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  • 1
    Electronic Resource
    Electronic Resource
    Solution of the associative mean spherical approximation for a multicomponent dimerizing hard-sphere multi-Yukawa fluid (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 1135-1142 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The analytical solution of the associative mean spherical approximation (AMSA) for a Yukawa dimerizing multicomponent hard-sphere fluid is derived. The general multi-Yukawa case is discussed. The simpler one-Yukawa case with factorizable coefficients is explicitly solved. As in the previously discussed electrolyte case the solution of the AMSA reduces to the solution of only one nonlinear algebraic equation for the scaling parameter ΓB. The analytical results for the AMSA closure is illustrated by numerical examples and computer simulation for the one-component one-Yukawa dimerizing fluid. Good agreement between theoretical and computer simulation results was found for both the thermodynamic properties and the structure of the system. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.481892
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  • 2
    Electronic Resource
    Electronic Resource
    Erratum: "Multicomponent mixture of charged hard-sphere chain molecules in the polymer mean-spherical approximation" [J. Chem. Phys. 115, 540 (2001)] (2002)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 116 (2002), S. 8637-8637 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1471902
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  • 3
    Electronic Resource
    Electronic Resource
    Multicomponent mixture of charged hard-sphere chain molecules in the polymer mean-spherical approximation (2001)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 115 (2001), S. 540-551 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The analytical solution of the recently proposed ideal chain polymer mean-spherical approximation [Kalyuzhnyi, Mol. Phys. 94, 735 (1998)] is presented for the multicomponent mixture of charged hard-sphere linear chain flexible molecules. The solution applies to any mixture of chain molecules with arbitrary distribution of the charge and size of the beads along the molecular backbone. Closed form analytical expressions for the internal energy, Helmholtz free energy, chemical potentials, and pressure are derived. By way of illustration thermodynamical properties of several versions of the fluid of charged chain molecules of different length, including the molecules with uniform, diblock, and alternating distribution of the charge, are studied. Theoretical predictions are in reasonable agreement with available computer simulation predictions. We also present the liquid–gas phase diagrams for systems with diblock and alternating distribution of the charge. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1376426
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  • 4
    Electronic Resource
    Electronic Resource
    Primitive models of chemical association. I. Theory and simulation for dimerization (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 7939-7952 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The structure and thermodynamic properties of a model of associating particles that dimerize into fused-sphere dumbbells are investigated by MC simulation and by integral-equation theory. The model particles, introduced by Cummings and Stell, associate as a result of shielded attractive shells. The integral equation theories are of two types. The first is an extension of Wertheim's associative Percus–Yevick (APY) equation to the case of the shielded sticky shell model, which is the limiting case of the shielded attractive shell model that can be handled analytically. The second is the extended mean spherical approximation (EMSA) of Zhou and Stell applied to the shielded sticky shell model. In the case of partially associated systems, the EMSA requires as input the equilibrium association constant, which is obtained here using an exact relation between monomer density and a cavity correlation function, together with an equation of state due to Boublik. The structure obtained from the EMSA is in good agreement with the predictions of the MC simulation over a substantial density range that includes liquid-state densities, while the thermodynamic input from Boublik's equation is in excellent agreement with the simulation results for all densities. Predictions of the APY approximation are also in good agreement with the simulation results as long as the density of the system is relatively low or, at high density, when the hard-core volume of a dimer is not substantially less than that of the two free monomers from which it is formed. There is an intermediate density range in which neither integral-equation theory gives correlation functions of high quantitative accuracy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.468221
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  • 5
    Electronic Resource
    Electronic Resource
    Multidensity integral equation theory for highly asymmetric electrolyte solutions (1995)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 102 (1995), S. 5770-5780 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Integral equation theory based on a recently developed multidensity formalism [Mol. Phys. 78, 1247 (1993)] is proposed to study highly asymmetric electrolyte (polyelectrolyte) solutions. The system studied consists of large and highly charged polyions and small counterions having one or two elementary charges. The potential energy of interaction between counterions and polyions is separated into two parts, a strongly attractive part responsible for the association and a nonassociative part. Due to the strong asymmetry in size we can treat each counterion as bondable to a limited number of polyions n, while each polyion can bond arbitrary number of counterions. In our cluster expansion appropriate to the problem the diagrams appearing in the activity expansion of the one-point counterion density are classified in terms of the number of associating bonds incident upon the labeled white counterion circle. The corresponding diagrams for the one-point polyion density are classified in the usual way. A generalized version of the Ornstein–Zernike equation, which involves n+1 counterion densities and one polyion density, together with hypernetted-chain-like (HNC) closure conditions are derived. The simplest two-density version of the theory yields very good agreement with new and existing computer simulations for both thermodynamical and structural properties of these systems. This good agreement extends into the region of parameter space where the ordinary HNC approximation does not have a convergent solution. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.469308
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  • 6
    Electronic Resource
    Electronic Resource
    Integral equation theory for associating liquids: Weakly associating 2–2 electrolytes (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 9151-9164 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Formation of ion pairs in a 2–2 aqueous electrolyte is studied using a generalization of Wertheim's formalism, designed to treat explicitly association between molecules. The ions in the model electrolyte interact via a continuous potential energy (unlike previous studies), which combines the long-range Coulomb interaction with a soft repulsive potential at short distances. Both the derivation of new equations, including approximately the formation of trimers, and numerical solution of the resultant equations are presented here. The predictions of the theory are in excellent agreement with new molecular dynamics (MD) simulations of the same electrolyte. Explicit predictions are made for the fraction of monomers, dimers, and trimers in the electrolyte, over the full range of concentrations of interest for association, from 0.001 to 0.2 M.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.461195
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  • 7
    Electronic Resource
    Electronic Resource
    Computer simulation of a model 2–2 electrolyte: Multiple time-step molecular dynamics (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 9165-9171 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A popular model of a 2–2 electrolyte is simulated using a multiple time-step molecular dynamics algorithm. Many authors have used this particular model to test approximate statistical mechanical theories. The ions are assumed to be the same size, and to interact via a continuous potential which behaves as a Coulomb potential at large distances and as an inverse ninth power repulsion at short distances. The ions are embedded in a dielectric continuum of fixed dielectric constant, here taken to be 78.358 to model water at 25 °C. The multiple time-step algorithm outlined here is essential to the success of the simulation. The structure, thermodynamics, and clustering of ions in the electrolyte are examined over the full range of concentrations. Significant corrections are found to earlier Monte Carlo simulations at the concentration 0.005 M, and new results are presented at the concentration 0.001 M.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.461196
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  • 8
    Electronic Resource
    Electronic Resource
    Primitive models of chemical association. IV. Polymer Percus–Yevick ideal-chain approximation for heteronuclear hard-sphere chain fluids (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 6525-6534 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We continue here our series of studies in which integral-equation theory is developed and used for the monomer-monomer correlation functions in a fluid of multicomponent freely jointed hard-sphere polymers. In this study our approach is based on Wertheim's polymer Percus–Yevick (PPY) theory supplemented by the ideal-chain approximation; it can be regarded as a simplified version of Wertheim's four-density PPY approximation for associating fluids considered in the complete-association limit. The numerical procedure of this simplified theory is much easier than that of the original Wertheim's four-density PPY approximation, but the degree of accuracy is reduced. The theory can also be regarded as an extension of the PPY theory for the homonuclear polymer system proposed by Chang and Sandler [J. Chem. Phys. 102, 437 (1995)]. Their work is based upon a description of a system of hard-sphere monomers that associate into a polydisperse system of chains of prescribed mean length. Our theory instead directly describes a multicomponent system of associating monomers that form monodisperse chains of prescribed length upon complete association. An analytical solution of the PPY ideal-chain approximation for the general case of a multicomponent mixture of heteronuclear hard-sphere linear chain molecules is given. Its use is illustrated by numerical results for two models of copolymer fluids, a symmetrical diblock copolymer system, and an alternating copolymer system. The comparison with Monte Carlo simulations is given to gauge the accuracy of the theory. We find for the molecules we study here that predictions of our theory for heteronuclear chain systems have the same degree of accuracy as Chang and Sandler's theory for homonuclear chain systems. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.476059
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  • 9
    Electronic Resource
    Electronic Resource
    Primitive models of chemical association. II. Polymerization into flexible chain molecules of prescribed length (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 106 (1997), S. 1940-1949 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The structural properties of the totally flexible sticky two-point (S2P) model for polymerization into chain molecules of fixed length are studied. The model is represented by an n-component mixture of hard spheres of the same size with species 2,...,n−1 bearing two attractive sticky sites A and B, randomly distributed on the surface. The hard spheres of species 1 and n have only one site per particle, site B for species 1 and site A for species n. Due to the specific choice for the attractive interaction, which is present only between site B of the particles of species a and site A of the particles of species a+1, this version of the S2P model represents an associating fluid that polymerizes into freely jointed tangent hard-sphere chain molecules. The correlation functions of this model are studied at all degrees of association using a recently obtained general solution of the polymer Percus–Yevick (PPY) approximation [Yu. Kalyuzhnyi and P. Cummings, J. Chem. Phys. 103, 3265 (1995)]. Comparison of the results of the present theory in the complete association limit with corresponding computer-simulation results and results of other theories is presented and discussed. The complete-association results constitute a quantitatively successful theory of the mean monomer–monomer distribution functions for n≤16 but for n=50 these functions are no longer quantitatively accurate. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.473331
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  • 10
    Electronic Resource
    Electronic Resource
    Thermodynamics of the associative mean spherical approximation for the fluid of dimerizing particles (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 3709-3715 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Analytical expressions for the thermodynamic properties of the n-component mixture of dimerizing hard spheres with a long-range potential are derived within the associative mean spherical approximation. The derivation is based on the extension of the Høye–Stell scheme [J. Chem. Phys. 67, 439 (1977)] in the framework of the Wertheim's two-density formalism for associating fluids and the exponential approximation recently suggested by Bernard and Blum [J. Chem. Phys. 104, 4746 (1996)]. In the complete association limit, in which the two-density associative mean spherical approximation reduces to Chandler–Silbey–Ladanyi mean spherical approximation, results of the present study coincide with the corresponding results obtained earlier by the other authors. Closed form expressions for the Helmholtz free energy, chemical potential, and pressure of the complete association version of the electrolyte restricted primitive model with the additional sticky-point attraction are derived. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.475764
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