Johan S. Høye

Theory of polar liquids

Two recent contributions to the statistical theory of polar fluids, namely the perturbation theory of Stell, Rasaiah and Narang (SRN) and the meanspherical-approximation (MSA) results of Wertheim, and of Nienhuis and Deutch, are compared and contrasted for the conceptually simple model of hard spheres, diameter R, with central point dipoles, of strength μ (dipolar hard spheres). It is shown that the MSA approach replaces correlation functions which enter correctly into the SRN theory by their low-density limits : to this extent it is unsatisfactory. On the other hand the MSA work does suggest reasons why the naive Pade approximant featuring in SRN theory may be expected to do reasonable justice to the physics of the problem. Numerical comparisons of the excess free-energy (as compared with non-polar hard spheres) as a function of reduced density, ρ* = ρR 3, are given at two temperatures, T* = 2 and T* = 0·25, where T* = kTR 3/μ2. Similar curves, for T* = 1 and T* = 0·5, are available from the authors. The...

Further investigations into the low-density behaviour of the hypernetted chain equation for ionic fluids

We describe the low-density behaviour of the hypernetted chain equation (HNC) for the restricted primitive model (RPM) of ionic fluids. An efficient computational procedure is developed and applied to the study of the thermodynamics and convergency behaviour in the low density and low temperature (or high ionic strength) region in which there is evidence of liquid-gas coexistence. After a careful study, we attribute the divergence found on the liquid side of the coexistence curve to the presence of a spinodal line. In contrast, divergences on the gas side (low density) are unphysical and appear to result from intrinsic inconsistencies in the HNC approximation. We remark upon the effect that the presence of a ‘cavity term’ added to the RPM pair potential can be expected to have upon the phase-separation behaviour in the HNC approximation as well in a more exact analysis.

Temperature dependence of the Casimir effect.

The temperature dependence of the Casimir force between a real metallic plate and a metallic sphere is analyzed on the basis of optical data concerning the dispersion relation of metals such as gold and copper. Realistic permittivities imply, together with basic thermodynamic considerations, that the transverse electric zero mode does not contribute. This results in observable differences from the conventional prediction, which does not take this physical requirement into account. The results are shown to be consistent with the third law of thermodynamics, as well as being not inconsistent with current experiments. However, the predicted temperature dependence should be detectable in future experiments. The inadequacies of approaches based on ad hoc assumptions, such as the plasma dispersion relation and the use of surface impedance without transverse momentum dependence, are discussed.

SCOZA critical exponents and scaling in three dimensions

The critical behavior of a self-consistent Ornstein–Zernike approach (SCOZA) that describes the pair correlation function and thermodynamics of a classical fluid, lattice gas, or Ising model is analyzed in three dimensions below the critical temperature, complementing our earlier analysis of the supercritical behavior. The SCOZA subcritical exponents describing the coexistence curve, susceptibility (compressibility), and specific heat are obtained analytically (β=7/20,γ′=7/5,α′=−1/10). These are in remarkable agreement with the exact values (β≈0.326,γ′≈1.24,α′≈0.11) considering that the SCOZA uses no renormalization group concepts. The scaling behavior that describes the singular parts of the thermodynamic functions as the critical point is approached is also analyzed. The subcritical scaling behavior in the SCOZA is somewhat less simple than that expected in an exact theory, involving two scaling functions rather than one.

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.

Analysis of the hypernetted chain equation for ionic fluids

It is well known that the numerical solution of the hypernetted chain (HNC) equations yields satisfactory results for the pair correlation function of the primitive model of electrolytes and similar models of ionic particles over a considerable range of thermodynamic states. Despite this, it has become apparent that for low densities (or low ionic concentration in electrolytes) the numerical solution breaks down for temperatures well above the expected coexistence region between gas and liquid phases. Here we study the situation by analytic means, comparing it to a similar problem for sticky hard spheres in the Percus-Yevick (PY) approximation. On the basis of our analysis we conclude that the failure of the HNC is of the same nature and is connected to the existence of two possible solutions for low densities. When the temperature is lowered these solutions will merge into one at a particular temperature, below which a real solution is no longer possible. By extending our analysis to systems like the mon...

Van der Waals force derived from a quantum statistical mechanical path integral method

Abstract The main purpose of this paper is to apply the quantum statistical mechanical model for polarizable fluids, used by Hoye-Stell and others, to the calculation of the van der Waals force (dispersion force) between monatomics. The results are in agreement with those obtained by quantum perturbation theory. The quantum statistical method implies considerable formal simplifications. The introductory sections of the paper show, for illustrative purposes, how the dispersion forces in limiting cases also can be obtained from macroscopic quantum electromagnetic theory when two dilute dielectric media with plane-parallel surfaces are separated by a vacuum (Casimir effect).

Casimir problem of spherical dielectrics: quantum statistical and field theoretical approaches.

The Casimir free energy for a system of two dielectric concentric nonmagnetic spherical bodies is calculated with use of a quantum statistical mechanical method, at arbitrary temperature. By means of this rather novel method, which turns out to be quite powerful (we have shown this to be true in other situations also), we consider first an explicit evaluation of the free energy for the static case, corresponding to zero Matsubara frequency (n=0). Thereafter, the time-dependent case is examined. For comparison we consider the calculation of the free energy with use of the more commonly known field theoretical method, assuming for simplicity metallic boundary surfaces.

Pathways in Two-State Protein Folding

Thermodynamic measurements of proteins indicate that the folding to the native state takes place either through stable intermediates or through a two-state process without intermediates. The rather short folding times of proteins indicate that folding is guided through some sequence of contact bindings. We discuss the possibility of reconciling a two-state folding event with a sequential folding process in a schematic model of protein folding. We propose a new dynamical transition temperature that is lower than the temperature at which proteins in equilibrium unfold. This is in qualitative agreement with observations of in vivo protein folding activity quantified by chaperone concentration in Escherichia coli. Finally, we discuss our framework in connection with the unfolding of proteins at low temperatures.

Achieving a simple development model for 3D shapes: are chemicals necessary?

Artificial Development Systems have been introduced as a technique aimed at increasing the scalability of evolutionary algorithms. Most commonly the development model is part of the evolutionary process, each individual developed during fitness evaluation. To achieve scalability it may be argued that the implicit requirements of evolvability and effectivity ( in terms of its resource requirements) are thus placed on the development model. To achieve an effective development model, one of the challenges is to find appropriate mechanisms from developmental biology and ways to implement them for the application in hand. This work presents a development model for the evolution and development of 3D shapes. The goal being to create a simple development model for any 3D shape. Further, this work provides a preliminary investigation into the usefulness of one of the mechanisms implemented in this model, that of chemicals.