Individual ion species chemical potentials in the Mean Spherical Approximation.

The Mean Spherical Approximation (MSA) is a commonly used thermodynamic theory for computing the energetics of ions in the primitive model (i.e., charged hard-sphere ions in a background dielectric). For the excess chemical potential, however, the early MSA formulations (which were widely adopted) only included the terms needed to compute the mean excess chemical potential (or the mean activity coefficient). Other terms for the chemical potential µi of individual species i were not included because they sum to 0 in the mean chemical potential. Here, we derive these terms to give a complete MSA formulation of the chemical potential. The result is a simple additive term for µi that we show is a qualitative improvement over the previous MSA version. In addition, our derivation shows that the MSA's assumption of global charge neutrality is not strictly necessary, so that the MSA is also valid for systems close to neutrality.

Full solution to the mean spherical approximation (MSA) for an arbitrary mixture of ions in a dipolar solvent.

The complete solution to the mean-spherical approximation is given for an arbitrary mixture of ions in a dipolar solvent. The calculation is done for an overall neutral collection of charged hard spheres (ions) and dipoles (solvent) that bear a central point dipole. Previous solutions to this problem were not consistent because they did not include the solvent particles as a (neutral) solute in the mixture. The present solution accounts for this peculiar counterintuitive feature, fully and consistently. Complete expressions for the chemical potentials of the ions and solvent are provided for the first time. To illustrate, a binary 1-1 asymmetric electrolyte solution in a water-like dipolar solvent is considered, and some numerical results are examined. In particular, it is verified that a set of thermodynamic consistency relations are accurately fulfilled.

The uniform quantized electron gas revisited.

In this article we continue and extend our recent work on the correlation energy of the quantized electron gas of uniform density at temperature [Formula: see text]. As before, we utilize the methods, properties, and results obtained by means of classical statistical mechanics. These were extended to quantized systems via the Feynman path integral formalism. The latter translates the quantum problem into a classical polymer problem in four dimensions. Again, the well known RPA (random phase approximation) is recovered as a basic result which we then modify and improve upon. Here we analyze the condition of thermodynamic self-consistency. Our numerical calculations exhibit a remarkable agreement with well known results of a standard parameterization of Monte Carlo correlation energies.

Uniform quantized electron gas.

In this work we study the correlation energy of the quantized electron gas of uniform density at temperature T = 0. To do so we utilize methods from classical statistical mechanics. The basis for this is the Feynman path integral for the partition function of quantized systems. With this representation the quantum mechanical problem can be interpreted as, and is equivalent to, a classical polymer problem in four dimensions where the fourth dimension is imaginary time. Thus methods, results, and properties obtained in the statistical mechanics of classical fluids can be utilized. From this viewpoint we recover the well known RPA (random phase approximation). Then to improve it we modify the RPA by requiring the corresponding correlation function to be such that electrons with equal spins can not be on the same position. Numerical evaluations are compared with well known results of a standard parameterization of Monte Carlo correlation energies.

Casimir friction: relative motion more generally.

This paper extends our recent study on Casimir friction forces for dielectric plates moving parallel to each other (Høye and Brevik 2014 Eur. Phys. J. D 68 61), to a case where the plates are no longer restricted to rectilinear motion. Part of the mathematical formalism thereby becomes more cumbersome, but reduces in the end to the form that we expected to be the natural one in advance. As an example, we calculate the Casimir torque on a planar disc rotating with constant angular velocity around its vertical symmetry axis next to another plate.

Van der Waals interactions: evaluations by use of a statistical mechanical method.

In this work the induced van der Waals interaction between a pair of neutral atoms or molecules is considered by use of a statistical mechanical method. With use of the Schrödinger equation this interaction can be obtained by standard quantum mechanical perturbation theory to second order. However, the latter is restricted to electrostatic interactions between dipole moments. So with radiating dipole-dipole interaction where retardation effects are important for large separations of the particles, other methods are needed, and the resulting induced interaction is the Casimir-Polder interaction usually obtained by field theory. It can also be evaluated, however, by a statistical mechanical method that utilizes the path integral representation. We here show explicitly by use of this method the equivalence of the Casimir-Polder interaction and the van der Waals interaction based upon the Schrödinger equation. The equivalence is to leading order for short separations where retardation effects can be neglected. In recent works [J. S. Høye, Physica A 389, 1380 (2010); Phys. Rev. E 81, 061114 (2010)], the Casimir-Polder or Casimir energy was added as a correction to calculations of systems like the electron clouds of molecules. The equivalence to van der Waals interactions indicates that the added Casimir energy will improve the accuracy of calculated molecular energies. Thus, we give numerical estimates of this energy including analysis and estimates for the uniform electron gas.

Dielectric properties of classical and quantized ionic fluids.

We study time-dependent correlation functions of classical and quantum gases using methods of equilibrium statistical mechanics for systems of uniform as well as nonuniform densities. The basis for our approach is the path integral formalism of quantum mechanical systems. With this approach the statistical mechanics of a quantum mechanical system becomes the equivalent of a classical polymer problem in four dimensions where imaginary time is the fourth dimension. Several nontrivial results for quantum systems have been obtained earlier by this analogy. Here, we will focus upon the presence of a time-dependent electromagnetic pair interaction where the electromagnetic vector potential that depends upon currents, will be present. Thus both density and current correlations are needed to evaluate the influence of this interaction. Then we utilize that densities and currents can be expressed by polarizations by which the ionic fluid can be regarded as a dielectric one for which a nonlocal susceptibility is found. This nonlocality has as a consequence that we find no contribution from a possible transverse electric zero-frequency mode for the Casimir force between metallic plates. Further, we establish expressions for a leading correction to ab initio calculations for the energies of the quantized electrons of molecules where now retardation effects also are taken into account.

Casimir force between dielectric media with free charges.

The statistical mechanical approach to Casimir problems for dielectrics separated by a vacuum gap turns out to be compact and effective. A central ingredient of this method is the effect of interacting fluctuating dipole moments of the polarizable particles. At arbitrary temperature the path-integral formulation of quantized particles, developed by Høye-Stell and others, is needed. At high temperature-the limit considered in the present paper-the classical theory is, however, sufficient. Our present theory is related to an idea put forward earlier by Jancovici and Samaj (2004), namely, to evaluate the Casimir force between parallel plates invoking an electronic plasma model and the Debye-Hückel theory for electrolytes. Their result was recently recovered by Høye (2008), using a related statistical mechanical method. In the present paper we generalize this by including a constant permittivity in the description. The present paper generalizes our earlier theory for parallel plates (1998), as well as for spherical dielectrics (2001). We also consider the Casimir force between a polarizable particle and a conductor with a small density of charges, finding agreement with the result recently derived by Pitaevskii (2008).

Temperature correction to Casimir-Lifshitz free energy at low temperatures: semiconductors.

The Casimir force and free energy at low temperatures have been the subject of focus for some time. We calculate the temperature correction to the Casimir-Lifshitz free energy between two parallel plates made of dielectric material possessing a constant conductivity at low temperatures, described through a Drude-type dielectric function. For the transverse magnetic (TM) mode such a calculation is made. A further calculation for the case of the TE mode is thereafter presented which extends and generalizes previous work for metals. A numerical study is undertaken to verify the correctness of the analytic results.

Analytical and numerical verification of the Nernst theorem for metals.

In view of the current discussion on the subject, an effort is made to show very accurately both analytically and numerically how the Drude dispersion model gives consistent results for the Casimir free energy at low temperatures. Specifically, for the free energy near T=0 we find the leading term proportional to T2 and the next-to-leading term proportional to T(5/2). These terms give rise to zero Casimir entropy as T-->0 and are thus in accordance with Nernst's theorem.

Apolar and polar solvation thermodynamics related to the protein unfolding process.

Thermodynamics related to hydrated water upon protein unfolding is studied over a broad temperature range (5-125 degrees C). The hydration effect arising from the apolar interior is modeled as an increased number of hydrogen bonds between water molecules compared with bulk water. The corresponding contribution from the polar interior is modeled as a two-step process. First, the polar interior breaks hydrogen bonds in bulk water upon unfolding. Second, due to strong bonds between the polar surface and the nearest water molecules, we assume quantization using a simplified two-state picture. The heat capacity change upon hydration is compared with model compound data evaluated previously for 20 different proteins. We obtain good correspondence with the data for both the apolar and the polar interior. We note that the effective coupling constants for both models have small variations among the proteins we have investigated.