residual. Guinier approximation error given in black.
In order to determine interparticle interactions via light scattering, the second virial
coefficient must be derived. For a well-dispersed system in the dilute regime, the proper
form factor expression can be fit to the data (R(q), in cm-1) and extrapolated to zero angle
at several concentrations. The resulting values for R(q)=0 can be graphed as Kc/R(q)=0
(K calculated using measured (dn/dc)) versus concentration to determine the slope, and
therefore, the value for the second virial coefficient(A2). This process is synonymous
with the Zimm plot for macromolecules, but substituting the correct form factor for the
Guinier approximation.[110]
The second virial coefficient determined for the effective sphere model was 2.4510-7
cm3 mol/g2. The core shell model resulting in a slightly higher A2 value of 2.5610-7 cm3
106
mol/g2. These numbers are very similar in comparison to the A2 resulting from the
typical Zimm plot (2.3410-6 cm3 mo/g2). The positive value of A2 confirms that toluene
presents a good solvent for DP150 and repulsive interactions dominate for this sample
(A2>0).
In summary, while the DP140 sample (and to a lesser degree, DP10) allowed for the
validation of the effective medium approach to quasi-transparency, the DP150 sample
was a prime candidate to determine the accuracy of the available form factor expressions.
From the DP150 data it was determined that the core-shell model is slightly more
accurate for angular dependence than the effective sphere approach. Both models were
nearly equivalent in the determination of the second virial coefficient and molecular
weight.
107
CHAPTER 5. CONCLUSIONS AND SUGGESTIONS FOR FUTURE STUDIES
This study has been the first of its kind in both the successful development, and
characterization of quasi-transparent materials. Applying the effective medium theory,
particle additives formerly known to produce scatter and opacity were altered to low,
quasi-transparent materials. Maxwell-Garnett theory was applied to predict nullscattering conditions. ARGET ATRP was capable of reducing the catalyst contamination
and further increased the purity and precision control to the AGET approach at the
sacrifice of accelerated reaction times. This method yielded composites nearly free of
metal residue known to absorb and scatter light which made it the ideal choice for our
study.
A reduction of scattering as compared to the bare, inorganic silica particle was achieved
for two composite materials that most closely satisfied the prediction (DP10 and DP140).
GPC of detached polymer chains, TGA of the functionalized particles, and TEM
micrographs were in good agreement with the findings from light scattering. The
scattering strength of the particles was determined independently by measurement of the
Rayleigh ratio at small angles and the differential refractive index increment. Both
techniques confirmed the near suppression of scattering when the effective index of the
core-shell particle is matched to the refractive index of the embedding medium. A
MATLAB program was developed to quantitatively compare the predictive strength of
various form factor models and confirmed that the assumption of discrete core-shell
108
geometry provides good agreement with the experimental data (within experimental
error).
5.1 CONCLUSION
The presented results demonstrate that the scattering cross-section of nanoparticle
inclusions within an embedding medium can be dramatically reduced by appropriate
surface modification such as to match the effective refractive index of the resulting coreshell particle to the refractive index of the embedding medium (quasi-transparency
condition) and that classical effective medium theory provides a viable means to predict
null-scattering conditions. This approach pertains to a wide variety of embedding media
(such as polymers, polymer gels, or ceramic glasses); as long as the dispersion state of
the particle inclusions is maintained. This will offer new opportunities for the design of
multi-functional particle coatings in which the polymer-functionalization serves a dual
purpose: First, to facilitate compatibilization with the embedding medium, and second, to
suppress scattering contributions of the inorganic core by index-matching the core-shell
particle with the embedding medium (e.g. those given in Table 5.1). While synthetic
methodologies to achieve appropriate architectures are a challenge, the further
development of polymerization techniques such as controlled radical polymerization that
facilitate the control of both, grafting density and molecular weight of the surface-bound
polymer holds the promise to realize the potential of quasi-transparent particle additives
for a wide array of filler and polymer compositions.
109
5.2 FUTURE STUDIES
In future materials, the method described herein will be utilized to develop solid-state
composites containing quasi-transparent filler materials. Although this study
concentrated on scattering in a toluene solution, application to embedded particles in
solid matrices is of particular interest. The idea to tailor the refractive index of core-shell
particle architectures in order to reduce particle-inclusion scattering has first been
discussed in the context of glass-matrix composites. [125-127] Maurer first compared
scattering of liquids with glasses (containing particle inhomogeneities) which confirmed
the Rayleigh prediction of reduced scatter for particles smaller than the wavelength of
light.[128] In 1969, Beall and Duke described the observance of transparency of
aluminosilicate glasses containing growing particle crystallites could be extended to
slightly larger particles if they closely matched the refractive index of the medium.[129]
This was verified experimentally by several groups who studied the properties of
transparent materials including: 14.7-17 nm cadmium and lead fluoride particles in
SiO2/Al2O3 glasses[130] and barium chloride nanoparticles in fluorozirconate glasses[131]
containing 20~29 mol % of the inclusions. The concentration limit (S(q) ≈ 1) at small q
for the Rayleigh scattering approximation for such materials has been discussed in detail
in recent publications.[132] This work confirms that quasi-transparent filler inclusions can
be mapped to organic embedding media. Of particular interest for future applications will
be demonstration of the approach’s viability for solid polymer embedding media.
Polymer matrix materials are particularly interesting since polymer-grafting techniques
110
already are routinely being applied to facilitate the compatibility of filler particle
inclusions.
Table 5.1 summarizes a set of inorganic core, graft- and matrix-polymer combinations
that correspond to the null scattering condition. The respective polymer pairs are chosen
because of their respective negative Flory–Huggins interaction parameter as well as
suitability of their refractive indices to facilitate matching of the effective refractive
indices.[133]
Table 5.1. Composition and architecture of selected polymer-coated particle systems for
compatibilization and index-matching with the respective matrix polymer (calculated
using Equation 1.4 and assuming an inorganic particle diameter of d = 20 nm). n denotes
the refractive index. Polymers listed are abbreviated as such: polymethyl methacrylate
(PMMA), polystyrene (PS), acrylonitrile (A), polyvinyl alcohol (PVA), polyacetic acid
(PAA), and polypropylene oxide (PPO).
Upcoming studies will undoubtedly probe the limitations of the application of the
effective medium theory in various systems. Materials where the addition of filler
111
particles increases the affordability or other properties will demand a greater
understanding of the size limitations for the inorganic core and relative size restraints for
polymer chain length. Ternary systems applying the quasi-transparent colloids to a target
matrix are inevitable. Solutions to these questions will inevitably involve a balance
between chain density and miscibility limitations.
Another area of interest developed from this study’s results, is the validity of the form
factor expressions for core-shell materials. Although the expressions fit the raw intensity
of our model material well enough to generate an agreeable second virial coefficient,
additional materials will be necessary to elucidate the applicability of these models for
different core-shell compositions and grafting densities.
112
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APPENDIX A: SUPPLEMENTAL INFORMATION
Additional TEM of HD 150 (size bar below is 50 nm):
Additional TEM of DP760 (size bar is 100 nm).
More Images DP150:
118
DP = 150:
DP =760:
119
DP = 760:
Supplemental Calculations:
General Calculations for 20 nm Silica:
DLS= 20 nm
Vol. Silica Sphere= 4/3  r3 = 4/3  103 = 4186 nm 3
Density= 1.9 g/cm3 (for bulk silica) = 1.9 X 10 -21 g/nm 3
wSiO2 = Mn (for silica)= density * vol.= 1.9 X 10 -21 g/nm 3 * 4186 nm 3
wSiO2 = Mn (for silica)= 7.95 X 10 -18 g
wSiO2 = Mn (for silica)= 4.78 X 106 g/mol
Section 1: Molecular weights and dilute regime for PS-Silica.
DP =10
(GPC Mn= 1000 g/mol):
Dshell (from .5 distance TEM): 5 nm
Rshell= 2.5 nm
120
Vol. Silica/PS Sphere= 4/3  (Rsphere + Rshell)3 = 4/3  (12.5)3 = 8.18 X 10 3 nm 3
Vol. Silica/PS Sphere = 8.18 X 10 -18 cm 3
wPS-SiO2 = Mn (for silica + PS)= 4.78 X 106 g/mol + (1,000 g/mol * 892.5 chains/SiO2) =
wPS-SiO2 = 5.67 X 10 6 g/mol = 9.42 X 10 -18 g
MassCrossover = 1 PSSiO2 mass/ 1 PSSiO2 vol = 9.42 X 10 -18 g / 8.18 X 10 -18 cm 3 =
MassCrossover = 1.15 X 10 0 g/ cm 3
Used 3 X 10 -4 g/ cm 3 – 1.5 X 10 -3 g/ cm 3 for SLS measurements. Far below (~115-3800
times less than), overlap conc.
The theoretical size (from 0.5 * avg. TEM core distance) is 20nm + ~2.5-5nm of PS-SiO2 = ~22.530 nm.
DP = 140
(GPC Mn= 14400 g/mol):
Dshell (from .5 distance TEM): 5 nm
Rshell= 2.5 nm
wPS-SiO2 = Mn (for silica + PS)= 4.78 X 106 g/mol + (14,400 g/mol * 1055. 9 chains/SiO2) =
wPS-SiO2 = 2.00 X 10 7 g/mol = 3.32 X 10 -17 g
Vol. Silica/PS Sphere= 4/3  (Rsphere + Rshell)3 = 4/3  (31.5)3 = 1.31 X 10 5 nm 3
Vol. Silica/PS Sphere = 1.31 X 10 -16 cm 3
MassCrossover = 1 PSSiO2 mass/ 1 PSSiO2 vol = 3.32 X 10 -17 g / 1.31 X 10 -16 cm 3 =
MassCrossover = 2.53 X 10 -1 g/ cm 3
Used 3 X 10 -4 g/ cm 3 - 1 X 10 -3 g/ cm 3 for SLS measurements. Far below (~270-900
times less than), overlap conc.
The theoretical size (from 5nm * avg. TEM core distance) of PS-SiO2 = ~ 25 nm.
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DP = 150
(GPC Mn= 15500 g/mol):
Dshell (from .5 distance TEM): 43 nm
Rshell= 21.5 nm
wPS-SiO2 = Mn (for silica + PS)= 4.78 X 106 g/mol + (15,500 g/mol * 1055. 9 chains/SiO2) =
wPS-SiO2 = 2.11 X 10 7 g/mol = 3.51 X 10 -17 g
Vol. Silica/PS Sphere= 4/3  (Rsphere + Rshell)3 = 4/3  (31.5)3 = 1.31 X 10 5 nm 3
Vol. Silica/PS Sphere = 1.31 X 10 -16 cm 3
MassCrossover = 1 PSSiO2 mass/ 1 PSSiO2 vol = 3.51 X 10 -17 g / 1.31 X 10 -16 cm 3 =
MassCrossover = 2.68 X 10 -1 g/ cm 3
Used 3 X 10 -4 g/ cm 3 - 1 X 10 -3 g/ cm 3 for SLS measurements. Far below (~270-900
times less than), overlap conc.
The theoretical size (from 0.5 * avg. TEM core distance) is 20nm + ~43 nm of PS-SiO2 = ~63 nm.
DP = 760
(GPC Mn= 76000 g/mol):
Dshell (from .5 distance TEM): 57 nm
Rshell= 28.5 nm
Vol. Silica/PS Sphere= 4/3  (Rsphere + Rshell)3 = 4/3  (38.5)3 = 2.39 X 10 5 nm 3
Vol. Silica/PS Sphere = 2.39 X 10 -16 cm 3
wPS-SiO2 = Mn (for silica + PS)= 4.78 X 106 g/mol + (76,000 g/mol * 628.5 chains/SiO2) =
wPS-SiO2 = 5.25 X 10 7 g/mol = 8.73 X 10 -17 g
MassCrossover = 1 PSSiO2 mass/ 1 PSSiO2 vol = 8.73 X 10 -17 g / 2.39 X 10 -16 cm 3 =
MassCrossover = 3.65 X 10 -1 g/ cm 3
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Used 3 X 10 -5 g/ cm 3 - 2 X 10 -3 g/ cm 3 for SLS measurements. Far below (~200-1200
times less than), overlap conc.
The theoretical size is 20nm + ~57nm of PS-SiO2 = ~77 nm.
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