Sarika Maitra Bhattacharyya

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.

Facilitation, complexity growth, mode coupling, and activated dynamics in supercooled liquids.

In low-temperature-supercooled liquids, below the ideal mode-coupling theory transition temperature, hopping and continuous diffusion are seen to coexist. Here, we present a theory that shows explicitly the interplay between the two processes and shows that activated hopping facilitates continuous diffusion in the otherwise frozen liquid. Several universal features arise from nonlinear interactions between the continuous diffusive dynamics described here by the mode coupling theory (MCT)] and the activated hopping (described here by the random first-order transition theory). We apply the theory to a specific system, Salol, to show that the theory correctly predicts the temperature dependence of the nonexponential stretching parameter, β, and the primary α relaxation timescale, τ. The study explains why, even below the mean field ergodic to nonergodic transition, the dynamics is well described by MCT. The nonlinear coupling between the two dynamical processes modifies the relaxation behavior of the structural relaxation 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. Furthermore, the theory correctly predicts the observed variation of the stretching exponent β with the fragility parameter, D. These two predictions also allow the complexity growth to be predicted, in good agreement with the results of Capaccioli et al. [Capaccioli S, Ruocco G, Zamponi F (2008) J Phys Chem B 112:10652-10658].

Pressure and temperature dependence of viscosity and diffusion coefficients of a glassy binary mixture

Extensive isothermal-isobaric (NPT) molecular dynamics simulations at many different temperatures and pressures have been carried out in the well-known Kob-Andersen binary mixture model to monitor the effect of pressure (P) and temperature (T) on the dynamic properties such as the viscosity (\eta) and the self-diffusion (Di) coefficients of the binary system. The following results have been obtained: (i) Compared to temperature, pressure is found to have a weaker effect on the dynamical properties. Viscosity and diffusion coefficients are found to vary exponentially with pressure up to a certain high pressure after which the nature of exponential dependence changes. This change is rather sharp. (ii) With temperature, on the other hand, both viscosity and diffusion show super-Arrhenius dependence. Viscosity and diffusion coefficients fit well also to the mode coupling theory (MCT) prediction of a power law dependence on the temperature. The MCT critical temperature (Tc) for both the two dynamical properties are significantly higher than the corresponding critical temperature T\eta 0 obtained by fitting to the Vogel-Fulcher-Tammann (VFT) equation. (iii) The critical temperature for viscosity (T\eta 0) is considerably larger than that for the diffusion coefficients (T D4 0) implying the decoupling between diffusion and viscosity in deeply supercooled liquid. (iv) The nature of the motion of small particles change from continuous to hopping dominated once the larger ones are frozen. (v) The potential energy of the system shows a minimum against density at a relatively high density when the latter is changed by applying pressure at a constant temperature.

Vibrational energy relaxation, nonpolar solvation dynamics and instantaneous normal modes: Role of binary interaction in the ultrafast response of a dense liquid

Recently instantaneous normal mode analysis has revealed an interesting similarity of the solvent dynamical influence on two rather different phenomena, namely vibrational energy relaxation (VER) and nonpolar solvation dynamics (NPSD). In this work we show that this similarity can be rationalized from a mode coupling theoretic analysis of the dynamic response of a dense liquid. The present analysis demonstrates that VER and the initial NPSD are coupled primarily to the binary part of the frequency dependent frictional response of the liquid. It is found that for strong solute–solvent interaction, the initial decay of nonpolar solvation dynamics can proceed with time constant less than 100 fs. In addition, a very good agreement between the calculated and the simulated VER rates have been obtained for a large range of frequency.

Computer simulation and mode coupling theory study of the effects of specific solute–solvent interactions on diffusion: Crossover from a sub-slip to a super-stick limit of diffusion

In many experimental situations, the interaction potential between the tagged solute and the solvent molecules is often different from that between the two solvent molecules. In such cases, the Stokes–Einstein relation attempts to describe the self-diffusion of the solute in terms of an effective hydrodynamic radius which, along with the hydrodynamic boundary condition (slip or stick), are varied to fit the experimental results. Extensive molecular dynamics (MD) simulations have been carried out to obtain the diffusion coefficient by varying interaction between the solute and the solvent. It is found that when this interaction is more repulsive than that between solvent–solvent, the diffusion can be significantly faster, leading to a complete breakdown of the Stokes–Einstein relation. In the limit of strong attractive interaction, we recover a dynamic version of the solvent–berg picture. The diffusion coefficient of the solute is found to depend strongly and nonlinearly on the magnitude of this specific i...

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 argonlike 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.

Isomerization dynamics in viscous liquids: Microscopic investigation of the coupling and decoupling of the rate to and from solvent viscosity and dependence on the intermolecular potential

A detailed investigation of viscosity dependence of the isomerization rate is carried out for continuous potentials by using a fully microscopic, self-consistent mode-coupling theory calculation of both the friction on the reactant and the viscosity of the medium. In this calculation we avoid approximating the short time response by the Enskog limit, which overestimates the friction at high frequencies. The isomerization rate is obtained by using the Grote–Hynes formula. The viscosity dependence of the rate has been investigated for a large number of thermodynamic state points. Since the activated barrier crossing dynamics probes the high-frequency frictional response of the liquid, the barrier crossing rate is found to be sensitive to the nature of the reactant–solvent interaction potential. When the solute–solvent interaction is modeled by a 6–12 Lennard-Jones potential, we find that over a large variation of viscosity (η), the rate (k) can indeed be fitted very well to a fractional viscosity dependence...

Role of Structure and Entropy in Determining Differences in Dynamics for Glass Formers with Different Interaction Potentials.

We present a study of two model liquids with different interaction potentials, exhibiting similar structure but significantly different dynamics at low temperatures. By evaluating the configurational entropy, we show that the differences in the dynamics of these systems can be understood in terms of their thermodynamic differences. Analyzing their structure, we demonstrate that differences in pair correlation functions between the two systems, through their contribution to the entropy, dominate the differences in their dynamics, and indeed overestimate the differences. Including the contribution of higher order structural correlations to the entropy leads to smaller estimates for the relaxation times, as well as smaller differences between the two studied systems.

Anisotropic local stress and particle hopping in a deeply supercooled liquid

The origin of the microscopic motions that lead to stress relaxation in deeply supercooled liquid remains unclear. We show that in such a liquid the stress relaxation is locally anisotropic which can serve as the driving force for the hopping of the system on its free energy surface. However, not all hoppings are equally effective in relaxing the local stress, suggesting that diffusion can decouple from viscosity even at the local level. On the other hand, orientational relaxation is found to be always coupled to stress relaxation.

Unraveling the success and failure of mode coupling theory from consideration of entropy

We analyze the dynamics of model supercooled liquids in a temperature regime where predictions of mode coupling theory (MCT) are known to be valid qualitatively. In this regime, the Adam-Gibbs (AG) relation, based on an activation picture of dynamics, also describes the dynamics satisfactorily, and we explore the mutual consistency and interrelation of these descriptions. Although entropy and dynamics are related via phenomenological theories, the connection between MCT and entropy has not been argued for. In this work, we explore this connection and provide a microscopic derivation of the phenomenological Rosenfeld theory. At low temperatures, the overlap between the MCT power law regime and AG relation implies that the AG relation predicts an avoided divergence at Tc, the origin of which can be related to the vanishing of pair configurational entropy, which we find occurring at the same temperature. We also show that the residual multiparticle entropy plays an important role in describing the relaxation time.