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In this talk, I will outline some of my past and ongoing research projects on statistical mechanical modeling of complex systems. First, I will briefly summarize my work on some fundamental problems in condensed matter physics-- packing of anisotropic objects and the origin of dynamical slowdown in glass forming supercooled liquids. The primary focus would be on recent developments to beat dynamical sluggishness present in both the systems. Next, I will quickly move on to the main part of my talk dealing with problems in material science where statistical mechanics has a lot to offer. We will start by constructing simple equilibrium polymerization models parameterized by first principle quantum mechanical calculations, to reveal thermodynamics and kinetics of gas capture within a class of porous crystalline materials, namely Metal-organic frameworks (MOFs). They are excellent candidates for gas capture and separation applications. Among them, MOFs with cooperative or step-like adsorption property, usually attributed to an underlying phase transition, permits more efficient gas uptake and removal than those with the more usual non-cooperative (Langmuir-type) adsorption. Using exact solution and computer simulations, we derive a general mechanism of obtaining step-like adsorption isotherm in the absence of a phase transition. We further establish the connection between thermodynamics and kinetics to explain the origin of (experimentally observed) hysteresis in these materials. Such an efficient equilibrium cooperative adsorption mechanism, however, can not be realized for all desired gas-framework combinations. Using a diffusion-binding simulation model and the emergent gas-separation mechanism, we explore the possibility of selective gas capture under nonequilibrium conditions.
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