The role of pair correlation function in the dynamical transition predicted by the mode coupling theory

  • In a recent study we have found that for a large number of systems the configuration entropy at pair level, Sc, which is primarily determined by the structural information, vanishes at the mode coupling transition temperature Tc. Sc, which is primarily determined by the structural information, vanishes at the mode coupling transition temperature Tc Thus it appears that the information of the transition temperature is embedded in the structure of the liquid. In order to investigate this we describe the dynamics of the system at the mean field level and using the concepts of the dynamical density functional theory show that the dynamics depends only on the structure of the liquid. Thus this theory is similar in spirit to the microscopic MCT. However unlike microscopic MCT, which predicts a very high transition temperature, the present theory predicts a transition temperature which is similar to Tc. Thus our study reveals that the information of the mode coupling transition temperature is embedded in the structure of the liquid.

  1. Auhor: Manoj Kumar NandiAtreyee BanerjeeChandan DasguptaSarika Maitra Bhattacharyya (arxiv:1706.027728)



Interplay between crystallization and glass transition in binary Lennard-Jones mixtures


  •  We explore the interplay between crystallization and glass transition in different binary mixtures by changing their inter-species interaction length and also the composition. We find that only those systems which form bcc crystal in the equimolar mixture and whose global structure for larger, whereis the mole fraction of the bigger particles) is a mixed fcc+bcc phase, do not crystallize at this higher composition. However, the systems whose equimolar structure is a variant of fcc (NaCl type crystal) and whose global structure at larger xA is a mixed NaCl+fcc phase, crystallize easily to this mixed structure. We find that the stability against crystallization of this "bcc zone" is due to the frustration between the locally preferred structure (LPS) and the mixed bcc+fcc crystal. Our study suggests that when the global structure is a mixed crystal where a single species contributes to both the crystal forms and where the two crystal forms have large difference in some order parameter related to that species then this induces frustration between the LPS and the global structure. This frustration makes the systems good glass former. When xA is further increased systems show a tendency towards mixed fcc crystal formation. However, the "bcc zone" even for this higher composition is found to be sitting at the bottom of a V shaped phase diagram formed by two different variants of the fcc crystal structure, leading to its stability against crystallization. Now we want to study the nucleation barrier height of the no crystal zone. 
  1.  Atreyee Banerjee, Suman Chakrabarty And Sarika Maitra Bhattacharyya, Interplay between crystallization and glass transition in binary Lennard-Jones mixtures, J. Chem. Phys., 139, 104501 (2013).
  2. Ujjwal Kumar Nandi, Atreyee Banerjee, Suman Chakrabarty And and Sarika Maitra Bhattacharyya, Composition dependence of the glass forming ability in binary mixtures: The role of demixing entropy, The Journal of Chemical Physics., 145, 034503 (2016), DOI:




The 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.
  1. Atreyee Banerjee, Manoj Kumar Nandi, Srikanth Sastry And and Sarika Maitra Bhattacharyya, Effect of total and pair configurational entropy in determining dynamics of supercooled liquids over a range of densities, The Journal of Chemical Physics., 145, 034502 (2016), DOI:
  2. Atreyee Banerjee, Shiladitya Sengupta, Srikanth Sastry And Sarika Maitra Bhattacharyya, The role of structure and entropy in determining differences in dynamics for glass formers with different interaction potentials, Phys.Rev.Let.., 113, 225701 (2014)





Interplay between activated and diffusive dynamics


  • Simulation studies of particle trajectories have shown a decoupling between persistence and exchange time thus predicting a hierarchy of events . The persistence time has been identified with the activated motion and the exchange time with the diffusive motion. The unified theory (1) did predict hopping induced diffusion but it failed to incorporate in the formulation the hierarchy of the events. The extended mode coupling theory and the unified theory, consider that diffusive and activated motions take place simultaneously and independently. A modified version of the continuous time random walk (CTRW) model incorporated this hierarchy, considering that the first jump is different from the subsequent jumps. We propose a model where the dynamics is formulated using the concepts of a further modified CTRW and the continuous and activated motions are calculated using the concepts of the unified theory.
  • The theory predicts the decoupling between diffusion and viscosity. We also calculate the dynamic correlation length. As the temperature is decreased, the dynamic correlation length is found to grow faster than the static correlation length. 
  1.  Sarika Maitra Bhattacharyya,Biman Bagchi, Peter G. Wolynes, “Facilitation, Complexity Growth, Mode Coupling and Activated Dynamics in Supercooled Liquids”. Proc. National Acad. Sciences United States Am. 105, 16077–16082 (2008).
  2. Manoj Kumar Nandi, Sarika Maitra bhattacharyya, ongoing project.


Effect of Interaction on Slow Dynamics


  • The structure and dynamics of model glass formers with pairwise additive Lennard Jones (LJ) potential and repulsive Week Chandler Anderson (WCA) potential was studied earlier. It was found that although both the systems have the same static structures at higher and lower temperatures the dynamics are dramatically different at lower temperatures. In the supercooled liquid it has been already shown that the dynamics can be described by diffusive and many body activated motions. Some regions in the glassy system tend to be jammed or be inactive where as some regions are liquid like or active. The regions are dynamic and flip between being active and inactive. According to Random First Order Transition theory (RFOT) the timescale of this flip is determined by the configurational entropy. To find the origin of the difference in dynamics between the WCA and LJ system we study the difference in their activated and diffusive motions. We also study the relation between thermodynamics and dynamics in both these types of interactions.



Explaining The Breakdown of Stokes-Eintsein Law in The Light of Sovent-Cage Effect, Levitation Effect


  • It has been shown both using molecular dynamics simulation and experiments that the self diffusivity D, of small solute particle in a sea of large solvent molecules show a non-monotonic behaviour with size variation. This anomalous behaviour comes due to the symmetry of the force when the solute diffuses through a neck created by the solvent molecules. This anomalous behavior was first noticed in the diffusion of solutes through Zeolites and was coined as the levitation effect. In Zeolites it is found that when the solute is about 80 % of the size of the neck of the Zeolite then the diffusion is maximum. We use a self-consistent microscopic theory (Mode coupling theory –MCT) to calculate the self diffusion co-efficient of a small tagged particle in a dense liquid of larger particles. In this the motion of solute is coupled with both the density and transverse and longitudinal current modes of the liquid.. The theoretical study shows a non-monotonic size dependence of diffusion and thus we obtain this levitation effect. We also simulate and do analytical calculation of other systems to understand the origin of levitation.
  1.  Manoj Kumar Nandi, Atreyee Banerjee And Sarika Maitra Bhattacharyya, Non-monotonic size dependence of diffusion and levitation effect: A mode- coupling theory analysis, J . Chem .Phys., 138, 124505 (2012).
  2. Sayantan Acharya, Manoj K. Nandi, Arkajit Mandal, Sucharita Sarkar And and Sarika Maitra Bhattacharyya*, Diffusion of Small Solute Particles in Viscous Liquids: Cage Diffusion, a Result of Decoupling of Solute–Solvent Dynamics, Leads to Amplification of Solute Diffusion, J.Phys.Chem. B., 119, 11169 - 11175 (2015).