A two-fluid model for the formation of clusters close to a continuous or almost continuous transition

Abstract

Experiments have shown that spatial heterogeneities can arise when the glass transition in polymers as well as in a number of low molecular weight compounds is approached by lowering the temperature. This formation of “clusters” has been detected predominantly by small angle light scattering and ultrasmall angle x-ray scattering from the central peak on length scales up to about 200 nm and by mechanical measurements including, in particular, piezorheometry for length scales up to several microns. Here we use a macroscopic two-fluid model to study the formation of clusters observed by the various experimental techniques. As additional macroscopic variables, when compared to simple fluids, we use a transient strain field to incorporate transient positional order, along with the velocity difference and a relaxing concentration field for the two subsystems. We show that an external homogeneous shear, as it is applied in piezorheometry, can lead to the onset of spatial pattern formation. To address the issue of additional spectral weight under the central peak we investigate the coupling to all macroscopic variables. We find that there are additional static as well as dissipative contributions from both, transient positional order, as well as from concentration variations due to cluster formation, and additional reversible couplings from the velocity difference. We also briefly discuss the influence of transient orientational order. Finally, we point out that our description is more general, and could be applied above continuous or almost continuous transitions

Structural Relaxation and Thermodynamics of Viscous Aqueous Systems: A Simplified Reappraisal

“…More intriguing and appealing seems the approach that relates thermodynamic equilibrium to the time scale considered [24][25][26][27][28][29]. Assuming the ergodicity of the system, this approach allows a connection between long wave relaxation processes that deal with the viscoelastic behavior and thermodynamic properties of many materials, which imply two time scales, one related to the linear dependence on time of the mean squared displacement, the other related to the Gaussian distribution of the particle displacements.…”

“…Longrange strains within the system depend on its thermo-rheological history and affect its internal energy for periods that are much longer than the relaxation times of processes at the molecular scale. However, the relaxation mechanism of long-range strains implies a concerted cooperation of short-range relaxations within mesoscopic regions of the system [6]. This justifies the search of a correlation between local relaxation processes, in the so called "zero shear conditions", and thermodynamic excess properties, like excess configuration entropy or excess Gibbs free energy.…”