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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.

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.

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.

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)].

An electrolytic solution is simulated by a mixture of charged hard spheres and hard dipoles, all of the same size. This model can be solved exactly in the mean spherical approximation (MSA), yielding a set of three coupled high order algebraic equations for three unknowns, which are essentially the excess internal energies due to the charges alone, the dipoles alone, and the charge‐dipole cross interaction. A rapidly converging series solution of these equations is proposed for the dilute solution regime. The first term in this series is the hard‐core Debye‐Huckel theory term, with electrostrictive corrections. We also obtain the leading term in the expansion for the infinite dilution limit of the ion‐solvent excess chemical potential. Other relevant information could be obtained using standard formulas.

The solvation force between neutral surfaces in water is studied by running the grand canonical ensemble Monte Carlo simulations on the system containing up to 102 water‐like particles between parallel smooth plates immersed in the fluid. The water molecules are modeled like hard spheres with embedded point dipoles and orientation dependent adhesion potential. The pressure between the walls as a function of the distance displays oscillations resembling those observed experimentally, The overall attraction between the plates is observed despite the absence of direct wall–wall or wall–fluid attractive forces.

We show that in the mean spherical approximation for a mixture of arbitrary size and charge hard ions in a dipolar solvent all the properties are expressible in terms of three parameters; a screening parameter Γ, a ion‐dipole interaction parameter B10, and a dipole–dipole interaction parameter b2, which are given by the solution of a set of algebraic equations. In the case of equal ionic size, the solution is quite simple and very similar to previous results which the size of ion are equal to the size of dipole (σ=σn=1). In the low density and high coupling limits, explicit results are given for the three parameters and for the thermodynamics. The calculations show that the model becomes the primitive model for infinite dilution and vanishingly small solvent molecules.

The expansion of the exponential of a tensorial expression such as the interaction or pair correlation function between two nonspherical molecules 1, 2 is of the form ∑mnl λmnlΦmnl(12), where Φmnl(12) are invariant tensorial expressions that depend only on the orientation of 1 and 2. The generating function e−∑mnl λmnlΦmnl =∑pqt ipqt(λ) Φpqt defines a generalized Bessel function (GBF). We discuss integral representations and recurrence relations for the GBF. The first GBFs for dipolar and linear quadrupolar exponents, which are of interest in the theory of ionic solutions are computed explicitly.

The structure of hard sphere fluid confined to cylindrical capillaries in equilibrium with the bulk fluid phase is considered. Simple analytical approaches are examined and compared with the results of simultaneous grand canonical ensemble Monte Carlo simulations. The validity of the limiting law according to which the fluid density in the capillary approaches its fugacity in vanishingly narrow pores is confirmed. The truncated graphical expansion around the exact narrow pore limit is found to represent a useful approximation for very narrow capillaries. In systems with the pore diameter exceeding a few diameters of the spheres and at the reduced bulk densities of the fluid ρbσ3≤0.6, the Percus–Yevick approximation provides a satisfactory description of the fluid distribution.

A model for an ideally polarizable interface is proposed where the two sides of the interface are described by two interacting classical one component plasmas of different neutralizing background densities separated by an impermeable membrane. The statistical mechanics of this system is solved exactly in two dimensions at the reduced temperature 2. The one and two body distribution functions, the potential drop, the differential capacity, and the interfacial tension are computed. The main feature of this model is that the potential drop and not the surface charge appears as the natural external variable. Several sum rules are discussed, such as the screening theorems for multipoles, the contact theorem, and the Lippmann equation. A general thermodynamic argument shows that these sum rules remain valid in three dimensions and for any value of the coupling parameter.

We develop a quantum mechanical theory for the inelasticity or Placzek correction for an asymmetric top rigid rotator, and give a formula to compute this correction for neutron scattering. We have, however, used a sphericalized model which satisfies Mecke’s sum rule to compute the correction for H2O and D2O. Since this rigid rotor model fails to satisfy the exact first sum rule, we introduce a form that does satisfy this condition. Good agreement with the large momentum exchange (k) behavior in the case of D2O is obtained. However, for the H2O this is not so and adjustable parameters have to be introduced to obtain the correction asymptotic behavior.

A model for the interface of two media with different background densities, separated by a charged bilayer, is solved exactly in a two dimensional, one component plasma at reduced temperature 2. When the two media are in direct contact (no gap), then we can think of it as a model of a classical metal and an electrolytic solution or just two metals. The contact potential, or potential of zero charge appears to be a very simple function of the ratio of the background densities. We also find that the potential does not depend on the surface charge, a fact that we explain using a corollary of the perfect screening theorem. A second case of interest is the case of the two media separated by a gap that in our case could be charged: this is a model of a two dimensional membrane, or the polarization layer of the inner Helmholtz region. Very surprisingly, we find that also the surface dipole is completely screened by the charges surrounding the interface, so that the potential drop across the interface only depends on the logarithm of the charge densities, as found by Ballone, Senatore, and Tosi for the most simple case of a discharged contact.

The scattering function I (k) for all k is given in the Percus–Yevick approximation for a polydisperse fluid of hard spheres. The extension to a simple model of interpenetrable particles introduced herein, the permeable‐sphere model, is made in order to widen the applicability of our results to colloid and polymer problems.

The modified hypernetted chain theory (MHNC) for density profiles of fluids in contact with a hard, smooth surface is found to possess a remarkably simple and interesting property: The accuracy of the MHNC and the universality of the bridge functions for the density profiles can be tested without resort to any detailed solution of the integral equations. It is given by the degree of universality of the bulk bridge parameter (e.g., η for the Percus–Yevick hard‐sphere bridge function) when expressed in terms of the second partial derivative of the free energy with respect to the density F. The function η (F) as obtained from MHNC calculations for bulk simple fluids is found to be remarkably independent of the pair potential. As an example for the accuracy of the resulting method, the one‐component plasma near a hard wall is discussed.

An extensive series of calculations are made to compare an improved closure of the Born–Green–Yvon (BGY) equation for the electric double layer of primitive electrolytes to existing Monte Carlo simulation and other theories, such as the modified Poisson–Boltzmann (version 5) (MPB5) and the hypernetted chain/mean spherical approximation (HNC/MSA), and its recent improvements. In contrast to these theories the BGY equation satisfies the contact theorem always. Furthermore, the bulk pair correlation functions used are the most accurate available, namely, the HNC bulk results. The results show very good general agreement to the computer work for high densities and surface charges. In particular, we are able to go to higher densities than those hitherto published in the literature. For low density 2–2 and 2–1 electrolytes, the agreement is not as good as for the other theories.

Some improvements in the primitive model of electrolyte solutions are discussed within the framework of the mean spherical approximation. Excellent agreement has been found between experimental and calculated osmotic and activity coefficients of 16 alkali halides in H2O at 25 °C, whenever a density dependent hard core ionic diameter is combined with an adjustable but not density dependent dielectric constant. Promising agreement is also found when Pauling crystallographic radii are used for the ions.

An analytical form of the HNC pair correlation function for the primitive ionic solution is proposed. This form interpolates between the EXP and MSA approximations. For 2:2 electrolytes it gives very good agreement to the thermodynamics and pair correlation function of the HNC.

A simple potential for the pair interaction of two water molecules is proposed. This model is intended for use in ionic solvation problems, and is a step beyond the ion dipole model proposed by Adelman, Deutch, and Blum to study molecular effects in solvation. It consists in adding to the hard spheres with a point dipole a narrow potential well with a tetrahedral octupole of the form v(θ,φ)=A(r)sin θ sin 2θ cos 2φ. We test this potential and two improvements by running a Monte Carlo simulation on a system of 70 molecules. The results show that our model reproduces surprisingly well the essential features of the structure of water, namely the rather well defined tetrahedral structure of the first coordination shell, and the very poorly structured second and third coordination shells.

The partial solution for the mean spherical model of neutral spheres with electrostatic interactions obtained in a previous communication [L. Blum, J. Chem. Phys. 57, 1862 (1972).] is extended to the general case, in which the electrostatic interactions of odd parity, like the dipole‐quadrupole interaction, are included. The solution is given in terms of a linear transform of the direct correlation function, which is shown to be a polynomial in r inside the hard core diameter. The coefficients of this polynomial are determined from a sufficient number of boundary conditions. The method of solution employs the so‐called second Baxter form of the Ornstein‐Zernike equation [Australian J. Phys. 21, 563 (1968).] which is derived for this particular case. Also, alternative forms of the Ornstein‐Zernike equation in coordinate space are obtained. The case of molecules with linear dipole and quadrupole moments is summarily illustrated.

The spectral distribution of light scattered by fluctuations about equilibrium in a chemically reactive fluid is calculated from the time dependence of the fluctuations predicted by the linearized hydrodynamic equations of irreversible thermodynamics. The theory treats a system with an arbitrary number, n, of independent chemical reactions which are coupled to the hydrodynamic processes involving viscosity and thermal conductivity. However, diffusion and any frequency dependence of the transport coefficients are neglected. The scattered light as a function of frequency has a central component and two side or Brillouin components. The central component is analyzed as a sum of n + 1 Lorentzian lines, one associated with a thermal diffusion relaxation process and n lines associated with the relaxation of the chemical reactions. In the limit of zero angle of scattering the widths of all Lorentzian lines associated with transport properties (thermal conductivity, viscosity, etc.,) vanish, and the entire width ...

A general theory of elastic light scattering is presented. The incoming and scattered light are described by the coherency matrix, which is written in spherical tensor form. The coherency matrix has three tensorial components in our representation: a scalar (the intensity), an axial vector (the ellipticity), and a second rank tensor (directly related to the inclination of the optical axes). It is shown that using Racah algebra, the components of the coherency matrix for the incident and scattered light can be related by rather compact formulas, involving Wigner's 9‐J symbols. The simplicity of the treatment allows us to include any higher multipole effects in the scattering, like the magnetic dipole and electric quadrupole contributions. For the pure electric dipole scattering, our theory gives a unique interpretation of the scattering in terms of moments of the molecular correlation function. Only two moments can be observed when the correlations are short compared to the wavelength of the light, while, ...

Using standard perturbation theory for degenerate matrices, an expansion for the eigenvectors corresponding to the thermodynamic fluctuation modes in a chemically reactive fluid is obtained. The expansion is valid for small scattering angles, that is, vanishing spatial gradients. These eigenvectors give rather complicated expressions for the intensities of the individual lines, making it rather impractical to get these intensities. We have therefore evaluated partial sums of integrated intensities, which depend only on thermodynamic equilibrium parameters and stoichiometric coefficients. We evaluate explicitly the ratio of the intensity contribution due to the chemical reactions and diffusion processes (Berne–Frisch approximation). For the case of the reaction AB⇆A + B, the intensity is proportional to the net change in the dielectric polarizability in the reaction, in accordance with the result obtained by Berne, Deutch, Hynes, and Frisch for a simpler case. Our method is, however, general and can be use...

The spectrum of the light scattered by a multicomponent fluid is discussed using the thermodynamic approach originally suggested by Landau and Placzek. The structure of the central Rayleigh line is discussed for two particular cases; the infinitely dilute solution of rigid polymers and a binary mixture.

An invariant expansion of the two‐body statistical correlation function of a fluid is proposed. This expansion does not depend on any particular reference frame used to define the orientation of the molecules, and therefore can be reduced to the expansions of the literature in a simple way. The new expansion permits a rather convenient way of including the effects of molecular symmetry into it. The expressions for a few thermodynamic properties in terms of this expansion are obtained. The equations for x‐ray, neutron, and light scattering are somewhat simpler using this expansion. The Ornstein—Zernike equation has a very convenient form, and is given in Fourier transformed form in terms of 6j angular recoupling coefficients.

A rigorous theory for the light scattered from a solution of an optically active species is presented. The theory is based on the quantum‐mechanical time displaced correlation function for the suceptibility tensors. This formalism leads to the correct form of the Kronig–Kramers relations. Otherwise, the procedure follows the usual theory of light scattered from inactive solutions. The result shows that the parameters usually associated with the optical rotatory power and the ellipticity are linear combinations of two rotational invariants of the fourth‐rank tensor formed by the direct product of the dielectric polarizability tensor and the pseudotensor that gives the optical activity. Only for isotropic molecules do we recover the classical result. The depolarization of the light (or ellipticity) is due both to the dielectric polarizability and to the optical activity pseudotensor. If the scattering experiment is done at an angle different from zero, then information about the anisotropy of the molecular ...

The Ornstein‐Zernike equation for fluids with nonspherical molecules obtained in a former publication [L. Blum and A. J. Torruella, J. Chem. Phys. 56, 303 (1972)] is written in coordinate space as a convolution matrix equation. A rather simple property of the angular coupling coefficients of our former work allows us to write the Ornstein‐Zernike equation in irreducible form, as a set of uncoupled matrix equations, of rather small size. A generalization of Baxter's form of the Ornstein‐Zernike equation to matrices allows us to write a formal solution to the mean spherical model of neutral hard spheres with almost arbitrary electrostatic multipoles. This is an extension of Wertheim's solution for dipoles [J. Chem. Phys. 55, 4291 (1971)]. The formal solution consists in showing that the direct correlation function inside the hard core is a polynomial in the interatomic distance r. The coefficients of the polynomials are obtained by solving a set of quadratic matrix equations. The class of potentials that ad...

The Placzek corrections for neutron scattering from atomic systems have been generalized to include molecular fluids. The correction terms include spherical Bessel functions of the zeroth and second order. As a consequence, the dynamic corrections for molecular systems show sizeable oscillations with a period determined by the internuclear distances within a molecule. These results are compared with neutron diffraction data for liquid carbon tetrachloride.