The conformations of grafted polymers play an important role in determining the physical properties of polymer nanocomposites.  Small-angle neutron scattering (SANS) is performed to quantify the conformation of poly(methyl methacrylate)($M_{w} > $ 27,000 g/mol) and polystyrene chains ($M_{w} >$ 57,000 g/mol) which are attached to iron oxide nanoparticles ($R_{np} = 2.5$ nm, $\sigma = 0.73$ chains/$\mathrm{nm^{2}}$) and small fractal aggregates ($R \approx 11$ nm, $\sigma = 0.2$ chains/$\mathrm{nm^{2}}$), respectively.  Unlike light scattering or microscopy, SANS can directly measure the grafted polymer chain conformations.  In a homopolymer melt, we find the grafted chains adopt stretched conformations near the nanoparticle surface, and transition to ideal, random coils past a cutoff distance $r_{c}$, in agreement with scaling arguments in the literature.  We find the conformation of the polymer chains is largely unaffected by the ratio of the degree of polymerization of the matrix ($P$) to that of the brush ($N$).  Finally, we extend this work to measure grafted polymer conformation in solution as a function of solvent quality, and find the grafted chains behave as swollen coils with an excluded volume parameter $\nu$ that decreases as the solvent cools to the $\Theta$ temperature. [ Preview Abstract]

Recent statistical mechanical theories of nanoparticle motion in polymer melts and networks have focused on the dilute particle limit.  By combining PRISM theory predictions for microscopic structural correlations, and a new formulation of self-consistent dynamical mode coupling theory, we extend dilute theories to finite filler loading.  As a minimalist model, the polymer dynamics are first assumed to be unperturbed by the presence of the nanoparticles.  The long time particle diffusivity in unentangled and entangled melts is determined as a function of polymer tube diameter and radius of gyration, nanoparticle diameter, and polymer-filler attraction strength under both constant volume and constant pressure situations.  The influence of nanocomposite statistical structure (depletion, steric stabilization, bridging) on dynamics is also investigated.  Using recent theoretical developments for predicting tube diameters in nanocomposites, the consequences of filler-induced tube dilation on nanoparticle motion is established.  In entangled melts, increasing filler loading first modestly speeds up diffusion, and then dramatically when the inter-filler separation becomes smaller than the tube diameter.  At very high loadings, a filler glass transition is generically predicted. [ Preview Abstract]

Using Rutherford backscattering spectroscopy (RBS), the translational
diffusion of titanium oxide (TiO$_{2})$ nanorods ($l=$43.1 nm and $d=$4.6 nm)
is measured in entangled and unentangled polymer melts, polystyrene (PS;
$M_{n}=$9-2000 kg/mol).  Nanorods in entangled systems ($M_{n}=$160, 650,
and 2000 kg/mol) are found to diffuse up to two orders of magnitude faster
than predicted by classical theory.  However, diffusion of nanorods in
unentangled systems ($M_{n}=$9 and 65 kg/mol) is captured by this continuum
theory.  Below or near the entanglement limitation, $M_{n} \quad \le \quad M_{e}$
($M_{e}$: entanglement molecular weight), unentangled polymer melts described
by Rouse dynamics can be modeled as a continuum matrix against nanoscale
inclusions.  However, in highly entangled systems ($M_{n}$ \textgreater
\textgreater $M_{e})$ the standard continuum models are no longer valid and
lead to local non-hydrodynamic friction at the length scale of the tube
diameter (i.e., $d_{t}=$8 nm for PS) [1].  Thus, enhanced diffusion of
nanorods parallel to the tubes may be responsible for the faster than
expected translational diffusion in entangled polymer melts.  These
experiments provide new insight into the relevant parameters that govern the
diffusion of anisotropic nanoparticles in complex fluids. [ 1] Yamamoto et. 
al.,  J. Chem.  Phys.,  135, 224902 (2011). [ Preview Abstract]

Polymer nanocomposites (PNCs) has received a lot of attention in the recent
years because of their potential applications in fabricating materials with
novel mechanical, electrical, and photonic properties.  The mobility of
nanoparticles (NPs) play crucial role in determining various properties of
PNC systems.  Computer simulations and recent experiments have suggested that
properties such as the toughness of a composite depend upon particle
mobility.  Even nanocomposites with ``self-healing'' properties that can
restore strength in damaged regions have been proposed and some early work
of their feasibility has been demonstrated.  In this talk I will present some
of our experimental work on the diffusion of nano-sized gold particles in
polymer solutions and melt.  Unusually fast diffusion of NPs when their size
is smaller than the tube diameter in an entangled polymer was observed. 
Comparison with current theories and simulations will be shown.  If time
permits, our recent results on gold nanorod diffusion in polymer solution
using polarized fluorescence correlation spectroscopy will be presented. [ Preview Abstract]

The intriguing thermodynamic properties of polymer nanocomposites (PNCs)
have often been attributed to the formation of an interfacial polymer region
at the nanoparticle surface and a better understanding of how the
interfacial region affects the PNC dynamics is desired.  The static and
dynamic properties of poly(2-vinylpyridine)/silica nanocomposites are
investigated by temperature modulated differential scanning calorimetry,
broadband dielectric spectroscopy (BDS), and small angle x-ray scattering
(SAXS).  The SAXS data revealed a core-shell structure formed in interfacial
region and BDS data detected the slower relaxation process associated with
the interfacial polymer layer.  Both static and dynamic measurements
estimated the layer thickness to be 4-6 nm.  We also demonstrated that the
presence of interfacial polymer layer has negligible influence on the glass
transition temperature and segmental dynamics of the remaining polymer. 
These results potentially offer an explanation to recent controversies in
studies of polymer nanocomposites due to different experimental techniques. [ Preview Abstract]

Polymer-particle composites are used today in virtually every field of
technology.  When the particles approach nanometer dimensions, large
interfacial regions are created in their polymer hosts, which present
opportunities and challenges for research, as well as for applications.  This
talk will focus on a novel class of polymer-particle composite fluids
created by densely grafting short organic polymer chains or ionic liquid
molecules to inorganic nanostructures.  By manipulating the nanoparticle
size, polymer molecular weight and surface chemistry, we show that it is
possible to create self-suspended suspensions of nanoparticles in which each
particle in suspension carries around a discrete share of the suspending
medium.  The talk will explore consequences of the self-suspended state on
fluid structure, rheology, and tethered polymer {\&} particle dynamics in
these so-called \textit{nanoscale organic hybrid materials} (NOHMs).  The talk will also discuss particle and tethered
polymer dynamics in single-component NOHMs and phase stability, structure,
and rheology of NOHMs/polymer blends. [ Preview Abstract]

We have observed that, for a wide range of spherical nanoparticles, the
polymer diffusion coefficient relative to the pure melt value as a function
of the interparticle distance relative to the chain radius of gyration
collapses onto a master curve.  In order to gain insight into the molecular
basis for this behaviour, we use the Evans-Edwards Monte Carlo model for
reptation dynamics in which the chains are coarse-grained such that each
bead within the simulation represents one entanglement segment.  We
investigate the long time diffusion behaviour when the chains are
constrained by a lattice structure with regularly spaced holes each the size
of an entanglement spacing.  We find that as the dimensions of the lattice
decreases, the power law for the scaling of the diffusion coefficient with
molecular weight changes from the well known result for melt diffusion of
entangled chains of approximately -2 to approximately -3.  We present a
simple physical model that captures this result. [ Preview Abstract]

Controlling the dispersion of nanoparticles throughout a polymer matrix is
difficult.  We have found that nanoparticle dispersion can be achieved by
incorporating soft, organic nanoparticles with complementary chemical
moieties, thus achieving favorable enthalpic interactions.  The rational
design of soft nanoparticles can create an interface that allows
interpenetration of the polymer chains and particles reducing the depletion
of entropy that is the main contributing force to the flocculation of
nanoparticles.  The nanoparticles are produced by intra-molecularly
crosslinking a single polystyrene chain via a nano-emulsion technique with
divinyl benzene.  This synthetic approach allows the effects from structure,
size and softness of the nanoparticle to be examined as they contribute to
the dynamics of the polymer matrix by varying the crosslink density.  This
report focuses on the effect that these nanoparticles have on the diffusion
coefficient of polystyrene.  Neutron reflectivity was used to monitor the
interdiffusion of deuterated polystyrene and protonated polystyrene with and
without the soft nanoparticles in the respective layers.  It has been
proposed that the ratio of the radius of gyration (Rg) of the polymer chain
to the nanoparticle controls the dynamics, thus the molecular weights of the
matrix in this study have been varied from 535, 173, to 68 kg/mol.  Initial
results suggest when the Rg of the polymer is larger than that of the
nanoparticle Rg the dynamics are impacted the most. [ Preview Abstract]

We report x-ray photon correlation spectroscopy (XPCS) experiments to investigate the motion of nanoscale gold particles within polystyrene (PS) melts of molecular weight between 30K and 900K g/mol.  The particles, with diameter span from 5 nm to 22 nm, are dispersed in a highly dilute concentration (volume fraction 0.005) and are functionalized with PS chains to stabilize them against aggregation.  We already know that for low molecular weight PS melts there are dynamics crossovers from diffusive motion to hyper-diffusive motion when quenching to lower temperature.  When polymer chains are longer than the entanglement length, things are more complicated.  At low temperature, similar hyper-diffusive motion are observed.  At high temperature, i.e. 70 K higher than Tg, the dynamics changed from overdamped behavior to underdamped oscillatory behavior, indicating that entanglement strongly affects the particle motion. [ Preview Abstract]

We have developed a self-consistent microscopic theory for the long-time
dynamics of needles in an array of static spherical fillers.  The approach
exactly enforces the dynamical two-body rod topological uncrossability and
sphere impenetrability constraints, leading to a generalized concept of
entanglements that includes the filler excluded volume effect.  How the
diffusion anisotropy (transverse versus longitudinal motion) depends on the
filler-needle aspect ratio, polymer concentration, and filler volume
fraction is established.  Due to the steric blocking of the longitudinal
reptative motion by obstacles, a literal localization transition is
predicted that is generically controlled by the ratio of filler diameter to
the pure polymer tube diameter or needle length.  For a window of filler
sizes and loadings, the needle is predicted to diffuse via a
``renormalized'' reptation dynamics where the tube is compressed and the
longitudinal motion is retarded in a manner that depends on all system
variables.  At high filler volume fractions the needle diffusivity is
strongly suppressed, and localization ultimately occurs in the unentangled
needle regime.  Generalization of the approach to treat mobile fillers,
flexible chains, and nonrandom microstructure is also possible. [ Preview Abstract]

The tracer diffusion of deuterated polystyrene (dPS; 168-3200 kg/mol) is
measured in polystyrene (650 kg/mol) nanocomposites containing phenyl-capped
nanorods with a similar aspect ratio (AR $=$ 9) but different sizes,
NR-short (TiO$_{2}$; $l=$43.1 nm and $d=$4.6 nm) and NR-long
(SiO$_{2}$-[Ni(N$_{2}$H$_{4})_{3}$]Cl$_{2}$; $l=$371 nm and $d=$43 nm).  For
NR-long where $l$ \textgreater 2$R_{g}$, the diffusion coefficient initially
decreases as nanorod volume fraction increases but then begins to increase
for near the percolation threshold.  In this system, $R$ \textless $R_{g}$ and
the diffusion behavior is consistent with previous studies of carbon
nanotubes (i.e., $l $\textgreater \textgreater 2$R_{g})$. However, for NR-short
(i.e., $l$ \textless 2$R_{g})$, diffusion shows a monotonic slowing down as the
volume fraction increases despite the small values of $R$/$R_{g}$. This behavior
is similar to the slowing down observed for isotropic nanoparticles.  These
experiments demonstrate that not only radius but also length of the
nanoparticle plays a key role in diffusion.  Moreover, these results indicate
that a comprehensive model for polymer dynamics should include the geometry
of the nanoparticle relative to $R_{g}$. [Preview Abstract]

The tracer diffusion of deuterated polystyrene (dPS; 49-532 kg/mol) is
measured in polystyrene (PS: 270 kg/mol) nanocomposites containing
PS-grafted (132 kg/mol) anisotropic nanoparticles (NP).  The NP's are small
aggregates containing iron oxide spheres (5nm).  These NP's uniformly
disperse in PS up to 100{\%} loading.  The structure of the polymer
nanocomposites is probed using (ultra)small angle x-ray scattering
(USAXS,SAXS).  Peaks shift to high Q region with increasing NP loadings,
indicating a decrease in spacing between particles.  The interparticle
distance for the pure NP case is 30nm, consistent with TEM, and a brush
thickness of 15nm.  The brush profile is also measured using SANS.  The
reduced tracer diffusion coefficient initially decreases as NP loadings
increase and then reaches a minimum (35{\%} reduction) near 0.25 vol{\%}
(core) for all dPS.  With a further increase in NP loading, diffusion
recovers to 90{\%} of the unfilled case.  Penetration of the tracer (i.e.,
wetting) into the brush will affect the effective interparticle distance. 
Diffusion of dPS (1866 kg/mol) will be examined to determine if the dry
brush case influences the recovery at high loading.  These experiments
demonstrate that polymer brushes grafted to anisotropic nano particles can
affect the tracer diffusion pathway and indicate that diffusion models
should incorporate the interfacial structure between brush and matrix. 
[Preview Abstract]