Research | RSSLAB

Phase transition in equilibrium and driven out-of-equilibrium systems

The formation of many of the complex hierarchical structures in nature involves either complex/rugged free energy landscape (e.g., zeolites, proteins, etc.) or driven out-of-equilibrium conditions (e.g., intra-cellular self-organization of cytoskeletons, birds flocking, etc.). These complex self-organized structures play key functional roles in many of the physical, chemical and biological processes in nature. Understanding the principles governing the self-assembly and self-organization in these complex (equilibrium and driven out-of-equilibrium) systems remains one of the central challenges of statistical mechanics. Using computational modeling and theoretical tools rooted in statistical mechanics we are interested in gaining fundamental understanding of self-assembly processes involving complex free energy landscape at equilibrium conditions and self-organization processes at driven out-of-equilibrium conditions.

Order parameter

Surrey et al., Science, 2001

Anomalous behavior of supercooled liquids

Liquid water is often described as anomalous because its behavior frequently departs from that of conventional “simple” liquids. Examples of water anomalies include a temperature of maximum density and increases in thermodynamic response functions (e.g., isothermal compressibility, isobaric heat capacity, etc.) upon isobaric cooling. One influential hypothesis that explains water’s anomalous behavior posits the existence of metastable liquid-liquid phase transition between two (high- and low-density) forms of liquid water (a phenomenon known as “liquid water polymorphism") at deeply supercooled conditions. We are trying to develop an energy landscape perspective of the anomalous thermodynamic and dynamic behavior of water at supercooled conditions.

Self-assembly at nanoscales

Self-assembly processes play a crucial role in designing many of the multi-scale complex structures in nature. In these processes, solvent-mediated effective inter-particle interactions guide the nanoscale building blocks to spontaneously assemble into the target structure. Therefore, it is crucial to have control of the inter-particle interactions between the self-assembling agents to get the target structure. Soft nanoscale particles are very promising for designing functional materials because the interaction between the building blocks can be easily altered. Using computational modelling, my research group is currently working on to develop rational design and selection criteria for solvent-mediated pair interactions between the nanoscale building blocks that would lead to the desired free-energy landscape, and in turn, the desired structure and properties.

Target Structure

Self-assembling agents

Effective interaction?

Dynamics on complex free energy landscape

Many of the dynamical processes in nature are described by diffusion along some collective variable(s) (reaction coordinate or order parameter). These dynamical processes can be activated or barrierless, Markovian or non-Markovian. We recently studied a very simple and ubiquitous diffusion-controlled phenomenon - ion recombination reactions in polar solvent - where the free energy surface consists of only two (solvent-separated reactant ion pair and neutral product) states (Singh et al. JPCB 2010). However, many rate processes (e.g., enzymatic reactions) involve a complex free energy landscape with intermediate states between the reactant and the product states. Using computational and theoretical (based on nonequilibrium statistical mechanics) modeling of the system, we are probing dynamic solvent effects and the validity of the existing rate theories in describing the diffusion-controlled processes involving complex a free energy surface consisting of many intermediate states.

Englander et al. PNAS (2014)