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We present a new method to compute the absolute free energy of arbitrary solid phases by Monte Carlo simulation. The method is based on the construction of a reversible path from the solid phase under consideration to an Einstein crystal with the same crystallographic structure. As an application of the method we have recomputed the free energy of the fcc hard-sphere solid at melting. Our results agree well with the single occupancy cell results of Hoover and Ree. The major source of error is the nature of the extrapolation procedure to the thermodynamic limit. We have also computed the free energy difference between hcp and fcc hard-sphere solids at densities close to melting. We find that this free energy difference is not significantly different from zero: –0.001
A three-dimensional lattice-gas model has been used to determine the dissipative hydrodynamic interactions between spherical particles. When the particles are close together the accuracy of the lattice-gas simulations is superior to typical integral-equation solutions of the creeping-flow equations. Moreover, the computational requirements scale linearly with system size, instead of quadratically or cubically. A new set of microrules have been implemented, which simulate a constant-velocity, no-slip boundary condition at the solid–fluid surfaces. Numerical results for various drag coefficients are reported. Physics of Fluids A: Fluid Dynamics is copyrighted by The American Institute of Physics.
We have used a novel Monte Carlo method to compute the gyration radius Rg and the hydrodynamic radius RH of excluded-volume polymer chains. The hydrodynamic radius scales as Ng05s (N is the number of bonds) over at least a decade of chain lengths, whereas the gyration radius exponent is close to the theoretical value of 0.59. The anomalous behavior Of RH is well-known experimentally; it is commonly attributed to the belief that polymers in mediocre solvents are not swollen on short length scales. However, the polymer chains in our simulations are uniformly swollen on all length scales; we suggest that the discreteness of the polymer chain is sufficient to explain the behavior of RH.
An adaptation of lattice-gas cellular automata to the simulation of solid-fluid suspensions is described. The method incorporates both dissipative hydrodynamic forces and thermal fluctuations. At low solid densities, theoretical results for the drag force on a single disk and the viscosity of a suspension of disks are reproduced. The zero–shear-rate viscosity has been obtained over a range of packing fractions and results indicate that simulations of three-dimensional suspensions are feasible.
Simulations of a colloidal particle suspended in a two-dimensional fluid are reported. The dissipative and fluctuating hydrodynamic forces acting on the particle are modeled by a lattice gas. Our results indicate that large long-time tails are present in both the translational and the rotational velocity correlation functions; these are the first observations of a rotational long-time tail. The strong translational tail leads to an observable renormalization of the diffusion coefficient; our results suggest that experimental observation of the latter effect is possible.
We present an accurate new method to compute absolute free energies of molecular solids by computer simulations. As a first application, we computed the thermodynamic phase transition between the fluid phase and the orientational disordered solid phase of nitrogen at 300 K, using a well tested pair potential. The computed coexistence pressure and the volume change coincides within the error margins with the experimental values. The coexistence volume differed by 2% from the experimental value. To our knowledge these results constitutes the first numerical calculation of the thermodynamic stability for a model of a realistic molecular solid
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