Molecular Theory of Hydrophobic Effects: ``She is too mean to have her name repeated.''

This paper reviews the molecular theory of hydrophobic effects relevant to biomolecular structure and assembly in aqueous solution. Recent progress has resulted in simple, validated molecular statistical thermodynamic theories and clarification of confusing theories of decades ago. Current work is resolving effects of wider variations of thermodynamic state, e.g. pressure denaturation of soluble proteins, and more exotic questions such as effects of surface chemistry in treating stability of macromolecular structures in aqueous solutionComment: submitted to Ann. Rev. Phys. Chem., 31 pages, 245 references, 2 figure

New mean field theories for the liquid-vapor transition of charged hard spheres

The phase behavior of the primitive model of electrolytes is studied in the framework of various mean field approximations obtained recently by means of methods pertaining to statistical field theory (CAILLOL, J.-M., 2004, \textit{J. Stat. Phys.}, \textbf{115}, 1461). The role of the regularization of the Coulomb potential at short distances is discussed in details and the link with more traditional approximations of the theory of liquids is discussed. The values computed for the critical temperatures, chemical potentials, and densities are compared with available Monte Carlo data and other theoretical predictions.Comment: 17 pages, 4 figures, 3 table

Translation invariant extensions of finite volume measures

We investigate the following questions: Given a measure μΛ on configurations on a subset Λ of a lattice L, where a configuration is an element of ΩΛ for some fixed set Ω, does there exist a measure μ on configurations on all of L, invariant under some specified symme- try group of L, such that μΛ is its marginal on configurations on Λ? When the answer is yes, what are the properties, e.g., the entropies, of such measures? Our primary focus is the case in which L = Zd and the symmetries are the translations. For the case in which Λ is an interval in Z we give a simple necessary and sufficient condition, local translation invariance (LTI), for extendibility. For LTI measures we construct extensions having maximal entropy, which we show are Gibbs measures; this construction extends to the case in which L is the Bethe lattice. On Z we also consider extensions supported on periodic configurations, which are analyzed using de Bruijn graphs and which include the extensions with minimal entropy. When Λ ⊂ Z is not an interval, or when Λ ⊂ Zd with d > 1, the LTI condition is necessary but not sufficient for extendibility. For Zd with d > 1, extendibility is in some sense undecidable

Convergence of density expansions of correlation functions and the Ornstein-Zernike equation

We prove absolute convergence of the multi-body correlation functions as a power series in the density uniformly in their arguments. This is done by working in the context of the cluster expansion in the canonical ensemble and by expressing the correlation functions as the derivative of the logarithm of an appropriately extended partition function. In the thermodynamic limit, due to combinatorial cancellations, we show that the coeffi- cients of the above series are expressed by sums over some class of two-connected graphs. Furthermore, we prove the convergence of the density expansion of the “direct correlation function” which is based on a completely different approach and it is valid only for some inte- gral norm. Precisely, this integral norm is suitable to derive the Ornstein-Zernike equation. As a further outcome, we obtain a rigorous quantification of the error in the Percus-Yevick approximation

Structural studies of thermally stable, combustion-resistant polymer composites

Composites of the industrially important polymer, poly(methyl methacrylate) (PMMA), were prepared by free-radical polymerization of MMA with varying amounts (1–30 wt. %) of sodium dioctylsulfosuccinate (Aerosol OT or AOT) surfactant added to the reaction mixture. The composites with AOT incorporated show enhanced resistance to thermal degradation compared to pure PMMA homopolymer, and micro-cone combustion calorimetry measurements also show that the composites are combustion-resistant. The physical properties of the polymers, particularly at low concentrations of surfactant, are not significantly modified by the incorporation of AOT, whereas the degradation is modified considerably for even the smallest concentration of AOT (1 wt. %). Structural analyses over very different lengthscales were performed. X-ray scattering was used to determine nm-scale structure, and scanning electron microscopy was used to determine μm-scale structure. Two self-assembled species were observed: large phase-separated regions of AOT using electron microscopy and regions of hexagonally packed rods of AOT using X-ray scattering. Therefore, the combustion resistance is observed whenever AOT self-assembles. These results demonstrate a promising method of physically incorporating a small organic molecule to obtain a highly thermally stable and combustion-resistant material without significantly changing the properties of the polymer

A probability-conserving cross-section biasing mechanism for variance reduction in Monte Carlo particle transport calculations

In Monte Carlo particle transport codes, it is often important to adjust reaction cross sections to reduce the variance of calculations of relatively rare events, in a technique known as non-analogous Monte Carlo. We present the theory and sample code for a Geant4 process which allows the cross section of a G4VDiscreteProcess to be scaled, while adjusting track weights so as to mitigate the effects of altered primary beam depletion induced by the cross section change. This makes it possible to increase the cross section of nuclear reactions by factors exceeding 10^4 (in appropriate cases), without distorting the results of energy deposition calculations or coincidence rates. The procedure is also valid for bias factors less than unity, which is useful, for example, in problems that involve computation of particle penetration deep into a target, such as occurs in atmospheric showers or in shielding