Article

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

Department of Chemical and Biomolecular Engineering, University of Illinois, 1304 West Green Street, Urbana, Illinois 61801, USA.

The Journal of Chemical Physics (Impact Factor: 3.12). 03/2008; 128(8):084509. DOI: 10.1063/1.2837295 Source: PubMed

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**ABSTRACT:**We analyze the influence of residual attractions on the static and some dynamic properties of size asymmetric mixtures of "hard-sphere-like" colloids. These attractions, usually neglected in the theoretical analysis, are characterized by a very short range and a moderate strength reflecting the underlying microscopic structure of the colloidal particles. Their effect on the potentials of mean force is analyzed from analytical expressions obtained from low density expansions. The effective potential of the big particle fluid is next considered. An analytical expression is proposed for estimating the deviation with respect to the hard sphere depletion potential. This case is compared to that of mixtures with noninteracting depletants. The important consequences on the binodals and the glass transition lines of the effective fluid are discussed in both cases. This study is next extended to other properties-the specific heat and the low shear viscosity-which incorporate contributions from the two components of the binary mixture.The Journal of Chemical Physics 07/2010; 133(4):044905. · 3.12 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We generalize the nonlinear Langevin equation theory of activated single particle dynamics to describe the correlated motion of two tagged spherical particles in a glass- or gel-forming fluid as a function of their initial separation. The theory is built on the concept of a two-dimensional dynamic free energy surface which quantifies the forces on two particles moving in a cooperative manner. For the hard sphere fluid, above a threshold volume fraction we generically find two relaxation channels corresponding largely, but not exclusively, to a center-of-mass-like displacement and a radial separation of the two tagged particles. The entropic barriers and mean first passage times are computed and found to systematically vary with volume fraction and initial particle separation; both oscillate as a function of the latter in a manner related to the equilibrium pair correlation function. A dynamic correlation length is estimated as the length scale beyond which the two-particle activated dynamics becomes uncorrelated in space and time, and is found to modestly grow with increasing mean relaxation time. The theory is also applied to a simplified model of cage escape, the elementary step of structural relaxation. Predictions for characteristic relaxation times, translation-relaxation decoupling, and stretched-exponential decay of time correlation functions are obtained. A novel mechanism for understanding why strong decoupling emerges in the activated regime, but stretched nonexponential time correlation functions do not change shape as the mean relaxation time grows, is presented and favorably compared with experiment. The theory may serve as a starting point for constructing a predictive model of multiple correlated caging and hopping (forward and backward) events of a pair of tagged particles.The Journal of Chemical Physics 02/2011; 134(6):064516. · 3.12 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We generalize the microscopic naïve mode coupling and nonlinear Langevin equation theories of the coupled translation-rotation dynamics of dense suspensions of uniaxial colloids to treat the effect of applied stress on shear elasticity, cooperative cage escape, structural relaxation, and dynamic and static yielding. The key concept is a stress-dependent dynamic free energy surface that quantifies the center-of-mass force and torque on a moving colloid. The consequences of variable particle aspect ratio and volume fraction, and the role of plastic versus double glasses, are established in the context of dense, glass-forming suspensions of hard-core dicolloids. For low aspect ratios, the theory provides a microscopic basis for the recently observed phenomenon of double yielding as a consequence of stress-driven sequential unlocking of caging constraints via reduction of the distinct entropic barriers associated with the rotational and translational degrees of freedom. The existence, and breadth in volume fraction, of the double yielding phenomena is predicted to generally depend on both the degree of particle anisotropy and experimental probing frequency, and as a consequence typically occurs only over a window of (high) volume fractions where there is strong decoupling of rotational and translational activated relaxation. At high enough concentrations, a return to single yielding is predicted. For large aspect ratio dicolloids, rotation and translation are always strongly coupled in the activated barrier hopping event, and hence for all stresses only a single yielding process is predicted.The Journal of Chemical Physics 04/2012; 136(15):154902. · 3.12 Impact Factor

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