Scaled-Particle Theory and the Length-scales Involved in Hydrophobic Hydration of Aqueous Biomolecular Assemblies

Hydrophobic hydration plays a crucial role in self-assembly processes over multiple length-scales, but the extrapolation of molecular-scale models to larger length-scale hydration phenomena is sometimes not warranted. Scaled-particle theories are based upon an interpolative view of that issue. We revisit the scaled-particle theory proposed thirty years ago by Stillinger, adopt a practical generalization, and consider the implications for hydrophobic hydration in light of our current understanding. The generalization is based upon identifying a molecular length, implicit in previous applications of scaled-particle models, that provides an effective radius for joining microscopic and macroscopic descriptions. We demonstrate that the generalized theory correctly reproduces many of the anomalous thermodynamic properties of hydrophobic hydration for molecularly sized solutes, including solubility minima and entropy convergence, successfully interpolates between the microscopic and macroscopic extremes, and provides new insights into the underlying molecular mechanisms. The results are discussed in terms of length-scales associated with component phenomena; in particular we first discuss the micro-macroscopic joining radius identified by the theory, then we discuss in turn the Tolman length that leads to an analogous length describing curvature corrections of a surface area model of hydrophobic hydration free energies, and the length-scales on which entropy convergence of hydration free energies are expected.Comment: 19 pages, 14 figures, one figure added, submitted to Rev. Mod. Phy

Balancing Local Order and Long-Ranged Interactions in the Molecular Theory of Liquid Water

A molecular theory of liquid water is identified and studied on the basis of computer simulation of the TIP3P model of liquid water. This theory would be exact for models of liquid water in which the intermolecular interactions vanish outside a finite spatial range, and therefore provides a precise analysis tool for investigating the effects of longer-ranged intermolecular interactions. We show how local order can be introduced through quasi-chemical theory. Long-ranged interactions are characterized generally by a conditional distribution of binding energies, and this formulation is interpreted as a regularization of the primitive statistical thermodynamic problem. These binding-energy distributions for liquid water are observed to be unimodal. The gaussian approximation proposed is remarkably successful in predicting the Gibbs free energy and the molar entropy of liquid water, as judged by comparison with numerically exact results. The remaining discrepancies are subtle quantitative problems that do have significant consequences for the thermodynamic properties that distinguish water from many other liquids. The basic subtlety of liquid water is found then in the competition of several effects which must be quantitatively balanced for realistic results.Comment: 8 pages, 6 figure

Structure/permeability relationships of silicon-containing polyimides

The permeability to H2, O2, N2, CO2 and CH4 of three silicone-polyimide random copolymers and two polyimides containing silicon atoms in their backbone chains, was determined at 35.0 C and at pressures up to about 120 psig (approximately 8.2 atm). The copolymers contained different amounts of BPADA-m-PDA and amine-terminated poly (dimethyl siloxane) and also had different numbers of siloxane linkages in their silicone component. The polyimides containing silicon atoms (silicon-modified polyimides) were SiDA-4,4'-ODA and SiDA-p-PDA. The gas permeability and selectivity of the copolymers are more similar to those of their silicone component than of the polyimide component. By contrast, the permeability and selectivity of the silicon-modified polyimides are more similar to those of their parent polyimides, PMDA-4,4'-ODA and SiDA-p-PDA. The substitution of SiDA for the PMDA moiety in a polyimide appears to result in a significant increase in gas permeability, without a correspondingly large decrease in selectivity. The potential usefulness of the above polymers and copolymers as gas separation membranes is discussed

Final state interactions in two-particle interferometry

We reconsider the influence of two-particle final state interactions (FSI) on two-particle Bose-Einstein interferometry. We concentrate in particular on the problem of particle emission at different times. Assuming chaoticity of the source, we derive a new general expression for the symmetrized two-particle cross section. We discuss the approximations needed to derive from the general result the Koonin-Pratt formula. Introducing a less stringent version of the so-called smoothness approximation we also derive a more accurate formula. It can be implemented into classical event generators and allows to calculate FSI corrected two-particle correlation functions via modified Bose-Einstein "weights".Comment: 12 pages RevTeX, 2 ps-figures included, submitted to Phys. Rev.

Quasi-chemical theory with a soft cutoff

In view of the wide success of molecular quasi-chemical theory of liquids, this paper develops the soft-cutoff version of that theory. This development has important practical consequences in the common cases that the packing contribution dominates the solvation free energy of realistically-modeled molecules because treatment of hard-core interactions usually requires special purpose simulation methods. In contrast, treatment of smooth repulsive interactions is typically straightforward on the basis of widely available software. This development also shows how fluids composed of molecules with smooth repulsive interactions can be treated analogously to the molecular-field theory of the hard-sphere fluid. In the treatment of liquid water, quasi-chemical theory with soft-cutoff conditioning doesn't change the fundamental convergence characteristics of the theory using hard-cutoff conditioning. In fact, hard cutoffs are found here to work better than softer ones.Comment: 5 pages, 2 figure

Molecular Realism in Default Models for Information Theories of Hydrophobic Effects

This letter considers several physical arguments about contributions to hydrophobic hydration of inert gases, constructs default models to test them within information theories, and gives information theory predictions using those default models with moment information drawn from simulation of liquid water. Tested physical features include: packing or steric effects, the role of attractive forces that lower the solvent pressure, and the roughly tetrahedral coordination of water molecules in liquid water. Packing effects (hard sphere default model) and packing effects plus attractive forces (Lennard-Jones default model) are ineffective in improving the prediction of hydrophobic hydration free energies of inert gases over the previously used Gibbs and flat default models. However, a conceptually simple cluster Poisson model that incorporates tetrahedral coordination structure in the default model is one of the better performers for these predictions. These results provide a partial rationalization of the remarkable performance of the flat default model with two moments in previous applications. The cluster Poisson default model thus will be the subject of further refinement.Comment: 5 pages including 3 figure

Towards the 3D-Imaging of Sources

Geometric details of a nuclear reaction zone, at the time of particle emission, can be restored from low relative-velocity particle-correlations, following imaging. Some of the source details get erased and are a potential cause of problems in the imaging, in the form of instabilities. These can be coped with by following the method of discretized optimization for the restored sources. So far it has been possible to produce 1-dimensional emission source images, corresponding to the reactions averaged over all possible spatial directions. Currently, efforts are in progress to restore angular details.Comment: Talk given at the Int. Workshop on Hot and Dense Matter in Relativistic Heavy Ion Collisions, March 24-27, 2004, Budapest; 10 pages, 6 figure