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  • 1
    ISSN: 1572-9567
    Keywords: freezing ; hard disks ; Ornstein-Zernike equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present a new freezing theory based on the inhomogeneous Ornstein-Zernike equation. The new theory is nonperturbative, in the sense that crystal and liquid are treated at the same level of approximation. This is in contrast to the popular density functional theory of freezing, which uses the liquid as a reference state for perturbation theory. Due to the demanding nature of the numerical method, preliminary calculations are presented for a model problem — which, in the strictest sense, is unphysical — namely, the freezing of hard disks in two dimensions. We also explore a generalized Percus-Yevick closure appropriate for the crystal.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1520-5126
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 97 (1992), S. 2153-2155 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We evaluate the entropy of several binary hard sphere fluid mixtures using two approximate expressions that require as input only the pair correlation functions, gαβ(r). An approximation based on the incompressible limit is found to be accurate for medium to high density fluids.
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 97 (1992), S. 7716-7729 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The integral equation theory for a model 2–2 electrolyte is studied in detail. In this model electrolyte, the ions are assumed to be the same size, and interact via a continuous potential energy which behaves as the Coulomb potential at large distances and an inverse ninth power repulsion at short distances. The ions are embedded in a dielectric continuum of fixed dielectric constant, here taken to be 78.3 ε0 in order to model water at 25 °C. The bridge function for this model is studied as a function of concentration (a) for six proposed closures, and (b) via "exact'' inversion of data from computer simulations. A proposed closure derived from examination of the inverted bridge function yields predictions in good agreement with computer simulations. We emphasize the importance of choosing an "optimized'' long-range potential, as opposed to the traditional Coulomb choice. A simple functional form for the bridge function results from this optimized choice of long-range potential.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 96 (1992), S. 8450-8459 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The role molecular flexibility plays in the chemistry of bulk water and ionic solutions is evaluated using molecular dynamics simulations. For simplicity the flexible water model used here is the revised central force (CF) model of Stillinger and Rahman [J. Chem. Phys. 68, 666 (1977)]. A companion, rigid central force (RCF) model is invented to provide the most accurate average description of CF water. Discussion of the role of flexibility is divided into effects due to Coulombic and non-Coulombic parts of the potential energy. The Coulombic part provides the connection between flexibility and nuclear polarizability. A variety of thermodynamic and dynamical properties of the two models are compared. These include the static dielectric constant, orientational correlation functions, self-diffusion coefficient, pressure, intermolecular energy, and pair correlation functions. The effect of flexibility is greatest for dielectric properties, but in general it is found to be small. The dielectric constant of CF water is measured to be approximately 77, in good—perhaps fortuitous—agreement with the experimental value. A variety of ionic solution properties, including the free energy and dynamics of ionic association, are reported for model sodium chloride solutions at two concentrations. For these quantities also the effect of water flexibility is found to be small.
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 5961-5966 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The translational and rotational dynamics of an aqueous ammonium ion are examined using an NVE molecular dynamics computer simulation and a rigid model of water. The linear momentum, angular momentum and reorientational autocorrelation functions of the ammonium ion have been measured. From these, the memory functions for the linear and angular momentum correlation functions are calculated. Reorientation of the ammonium ion about its center of mass shows unambiguous departure from Debye rotational behavior. The translational and rotational diffusion constants have been calculated.
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 3638-3646 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The interfaces between a bcc crystal and its melt are studied by molecular dynamics simulation. Three distinct crystal/melt interfaces, (100), (111), and (110) are studied. For all interfaces the variation with z, the coordinate perpendicular to the interfacial plane, of the single particle density (averaged over the directions perpendicular to z) and the diffusion constant are measured. Although the 10–90 widths of the density peak-height profiles differ significantly among the three interfaces (6, 9, and 7 molecular diameters, respectively), the corresponding 10–90 widths of the diffusion constant profiles are nearly identical with a common value of about four molecular diameters. This leads to the conclusion that the differences in apparent structural width are due primarily to geometric considerations and not to differences in average local molecular environments.
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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 7854-7860 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present a formalism for molecular liquids in which the interatomic force depends upon both the internuclear separation and on internal, quantum degrees of freedom. The internal degrees of freedom are spin and orbital angular momenta, and they are eventually approximated to yield a purely classical function for the interatomic interaction. We show that the interpolative character of the classical energy function is derived from a resolution of a model Hamiltonian. The formal derivation of the potential energy function is illustrated with an explicit calculation for some nonpolar and polar systems, and with discussion for ionic systems. Our derivation emphasizes an alternative to the ever more popular three-body potential energy functions for statistical mechanics studies of liquids. We outline the path to be followed in computer simulations and analytical studies of liquids with our pairwise-additive, spin-dependent potential energy functions.
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  • 9
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 1901-1908 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The Ornstein–Zernike equation is solved in the mean spherical approximation (MSA) for a model liquid with an internal degree of freedom. The spatial variation of the potential outside the hard core is given by a combination of Yukawa potentials. We compute the equations of state from analytic expressions derived in this work, and also the spin-dependent pair correlation function and its value averaged over the internal degrees of freedom. The model system displays an increase of the pressure over the hard-sphere system, and the pair correlation function that depends on the internal degrees of freedom shows a structure consistent with the effect of such degrees of freedom on interparticle interactions. The usual strengths and inconsistencies of the MSA are observed in this work. These calculations provide a starting point, other than computer simulations, for treatment of liquid models with many internal degrees of freedom, for the study of polar liquids and chemical reactions in solution.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 89 (1988), S. 4315-4324 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The atom–atom pair correlation functions and thermodynamics of the central force model of water, introduced by Lemberg, Stillinger, and Rahman, have been calculated accurately by an integral equation method which incorporates two new developments. First, a rapid new scheme has been used to solve the Ornstein–Zernike equation. This scheme combines the renormalization methods of Allnatt, and Rossky and Friedman with an extension of the trigonometric basis-set solution of Labik and co-workers. Second, by adding approximate "bridge'' functions to the hypernetted-chain (HNC) integral equation, we have obtained predictions for liquid water in which the hydrogen bond length and number are in good agreement with "exact'' computer simulations of the same model force laws. In addition, for dilute ionic solutions, the ion–oxygen and ion–hydrogen coordination numbers display both the physically correct stoichiometry and good agreement with earlier simulations. These results represent a measurable improvement over both a previous HNC solution of the central force model and the ex-RISM integral equation solutions for the TIPS and other rigid molecule models of water.
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