Thermodynamic Properties Of Hard Sphere Fluid Near Hard Surface

<p dir="ltr">The system of hard-spheres is a commonly used model in statistical mechanics to ,describe the quasi-universal structure, the phase behaviour, physical properties and the particle dynamics of a wide range of systems such as atomic liquids and solids. The model of hard-spheres or hard disks (hard-sphere in 2d) forms an important part in the history of computation, as it is one of the first systems to be simulated by a computer. A hard-sphere fluid in a cavity or a particle solvated in hard-sphere fluid both describe a system at curved wall (with negative or positive curvatures). The curvature dependence of the thermodynamics of a hard-sphere system is a crucial aspect in understanding physical processes. In this work, I presented a picture of this dependence, where it was shown that the surface free energy of a con?ned hard-sphere system is linear in curvature with deviations only at high negative curvatures and high densities. The slope was the same as the positive curvature case studied before. Results for two different confinements (spherical and cylindrical) of different sizes were obtained using grand canonical Monte Carlo simulations. The excess chemical potential of a test hard-sphere immersed in a hard-sphere fluid, is traditionally obtained by Widom's particle insertion method, In this work I presented a more precise way to calculate this quantity using the insertion probability by applying the inclusion-exclusion principle. Those results allow me to derive higher-order terms in the expansion of the chemical potential.</p>