Bridging the Gap Between the Mode Coupling and the Random First Order Transition Theories of Structural Relaxation in Liquids

A unified treatment of structural relaxation in a deeply supercooled glassy liquid is developed which extends the existing mode coupling theory (MCT) by incorporating the effects of activated events by using the concepts from the random first order transition (RFOT) theory. We show how the decay of the dynamic structure factor is modified by localized activated events (called instantons) which lead to the spatial reorganization of molecules in the region where the instanton pops up. The instanton vertex added to the usual MCT depicts the probability and consequences of such an event which can be derived from the random first order transition theory. The vertex is proportional to $exp(-A/s_{c})$ where $s_{c}$ is the configurational entropy. Close to the glass transition temperature, $T_{g}$, since $s_{c}$ is diminishing, the activated process slows beyond the time window and this eventually leads to an arrest of the structural relaxation as expected for glasses. The combined treatment describes the dynamic structure factor in deeply supercooled liquid fairly well, with a hopping dominated decay following the MCT plateau.Comment: 11 pages, 5 figures, 1 tabl

Dynamical Heterogeneity and the interplay between activated and mode coupling dynamics in supercooled liquids

We present a theoretical analysis of the dynamic structure factor (DSF) of a liquid at and below the mode coupling critical temperature $T_c$, by developing a self-consistent theoretical treatment which includes the contributions both from continuous diffusion, described using general two coupling parameter ($F_{12}$) mode coupling theory (MCT), and from the activated hopping, described using the random first order transition (RFOT) theory, incorporating the effect of dynamical heterogeneity. The theory is valid over the whole temperature plane and shows correct limiting MCT like behavior above $T_{c}$ and goes over to the RFOT theory near the glass transition temperature, $T_{g}$. Between $T_{c}$ and $T_{g}$, the theory predicts that neither the continuous diffusion, described by pure mode coupling theory, nor the hopping motion alone suffices but both contribute to the dynamics while interacting with each other. We show that the interplay between the two contributions conspires to modify the relaxation behavior of the DSF from what would be predicted by a theory with a complete static Gaussian barrier distribution in a manner that may be described as a facilitation effect. Close to $T_c$, coupling between the short time part of MCT dynamics and hopping reduces the stretching given by the F$_{12}$-MCT theory significantly and accelerates structural relaxation. As the temperature is progressively lowered below $T_c$, the equations yield a crossover from MCT dominated regime to the hopping dominated regime. In the combined theory the dynamical heterogeneity is modified because the low barrier components interact with the MCT dynamics to enhance the relaxation rate below $T_c$ and reduces the stretching that would otherwise arise from an input static barrier height distribution.Comment: 7 pages, 4 figure

Bimodality of the viscoelastic response of a dense liquid and comparison with the frictional responses at short times

While the time dependence of the friction on a tagged particle in a dense liquid has been investigated in great detail, a similar analysis for the viscosity of the medium and the interrelationship between the two has not been carried out. This is despite the close relation always assumed, both in theoretical and experimental studies, between friction and viscosity. In this article a detailed study of the time and frequency dependencies of the viscosity has been carried out and compared with those of the friction. The analysis is fully microscopic and is based on the mode coupling theory (MCT). It is found that for an argon like liquid near its triple point, the initial decay of the viscosity occurs with a time constant of the order of 100 fs, which is close to that of the friction. The frequency dependent viscosity shows a pronounced bimodality with a sharp peak at the low frequency and a broad peak at the high frequency; the usually employed Maxwell's relation fails to describe the peak at the high frequency. A surprising result of the present study is that both the bare and the MCT values of viscosity and friction individually sustain a ratio which is close to the value predicted by the Stokes relation, even when Navier-Stokes hydrodynamics itself seems to have little validity

Anomalous diffusion of small particles in dense liquids

We present here a microscopic and self-consistent calculation of the self-diffusion coefficient of a small tagged particle in a dense liquid of much larger particles. In this calculation the solute motion is coupled to both the collective density fluctuation and the transverse current mode of the liquid. The theoretical results are found to be in good agreement with the known computer simulation studies for a wide range of solute-solvent size ratio. In addition, the theory can explain the anomalous enhancement of the self-diffusion over the Stokes-Einstein value for small solutes, for the first time. Further, we find that for large solutes the crossover to Stokes-Einstein behavior occurs only when the solute is 2-3 times bigger than the solvent molecules. The applicability of the present approach to the study of self-diffusion in supercooled liquids is discussed

Diffusion of small light particles in a solvent of large massive molecules

We study diffusion of small light particles in a solvent which consists of large heavy particles. The intermolecular interactions are chosen to approximately mimic a water-sucrose (or water-polysaccharide) mixture. Both computer simulation and mode coupling theoretical (MCT) calculations have been performed for a solvent-to-solute size ratio five and for a large variation of the mass ratio, keeping the mass of the solute fixed. Even in the limit of large mass ratio the solute motion is found to remain surprisingly coupled to the solvent dynamics. Interestingly, at intermediate values of the mass ratio, the self-intermediate scattering function of the solute, F_{s}(k,t) (where k is the wavenumber and t the time), develops a stretching at long time which could be fitted to a stretched exponential function with a k-dependent exponent, \beta. For very large mass ratio, we find the existence of two stretched exponentials separated by a power law type plateau. The analysis of the trajectory shows the coexistence of both hopping and continuous motions for both the solute and the solvent particles. It is found that for mass ratio five, the MCT calculations of the self-diffusion underestimates the simulated value by about 20 %, which appears to be reasonable because the conventional form of MCT does not include the hopping mode. However, for larger mass ratio, MCT appears to breakdown more severely. The breakdown of the MCT for large mass ratio can be connected to a similar breakdown near the glass transition.Comment: RevTex4, 9 pages, 10 figure