Coherent neutron scattering and collective dynamics on mesoscale

By combining, and modestly extending, a variety of theoretical concepts for the dynamics of liquids in the supercooled regime, we formulate a simple analytic model for the temperature and wavevector dependent collective density fluctuation relaxation time that is measurable using coherent dynamic neutron scattering. Comparison with experiments on the ionic glass-forming liquid Ca-K-NO3 in the lightly supercooled regime suggests the model captures the key physics in both the local cage and mesoscopic regimes, including the unusual wavevector dependence of the collective structural relaxation time. The model is consistent with the idea that the decoupling between diffusion and viscosity is reflected in a different temperature dependence of the collective relaxation time at intermediate wavevectors and near the main (cage) peak of the static structure factor. More generally, our analysis provides support for the ideas that decoupling information and growing dynamic length scales can be at least qualitatively deduced by analyzing the collective relaxation time as a function of temperature and wavevector, and that there is a strong link between dynamic heterogeneity phenomena at the single and many particle level. Though very simple, the model can be applied to other systems, such as molecular liquids.

Glass formation and shear elasticity in dense suspensions of repulsive anisotropic particles

Kinetic vitrification, shear elasticity, and the approach to jamming are investigated for repulsive nonspherical colloids and contrasted with their spherical analog. Particle anisotropy dramatically increases the volume fraction for kinetic arrest. The shear modulus of all systems increases roughly exponentially with volume fraction, and a universal collapse is achieved based on either the dynamic crossover or random close packing volume fraction as the key nondimensionalizing quantity. Quantitative comparisons with recent microscopic theories are performed and good agreement demonstrated.

Segmental dynamics in polymers: from cold melts to ageing and stressed glasses

Recent progress in developing statistical mechanical theories of supercooled polymer melts and glasses is reviewed. The focus is on those approaches that are either explicitly formulated for polymers, or are applications of more generic theories to interpret polymeric phenomena. These include two configurational entropy theories, a percolated free volume distribution model, and the activated barrier hopping nonlinear Langevin theory. Both chemically-specific and universal aspects are discussed. After a brief summary of classic phenomenological approaches, a discussion of the relevant length scales and key experimental phenomena in both the supercooled liquid and glassy solid state is presented including ageing and nonlinear mechanical response. The central concepts that underlie the theories in the molten state are then summarized and key predictions discussed, including the glass transition in oriented polymer liquids and deformed rubber networks. Physical ageing occurs in the nonequilibrium glass, and theories for its consequences on the alpha relaxation are discussed. Very recent progress in developing a segment scale theory for the dramatic effects of external stress on polymer glasses, including acceleration of relaxation, yielding, plastic flow and strain hardening, is summarized. The article concludes with a discussion of outstanding theoretical challenges.

Collective diffusion in colloid-polymer suspensions: relative role of thermodynamics and hydrodynamics

Theories such as the mode coupling theory (MCT) have seen recent success in predicting the kinetic arrest boundaries and resultant flow properties of colloidal suspensions. A key assumption of such theories is that interparticle forces and equilibrium structure control slow dynamics and gelation, not long-time many-body hydrodynamics. Here we report measurements of short-time collective diffusivities of colloid-polymer suspensions aimed at elucidating the relative contributions of hydrodynamics and thermodynamics as a phase transition or gelation boundary is approached. The experimental system is a hard sphere octadecyl silica suspension to which nonadsorbing polystyrene is added. Two different polymer molecular weights are chosen such that they give rise to a liquid-liquid or a gel transition as the colloid volume fraction or polymer concentration is increased. The short-time diffusivities are measured for each polymer molecular weight as a function of polymer concentration and colloid volume fraction. At a fixed polymer molecular weight and concentration, the colloid volume fraction is varied from dilute to concentrated and near the phase separation boundary. It is found for all measured colloid volume fractions that the diffusivities decrease linearly with increasing strength of the polymer-mediated depletion attraction at a fixed polymer molecular weight. Comparisons are made with theoretical predictions in the dilute limit. When the effects of thermodynamics are normalized out by multiplying the measured diffusivities with the suspension structure factor, it is found that the hydrodynamic effects are essentially those of hard spheres independent of the range and strength of depletion attraction.

Structure, surface excess and effective interactions in polymer nanocomposite melts and concentrated solutions

The Polymer Reference Interaction Site Model (PRISM) theory is employed to investigate structure, effective forces, and thermodynamics in dense polymer-particle mixtures in the one and two particle limit. The influence of particle size, degree of polymerization, and polymer reduced density is established. In the athermal limit, the surface excess is negative implying an entropic dewetting interface. Polymer induced depletion interactions are quantified via the particle-particle pair correlation function and potential of mean force. A transition from (nearly) monotonic decaying, attractive depletion interactions to much stronger repulsive-attractive oscillatory depletion forces occurs at roughly the semidilute-concentrated solution boundary. Under melt conditions, the depletion force is extremely large and attractive at contact, but is proceeded by a high repulsive barrier. For particle diameters larger than roughly five monomer diameters, division of the force by the particle radius results in a nearly universal collapse of the depletion force for all interparticle separations. Molecular dynamics simulations have been employed to determine the depletion force for nanoparticles of a diameter five times the monomer size over a wide range of polymer densities spanning the semidilute, concentrated, and melt regimes. PRISM calculations based on the spatially nonlocal hypernetted chain closure for particle-particle direct correlations capture all the rich features found in the simulations, with quantitative errors for the amplitude of the depletion forces at the level of a factor of 2 or less. The consequences of monomer-particle attractions are briefly explored. Modification of the polymer-particle pair correlations is relatively small, but much larger effects are found for the surface excess including an energetic driven transition to a wetting polymer-particle interface. The particle-particle potential of mean force exhibits multiple qualitatively different behaviors (contact aggregation, steric stabilization, local bridging attraction) depending on the strength and spatial range of the polymer-particle attraction.

Barrier hopping, viscous flow, and kinetic gelation in particle-polymer suspensions

The naive mode coupling-polymer reference interaction site model (MCT-PRISM) theory of gelation and elasticity of suspensions of hard sphere colloids or nanoparticles mixed with nonadsorbing polymers has been extended to treat the emergence of barriers, activated transport, and viscous flow. The barrier makes the dominant contribution to the single particle relaxation time and shear viscosity, and is a rich function of the depletion attraction strength via the polymer concentration, polymer-particle size asymmetry ratio, and particle volume fraction. The dependences of the barrier on these three system parameters can be accurately collapsed onto a single scaling variable, and the resultant master curve is well described by a power law. Nearly universal master curves are also constructed for the hopping or alpha relaxation time for system conditions not too close to the ideal MCT transition. Based on the calculated barrier hopping time, a theory for kinetic gel boundaries is proposed. The form and dependence on system parameters of the kinetic gel lines are qualitatively the same as obtained from prior ideal MCT-PRISM studies. The possible relevance of our results to the phenomenon of gravity-driven gel collapse is studied. The general approach can be extended to treat nonlinear viscoelasticity and rheology of polymer-colloid suspensions and gels.

Elasticity and clustering in concentrated depletion gels

X-ray scattering and rheology are employed to study the volume fraction dependence of the collective structure and elastic moduli of concentrated nanoparticle-polymer depletion gels. The nonequilibrium gel structure consists of locally densified nonfractal clusters and narrow random interfaces. The elastic moduli display a power law dependence on volume fraction with effective exponents that decrease with increasing depletion attraction strength. A microscopic theory that combines local structural information with a dynamic treatment of gelation is in good agreement with the observations.

Macromolecular theory of solvation and structure in mixtures of colloids and polymers

The structural and thermodynamic properties of mixtures of colloidal spheres and nonadsorbing polymer chains are studied within a general two-component macromolecular liquid state approach applicable for all size asymmetry ratios. The dilute limits, when one of the components is at infinite dilution but the other concentrated, are presented and compared to field theory and to models that replace polymer coils with spheres. Whereas the derived analytical results compare well, qualitatively and quantitatively, with mean-field scaling laws where available, important differences from "effective sphere" approaches are found for large polymer sizes or semidilute concentrations.