Lesser Blum

Equation of state of a hard-core fluid with a Yukawa tail

We present Monte Carlo results for the equation of state of a fluid in which the intermolecular potential consists of a hard core of diameter σ and an attractive tail which is of the form of a Yukawa function, - e exp -λ(r - σ)tr with λ=1·8/σ. These results are compared with those obtained from perturbation theory, the mean spherical approximation (MSA), and three related approximation schemes. While perturbation theory works rather well for this system, the MSA is considerably less satisfactory. However, the exponential and linearized exponential modifications of the MSA and the generalized MSA all give good results for this system.

Thermodynamic properties and phase equilibria of charged hard sphere chain model for polyelectrolyte solutions

A recent thermodynamic perturbation theory for flexible polyelectrolyte solutions is extended to study thermodynamic properties and phase equilibria for polyelectrolyte solutions with different polyion, chain lengths. Osmotic pressure, activity coefficient of an individual ion (polyion or counterion) and average activity coefficient are calculated. Except for the activity coefficient of the polyion, the chain length dependence of the properties is small. Also presented are vapour-liquid equilibrium coexisting curves, vapour pressures and critical points. As the polyion chain length approaches infinity the critical properties (temperature, pressure and density) become constants.

Sticky electrolyte mixtures in the Percus-Yevick/mean spherical approximation

The analytical solution of the sticky‐electrolyte model is obtained in the mean spherical/Percus–Yecvick approximation. This model can be used to represent chemical association in electrolytes. As in the case of the simple mean spherical approximation (MSA), the general solution is given in terms of a single scaling parameter Γ, which is now also a function of the stickiness parameters. We obtain analytic expressions for the thermodynamic functions ΔA, ΔP, and ΔEex. These expressions give the correct limits when the charge is zero (Barboy–Tenne) and when the sticky parameter vanishes. A particularly simple form of the thermodynamic functions is obtained in which the expressions are identical to those of the MSA, but with a different value of Γ, which now depends on the sticky interactions.

Monte Carlo and simple theoretical calculations for ion-dipole mixtures

The mixture of charged hard spheres and dipolar hard spheres is the simplest extension of the primitive model of an electrolyte. Only a few theoretical calculations are available. Here, we report the first computer simulations for this system. The simulation calculations were performed on the Cornell super-computer with the long-range coulombic forces calculated using an Ewald resummation technique. Also, a hybrid theory based on perturbation theory, but with the high-order terms estimated from the mean spherical approximation, is developed and compared with the simulation results. Where possible, comparison with recent reference hypernetted chain results is also made.

Equation of state for a Yukawa fluid in the mean spherical approximation

The analytical solution of the mean spherical approximation (MSA) for a fluid of hard spheres and a Yukawa potential is obtained by solving a quartic equation for an inverse length parameter Γ. Simple expressions for the thermodynamics and correlation functions in terms of Γ exist in the literature. In this paper we obtain a simple form of the equation of state via the energy. This is compared with the result of Henderson et al. [D. Henderson, L. Blum, and J. P. Noworyta, J. Chem. Phys. 102, 4973 (1995)].

Analytical solution of the Yukawa closure of the Ornstein—Zernike equation III: the one-component case

In previous work we have studied the solution of the Ornstein-Zernike equation with a general multiyukawa closure. Here the direct correlation function is expressed by a rapidly converging sum of M (complex) exponentials. For a simple fluid the mathematical problem of solving the Ornstein-Zernike equation is equivalent to finding the solution of a linear algebraic equation of order M. The solution for the arbitrary case is given in terms of a scaling matrix Γ. For only one component this matrix is diagonal and the general solution using the properties of M-dimensional SOM Lie group is given. In the Mean Spherical Approximation (MSA) the excess entropy is obtained and expressed as a sum of 1-dimensional integrals of algebraic functions. We remark that the general solution of the M exponents-1 component case was found in our early work (Blum, L., and Hoye, J. S.,1978, J. stat. Phys., 19, 317) in implicit form. The present explicit solution agrees completely with the early one. Other thermodynamic properties such as the energy equation of state are also obtained, explicitly for 2 and 3 exponentials. The analytical solution of the effective MSA is also obtained from the simple variational form for the Helmholtz excess free energy δA (1) where (2) where both the excess energy ΔE(Γ) and the excess entropy ΔS(Γ) are functionals of Γ, which opens interesting possibilities that are discussed elsewhere. We remark that this is a non-trivial property, which is certainly true for the MSA (Chandler, D., and Andersen, H. C., 1972, J. chem. Phys., 57, 1930). It implies cross-derivative properties for the closure equations, which have been verified in all cases.

Light Scattering from Chemically Reactive Fluids. II. Case with Diffusion

The thermodynamic approach for light scattering developed in a previous paper is extended to include the diffusion process. The results for zero angle are the same as stated before [B. J. Berne and H. L. Frisch, J. Chem. Phys. 47, 3675 (1967); L. Blum and Z. W. Salsburg, ibid. 48, 2292 (1968)], that is, the only remaining contribution to the central Rayleigh line is due to the chemical reactions.

On the properties of inhomogeneous charged systems

We give a proof and an extension of equations previously derived by Wertheim and Lovett, Mou and Buff, relating the gradient of the density to an integral of the external force over the pair correlation function; when the system has boundaries it also involves a surface contribution. These equations are derived and used for systems which may contain free charges, dipoles, and a rigid background (jellium). In particular, we derive an equation for the density profile near a plane electrode and we show that the correlation function has to decay no faster than ‖x‖−N(N=space dimension) parallel to the electode.

Thermodynamic properties of an asymmetric fluid mixture with Yukawa interaction in the mean spherical approximation

The analytical solution of mean spherical approximation of the Ornstein–Zernike equation for a Yukawa fluid with factorizable coefficients is used to obtain a simple form of the equation of state for the mixture. These results are an extension of Ginoza’s work.

A solvable model of polydisperse charged particles with sticky interactions

The statistical mechanics of a polydisperse system of charged particles with sticky interactions is studied in the mean spherical/Percus–Yevick approximation. The excess thermodynamic properties are calculated, taking as a reference system the sticky hard spheres mixture and are given in terms of a single scaling parameter ΓT. When the sticking probability is of the form λij=λiλj, then all the equations are explicitly solvable for arbitrary mixtures of charged systems. We obtain explicit expressions for the thermodynamic properties, structure function, and the Laplace transform of the pair distribution function.