Mithun K. Mitra

Theory of volume transition in polyelectrolyte gels with charge regularization

We present a theory for polyelectrolyte gels that allow the effective charge of the polymer backbone to self-regulate. Using a variational approach, we obtain an expression for the free energy of gels that accounts for the gel elasticity, free energy of mixing, counterion adsorption, local dielectric constant, electrostatic interaction among polymer segments, electrolyte ion correlations, and self-consistent charge regularization on the polymer strands. This free energy is then minimized to predict the behavior of the system as characterized by the gel volume fraction as a function of external variables such as temperature and salt concentration. We present results for the volume transition of polyelectrolyte gels in salt-free solvents, solvents with monovalent salts, and solvents with divalent salts. The results of our theoretical analysis capture the essential features of existing experimental results and also provide predictions for further experimentation. Our analysis highlights the importance of the self-regularization of the effective charge for the volume transition of gels in particular, and for charged polymer systems in general. Our analysis also enables us to identify the dominant free energy contributions for charged polymer networks and provides a framework for further investigation of specific experimental systems.

Theory of spinodal decomposition assisted crystallization in binary mixtures

We propose a general theory of crystallization of one component from an unstable mixture of two components by addressing the coupling between the spinodal decomposition associated with concentration fluctuations in the mixture and the nucleation kinetics for the crystallization. We propose that the domains created spontaneously by spinodal decomposition then present interfaces on which heterogeneous nucleation of the crystallizable component takes place with a much reduced nucleation barrier. Combining the theories of heterogeneous nucleation and spinodal decomposition kinetics, we present an analytic calculation of the nucleation rate as a function of the allowed duration of spinodal decomposition as well as the spinodal quench depth. In the present theory, shorter time evolution of spinodal decomposition or, equivalently, larger propensity of heterogeneous nucleation, results in faster crystallization. This is in contrast to the expectation of faster nucleation in more pure phases at later stages of spi...

Monte Carlo study of the molecular mechanisms of surface-layer protein self-assembly

The molecular mechanisms guiding the self-assembly of proteins into functional or pathogenic large-scale structures can be only understood by studying the correlation between the structural details of the monomer and the eventual mesoscopic morphologies. Among the myriad structural details of protein monomers and their manifestations in the self-assembled morphologies, we seek to identify the most crucial set of structural features necessary for the spontaneous selection of desired morphologies. Using a combination of the structural information and a Monte Carlo method with a coarse-grained model, we have studied the functional protein self-assembly into S(surface)-layers, which constitute the crystallized outer most cell envelope of a great variety of bacterial cells. We discover that only few and mainly hydrophobic amino acids, located on the surface of the monomer, are responsible for the formation of a highly ordered anisotropic protein lattice. The coarse-grained model presented here reproduces accurately many experimentally observed features including the pore formation, chemical description of the pore structure, location of specific amino acid residues at the protein-protein interfaces, and surface accessibility of specific amino acid residues. In addition to elucidating the molecular mechanisms and explaining experimental findings in the S-layer assembly, the present work offers a tool, which is chemical enough to capture details of primary sequences and coarse-grained enough to explore morphological structures with thousands of protein monomers, to promulgate design rules for spontaneous formation of specific protein assemblies.

Long-time growth kinetics of first order phase transitions in the presence of a boundary layer.

The late stage growth mechanism for a first order phase transition, either through nucleation growth or spinodal decomposition, is well understood to be an Ostwald ripening or coarsening process, in which larger domains grow at the expense of smaller ones. The growth kinetics in this regime was shown by Lifshitz and Slyozov to follow at(1/3) law. However, the kinetics is altered if there exists a barrier ahead of the growth front, irrespective of the physical origin of the boundary layer. We present an analytic calculation for the growth kinetics in the presence of a boundary layer, showing that in the limit of barrier-dominated growth, the domains grow with at(1/2) law. This result holds true in the dilute regime independent of whether the growing nuclei are spherical or cylindrical.

Thermodynamic behaviour of two-dimensional vesicles revisited.

We study pressurised self-avoiding ring polymers in two dimensions using Monte Carlo simulations, scaling arguments and Flory-type theories, through models which generalise the model of Leibler, Singh and Fisher (Phys. Rev. Lett. 59, 1989 (1987)). We demonstrate the existence of a thermodynamic phase transition at a non-zero scaled pressure

Phase transitions in pressurized semiflexible polymer rings.

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Asymptotic behaviour of convex and column-convex lattice polygons with fixed area and varying perimeter

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Asymptotic Behavior of Inflated Lattice Polygons

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Theory of volume transitions in polyelectrolyte gels

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Diffusion dynamics and steady states of systems of hard rods on a square lattice

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