Hard Sphere Solvent Research Articles

Theoretical study of solvent-mediated Ising-like systems: One-dimensional version

We theoretically study physical properties of solutes placed in a straight line and at regular intervals. The solute is a rigid-body and has an arrow-like shape, which changes its direction up (↑) or down (↓). If the rigid solutes are immersed in a continuum solvent, nothing happens in the system (it is an obvious fact). However, the property of the directions differs in a granular solvent (e.g., hard-sphere solvent). Depending on the distance between the nearest-neighbor solutes, the directional correlation between them is periodically changed as follows: “parallel-tendency (↑↑)” ↔ “random” ↔ “antiparallel-tendency (↑↓)”. Studying a newly created nanosystem, it is able to discover interesting properties hiding in the nanosystem. We believe that such an approach contributes to the development of nanotechnology.

Excess properties of aqueous solutions: hard spheres versus pseudo-hard bodies

The effect of repulsive interactions (geometrical packing of molecules) on mixing properties is examined considering hard sphere solutes of different diameters in the hard sphere and pseudo-hard body solvents. It is shown that the fluid of pseudo-hard bodies, representing repulsive interactions in water, captures, without any parameter adjustment, the experimentally observed decrease of the partial molar volume of nonpolar solutes (hard spheres) at their low concentrations when compared to that in a nonpolar (hard sphere) solvent.

Hybrid MC−DFT Method for Studying Multidimensional Entropic Forces

Entropic force has been a focus of many recent theoretical studies because of its fundamental importance in solution thermodynamics and its close relevance to a broad range of practical applications. Whereas previous investigations are mostly concerned with the potential energy as a one-dimensional function of the separation, here we propose a hybrid method for studying multidimensional systems by combining Monte Carlo simulation for the microscopic configurations of the solvent and the density functional theory for the free energy. We demonstrate that the hybrid method predicts the potential of mean force between a test particle and various concave objects in a hard-sphere solvent in excellent agreement with the results from alternative but more expensive computational methods. In particular, the hybrid method captures the entropic force between asymmetric particles and its dependence on the particle size and shape that underlies the "lock and key" interactions. Because the same molecular model is used for the theory and simulation, we expect that the hybrid method provides a new avenue to efficient computation of entropic forces in complex molecular systems.

An efficient method for analyzing conformational properties of a polymer in solvent

We propose an efficient method for investigating conformational properties of a polymer in solvent. The method is a combination of a Monte Carlo (MC) simulation applied to the polymer alone and a statistical-thermodynamic approach for incorporating solvent effects. To illustrate it, we analyze conformations of a simple polymer chain stabilized in a hard-sphere solvent. The generation of polymer conformations is performed using the self-avoiding random walk on a cubic lattice. We argue that by introducing the generalized-ensemble techniques to the MC simulation part, the method can be applied to studies on protein conformations in aqueous solution under any thermodynamic condition.

An Effective Solvent Theory Connecting the Underlying Mechanisms of Osmolytes and Denaturants for Protein Stability

An all-atom Gō model of Trp-cage protein is simulated using discontinuous molecular dynamics in an explicit minimal solvent, using a single, contact-based interaction energy between protein and solvent particles. An effective denaturant or osmolyte solution can be constructed by making the interaction energy attractive or repulsive. A statistical mechanical equivalence is demonstrated between this effective solvent model and models in which proteins are immersed in solutions consisting of water and osmolytes or denaturants. Analysis of these studies yields the following conclusions: 1), Osmolytes impart extra stability to the protein by reducing the entropy of the unfolded state. 2), Unfolded states in the presence of osmolyte are more collapsed than in water. 3), The folding transition in osmolyte solutions tends to be less cooperative than in water, as determined by the ratio of van 't Hoff to calorimetric enthalpy changes. The decrease in cooperativity arises from an increase in native structure in the unfolded state, and thus a lower thermodynamic barrier at the transition midpoint. 4), Weak denaturants were observed to destabilize small proteins not by lowering the unfolded enthalpy, but primarily by swelling the unfolded state and raising its entropy. However, adding a strong denaturant destabilizes proteins enthalpically. 5), The folding transition in denaturant-containing solutions is more cooperative than in water. 6), Transfer to a concentrated osmolyte solution with purely hard-sphere steric repulsion significantly stabilizes the protein, due to excluded volume interactions not present in the canonical Tanford transfer model. 7), Although a solution with hard-sphere interactions adds a solvation barrier to native contacts, the folding is nevertheless less cooperative for reasons 1–3 above, because a hard-sphere solvent acts as a protecting osmolyte.

Theoretical study of solvent effects on the coil-globule transition

The coil-globule transition of a polymer in a solvent has been studied using Monte Carlo simulations of a single chain subject to intramolecular interactions as well as a solvent-mediated effective potential. This solvation potential was calculated using several different theoretical approaches for two simple polymer/solvent models, each employing hard-sphere chains and hard-sphere solvent particles as well as attractive square-well potentials between some interaction sites. For each model, collapse is driven by variation in a parameter which changes the energy mismatch between monomers and solvent particles. The solvation potentials were calculated using two fundamentally different methodologies, each designed to predict the conformational behavior of polymers in solution: (1) the polymer reference interaction site model (PRISM) theory and (2) a many-body solvation potential (MBSP) based on scaled particle theory introduced by Grayce [J. Chem. Phys. 106, 5171 (1997)]. For the PRISM calculations, two well-studied solvation monomer-monomer pair potentials were employed, each distinguished by the closure relation used in its derivation: (i) a hypernetted-chain (HNC)-type potential and (ii) a Percus-Yevick (PY)-type potential. The theoretical predictions were each compared to results obtained from explicit-solvent discontinuous molecular dynamics simulations on the same polymer/solvent model systems [J. Chem. Phys. 125, 194904 (2006)]. In each case, the variation in the coil-globule transition properties with solvent density is mostly qualitatively correct, though the quantitative agreement between the theory and prediction is typically poor. The HNC-type potential yields results that are more qualitatively consistent with simulation. The conformational behavior of the polymer upon collapse predicted by the MBSP approach is quantitatively correct for low and moderate solvent densities but is increasingly less accurate for higher densities. At high solvent densities, the PRISM-HNC and MBSP approaches tend to overestimate, while the PRISM-PY approach underestimates the tendency of the solvent to drive polymer collapse.

Depletion effects in a mixture of hard and attractive colloids

Monte Carlo simulation and theory were used to study the potential of mean force (PMF) between a pair of big colloidal (solute) particles suspended in a sea of smaller particles (solvent) interacting via Baxter's sticky hard sphere (SHS) potential. Simulation results were obtained by applying a special simulation technique developed for sampling the hard sphere collision force, while the theoretical predictions were calculated from the analytic solution of the Percus-Yevick/Ornstein-Zernike integral equation for spatial correlations in a two-component mixture at vanishing solute concentration. Both theory and simulation revealed oscillations of the solute-solute PMF with a period equal to the diameter of the solvent molecules. Further, the attractive PMF between solute particles in the SHS fluid decays slower than in a hard sphere solvent. Upon increasing the strength of attraction (stickiness) between the molecules of solvent, these oscillations gradually disappear, the PMF becoming long ranged and attractive at all separations.

Why χ Is Seldom Zero for Polymer−Solvent Mixtures

Typical good nonpolar solvents for nonpolar polymers have values of the Flory interaction parameter χ of 0.3 or higher. This is striking since miscible nonpolar polymer blends exist with well-matched solubility parameters and resulting very small χ values of 10−2 or less. Using a cell model, it has been previously argued that there is a generic contribution to χ in polymer−solvent systems of about 0.3, which ultimately arises from the difference in affinity for free volume of bonded chain mers and otherwise identical solvent mers. We explore this result with off-lattice MC simulations of hard-sphere freely jointed chains in identical hard-sphere solvent. We observe reductions in chain radii of gyration and of virial coefficients for dimers among hard-sphere solvents versus in vacuum, consistent with the cell model results. Finally, we extract free volume distributions and observe reduced free volume of chain mers compared to solvent. With a model of a single mer in a fluctuating cell surrounded by hard-sphere fluid, we construct free volume distributions in good agreement with our MC results and previous work of Sastry et al. on hard-sphere liquids.

Conformation of a polymer chain in explicit solvent: A solvation potential approach

AbstractIn much of the theoretical work on polymers in dilute solution the effects of solvent are treated in an implicit fashion: thus one studies an isolated chain interacting via an effective site–site potential. Although a formally exact mapping is possible between the chain‐in‐solvent system and a corresponding isolated effective‐potential‐chain, this mapping involves a many‐site solvation potential which is not practical to compute. Thus, one generally resorts to a two‐site potential approximation. In this article we test the validity of this two‐site approximation for a short hard‐sphere (HS) n‐mer chain (n ≤ 5) in a HS solvent. This test involves computing a set of “exact” site–site solvation potentials for an isolated chain. These potentials are shown to reproduce the conformation of a chain in explicit solvent. We make use of these exact short‐chain results (combining them with the solvent potential of mean force) to construct approximate two‐site solvation potentials for long chains. Monte Carlo simulations have been performed for HS chain‐in‐solvent systems and for the corresponding isolated effective‐potential n‐mer chain with n ≤ 50. These simulations show that our solvation potentials provide a quantitatively accurate description of the conformation of a HS chain in explicit (hard sphere) solvent. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3319–3326, 2007

Solvation of Proteins: Linking Thermodynamics to Geometry

We calculate the solvation free energy of proteins in the tube model of Banavar and Maritan [Rev. Mod. Phys. 75, 23 (2003)10.1103/RevModPhys.75.23] using morphological thermodynamics which is based on Hadwiger's theorem of integral geometry. Thereby we extend recent results by Snir and Kamien [Science 307, 1067 (2005)10.1126/science.1106243] to hard-sphere solvents at finite packing fractions and obtain new conclusions. Depending on the solvent properties, parameter regions are identified where the beta sheet, the optimal helix, or neither is favored.

Oscillatory structure of confined fluids

The confinement of fluids in pores and wedges is associated with exponentially damped oscillatory packing structure, as observed with the surface forces apparatus. This paper reviews the statistical mechanics of confined fluids and then illustrates the results with density functional data for hard-sphere solvent. The free energy of the pore fluid and its functional derivatives with respect to thermodynamic fields all oscillate, as a function of pore width, with a wavelength close to the solvent diameter. In contrast, the density at the centre of pores oscillates with twice this wavelength, as a function of pore width. The development of a unified physics of confined fluids is considered. Approximations based on one-dimensional physics do extraordinarily well in planar symmetry at three-dimensions.

Depletion forces between nonspherical objects

We extend the insertion approach for calculating depletion potentials to the case of nonspherical solutes. We suggest to employ the recently developed curvature expansion of density profiles close to complexly shaped walls. The approximations introduced in the calculation by the use of the curvature expansion and of weight functions for nonspherical objects can be tested independently. As an application for our approach we calculate and discuss the depletion potential between two hard oblate ellipsoids in a solvent of hard spheres. For this system we calculate the entropic force and torque acting on the objects.

Towards a microscopic theory of wetting by ionic solutions. I. Surface properties of the semi-primitive model

As a first step towards a density functional theory (DFT) of wetting by ionic solutions we examine the density profiles of ions and solvent molecules confined near a charged wall, or between two walls, and the corresponding interfacial properties, including adsorption, surface tension, solvation force and electrostatic properties, within the semi-primitive model (SPM) of solutions made up of hard sphere solvent particles and charged hard spheres. Both monovalent and divalent cations with species-dependent diameters are considered. The density functional includes the best available Rosenfeld hard-sphere functional, as well as mean-field and Coulomb correlation contributions. The simpler mean-field functional is found to be adequate, at least for monovalent ions. The size differences lead to an interesting ‘fine structure’ of the density and charge density profiles. Cohesive interactions between all species are shown to lead to significant changes in the density profiles.

Shape factors in equations of state : Part II. Repulsion phenomena in multicomponent chain fluids

An equation of state for the multicomponent fluid phase of nonattracting rigid particles of arbitrary shape is presented. The equation is a generalization of a previously presented equation of state for pure fluids of rigid particles; the approach describes the volumetric properties of a pure fluid in terms of a shape factor, zeta, which can be back calculated by scaling the volumetric properties of pure fluids to that of a hard sphere. The performance of the proposed equation is tested against mixtures of chain fluids immersed in a "monomeric" solvent of hard spheres of equal and different sizes. Extensive new Monte Carlo simulation data are presented for 19 binary mixtures of hard homonuclear tangent freely-jointed hard sphere chains (pearl-necklace) of various lengths (three to five segments), with spheres of several size ratios and at various compositions. The performance of the proposed equation is compared to the hard-sphere SAFT approach and found to be of comparable accuracy. The equation proposed is further tested for mixtures of spheres with spherocylinders. In all cases, the equation proved to be accurate and simple to use.

Transient cavities and the excess chemical potentials of hard-spheroid solutes in dipolar hard-sphere solvents

Monte Carlo computer simulations are used to study transient cavities and the solvation of hard-spheroid solutes in dipolar hard-sphere solvents. The probability distribution of spheroidal cavities in the solvent is shown to be well described by a Gaussian function, and the variations of fit parameters with cavity elongation and solvent properties are analyzed. The excess chemical potentials of hard-spheroid solutes with aspect ratios x in the range of 15< or =x< or =5, and with volumes between 1 and 20 times that of a solvent molecule, are presented. It is shown that for a given molecular volume and solvent dipole moment (or temperature) a spherical solute has the lowest excess chemical potential and hence the highest solubility, while a prolate solute with aspect ratio x should be more soluble than an oblate solute with aspect ratio 1x. For a given solute molecule, the excess chemical potential increases with increasing temperature; this same trend can be observed in hydrophobic solvation. A scaled-particle theory based on the solvent equation of state and a fitted solute-solvent interfacial tension shows excellent agreement with the simulation results over the whole range of solute elongations and volumes considered. An information-theoretic model based on the solvent density and radial distribution function is less successful, being accurate only for small solute volumes and low solvent densities.

Parametric Studies of Interaction Strengths in Polymer/CO2 Systems: Discontinuous Molecular Dynamics Simulations

Discontinuous molecular dynamics simulations are performed on homopolymer/solvent and surfactant/solvent systems. The homopolymer and surfactant molecules are modeled as freely jointed square-well chains. Solvent molecules are modeled as both hard spheres and square-well spheres. We explore how the various interaction parameters affect the types of phase behavior and micellization observed in the homopolymer/solvent and surfactant/solvent systems. Increasing the packing fraction of homopolymers in both hard-sphere solvents and square-well solvents increases the solvent's ability to dissolve homopolymers only when the segment-solvent interaction strength exceeds a critical value. Although only upper critical solution temperature (UCST) behavior is observed for homopolymers in hard-sphere solvents, both UCST and lower critical solution temperature (LCST) behavior are observed for homopolymers in square-well solvents, depending upon the interaction strengths and chain length. This indicates that it is necessary to account for the solvent-solvent attraction to model LCST behavior in supercritical CO2. Our simulation results on surfactants in hard-sphere solvents show that it is necessary to account for the interactions experienced by both the head and tail blocks in order to capture the essential features of surfactant/supercritical CO2 systems.

Isostructural solid–solid transitions in binary asymmetrical hard sphere system: Based on solvent-mediated potential

Size dependence is imparted onto a modified bridge functional, adopted for a recently proposed semi-analytical hard sphere reference system theory for calculation of solvent-mediated potential (SMP). The SMP for two large hard sphere particles immersed in a small hard sphere solvent bath predicted by the present improved version is in satisfactory agreement with the prediction from a theoretically based fitting formula. Isostructural solid–solid transitions in the binary asymmetrical hard sphere system are investigated based on a single-component macrofluid approximation combined with the improved version. It is found that the isostructural solid–solid transition appears when size asymmetry increases. The limiting asymmetry size ratio is near 1 / 8 . As the size asymmetry increases, critical density for both large and small hard sphere components for the fcc isostructural solid–solid transition increases and decreases, respectively.

Simulation and approximate formulae for the radial distribution functions of highly asymmetric hard sphere mixtures

The Henderson and Chan (HC) formulae for the contact values of the radial distribution functions (RDFs) of a highly asymmetric hard sphere mixture are reconsidered in light of a recent formula of Roth, Evans and Dietrich for the RDF of a pair of exceedingly large spheres at zero concentration in a solvent of small hard spheres. Two modifications of the HC formulae using this result give a large sphere–large sphere contact value that is considerably smaller than that of the original formulation. These new HC results are compared with the molecular dynamics simulations of Lue and Woodcock, for a diameter ratio of 1:10, supplemented by a few new results that are reported here. The new HC formulae are in much better agreement with the MD results than is the popular Boublik–Mansoori–Carnahan–Starling–Leland formula. Also, some simulation results for the RDFs as functions of separation are reported.

Conformation of a polymer chain in solution: An exact density expansion approach

The conformation of a polymer chain in solution is intrinsically coupled to the thermodynamic and structural properties of the solvent. Here we study such solvent effects in a system consisting of a flexible interaction-site n-mer chain immersed in a monomeric solvent. Chain conformation is described with a set of intramolecular site-site probability functions. We derive an exact density expansion for these intramolecular probability functions and give a diagrammatic representation of the terms contributing at each order of the expansion. The expansion is tested for a short hard-sphere chain (n=3 or 4) with site diameter sigma in a hard-sphere solvent with solvent diameter D. In comparison with Monte Carlo simulation results for 0.2< or =D/sigma< or =100, the expansion (taken to second order) is found to be quantitatively accurate for low to moderate solvent volume fractions for all size ratios. Average chain dimensions are predicted accurately up to liquidlike solvent densities. The hard-sphere chains are compressed with both increasing solvent density and decreasing solvent size. For small solvent (D<sigma), depletion effects are found and the chain structure is strongly perturbed even at low solvent volume fractions.

Interaction energy and force for a pair of colloidal particles in a bidisperse hard-sphere solvent

Interaction energy and force for a pair of colloidal particles in a bidisperse hard-sphere solvent