Analysis of probability of inserting a hard spherical particle with small diameter in hard-sphere fluid.

The probability of inserting, without overlap, a hard spherical particle of diameter σ in a hard-sphere fluid of diameter σ0 and packing fraction η determines its excess chemical potential at infinite dilution, μex(σ, η). In our previous work [R. L.

Chemical potential and surface free energy of a hard spherical particle in hard-sphere fluid over the full range of particle diameters.

The excess chemical potential μ(σ, η) of a test hard spherical particle of diameter σ in a fluid of hard spheres of diameter σ and packing fraction η can be computed with high precision using Widom's particle insertion method [B. Widom, J. Chem.

Cleaving Method for Molecular Crystals and Its Application to Calculation of the Surface Free Energy of Crystalline β-d-Mannitol at Room Temperature.

Calculation of the surface free energy (SFE) is an important application of the thermodynamic integration (TI) methodology, which was mainly employed for atomic crystals (such as Lennard-Jones or metals). In this work, we present the calculation of the SFE of a molecular crystal using the cleaving technique which we implemented in the LAMMPS molecular dynamics package. We apply this methodology to a crystal of β-d-mannitol at room temperature and report the results for two types of force fields belonging to the GROMOS family: all atoms and united atoms.

Shuttleworth equation: A molecular simulations perspective.

Even though the study of interfacial phenomena can be traced back to Laplace and was given a solid thermodynamic foundation by Gibbs, it appears that some concepts and relations among them are still causing some confusion and debates in the literature, particularly for interfaces involving solids. In particular, the definitions of the concepts of interfacial tension, free energy, and stress and the relationships between them sometimes lack clarity, and some authors even question their validity. So far, the debates about these relationships, in particular the Shuttleworth equation, have taken place within the framework of classical thermodynamics.

Surface free energy of a hard-sphere fluid at curved walls: Deviations from morphometric thermodynamics.

We report molecular-dynamics (MD) simulation results for the surface free energy of a hard-sphere fluid at cylindrical and spherical hard walls of different radii. The precision of the results is much higher than that in our previous study [B. B.

Properties of the hard-sphere fluid at a planar wall using virial series and molecular-dynamics simulation.

We study the hard-sphere fluid in contact with a planar hard wall. By combining the inhomogeneous virial series with simulation results, we achieve a new benchmark of accuracy for the calculation of surface thermodynamics properties such as surface adsorption Γ and the surface free energy (or surface tension), γ. We briefly introduce the problem of choosing a position for the dividing surface and avoid it by proposing the use of alternative functions to Γ and γ that are independent of the adopted frame of reference.

Reduction of SO(2) symmetry for spatially extended dynamical systems.

Spatially extended systems, such as channel or pipe flows, are often equivariant under continuous symmetry transformations, with each state of the flow having an infinite number of equivalent solutions obtained from it by a translation or a rotation. This multitude of equivalent solutions tends to obscure the dynamics of turbulence. Here we describe the "first Fourier mode slice," a very simple, easy to implement reduction of SO(2) symmetry.

Interfacial free energy of a hard-sphere fluid in contact with curved hard surfaces.

Using molecular-dynamics simulation, we have calculated the interfacial free energy γ between a hard-sphere fluid and hard spherical and cylindrical colloidal particles, as functions of the particle radius R and the fluid packing fraction η=ρσ(3)/6, where ρ and σ are the number density and hard-sphere diameter, respectively. These results verify that Hadwiger's theorem from integral geometry, which predicts that γ for a fluid at a surface, with certain restrictions, should be a linear combination of the average mean and Gaussian surface curvatures, is valid within the precision of the calculation for spherical and cylindrical surfaces up to η ≈ 0.42.

Ice Ih-Water Interfacial Free Energy of Simple Water Models with Full Electrostatic Interactions.

We employ the cleaving approach to calculate directly the ice Ih-water interfacial free energy for the simple models of water, TIP4P, TIP4P-Ew, and TIP5P-E, with full electrostatic interactions evaluated via the Ewald sums. The results are in good agreement with experimental values, but lower than previously obtained for TIP4P-Ew and TIP5P-E by indirect methods. We calculate the interfacial free energies for basal, prism, and {112̅0} interfaces and find that the anisotropy of the TIP5P-E model is different from that of the TIP4P models.

A molecular dynamics study of Young's modulus change of semi-crystalline polymers during degradation by chain scissions.

This paper presents a molecular dynamics study on the change in Young's modulus of semi-crystalline polymers during degradation by chain scissions, which is relevant to the study of mechanical properties of biodegrading polymers. Using a simple polymer model whose structural and mechanical properties are similar to that of a commonly used biodegrading polymer poly(glycolic acid), we combine molecular dynamics and Monte Carlo to model a system of two polymer crystals separated by an amorphous region between them. The polymer chains in the amorphous region are cut randomly to mimic hydrolysis chain scissions.

Hard spheres revisited: accurate calculation of the solid-liquid interfacial free energy.

We revise the earlier [R. L. Davidchack and B.

Calculation of the interfacial free energy of a fluid at a static wall by Gibbs-Cahn integration.

The interface between a fluid and a static wall is a useful model for a chemically heterogeneous solid-liquid interface. In this work, we outline the calculation of the wall-fluid interfacial free energy (gamma(wf)) for such systems using molecular simulation combined with adsorption equations based on Cahn's extension of the surface thermodynamics of Gibbs. As an example, we integrate such an adsorption equation to obtain gamma(wf) as a function of pressure for a hard-sphere fluid at a hard wall.

On the use of stabilizing transformations for detecting unstable periodic orbits in high-dimensional flows.

We explore the possibility of extending the stabilizing transformations approach [J. J. Crofts and R.

Determination of the solid-liquid interfacial free energy along a coexistence line by Gibbs-Cahn integration.

We calculate the solid-liquid interfacial free energy gamma(sl) for the Lennard-Jones (LJ) system at several points along the pressure-temperature coexistence curve using molecular-dynamics simulation and Gibbs-Cahn integration. This method uses the excess interfacial energy (e) and stress (tau) along the coexistence curve to determine a differential equation for gamma(sl) as a function of temperature. Given the values of gamma(sl) for the (100), (110), and (111) LJ interfaces at the triple-point temperature (T( *)=kT/varepsilon=0.

Langevin thermostat for rigid body dynamics.

We present a new method for isothermal rigid body simulations using the quaternion representation and Langevin dynamics. It can be combined with the traditional Langevin or gradient (Brownian) dynamics for the translational degrees of freedom to correctly sample the canonical distribution in a simulation of rigid molecules. We propose simple, quasisymplectic second-order numerical integrators and test their performance on the TIP4P model of water.

Direct calculation of solid-liquid interfacial free energy for molecular systems: TIP4P ice-water interface.

By extending the cleaving method to molecular systems, we perform direct calculations of the ice Ih-water interfacial free energy for the TIP4P model. The values for the basal, prism, and {112[over]0} faces are 23.3+/-0.

The anisotropic hard-sphere crystal-melt interfacial free energy from fluctuations.

We have calculated the interfacial free energy for the hard-sphere system, as a function of crystal interface orientation, using a method that examines the fluctuations in the height of the interface during molecular dynamics simulations. The approach is particularly sensitive for the anisotropy of the interfacial free energy. We find an average interfacial free energy of gamma=0.

Direct calculation of the crystal-melt interfacial free energy via molecular dynamics computer simulation.

We review our recent work on the direct calculation of the interfacial free energy, gamma, of the crystal-melt interface via molecular dynamics computer simulation for a number of model systems. The value of gamma as a function of crystal orientation is determined using a thermodynamic integration technique employing moving cleaving walls [Phys. Rev.

Crystal structure and interaction dependence of the crystal-melt interfacial free energy.

We examine via molecular simulation the dependence of the crystal-melt interfacial free energy gamma on molecular interaction and crystal structure (fcc vs bcc) for systems interacting with inverse-power repulsive potentials, u(r)=epsilon(sigma/r)(n), 6< or =n< or =100. Both the magnitude and anisotropy of gamma are found to increase as the range of the potential increases. Also we find that gamma(bcc) View Article and Find Full Text PDF