Sunil P. Singh

Hydrodynamic correlations and diffusion coefficient of star polymers in solution.

The center-of-mass dynamics of star polymers in dilute solution is analyzed by hybrid mesoscale simulations. The fluid is modeled by the multiparticle collision dynamics approach, a particle-based hydrodynamic simulation technique, which is combined with molecular dynamics simulations for the polymers. Star polymers of various functionalities are considered. We determine the center-of-mass velocity correlation functions, the corresponding mean square displacements, and diffusion coefficients. The velocity correlation functions exhibit a functionality-dependent and structure-specific intermediate time regime, with a slow decay. It is followed by the long-time tail t(-3/2), which is solely determined by the fluid. Infinite-system-size diffusion coefficients are determined from the velocity correlation function by a combination of simulation and analytical results, as well as from the center-of-mass mean square displacement for various systems sizes and extrapolation. In terms of the hydrodynamic radius, the star polymer hydrodynamic diffusion coefficient exhibits the same universal system-size dependence as a spherical colloid. The functionality dependence of the ratio of hydrodynamic radii and the radii of gyration agrees well with experimental predictions.

A density functional model for the binary crystal of hard spheres with vacancies

We study the stability of a binary mixture of hard spheres in the crystalline state in which a small fraction of lattice sites in the solid structure are vacant. The optimum vacancy concentration is obtained by minimizing the free energy of the inhomogeneous solid state. We use the modified weighted density functional approximation to compute the free energy. The necessary input for the theory is the thermodynamic properties of the homogeneous state of the mixture and is obtained from the solutions of the corresponding Percus-Yevick integral equations for the binary system. We compute the free energy for the crystal having two kinds of ordered structures in which (i) both the species lie in a disordered manner on a single face-centered-cubic lattice and (ii) each of the two species lie on a separate cubic lattice. Our theoretical model obtains equilibrium vacancy fraction of O(10(-5)) near the freezing point in both cases. The vacancy concentration decreases with the increase of density in both cases.

Nonequilibrium dynamics in an amorphous solid

The nonequilibrium dynamics of an amorphous solid is studied with a soft-spin model. We show that the aging behavior in the glassy state follows a modified Kohlrausch-Williams-Watts form similar to that obtained in Lunkenheimer [Phys. Rev. Lett. 95, 055702 (2005)] from analysis of the dielectric loss data. The nature of the fluctuation-dissipation theorem violation is also studied in time as well as correlation windows.

The hopping process of a vacancy defect in a crystal

The average time associated with the movement of a vacancy defect between two adjacent sites is estimated using a classical density functional model. Our calculation shows that this time is much faster than that of the typical vacancy diffusion process over longer distances in the crystal lattice. The process of movement of a vacancy defect from one lattice site to its neighbor is depicted as a series of readjustments in the local crystalline structure. The free energy barrier to this process is obtained here using the classical density functional theory. The theory requires the structure factor of the corresponding homogeneous liquid and can therefore be studied with the basic interaction potential as the only necessary input. In this work we consider mono-atomic systems interacting respectively with hard sphere and Lennard-Jones potentials. We show that as the location of the point vacancy shifts from a lattice site to its nearest neighbor on the face-centered cubic lattice, the corresponding free energy curve constitutes two symmetric minima separated by a barrier. The height of this barrier is obtained in terms of the interaction potential from the present density functional theory model. Assuming a low concentration of vacancies, the escape rate of the vacancy defect from one lattice site to the adjacent one is then estimated by using Kramers theory for crossing the energy barrier.