Extension of scaled particle theory to inhomogeneous hard particle fluids. I. Cavity growth at a hard wall

An equilibrium model for the combined effect of macromolecular crowding and surface adsorption on the formation of linear protein fibrils

The formation of linear protein fibrils has previously been shown to be enhanced by volume exclusion or crowding in the presence of a high concentration of chemically inert protein or polymer, and by adsorption to membrane surfaces. An equilibrium mesoscopic model for the combined effect of both crowding and adsorption upon the fibrillation of a dilute tracer protein is presented. The model exhibits behavior that differs qualitatively from that observed in the presence of crowding or adsorption alone. The model predicts that in a crowded solution, at critical values of the volume fraction of crowder or intrinsic energy of the tracer-wall interaction, the tracer protein will undergo an extremely cooperative transition-approaching a step function-from existence as a slightly self-associated species in solution to existence as a highly self-associated and completely adsorbed species. Criteria for a valid experimental test of these predictions are presented.

Scaled-particle theory analysis of cylindrical cavities in solution

The solvation of hard spherocylindrical solutes is analyzed within the context of scaled-particle theory, which takes the view that the free energy of solvating an empty cavitylike solute is equal to the pressure-volume work required to inflate a solute from nothing to the desired size and shape within the solvent. Based on our analysis, an end cap approximation is proposed to predict the solvation free energy as a function of the spherocylinder length from knowledge regarding only the solvent density in contact with a spherical solute. The framework developed is applied to extend Reiss's classic implementation of scaled-particle theory and a previously developed revised scaled-particle theory to spherocylindrical solutes. To test the theoretical descriptions developed, molecular simulations of the solvation of infinitely long cylindrical solutes are performed. In hard-sphere solvents classic scaled-particle theory is shown to provide a reasonably accurate description of the solvent contact correlation and resulting solvation free energy per unit length of cylinders, while the revised scaled-particle theory fitted to measured values of the contact correlation provides a quantitative free energy. Applied to the Lennard-Jones solvent at a state-point along the liquid-vapor coexistence curve, however, classic scaled-particle theory fails to correctly capture the dependence of the contact correlation. Revised scaled-particle theory, on the other hand, provides a quantitative description of cylinder solvation in the Lennard-Jones solvent with a fitted interfacial free energy in good agreement with that determined for purely spherical solutes. The breakdown of classical scaled-particle theory does not result from the failure of the end cap approximation, however, but is indicative of neglected higher-order curvature dependences on the solvation free energy.

Extension of scaled particle theory to inhomogeneous hard particle fluids. IV. Cavity growth at any distance relative to a planar hard wall

A completely generalized version of an inhomogeneous scaled particle theory (I-SPT) for hard particle fluids confined by hard walls is presented, whereby the reversible work of cavity insertion can be determined for a cavity of any radius located at any distance from the hard wall. New exact and approximate conditions on the central function Ḡ of I-SPT are developed, where Ḡ is related to the average value of the anisotropic density of hard-sphere centers at the surface of the cavity. The predictions of the work of insertion and the form of Ḡ are quite accurate up to moderate bulk densities as compared to molecular simulation results. The accuracy of I-SPT begins to decline at high densities, due to limitations of certain needed approximations required for a complete description of Ḡ. Finally, interesting insights into the origin of depletion effects between a hard-sphere solute and the hard wall are generated via this version of I-SPT. The oscillatory nature of depletion forces, exhibiting both attractive and repulsive domains, is found to arise from the interplay between bulk SPT and I-SPT relations.

Extension of scaled particle theory to inhomogeneous hard particle fluids. III. Entropic force exerted on a cavity that intersects a hard wall

We present a further development of an inhomogeneous scaled particle theory (I-SPT) for hard particle fluids confined by hard walls, such that the reversible work of cavity insertion can now be determined for all cavities that intersect one of the walls. Building upon a previous version of I-SPT [D. W. Siderius and D. S. Corti, Phys. Rev. E, 71, 036141 (2005)], a new function, F[over ] , is introduced, which is proportional to the net force on the surface of the cavity in the direction normal to the wall. The reversible work of cavity insertion is then determined by an integral over the force required to "push" the cavity of fixed size into the fluid starting from a position behind the wall. An exact relation for F[over ] at certain cavity locations and radii is derived and an accurate interpolation scheme is proposed for the computation of F[over ] beyond these exact limits. The chosen interpolation incorporates a large number of exact and nearly exact conditions, several of which follow from the surface thermodynamics of macroscopic cavities. Work predictions using F[over ] are highly accurate as compared to simulation results at low to moderate fluid densities. Good agreement still persists at densities near the hard-sphere freezing transition. The interpolation of F[over ] is also used to estimate the depletion force between a hard sphere solute and the wall. The I-SPT entropic force predictions are in good agreement with simulation results presented in the literature. Due to its reliance upon physical and geometric arguments, I-SPT provides important insights into the origin of various depletion effects such as how the interplay between geometry and the varying local density at the cavity surface gives rise to the appearance of multiple attractive regions at intermediate solute sizes and a universal repulsive region, both within solute to wall separations that are less than the diameter of a solvent particle. Finally, all of the scaled particle theory-based methods presented here can, in principle, be extended to describe hard particle fluids confined by nonplanar surfaces, thereby providing estimates of the depletion force between a solute and a variety of surfaces of interest.

Hard-sphere fluid adsorbed in an annular wedge: the depletion force of hard-body colloidal physics

Many important issues of colloidal physics can be expressed in the context of inhomogeneous fluid phenomena. When two large colloids approach one another in solvent, they interact at least partly by the response of the solvent to finding itself adsorbed in the annular wedge formed between the two colloids. At shortest range, this fluid mediated interaction is known as the depletion force/interaction because solvent is squeezed out of the wedge when the colloids approach closer than the diameter of a solvent molecule. An equivalent situation arises when a single colloid approaches a substrate/wall. Accurate treatment of this interaction is essential for any theory developed to model the phase diagrams of homogeneous and inhomogeneous colloidal systems. The aim of our paper is a test of whether or not we possess sufficient knowledge of statistical mechanics that can be trusted when applied to systems of large size asymmetry and the depletion force in particular. When the colloid particles are much larger than a solvent diameter, the depletion force is dominated by the effective two-body interaction experienced by a pair of solvated colloids. This low concentration limit of the depletion force has therefore received considerable attention. One route, which can be rigorously based on statistical mechanical sum rules, leads to an analytic result for the depletion force when evaluated by a key theoretical tool of colloidal science known as the Derjaguin approximation. A rival approach has been based on the assumption that modern density functional theories (DFT) can be trusted for systems of large size asymmetry. Unfortunately, these two theoretical predictions differ qualitatively for hard sphere models, as soon as the solvent density is higher than about 23 that at freezing. Recent theoretical attempts to understand this dramatic disagreement have led to the proposal that the Derjaguin and DFT routes represent opposite limiting behavior, for very large size asymmetry and molecular sized mixtures, respectively. This proposal implies that nanocolloidal systems lie in between the two limits, so that the depletion force no longer scales linearly with the colloid radius. That is, by decreasing the size ratio from mesoscopic to molecular sized solutes, one moves smoothly between the Derjaguin and the DFT predictions for the depletion force scaled by the colloid radius. We describe the results of a simulation study designed specifically as a test of compatibility with this complex scenario. Grand canonical simulation procedures applied to hard-sphere fluid adsorbed in a series of annular wedges, representing the depletion regime of hard-body colloidal physics, confirm that neither the Derjaguin approximation, nor advanced formulations of DFT, apply at moderate to high solvent density when the geometry is appropriate to nanosized colloids. Our simulations also allow us to report structural characteristics of hard-body solvent adsorbed in hard annular wedges. Both these aspects are key ingredients in the proposal that unifies the disparate predictions, via the introduction of new physics. Our data are consistent with this proposed physics, although as yet limited to a single colloidal size asymmetry.

Extension of scaled particle theory to inhomogeneous hard particle fluids. II. Theory and simulation of fluid structure surrounding a cavity that intersects a hard wall

Integral equations describing the structure of a hard sphere fluid surrounding a cavity that intersects a hard wall are derived from scaled particle theory (SPT). The new expressions are solved exactly for specific cavity radii and the predictions are compared to simulation-generated results, showing excellent agreement. Additional simulation studies are conducted for cavity radii that fall outside the range of exact solution. For all cavity sizes, an enhancement of the local density of hard spheres over that of the hard wall contact value is seen for positions near the point of intersection of the cavity and the hard wall. The local density in front of the cavity and away from the hard wall is depleted at small cavity sizes, but eventually approaches the density profile created by a cavity placed within a bulk hard sphere fluid at larger cavity radii. The exact solutions and simulation results are also used to understand why a minimum appears in the inhomogeneous SPT function G (lambda,h) [D. W. Siderius and D. S. Corti, preceding paper, Phys. Rev. E 71, 036141 (2005)].