Abstracts

I investigate the system-size dependence of the thermodynamic properties of classical Coulomb systems in three dimensions with periodic boundary conditions. The system of interest at given density, composition, and temperature is assumed to behave as a conductor in the thermodynamic limit V [right pointing arrow] [infinity symbol], where V is the volume of the unit cell. The leading-order finite-size correction to the Coulomb energy per unit volume is shown to be 1/2k[subscript B]T/V (with k[subscript B]T the thermal energy). This correction is the classical analog of the correction to the potential energy of the electron gas at zero temperature derived by Chiesa et al. [Phys. Rev. Lett. bf{97}, 076404 (2006)]. Also considered is the system-size dependence of the change in free energy due to the insertion of a localized charge distribution of net charge Q [does not equal] 0, which serves as a prototype for the size dependence of the chemical potential of an ion. It is found that the finite-size correction to the charging free energy is of order1/V. If the response of the system is linear, the leading-order correction is given by 1/2aQx/V, where x is the fourth moment of the static charge response function of the bulk fluid, and a is a constant that depends on the choice of units. This formula may provide a useful estimate of the system-size dependence of charging free energies (or ionic chemical potentials) when paired with an approximate theory that gives a closed-form expression for x. Finite-size corrections to excess thermodynamic properties obtained from the linearized Debye Huckel theory are reviewed; these analytic expressions are valid for ionic systems in the low-density limit. A subset of the theoretical results are compared with computer simulation data for two simple models: the classical one-component plasma and a symmetric primitive-model electrolyte solution. This work may have methodological implications for simulation studies of various models of charged fluids.Advisors/Committee Members: Sanchez, Isaac C., 1941- (advisor), Freeman, Benny D (committee member), Ganesan, Venkat (committee member), Makarov, Dmitrii E (committee member), Truskett, Thomas M (committee member).