**Jacinta C. Conrad, PhD**, University of Houston

This ACS PRF grant supported two research thrusts in our lab related
to the properties of colloidal suspensions in confined
geometries. While the primary thrust of our work was to investigate
solidification of concentrated attractive suspensions of micron-sized
particles in thin geometries, we also applied techniques and
algorithms developed in our primary thrust to study slowing of
dynamics of nanoparticles diffusing in nanopost arrays. Confinement in
both cases induced similar physics: as the suspensions were
increasingly confined, the dynamics of the particles became
increasingly solid-like. Remarkably, this was true even for the dilute
nanoparticle dispersions, as long as they were highly confined. Below,
we describe our major accomplishments over the past year.

(1) Dynamics of confined mixtures of monodispersed colloids and polymers

As models of attractive colloidal suspensions, we studied suspensions of micron-sized poly(methyl methacrylate) particles and non-adsorbing depletant polystyrene polymers in low-dielectric-constant solvents; the polymers induced an entropic depletion attraction between the colloidal particles. Using confocal microscopy and particle tracking, we measured mean-squared displacements and distributions of displacements of particles in mixtures in which particle volume fraction and polymer concentration were held constant, and showed that confinement in a thin wedge chamber induced slowing of the particle dynamics. Comparison with micrographs of samples at different confinement thicknesses indicated that slowing of particle dynamics was driven in part by clustering of particles en route to gelation. Figure 1 shows that as either the strength of the interparticle attraction (parameterized by the concentration of depletant polymer) or the confinement was increased, the suspension became increasingly solid-like, as indicated by the formation of large aggregated of particles. In both weakly- and strongly- attractive mixtures we also observed confinement-induced slowing of dynamics, suggesting that additional mechanisms beyond clustering and solidification contributed to changes in dynamics of confined colloid-polymer mixtures. Figure 2 shows that the distributions of particle displacements became increasingly non-Gaussian as either the strength of attraction was increased or as the confinement was increased, again consistent with the increasingly solid-like behavior.

Figure 1: Representative confocal micrographs of colloid-polymer
samples at constant colloid volume fraction φ = 0.15 and varying
concentration of polymer C_{p} and confinement thickness. Top row: C_{p} =
20.7 mg/mL; middle row: C_{p} = 15.5 mg/mL; bottom row: C_{p} = 10.4
mg/mL. The color of the border around each micrograph indicates the
phase: fluid (red), fluid of clusters (purple), or gel (blue). Scale
bars: 10 μm.

Figure 2: (a) Self-part of the van Hove correlation G_{s}(x,τ) at
Τ = 10 s for bulk (h/2a > 116) samples with concentration of
polymer C_{p} = 10.4 mg/mL (fluid, red) and 15.5 mg/mL (fluid of
clusters, purple) in bulk and for C_{p} = 23.6 mg/mL at confinement
thickness h/2a = 67 (gel, blue +). Lines indicate fits to single
Gaussian functions. (b)-(d) G_{s}(x,τ) for C_{p} = 15.5 mg/mL sample at
confinement thickness (b) h/2a > 116 (fluid of clusters), (c) h/2a =
35 (fluid of clusters), and (d) h/2a = 8.7 (gel) at varying lag
times. Lines indicate fits to single-Gaussian distributions. Colors
indicate the phase as in Figure 1.

(2) Dynamics of confined mixtures of bidispersed colloids and polymers

As an extension of the previous work, we investigated the effect of
confinement on solidification of mixtures of non-adsorbing polymers
and bidispersed colloidal particles (size ratio a_{S /} a_{L} ≅ 0.49) in a
low-dielectric-constant solvent. Holding the total volume fraction of
particles fixed, the dynamics of the large particles became
increasingly slow as either the volume ratio of small particles was
increased or the confinement thickness was decreased. Confinement to
ten large particle diameters induced gelation in all samples
investigated, with the most arrested dynamics appearing when both the
depletant concentration and volume ratio of small particles were
large, as shown by the magnitude of the mean-squared displacement at a
fixed lag time in Figure 3. To elucidate the mechanism driving
solidification, we investigated the effect of confinement on the
electrostatic interactions between the particles in the
low-dielectric-constant solvent. We found that the changes in dynamics
were consistent with an increase in the effective interparticle
attraction, driven by changes in the electrostatic repulsion between
particles as the suspension was confined. This result suggests that
even small changes in the number of charges on particles or in
solvents of low dielectric constant can drive macroscopic changes in
interparticle interactions and the resulting suspension phase
behavior.

Figure 3: Normalized mean-squared displacement at a lag time
Δt = 10 s of large particles as a function of confinement h/2a_{L}
for binary suspensions with concentration of depletant polymer C_{p}
≅ 5 mg/mL (closed symbols) and C_{p} ≅ 25 mg/mL (open
symbols) for varying volume percent of small particles r of 0.75
(circles), 0.50 (down-pointing triangles), and 0 (up-pointing
triangles).

(3) Diffusive dynamics of nanoparticles in arrays of nanoposts

We studied the dynamics of dilute dispersions of nanoparticles of
diameter 200-400 nm diffusing in square arrays of nanoposts. We
applied particle-tracking algorithms to validate the dynamical
measurements obtained using a new image-analysis technique, different
dynamic microscopy. As the spacing between posts was decreased, the
dynamics of the nanoparticles slowed. Moreover, the dynamics at all
length scales were best represented by a stretched exponential,
characterized by a stretching exponent r, rather than a simple
exponential. Figure 4 shows that both the diffusivity of particles
relative to their free diffusivity D/D_{0} and the stretching exponent
decreased linearly with increased confinement. Data for varying
particle diameters (d_{NP}) and varying nanopost spacings (S) could be
collapsed onto a master curve using a dimensionless confinement
parameter ζ = d_{NP}/S. The slowing of the overall diffusive dynamics and
the broadening distribution of nanoparticle displacements with
increased confinement were consistent with onset of dynamic
heterogeneity and approach to vitrification. Our results thus
suggested that extreme confinement may give rise to arrested dynamics
akin to those seen in colloidal glass transitions.

Figure 4: (a) Normalized diffusion coefficient D/D_{0} and (b) average
stretching exponent r (describing the distributions of displacements)
as a function of dimensionless confinement parameter ζ =
d_{NP}/S.

Copyright © 2014 American Chemical Society