Reference Interaction Site Model Theory Research Articles

Effect of attractive interactions on the structure of polymer melts confined between surfaces: A density-functional approach

A density-functional theory is presented to study the structure of polymers, having attractive interactions, confined between attractive surfaces. The theory treats the ideal-gas free-energy functional exactly and uses weighted density approximation for the hard-chain contribution to the excess free-energy functional. The bulk interactions of freely jointed hard spheres are obtained from generalized Flory equation of state and the attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions are found to be in quite good agreement with the Monte Carlo simulation results for varying densities, chain lengths, and different interaction potentials. The results confirm important implications of using different approximations for the hard-sphere and attractive interactions.

Barrier hopping, viscous flow, and kinetic gelation in particle-polymer suspensions

The naive mode coupling-polymer reference interaction site model (MCT-PRISM) theory of gelation and elasticity of suspensions of hard sphere colloids or nanoparticles mixed with nonadsorbing polymers has been extended to treat the emergence of barriers, activated transport, and viscous flow. The barrier makes the dominant contribution to the single particle relaxation time and shear viscosity, and is a rich function of the depletion attraction strength via the polymer concentration, polymer-particle size asymmetry ratio, and particle volume fraction. The dependences of the barrier on these three system parameters can be accurately collapsed onto a single scaling variable, and the resultant master curve is well described by a power law. Nearly universal master curves are also constructed for the hopping or alpha relaxation time for system conditions not too close to the ideal MCT transition. Based on the calculated barrier hopping time, a theory for kinetic gel boundaries is proposed. The form and dependence on system parameters of the kinetic gel lines are qualitatively the same as obtained from prior ideal MCT-PRISM studies. The possible relevance of our results to the phenomenon of gravity-driven gel collapse is studied. The general approach can be extended to treat nonlinear viscoelasticity and rheology of polymer-colloid suspensions and gels.

Solvation dynamics in water investigated by RISM/mode-coupling theory

The reference interaction site model (RISM) theory combined with the generalized Langevin/mode-coupling theory (MCT) is applied to the investigation of solvation dynamics in water. The dynamic response function S S( t) which measures the energy relaxation of the system is calculated with different model solutes. The RISM–MCT framework recently presented by Yamaguchi and coworkers [ J. Chem. Phys., 117 (2002) 2216; Mol. Phys., 101 (2003) 1211] is shown to be applicable well to the realistic description of solvation dynamics. S S( t) initially relaxes with a Gaussian decay followed by an overdamping oscillation with the time period of 30 fs. As the multiplicity of the solute pole is increased, the magnitude of the S S( t) damping becomes smaller and relaxation gets slower.

Integral equation theory for two-dimensional polymer melts

The polymer reference interaction site model theory is investigated for two-dimensional polymer melts composed of freely-jointed hard disk chains and tangent-disk rods. Exact results for the intramolecular pair correlation functions are input into the theory, and predictions of the theory for the intermolecular pair correlation functions are tested via comparison with simulation. The theory is not as accurate for this system as it is for three-dimensional polymer melts, and the quantitative predictions are not good except at the highest area fractions. Possible reasons for the deficiency in the theory are discussed.

Analysis of K+/Na+ selectivity of KcsA potassium channel with reference interaction site model theory

As a preliminary approach, we have successfully analysed K+/Na+ selectivity of the KcsA potassium channel for the most selective ion occupancy state (1010) at the atomic level by using the reference interaction site model (RISM) integral equation theory [Q. Cui, V.H. Smith, Chem. Phys. Lett. 365, 110 (2002)]. With similar methods, in this paper, we analyse seven other most relevant ion occupancy states: (0101), (0110), (1001), (1000), (0100), (0010) and (0001). By analysing all the most relevant states, we are able to characterize some dynamic properties of the systems. More detailed solvation structures of the selectivity filter are presented and more solvation energetic data are obtained and compared with the available molecular dynamics simulation data. We predict consistent results with the simulations in that ions are best dehydrated at binding site 2. For ion occupancy states of most interest, we obtain good relative solvation free energies in comparison with the simulation data. The results in this paper further support the conclusion in our previous paper that the selectivity filter favours K+ over Na+ from the point of view of solvation.

Partial Molar Volume of Proteins Studied by the Three-Dimensional Reference Interaction Site Model Theory

The three-dimensional reference interaction site model (3D-RISM) theory is applied to the analysis of hydration effects on the partial molar volume of proteins. For the native structure of some proteins, the partial molar volume is decomposed into geometric and hydration contributions using the 3D-RISM theory combined with the geometric volume calculation. The hydration contributions are correlated with the surface properties of the protein. The thermal volume, which is the volume of voids around the protein induced by the thermal fluctuation of water molecules, is directly proportional to the accessible surface area of the protein. The interaction volume, which is the contribution of electrostatic interactions between the protein and water molecules, is apparently governed by the charged atomic groups on the protein surface. The polar atomic groups do not make any contribution to the interaction volume. The volume differences between low- and high-pressure structures of lysozyme are also analyzed by the present method.

Density Functional Theory of Realistic Models of Polyethylene Liquids in Slit Pores: Comparison with Monte Carlo Simulations

Density functional theory is applied to study properties of fully detailed, realistic models of polyethylene liquids near surfaces and compared to results from Monte Carlo simulations. When the direct correlation functions from polymer reference interaction site model (PRISM) theory are used as input, the theory somewhat underpredicts the density oscillations near the surface. However, good agreement with simulation is obtained with empirical scaling of the PRISM-predicted direct correlation functions. Effects of attractive interactions are treated using the random-phase approximation. The results of theoretical predictions for the attractive system are also in reasonable agreement with simulation results. In general, the theory performs best when the wall-polymer interaction strength is comparable to polymer-polymer interactions.

Combination of the Replica-Exchange Monte Carlo Method and the Reference Interaction Site Model Theory for Simulating a Peptide Molecule in Aqueous Solution

This article reports the first attempt to combine the replica-exchange Monte Carlo method and the reference interaction site model (RISM) theory for simulating a peptide molecule in aqueous solution. The energy function is the sum of the conformational energy and the solvation free energy. The solvation free energy for a fixed conformation of the peptide molecule is calculated using the RISM theory. The replica-exchange method is modified so that the dependence of the energy function on the temperature can be incorporated. The effectiveness of the combined approach is demonstrated for Met-enkephalin in water. It is argued that the number of replicas required for a peptide molecule immersed in water is drastically reduced by employing the combined approach. Solvation properties and free energy surfaces of Met-enkephalin in water are discussed.

Structure, surface excess and effective interactions in polymer nanocomposite melts and concentrated solutions.

The Polymer Reference Interaction Site Model (PRISM) theory is employed to investigate structure, effective forces, and thermodynamics in dense polymer-particle mixtures in the one and two particle limit. The influence of particle size, degree of polymerization, and polymer reduced density is established. In the athermal limit, the surface excess is negative implying an entropic dewetting interface. Polymer induced depletion interactions are quantified via the particle-particle pair correlation function and potential of mean force. A transition from (nearly) monotonic decaying, attractive depletion interactions to much stronger repulsive-attractive oscillatory depletion forces occurs at roughly the semidilute-concentrated solution boundary. Under melt conditions, the depletion force is extremely large and attractive at contact, but is proceeded by a high repulsive barrier. For particle diameters larger than roughly five monomer diameters, division of the force by the particle radius results in a nearly universal collapse of the depletion force for all interparticle separations. Molecular dynamics simulations have been employed to determine the depletion force for nanoparticles of a diameter five times the monomer size over a wide range of polymer densities spanning the semidilute, concentrated, and melt regimes. PRISM calculations based on the spatially nonlocal hypernetted chain closure for particle-particle direct correlations capture all the rich features found in the simulations, with quantitative errors for the amplitude of the depletion forces at the level of a factor of 2 or less. The consequences of monomer-particle attractions are briefly explored. Modification of the polymer-particle pair correlations is relatively small, but much larger effects are found for the surface excess including an energetic driven transition to a wetting polymer-particle interface. The particle-particle potential of mean force exhibits multiple qualitatively different behaviors (contact aggregation, steric stabilization, local bridging attraction) depending on the strength and spatial range of the polymer-particle attraction.

Solvation thermodynamics of protein studied by the 3D-RISM theory

The partial molar volume and the solvation free energy of five globular proteins in aqueous solutions are calculated by the three-dimensional reference interaction site model theory, a modern integral equation theory of molecular liquids. The partial molar volume calculated by the theory shows quantitative agreement with the corresponding experimental data. Concerning the solvation free energy, the theoretical results are compared with estimations by an empirical method which uses the accessible surface area of atoms, because the corresponding experimental data are not available. Possible applications of the method to problems related to the solvation thermodynamics of protein are discussed.

Solute Dependence of Polar Solvation Dynamics Studied by RISM/Mode-Coupling Theory

We apply the combination of the reference interaction-site model (RISM) theory and mode-coupling theory (MCT) for the description of solvation dynamics in acetonitrile. The RISM theory is used for the static features of the solute–solvent system, whereas MCT is employed to capture solvent dynamics. We calculate the dynamic response function of the average-energy relaxation of the system, SS(t), a corresponding quantity which is experimentally measured through the dynamic Stokes shift of fluorescence spectra, for example. The RISM–MCT framework turns out to be very applicable for realistic estimation of SS(t). We vary the model solutes from a simple ion, to dumbbell dipoles, to quadrupole, to octapole. As a general feature, SS(t) begins to relax with the initial Gaussian decay, followed by the underdamped oscillation. Higher multiplicity of the pole or larger charges put on the solute-site causes SS(t) to relax more slowly. We suggest this behavior is related to an increased complexity of solvent–solvent interactions just around the charged sites on the solute. On the other hand, the amplitude of the underdamped oscillation becomes smaller as the multiplicity of the pole increases.

Microscopic theory of gelation and elasticity in polymer-particle suspensions.

A simplified mode-coupling theory (MCT) of ergodic-nonergodic transitions, in conjunction with an accurate two-component polymer reference interaction site model (PRISM) theory for equilibrium structural correlations, has been systematically applied to investigate gelation, localization, and elasticity of flexible polymer-hard particle suspensions. The particle volume fraction at the fluid-gel transition is predicted to depend exponentially on reduced polymer concentration and size asymmetry ratio at relatively high colloid concentrations. In contrast, at lower particle volume fractions, a power-law dependence on polymer concentration is found with effective exponents and prefactors that depend systematically on the polymer/particle size ratio. Remarkable power-law and near universal scaling behavior is found for the localization length and elastic shear modulus. Multiple experiments for gel boundaries and shear moduli are in good agreement with the no adjustable parameter theory. The one exception is the absolute magnitude of the shear modulus which is strongly overpredicted, apparently due to nonequilibrium dense cluster formation. The simplified MCT-PRISM theory also captures the qualitative aspects of the weak depletion-driven "glass melting" phenomenon at high particle volume fractions. Calculations based on an effective one-component model of structure within a low particle volume fraction framework yield qualitatively different features than the two-component approach and are apparently all in disagreement with experiments. This suggests that volume fraction and size asymmetry dependent many-body screening of polymer-mediated depletion attractions at finite particle concentrations are important.

Liquid-State Theory of Structure, Thermodynamics, and Phase Separation in Suspensions of Rod Polymers and Hard Spheres

A new formulation of the polymer reference interaction site model (PRISM) theory for suspensions of hard spheres and rigid rods has been developed. The nonlocal loss of orientational entropy when a rod is near an impenetrable particle is accounted for in a thermodynamically self-consistent manner. In the ideal needle limit, quantitative predictions and qualitative scaling behaviors are determined for the depletion potential, rod insertion chemical potential, intermolecular pair correlations, and fluid−fluid spinodal phase-separation boundaries as a function of rod−particle size-asymmetry and mixture variables. The needle-induced depletion potential of mean force between a pair of particles is in good agreement with exact numerical results and experiments on dilute silica−virus suspensions. Needle-induced clustering of colloidal particles is studied, and the PRISM results are in good agreement with the small amount of available simulation data. The behavior of spinodal boundaries in the extreme size-asymme...

Integral Equation Theory of Polymer Solutions: Application to Polyethylene/Benzene Solutions

Solutions of polyethylene macromolecules immersed in benzene were modeled with self-consistent polymer reference interaction site model (PRISM) theory. The PRISM integral equations for the solution were solved self-consistently for the polyethylene intramolecular chain structure and intermolecular polymer and solvent correlations at various mole fractions. We found that explicitly considering the solvent molecules leads to considerably more short-range structure in the radial distribution function of the polymer, relative to the polymer without solvent at the same concentration. The long-range intermolecular correlations between polymer sites in the correlation hole regime decreased inversely with the polymer concentration as expected. The solvent/solvent radial distribution function, however, showed unexpected changes in shape and intensity as the polymer concentration increased. By using the direct correlation functions from PRISM theory, along with the random phase approximation, we estimated the spinodal temperatures as a function of polymer concentration. PRISM theory, which includes compressibility and nonrandom mixing effects, predicted a significantly higher critical temperature than was obtained from the corresponding incompressible Flory−Huggins theory. The PRISM spinodal curves were in reasonable agreement with experimental dissolution temperatures for octacosane in benzene.

Liquid state theories for the structure of water

Liquid state theories are investigated for the local structure of the simple point charge (SPC) and a modified SPC (MSPC) model of water. The latter model includes a van der Waals repulsion between the oxygen (O) and hydrogen (H) atoms, which is necessary for the implementation of some integral equation theories. Two integral equation theories, the reference interaction site model (RISM) and the diagrammatically proper Chandler–Silbey–Ladanyi (CSL) theory, are tested by comparison with simulations of the MSPC model (neither theory converges for the SPC model when the hypernetted chain closure is used). The RISM theory is in reasonable agreement with simulations, and is more accurate than the CSL theory. A density functional theory (DFT) is investigated, which treats the ideal gas functional exactly and uses a truncated expansion for the excess free energy functional. The DFT is in excellent agreement with simulations for the structure of the MSPC water model at all temperatures studied, and for the structure of the SPC water model at high temperatures. At room temperature, the DFT is in good agreement with simulations (of SPC water) for gHH(r) and gOH(r), but misses the location of the second peak in gOO(r). We attribute this deficiency to the importance of three-body correlations that are not properly incorporated in the theory.

Viscoelasticity and rheology of depletion flocculated gels and fluids

The flow properties of high volume fraction hard sphere colloid–polymer suspensions are studied as a function of polymer concentration, depletion attraction range, and solvent quality up to, and well beyond, the gelation boundary. As the gel boundary is approached, the shear viscosity tends to diverge in a critical power law manner at a polymer concentration that is a function of the polymer radius of gyration and solvency condition. The shear viscosity for different polymer size suspensions can be collapsed onto a master curve motivated by mode coupling theory (MCT). The low frequency elastic modulus grows rapidly with increasing depletion attraction near the gel boundary, but becomes a dramatically weaker function of polymer concentration as the gel state is more deeply entered. A simplified version of MCT with accurate, no adjustable parameter polymer reference interaction site model (PRISM) theory structural input has been applied to predict the gelation boundaries and elastic shear moduli. The calculated gel lines are in semiquantitative agreement with experiment at high volume fractions, but increasingly deviate upon particle dilution. Calculations of the dependence of the gel elastic shear moduli on particle-polymer size asymmetry and scaled polymer concentration are in excellent agreement with experiment, and deep in the gel follow a power law dependence on polymer concentration. Quantitatively, MCT-PRISM elastic moduli are higher than experiment by a nearly constant large factor. This discrepancy is suggested to be due to the heterogeneous nature of the gel structure which small angle scattering experiments show consists of dense clusters and voids of characteristic length scales ∼4–7 particle diameters. A simple idea for correcting the particle level MCT modulus by employing cluster network concepts is proposed.

Partial molar volume and compressibility of a molecule with internal degrees of freedom

Statistical mechanical expressions for the partial molar volume (PMV) and the partial molar compressibility (PMC) of a solute molecule with internal degrees of freedom are derived. The equilibrium PMV is expressed simply by the conformational ensemble average of PMV. The equilibrium PMC consists of two terms: the conformational ensemble average of PMC and the mean square fluctuation of PMV along conformational axis. As an illustrative application of the theory, the equilibrium PMV and PMC of butane in aqueous solution are calculated from the relations, in which the thermodynamic quantities of each conformer appearing in the relations are obtained by the reference interaction site model theory. The conformational ensemble average of PMC is the predominant contribution to the equilibrium PMC in this particular example. Possibility of shedding light on the protein conformation in terms of PMV and PMC is discussed.

Scattering Studies of the Structure of Colloid−Polymer Suspensions and Gels

Depletion-driven changes in the structure of hard-sphere particles (radius R) mixed with a nonadsorbing polymer (radius of gyration Rg) dissolved in good (athermal) and ideal (theta) solvents are systematically studied. Colloidal structure factors, S(q), are determined using slit-smeared and pinhole-collimated ultra-small-angle X-ray scattering and small-angle neutron scattering. A comparison of the structure factors extracted from the three methods demonstrates the validity of the available desmearing algorithms. Polymer additives alter the colloidal structure more for larger particle volume fractions (φc) and smaller size asymmetry ratios Rg/R. At fixed φc ∼ 0.40 and Rg/R = 0.06, increasing the reduced polymer concentration (cp/cp*) results in a monotonic shift to higher wavevectors of the location of the first peak in the structure factor, q*, and a nonmonotonic variation of the cage order parameter, S(q*), in a nearly solvent quality independent manner. Local structural correlations arrest as the gel state is entered. The reduced polymer concentration required for gelation is smaller in athermal solvents compared to its theta analogue and, in both cases, is well below the fluid−fluid spinodal boundaries. Comparisons between the measured structure factors and no-adjustable-parameter predictions of the polymer reference interaction site model theory shows near quantitative agreement over all wavevectors. When the gel phase is entered, strong differences between the theory and the experiment emerge, indicating the nonequilibrium nature of structural correlations in the nonergodic gel. Relative to equilibrium expectations, enhanced (reduced) fluctuations occur at small (intermediate) wavevectors. The combined experimental and theoretical results suggest that neither long wavelength fluctuations nor the local cage structure are the primary origin of the gelation transition.

Stretching, Packing, and Thermodynamics in Highly Branched Polymer Melts

Within the framework of the polymer reference interaction site model (PRISM) theory, we formulate a simplified method for enforcing conformational self-consistency associated with screening of intrapolymer excluded-volume interactions. It is built on a utilization of the Flory ideality concept, preaveraging of site inequivalency, and the insensitivity of equation-of-state properties of chemically identical polymers to global architecture variation at constant temperature and pressure. The approach allows calculation of the influence of chain branching on average macromolecular stretching under meltlike conditions. Nonideal conformational swelling, intermolecular pair correlation functions, and the cohesive energy as a function of architectural variables have been studied for a variety of star and regular comb models. Predictions for a specific highly globular comb melt are in good agreement with a recent experiment. The relatively weak influence of the nonuniversal local aspect ratio and melt compressibility on polymer stretching is also established. Implications for the χ parameter in isotopic star or comb blends, and the miscibility of mixtures of linear and branched polymers, are briefly discussed.

Density functional theory for nonuniform polymers: Accurate treatment of the effect of attractive interactions

A density functional theory is presented for the effect of fluid–fluid and fluid–surface attractive interactions on the structure of polymers at surfaces. The theory treats the ideal gas free-energy functional exactly and uses a weighted density approximation for the hard chain contribution to the excess free-energy functional. The attractive interactions are calculated using the bulk fluid direct correlation function obtained from the polymer reference interaction site model theory. The predictions of the theory are in good agreement with computer simulation results for the density profiles of freely rotating fused-sphere chains at surfaces for a wide range of densities and temperatures. The results emphasize the importance of using different approximations for the hard sphere and attractive interactions in density functional theories for polymers.