Integral equation theory for atactic polystyrene melt with a coarse-grained model

In this work, an integral equation approach to investigate the atactic polystyrene (aPS) melt based on polymer reference interaction site model (PRISM) theory is proposed. The intramolecular structure factors, required as input to PRISM theory, are obtained from the semiflexible chain model. With a novel coarse-graining procedure and the explicit-atom molecular-dynamics (MD) simulations for aPS, the parameters needed for the coarse-grained model are obtained by using an automatic simplex optimization. These parameters can be used to describe the structure and thermodynamic properties of the complex aPS melt and good agreement is obtained between the theory and MD simulations. The proposed integral equation approach provides a basis for describing the structure and properties of PS nanocomposites where the application of molecular simulation is difficult.     

Structure factor and thermodynamics of rigid dendrimers in solution

The "polymer reference interaction site model" (PRISM) integral equation theory is used to determine the structure factor of rigid dendrimers in solution. The theory is quite successful in reproducing experimental structure factors for various dendrimer concentrations. In addition, the structure factor at vanishing scattering vector is calculated via the compressibility equation using scaled particle theory and fundamental measure theory. The results as predicted by both theories are systematically smaller than the experimental and PRISM data for platelike dendrimers.     

Characterization of polyolefin melts using the polymer reference interaction site model integral equation theory with a single‐site united atom model

A general approach, based on the polymer reference interaction site model (PRISM) integral equation theory, suitable for characterizing arbitrarily complex polyolefin melts is described. We tested the method by calculating the melt structures of linear polyethylene (PE) and isotactic polypropylene (iPP) and the spinodal decomposition temperatures for PE/iPP blends. The computational expense of the PRISM calculation was reduced with a single‐site united atom model in which the polyolefin CH, CH₂, and CH₃ groups were approximated as chemically equivalent sites with spherically symmetric energetic interactions. The site–site interactions were defined by a potential function comprising a hard core with an attractive Lennard–Jones term. These energetic parameters were optimized with a central composite design strategy that enabled a simultaneous fit of experimental melt density and structure factor data. Values were obtained for PE and iPP individually and for common universal parameters that could potentially be used for all polyolefins. The rotational isomeric state–metropolis Monte Carlo (RMMC) technique was used to generate sets of conformers at specified temperatures covering the melt‐temperature range of the polymers. The characteristic ratio was used to assess the quality of the conformers and the RMMC method. Values of 9.68 for PE and 9.27 for iPP were obtained. The single‐chain structure factors calculated by the RMMC method were used to calculate the total structure factor for each melt. These were validated against published X‐ray diffraction results. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1803–1814, 2001     

Integral equation theory of random copolymer melts: self-consistent treatment of intramolecular and intermolecular correlations

A self-consistent integral equation theory is presented for the conformational properties and spinodal lines of random copolymer melts. The theory combines field-theoretic methods with the polymer reference interaction site model (PRISM) theory. The many-chain problem is replaced by a single chain where the sites interact via a bare plus a self-consistently determined medium-induced potential, and the conformational properties are obtained using a variational method. The theoretical prediction for the spinodal line is qualitatively similar to that of non-self-consistent PRISM theory. The theory predicts macroscopic phase separation for all values of the monomer correlation strength, lambda. The inverse spinodal temperature is a nonmonotonic function of lambda with a maximum at lambda(max). For large values of lambda( approximately 1), the values of spinodal temperatures are almost identical to those of non-self-consistent PRISM theory. For low values of lambda, however, the theory predicts higher values for spinodal temperatures than non-self-consistent PRISM theory. The theory predicts significant changes in the mean-square end-to-end distance as the temperature is decreased.     

Monte Carlo simulation and self-consistent integral equation theory for polymers in quenched random media

The conformational properties and static structure of freely jointed hard-sphere chains in matrices composed of stationary hard spheres are studied using Monte Carlo simulations and integral equation theory. The simulations show that the chain size is a nonmonotonic function of the matrix density when the matrix spheres are the same size as the monomers. When the matrix spheres are of the order of the chain size the chain size decreases monotonically with increasing matrix volume fraction. The simulations are used to test the replica-symmetric polymer reference interaction site model (RSP) integral equation theory. When the simulation results for the intramolecular correlation functions are input into the theory, the agreement between theoretical predictions and simulation results for the pair-correlation functions is quantitative only at the highest fluid volume fractions and for small matrix sphere sizes. The RSP theory is also implemented in a self-consistent fashion, i.e., the intramolecular and intermolecular correlation functions are calculated self-consistently by combining a field theory with the integral equations. The theory captures qualitative trends observed in the simulations, such as the nonmonotonic dependence of the chain size on media fraction.     

An interaction site model integral equation study of molecular fluids explicitly considering the molecular orientation

We implemented an interaction site model integral equation for rigid molecules based on a density-functional theory where the molecular orientation is explicitly considered. In this implementation of the integral equation, multiple integral of the degree of freedom of the molecular orientation is performed using efficient quadrature methods, so that the site-site pair correlation functions are evaluated exactly in the limit of low density. We apply this method to Cl(2), HCl, and H(2)O molecular fluids that have been investigated by several integral equation studies using various models. The site-site pair correlation functions obtained from the integral equation are in good agreement with the one from a simulation of these molecules. Rotational invariant coefficients, which characterize the microscopic structure of molecular fluids, are determined from the integral equation and the simulation in order to investigate the accuracy of the integral equation.     

A Singlet-RISM theory for solid/liquid interfaces Part I: uncharged walls

We present a novel integral equation method for the calculation of fluid structure in the vicinity of a plane impenetrable wall. The theory is based on the well-known RISM equation and is capable of dealing with arbitrary interaction site model (ISM) fluids at a solid/liquid interface. In conjunction with several closure approximations, the equations are solved numerically and wall-fluid site density distributions as well as charge density, field, and potential profiles are calculated for pure water and aqueous electrolyte solutions with varying concentrations adjacent to an uncharged soft wall. The results show reasonable agreement with corresponding computer simulation data.     

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.     

Self‐Consistent Integral Equation Theory for Semiflexible Polyelectrolytes in Poor Solvent

Self‐consistent hybrid MC/PRISM method is presented for calculating properties of polyelectrolytes in semidilute and more concentrated regimes in a poor solvent. The static structure and conformational behavior of salt‐free polyelectrolyte solutions composed of semiflexible polyions and monovalent counterions are studied using the approach which combines the traditional Monte‐Carlo (MC) simulation with the numerical solution of the polymer integral PRISM equation. The MC technique is applied to generate the configurations of a single chain molecule and obtain the averaged intrapolymer correlation function. The PRISM equation is then numerically solved for a given monomer density to obtain the various correlation functions and the medium‐induced intrapolymer potential. This is used in a single chain MC simulation, where the polymer sites interact via the bare Coulomb potential together with the short range attractive potential and a self‐consistently determined medium‐induced potential. The monomer‐monomer pair correlation functions and static structure factors are calculated for a large variety of parameters. Conformational properties such as the radius of gyration and visual images are obtained as a function of attractive short‐range interaction, monomer density, Bjerrum length, and chain stiffness. The MC/PRISM study predicts that there is a range of hydrophobicity and monomer density for which polyion chains can form the toroidal structure in a poor solvent. Nonmonotonic dependence of the chain size on monomer density is predicted over the entire range of parameters. Polyion structure factor peak position as a function of density is described. Two concentration regimes in which the polyion structure factors exhibit physically different peaks were found. Over the entire concentration regime considered polyelectrolyte chains undergo strong compression with R_g ∝ lequation/tex2gif-stack-1.gif.

Conformation of a polyion chain for l_B = 2, ε = 0.18 at ρ* = 0.2 and α = 10°.     

Thermal properties and crystalline structure of syndiotactic polystyrene‐based miscible blends

This work examined the effect of the pre‐melting temperature (T_max) on the thermal properties and crystalline structure of four miscible syndiotactic polystyrene (sPS)‐based blends containing 80 wt % sPS. The counterparts for sPS included a high‐molecular‐weight atactic polystyrene [aPS(H)], a medium‐molecular‐weight atactic polystyrene [aPS(M)], a low‐molecular‐weight atactic polystyrene [aPS(L)], and a low‐molecular‐weight poly(styrene‐co‐α‐methyl styrene) [P(S‐co‐αMS)]. According to differential scanning calorimetry measurements, upon nonisothermal melt crystallization, the crystallization of sPS shifted to lower temperatures in the blends, and the shift followed this order of counterpart addition: P(S‐co‐αMS) > aPS(L) > aPS(M) > aPS(H). The change in T_max (from 285 to 315 °C) influenced the crystallization of sPS in the blends to different degrees, depending on the counterpart's molecular weight and cooling rate. The change in T_max also affected the complex melting behaviors of pure sPS and an sPS/aPS(H) blend, but it affected those of the other blends to a lesser extent. Microscopy investigations demonstrated that changing T_max slightly affected the blends' crystalline morphology, but it apparently altered that of pure sPS. Furthermore, the X‐ray diffraction results revealed that the α‐form sPS crystal content in the blends generally decreased with an increase in T_max, and it decreased with a decrease in the cooling rate as well. The blends showed a lower α‐form content than pure sPS; a counterpart of a lower molecular weight more effectively reduced the formation of α‐form crystals. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2798–2810, 2006     

Prediction of tautomer ratios by embedded-cluster integral equation theory

The “embedded cluster reference interaction site model” (EC-RISM) approach combines statistical-mechanical integral equation theory and quantum-chemical calculations for predicting thermodynamic data for chemical reactions in solution. The electronic structure of the solute is determined self-consistently with the structure of the solvent that is described by 3D RISM integral equation theory. The continuous solvent-site distribution is mapped onto a set of discrete background charges (“embedded cluster”) that represent an additional contribution to the molecular Hamiltonian. The EC-RISM analysis of the SAMPL2 challenge set of tautomers proceeds in three stages. Firstly, the group of compounds for which quantitative experimental free energy data was provided was taken to determine appropriate levels of quantum-chemical theory for geometry optimization and free energy prediction. Secondly, the resulting workflow was applied to the full set, allowing for chemical interpretations of the results. Thirdly, disclosure of experimental data for parts of the compounds facilitated a detailed analysis of methodical issues and suggestions for future improvements of the model. Without specifically adjusting parameters, the EC-RISM model yields the smallest value of the root mean square error for the first set (0.6 kcal mol⁻¹) as well as for the full set of quantitative reaction data (2.0 kcal mol⁻¹) among the SAMPL2 participants.     

Effective intramolecular interactions in weakly charged polyelectrolytes: Relation to structural behavior of solution

A self-consistent integral equation theory in the form of a hybrid Monte Carlo/PRISM computation scheme was used to study a polyelectrolyte solution. The static conformational and structural properties of polyions of different rigidities in a good solvent were studied with explicit allowance for counterions over a wide concentration range. An analysis of the calculated effective potentials and correlation functions confirms the presence of effective attraction between units of the charged polymer in semidilute and concentrated solutions; this attraction leads to the collapse of polyions under certain conditions. It was shown that the cause of effective attraction is the dipole-dipole interaction of ion pairs. For the region of polyelectrolyte transition from the semidilute to the concentrated state of solution, the results qualitatively agree with experimental data and theoretical predictions. Visualized images of conformations in the test range of parameters are given.     

Structure of short polymers at interfaces: a combined simulation and theoretical study

The structure of polymers confined between surfaces is studied using computer simulation and a density functional approach. The simple model system considers the polymer molecule as a pearl necklace of freely jointed hard spheres, having attractions among the beads, confined between attractive surfaces. This approach uses the universality of the free-energy functional to obtain the self-consistent field required in the single chain simulation. The second-order direct correlation function for the uniform bulk fluid required as input has been calculated from the reference interaction site model integral equation theory using mean spherical approximation. The theoretical results are shown to compare well with the Monte Carlo simulation results for varying densities, chain lengths, and with different attractive interaction parameters. The simulation results on the conformational properties give important indications regarding the behavior of chains as they approach the surfaces.     

Morphological and Structural Studies of sPS/aPS Blends

Inrecentyears,thenewsedricrystallinepolymersyndiotacticp0lystyrene(sPS)hasat-ITactedmuchattentionduetoitsg0odchendcalresistanceandenhancedmechanicalperformanceatelevatedtemPeratUre.'H0wever,itexhibitshighbrittlenessandpoorimPact-resistanceandtCar-resistance.2Therefore,itisnecessarytomodifyitwithtougheningpolyIners.AsimPlemeth0dto0verc0methedriscibilityofatwo-phaseblendofsPSandatougheningpolymristotwrovetheinterfacialaffmity,wheretheadditionofablockcoP0lymerisconsideredtobemosteffective.3…     

双流体高聚物配位溶液理论——纯物质的状态方程及其应用

以Ｆｌｏｒｙ局部组合型囚胞理论为雏形，引进空穴数，建立了更符合流体特性的双流体高聚物配位统计模型，以配位分数和局部位分数替代原局部组成中面积接触分数和局部面积接触分数概念，用拟化学近似处理局部配位分数，导出纯物质的状态方程，并应用于聚丙烯（ＰＰ）、聚丁烯－１（ＰＢＴ）、聚苯乙烯（ＰＳ）三个体系的关联，取得了良好的关联精度，根据ＰＰ和ＰＢＴ的链节结构与空穴数的关系，预言了高聚物的链节结构和空穴数与聚     

Density functional theory of polymer-polymer phase separation behavior

Polyatomic density functional theory is applied to a binary polymer blend. The polymer reference interaction site model (PRISM) liquid state theory provides the homogeneous state correlation functions necessary for the application of density functional theory. An effective chi parameter can be recognized from the density functional expression; however, the phase separation criteria does not depend solely upon the chi parameter, rather it depends upon various combinations of the species-dependent direct correlation functions of the blend. The Flory-Huggins chi parameter along with the associated phase diagram is obtained when the monomer volumes of the blend species are equal and for a range of monomer-monomer attractive interactions. Calculations are performed both with and without the assumption of incompressibility. The density functional theory along with the PRISM determined “input” predict that an isotopic polymer blend shows an upper critical solution temperature (UCST) phenomena. © 1995 John Wiley & Sons, Inc.     

Investigation of liquid–liquid transition process in atactic polystyrene by means of thermally stimulated depolarization current

Thermally stimulated depolarization current (TSDC) measurement was used to investigate the liquid–liquid transition process of atactic polystyrene (aPS). There are four distinct peaks (α, ρ₁, LL and ρ₂) showed in TSDC spectrum in the range of 300–480 K. Compared with the result of differential scanning calorimetry for aPS, the TSDC spectrum showed that the peak LL located at 422 K could be attributed to the movement of entire chain related to liquid–liquid transition. The isolated peak LL was separated from TSDC spectrum of aPS by curve fitting procedure of the kinetics equation. The distribution of relaxation time of liquid–liquid transition was obtained in terms of the principle of Debye relaxation process. Based on analysis of calculated results, it was confirmed that the relaxation time during the liquid–liquid transition of aPS changed gradually from following Vogel–Fulcher equation to Arrhenius rule with increasing temperature.     

An integral equation theory for inhomogeneous molecular fluids: the reference interaction site model approach

An integral equation theory which is applicable to inhomogeneous molecular liquids is proposed. The "inhomogeneous reference interaction site model (RISM)" equation derived here is a natural extension of the RISM equation to inhomogeneous systems. This theory makes it possible to calculate the pair correlation function between two molecules which are located at different density regions. We also propose approximations concerning the closure relation and the intramolecular susceptibility of inhomogeneous molecular liquids. As a preliminary application of the theory, the hydration structure around an ion is investigated. Lithium, sodium, and potassium cations are chosen as the solute. Using the Percus trick, the local density of solvent around an ion is expressed in terms of the solute-solvent pair correlation function calculated from the RISM theory. We then analyze the hydration structure around an ion through the triplet correlation function which is defined with the inhomogeneous pair correlation function and the local density of the solvent. The results of the triplet correlation functions for cations indicate that the thermal fluctuation of the hydration shell is closely related to the size of the solute ion. The triplet correlation function from the present theory is also compared with that from the Kirkwood superposition approximation, which substitutes the inhomogeneous pair correlation by the homogeneous one. For the lithium ion, the behavior of the triplet correlation functions from the present theory shows marked differences from the one calculated within the Kirkwood approximation.