Theory of gelation, vitrification, and activated barrier hopping in mixtures of hard and sticky spheres

Department of Materials Science and Engineering, University of Illinois, Urbana-Champaign, Urbana, Illinois, United States
The Journal of Chemical Physics (Impact Factor: 2.95). 03/2008; 128(8):084509. DOI: 10.1063/1.2837295
Source: PubMed


Naive mode coupling theory (NMCT) and the nonlinear stochastic Langevin equation theory of activated dynamics have been generalized to mixtures of spherical particles. Two types of ideal nonergodicity transitions are predicted corresponding to localization of both, or only one, species. The NMCT transition signals a dynamical crossover to activated barrier hopping dynamics. For binary mixtures of equal diameter hard and attractive spheres, a mixture composition sensitive "glass-melting" type of phenomenon is predicted at high total packing fractions and weak attractions. As the total packing fraction decreases, a transition to partial localization occurs corresponding to the coexistence of a tightly localized sticky species in a gel-like state with a fluid of hard spheres. Complex behavior of the localization lengths and shear moduli exist because of the competition between excluded volume caging forces and attraction-induced physical bond formation between sticky particles. Beyond the NMCT transition, a two-dimensional nonequilibrium free energy surface emerges, which quantifies cooperative activated motions. The barrier locations and heights are sensitive to the relative amplitude of the cooperative displacements of the different species.

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    • "Mode coupling theory has been successful in predicting the form of the two-step relaxation of the intermediate scattering function, but it predicts an ergodicity-breaking transition well-above the experimentally determined colloidal glass transition. Related theories are able to predict activated dynamics, but the location of the divergence in the structural and stress relaxation times is still an input parameter, not a prediction [26]. Models of dynamic facilitation, in which mobile regions increase the probability that nearby regions will also become mobile, are able to explain important aspects of dynamical heterogeneities and non-Arrhenius relaxation times. "
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    ABSTRACT: We describe numerical simulations and analyses of a quasi-one-dimensional (Q1D) model of glassy dynamics. In this model, hard rods undergo Brownian dynamics through a series of narrow channels connected by $J$ intersections. We do not allow the rods to turn at the intersections, and thus there is a single, continuous route through the system. This Q1D model displays caging behavior, collective particle rearrangements, and rapid growth of the structural relaxation time, which are also found in supercooled liquids and glasses. The mean-square displacement $\Sigma(t)$ for this Q1D model displays several dynamical regimes: 1) short-time diffusion $\Sigma(t) \sim t$, 2) a plateau in the mean-square displacement caused by caging behavior, 3) single-file diffusion characterized by anomalous scaling $\Sigma(t) \sim t^{0.5}$ at intermediate times, and 4) a crossover to long-time diffusion $\Sigma(t) \sim t$ for times $t$ that grow with the complexity of the circuit. We develop a general procedure for determining the structural relaxation time $t_D$, beyond which the system undergoes long-time diffusion, as a function of the packing fraction $\phi$ and system topology. This procedure involves several steps: 1) define a set of distinct microstates in configuration space of the system, 2) construct a directed network of microstates and transitions between them, 3) identify minimal, closed loops in the network that give rise to structural relaxation, 4) determine the frequencies of `bottleneck' microstates that control the slow dynamics and time required to transition out of them, and 5) use the microstate frequencies and lifetimes to deduce $t_D(\phi)$. We find that $t_D$ obeys power-law scaling, $t_D\sim (\phi^* - \phi)^{-\alpha}$, where both $\phi^*$ (signaling complete kinetic arrest) and $\alpha>0$ depend on the system topology.
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    • "Theoretical studies have been carried out to understand the glass transition and gelation in binary mixtures of hard spheres (e.g., those experience only excluded volume interactions) and attractive spheres with comparable size [Viehman and Schweizer (2008c)]. For weak strengths of attraction between the attractive spheres, at sufficiently high total volume fraction, the system enters a glassy state. "
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    ABSTRACT: We explore the flow properties of nanocomposite melts where the particles have bimodal size distributions and experience a weak attraction produced by suspending silica particles in polyethylene glycol melts with a molecular weight of 2000 (PEG2000). The polymer is unentangled and adsorbs to the particle surface. The volume fraction ratio of large particles to total particle volume fraction, R, is systematically varied to study the effects of this polymer-induced attraction on suspension rheology. The maximum volume fraction, ϕm , of the particles varies in a nonmonotonic manner of R as demonstrated in studies of the same mixtures when suspended in polyethylene glycol with a molecular weight of 400 (PEG400), where the particles experience excluded volume interactions. The dynamical arrest volume fraction ϕx , of nanocomposite melts in PEG2000 monotonically increases with R. In frequency sweep experiments, the plateau elastic modulus is dominated by attractive interactions and increases with the total particle volume fraction, ϕc , proportionally with 1/(h2 ), where is the volume average particle diameter and h is the average particle-particle surface separation. As R is varied, this universal yielding behavior occurs at constant surface separation, h, suggesting that the flow properties of the mixtures can be understood as being equivalent to flow properties of homogeneous particle suspensions experiencing short-range attractions with an extent independent of particle size.
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    ABSTRACT: A nonlinear Langevin equation (NLE) theory for the translational center-of-mass dynamics of hard nonspherical objects has been applied to isotropic fluids of rigid rods. The ideal kinetic glass transition volume fraction is predicted to be a monotonically decreasing function beyond an aspect ratio of two. The functional form of the decrease is weaker than the inverse aspect ratio. Vitrification occurs at lower volume fractions for corrugated tangent bead rods compared to their smooth spherocylinder analogs. The ideal glass transition signals a crossover to activated dynamics, which is estimated to be observable before the nematic phase boundary is encountered if the aspect ratio is less than roughly 25. Calculations of the glassy elastic shear modulus and absolute yield stress reveal a roughly exponential growth with volume fraction. The dependence of entropic barriers and mean barrier hopping times on concentration for rods of variable aspect ratios can be collapsed quite well based on a difference volume fraction variable that quantifies the distance from the ideal glass boundary. Full numerical solution of the NLE theory via stochastic trajectory simulation was performed for tangent bead rods, and the results were compared to their hard sphere analogs. With increasing shape anisotropy the characteristic length scales of the nonequilibrium free energy increase and the magnitude of the localization well and entropic barrier curvatures decreases. These changes result in a significant aspect ratio dependence of dynamical properties and time correlation functions including weaker intermediate time subdiffusive transport, stronger two-step decay of the incoherent dynamic structure factor, longer mean alpha relaxation time, and stronger wavevector-dependent decoupling of relaxation times and the self-diffusion constant. The theoretical results are potentially testable via computer simulation, confocal microscopy, and dynamic light scattering.
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