The static longitudinal dielectric function eL(k) is calculated for several polar interaction site model (ISM) fluids for comparison with related models having arbitrary short‐range interactions and a set of one or more lower‐order multipole moments at the centers (ΩM models). The requisite averages over the ISM fluids are calculated by the extended reference interaction site method (XRISM) using site–site hypernetted chain (HNC)‐like closures modified to reproduce the correct long‐range behavior of the site–site pair correlation functions. They are compared with averages over the ΩM models under the RHNC theory taken from the literature or calculated under the mean spherical approximation. We find for fluids of strong enough polarity that eL(k) is negative over a finite range of k, the low end being in agreement with recent computer simulation studies of both ISM and ΩM polar fluids. However, we confirm that the expected large‐k behavior eL(k)=1 governs the ISMs, but not the ΩM models. Based on an adapta...

Static longitudinal dielectric function of model molecular fluids

Based on a suitable density-functional theory for inhomogeneous fluids we investigate both the liquid-vapor coexistence curve of the bulk phase diagram and interfacial structures of molecular fluids in general and Stockmayer fluids in particular We derive a scheme which allows us to analyze one-component fluids composed of molecules with strong permanent dipole moments which are shown to affect significantly the bulk phase diagram The critical temperature increases as a function of the strength of the dipole moments, whereas the critical density remains unchanged if the repulsive interaction of the molecules at short distances is modeled by a constant hard-core potential A temperature-dependent diameter of the hard-core potential that mimics the actual soft repulsive potential is also considered It results in an additional enhancement of the critical temperature and a slight increase of the critical density at larger dipole strengths and higher temperatures Our analytic results turn out to be in good agreement with published Monte Carlo data The density profile and the orientational ordering at interfaces are shown to be determined by a system of coupled integral equations that are applicable for dipole moments of arbitrary strength Its corresponding numerical solution will be presented in a subsequent paper

Bulk and interfacial properties of polar and molecular fluids

Potentials of mean force between nonuniformly charged colloids or globular proteins are often estimated as a pairwise sum of distinct orientation averages for charge−dipole and dipole−dipole interactions. In systems with dipole-related interactions comparable to or exceeding the thermal energy, however, correlations between charge−dipole and dipole−dipole terms can render the additivity assumption highly inaccurate. On the basis of the third-order cumulant expansion of intercolloidal interactions, we derive an asymptotically exact relation for the potential of mean force that includes the correlation between distinct contributions. Using a simple discrete-orientation model, we obtain an approximate expression for the nonadditivity correction that reproduces correct behavior in weak and strong coupling limits and is sufficiently accurate for practical calculations over a wide range of interaction strengths including those characteristic of aqueous protein solutions.

Orientation-Averaged Pair Potentials between Dipolar Proteins or Colloids

It is customary in the physicochemical literature to define the static transverse dielectric function of a polar fluid according to the relation eT(k) = 1 + 4πβST(k), where β=(kBT)−1 and ST(k) is a measure of the static fluctuations of the Fourier components of the transverse part of the electric polarization field in the fluid. In this work we evaluate eT(k) for models of two classes. (1) In a DS model each molecule is a hard sphere with a point dipole at its center. It is the simplest representative of models in which the long range intermolecular interactions are generated by a set of point multipoles located at a single point in the molecule. In this case ST(k) is SM,T(k), the static correlation function of the transverse part of the dipole polarization density M(k). (2) In a ζDS model fluid, comprising nonideal dipolar hard spheres, the long range interactions are accounted for by two opposite partial charges on either side of the sphere’s center and separated by a distance l. The ζDS model is the s...

Static transverse dielectric function of model molecular fluids

The many degrees of freedom in fluid mixtures of nonspherical molecules can lead to different kinds of phase transition. We propose to characterize the phase transition uniquely by the eigenvector belonging to the vanishing eigenvalue of the coefficient matrix which multiplies the fluctuation in an expansion of the free energy up to second order. As an example we study the phase transition of a mixture of dipolar hard spheres and neutral hard spheres. We evaluate the coefficient matrix from the calculated correlation functions and find a demixing phase transition combined with small total density changes.

The phase instability of molecular fluid mixtures : dipolar and neutral hard spheres

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.

L. Blum

Papers

Invariant expansion. IV. The exponentials of tensorial expressions