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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 7589-7590 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: © 1999 American Institute of Physics.
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 7360-7370 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The potential distribution theorems for the test particles provide a connection to the chemical potentials and the cavity distribution functions y(r) much used in molecular theory. These relations can be capitalized for establishing the closure relations for the Ornstein–Zernike equation. In this study, we formulate a class of closures with built-in flexibilities in order to satisfy the potential distribution theorems (or the related zero separation theorems) and thermodynamic consistency. The theory is self-contained within the integral equation framework. We test it on the Lennard-Jones fluid over ranges of temperatures (down to T*=0.81) and densities (up to ρ*=0.9). To achieve self-sufficiency, we exploit the connections offered by writing down n members of the mixture Ornstein–Zernike equations for the coincident oligomers up to n-mers. Then the potential distribution theorems generate new conditions for use in determining the bridge function parameters. Five consistency conditions have been identified (three thermodynamic and two based on zero-separation values). This self-consistency allows for bootstrapping and generation of highly accurate structural and thermodynamic information. The same procedure can potentially be extended to soft-sphere potentials other than the Lennard-Jones type. © 1997 American Institute of Physics.
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 103 (1995), S. 9388-9396 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We evaluate a number of current closure relations used in the integral equations for hard sphere fluids, such as the Percus–Yevick, Martynov–Sarkisov, Ballone–Pastore–Galli–Gazillo, and Verlet modified (VM) closures with respect to their abilities of satisfying the zero-separation theorems for hard spheres. Only the VM closure is acceptable at high densities (ρ∼0.7), while all fail at lower densities (lim 0〈ρ〈0.5). These shall have deleterious effects when used in perturbation theories, especially at low densities. To improve upon this, we propose a closure, ZSEP, that is flexible and suited to satisfying the known zero separation theorems [e.g., the ones for the cavity function y(0) and the indirect correlation γ(0), and others for their derivatives dy(0)/dr, etc.], plus the pressure consistency condition. This particular closure, after numerical solution with the Ornstein–Zernike equation, is shown to perform well at high densities (ρ∼0.9) as well as low densities (0.1〈ρ〈0.5) for the cavity function y(r), the pair correlation function g(r), and the bridge function B(r). Derived thermodynamic properties: pressure, isothermal compressibility, and chemical potential are also highly accurate. Comparison with available Monte Carlo data bears this out. We have formulated a "consistent'' and accurate integral equation theory for hard spheres over a wide range of density states. © 1995 American Institute of Physics.
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 8058-8067 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present a class of closures specifically designed to satisfy the zero-separation theorems for the correlation functions y(r) (the cavity function), γ(r)=h(r)−C(r) (the indirect correlation), and B(r) (the bridge function) at coincidence r=0 for soft-sphere pair potentials. The rationale is to ensure the correct behavior of these correlation functions inside the core r〈σ. Since the coincidence theorems implicate the thermodynamic properties of the bulk fluid: the isothermal compressibility, the internal energy and the chemical potentials, we can hopefully enforce consistency between the structure and thermodynamic properties. We solve the Ornstein–Zernike equation for the Lennard-Jones molecules where plentiful Monte Carlo data are available for testing. It turns out that not only consistency is achieved, we also obtain accurate structures: the pair correlation function g(r), the cavity function, and the bridge function for wide ranges of fluid states (0.72〈T*〈1.5, ρ*〈0.9). Comparison with MC data attests to the accuracy. The closure of the zero-separation type (ZSEP), is sufficiently robust and flexible to ensure not only fulfillment of the zero-separation theorems but also pressure consistency. Success with the Lennard-Jones potential implies its applicability to other similar soft-sphere potentials. © 1996 American Institute of Physics.
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  • 5
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Industrial & engineering chemistry research 29 (1990), S. 977-988 
    ISSN: 1520-5045
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 114 (2001), S. 7109-7117 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new self-consistent closure is formulated for the additive hard sphere mixtures at high densities (η=0.49) within the Ornstein–Zernike integral equation approach. Diameter ratios (σSS/σBB) from 0.3 to 0.9 and several compositions are examined. The consistencies include the thermodynamic ones (e.g., pressure consistency, and Gibbs–Duhem relation), and the structural ones (e.g., the zero-separation theorems). The bridge functions have built-in "flexibility" that can be adapted to the consistency requirements. Comparison with Monte Carlo simulation shows that the present closure yields highly accurate results. The contact values and zero-separation values are more accurate than those obtained from the conventional closures, such as the Percus–Yevick and Martynov–Sarkisov closures. A structural theory for hard sphere mixtures has been formulated that is accurate and consistent at the same time. © 2001 American Institute of Physics.
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 97 (1992), S. 8606-8616 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A closed form for the chemical potentials of a fluid is presented that involves only integrals of the molecular distribution functions at the given state, (e.g., temperature and density). Thus no Kirkwood charging or thermodynamic integration is needed. An exact formula from a previous study is reanalyzed and a diagrammatical representation of the correlation functions involved is given. This representation involves, in addition to the usual total correlations, direct correlations, and the bridge function, B(r), a new star function, S(r). Analysis shows that the integral of the star function is the primitive of the bridge function, i.e., its functional derivative yields B(r). It is also related to the free-energy functional F[ρ] in density-functional theories for nonuniform systems. Methods for estimating the star function are given. Tests on uniform hard-sphere fluid are carried out to demonstrate the new formulas. We have examined several current closures: the Percus–Yevick, Martynov–Sarkisov, Ballone–Pastore–Galli–Gazzillo, and a Verlet-modified (VM) closure. The VM approach gives the best reproduction of the bridge function. Much improved results are obtained for the chemical potentials of hard spheres at densities ρd3 ranging from 0.3 to 0.85.
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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 2458-2464 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The possible connection between the equilibrium structure of a solution and the chemical reaction dynamics that occur in that solution has been discussed by Adelman and co-workers. In this work, we present a computational demonstration of this connection using molecular dynamics simulations and the generalized Langevin equation (GLE). A favorable example of a reaction loosely based on thermally activated Cl+Cl2→Cl2+Cl in argon solvent is used for this demonstration by (1) computing equilibrium solution structural information in terms of the Ar–Ar and Ar–Cl radial distribution functions, both from integral equations and from molecular dynamics; (2) deriving a memory function for Cl in argon solvent from the radial distribution functions and the Ar–Cl potential; and (3) using this memory function in a simple GLE to compute the dynamics of the reaction. Energy flow results both for climbing and descending the barrier are in gratifying agreement with the dynamics of the same reaction as computed by full deterministic molecular dynamics.
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  • 9
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 3114-3131 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Presented are the results of testing the method for estimating chemical potentials which was described in paper I. The method, which is based on scaled particle theory, provides accurate chemical potentials in mixtures of softly repulsive particles when used with the Rogers–Young integral equation. Calculated excess Gibbs energies agreed with simulations to an average of −0.67% for 2:1 diameter ratio mixtures. The method provides approximate results in Lennard-Jones mixtures when used with the hybrid mean spherical approximation integral equation theory. Results for supercritical isotherms reproduce simulation data to an average of −3.0%. For subcritical isotherms, vapor results are exact while liquid results are qualitatively correct. The method used with the integral equation theory correctly predicts the effect of energy ratio on the Henry's Law constant. The predicted effect of size ratio on the constant has an incorrect slope at subcritical temperatures when the solvent density is near the value for a saturated liquid. The incorrect slope results from inaccuracies in the predicted correlation functions for the fluid surrounding the test particle. The method allows estimates to be made of the work of cavity formation and of the strength of solvent–solute binding in near-critical mixtures.
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  • 10
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 477-488 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: It is shown that the potential distribution of a strong test particle leads to the zero separation values of the cavity distribution functions yab(0) in a mixture. This relation furnishes a direct means of computing by Monte Carlo simulations the coincidence values of the cavity function ln yab(0) and the potential distribution 〈exp[−βΨa−βΨb]〉. Test particle simulations have been carried out for mixtures of Lennard-Jones molecules differing considerably in size [(σab/σbb)3 =0.25, 0.5, 0.75, 1.00, 1.25, 1.50, 1.75, and 2.00] and in strength of interaction (εab/εbb =0.5, 1.0, 1.5, and 2.0). Alternative Monte Carlo methods are employed to check the statistics. In order to predict the behavior of the potential distribution, a distribution function theory, the reference hypernetted chain (RHNC) equation, is solved based on the universality of the bridge functions. Hard sphere mixtures are taken as reference fluids. The criteria recently proposed by Rosenfeld and Blum are used to select the equivalent hard sphere diameters. Close agreement with MC results is attained for most of the states considered. This provides further evidence that the RHNC equation is a reliable theory for mixtures of simple fluids.
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