Reference interaction site model theory of polymeric liquids: Self‐consistent formulation and nonideality effects in dense solutions and melts

RISMiCal: A software package to perform fast RISM/3D-RISM calculations

Solvent plays an essential role in a variety of chemical, physical, and biological processes that occur in the solution phase. The reference interaction site model (RISM) and its three-dimensional extension (3D-RISM) serve as powerful computational tools for modeling solvation effects in chemical reactions, biological functions, and structure formations. We present the RISM integrated calculator (RISMiCal) program package, which is based on RISM and 3D-RISM theories with fast GPU code. RISMiCal has been developed as an integrated RISM/3D-RISM program that has interfaces with external programs such as Gaussian16, GAMESS, and Tinker. Fast 3D-RISM programs for single- and multi-GPU codes written in CUDA would enhance the availability of these hybrid methods because they require the performance of many computationally expensive 3D-RISM calculations. We expect that our package can be widely applied for chemical and biological processes in solvent. The RISMiCal package is available at https://rismical-dev.github.io.

Coexistence of two coacervate phases of polyglycine in water suggested by polymer reference interaction site model theory

Mixing Gibbs energy and phase equilibria of aqueous solutions of polyglycine were studied theoretically by means of polymer reference interaction site model integral equation theory combined with the Gibbs-Duhem method. In addition to the ordinary liquid-liquid phase separation between dilute and concentrated solutions, the theoretical calculation predicted the coexistence of two coacervate phases, namely, the lower- and higher-density coacervates. The relative thermodynamic stabilities of these two phases change with the polymerization degree of polyglycine. The higher-density coacervate phase was rapidly stabilized by increasing the polymer length, and the lower-density phase became metastable at large polymers. The hydrogen bonds between the peptide chains were strengthened, and water was thermodynamically destabilized in the higher-density coacervate. A possible relation with the formation of amyloid fibril within a liquid droplet is also discussed.

Effects of intramolecular chain conformation on the hydration and miscibility of polyethylene glycol in water studied by means of polymer reference interaction site model theory

To examine the conventional idea that the gauche conformation of the OCCO dihedral angle promotes the dissolution of polyethylene glycol (PEG) in water through strong hydration, the thermodynamic properties of liquid mixtures of PEG and water were studied by means of polymer reference interaction site model (PRISM) theory. The intramolecular correlation functions required as input for PRISM theory were calculated by the generator matrix method, accompanied by changes in the distribution of dihedral angles. In the infinite dilution limit, the increased probability of gauche conformation of the OCCO dihedral angles stabilizes the hydration of PEG through enhanced hydrogen bonding between the ether oxygen of PEG and water. The mixing Gibbs energies of the liquid mixtures were also calculated in the whole concentration range based on the Gibbs-Duhem equation, as per our recent proposal. A liquid-liquid phase separation was observed when all the dihedral angles of PEG were in the trans conformation; for the liquid mixture to be miscible in the whole concentration range, the introduction of the OCCO gauche conformation was found to be indispensable. The above theoretical results support the conventional idea that the OCCO gauche conformation is important for the high miscibility of PEG and water.

Systematic and simulation-free coarse graining of homopolymer melts: a relative-entropy-based study

We applied the systematic and simulation-free strategy proposed in our previous work (D. Yang and Q. Wang, J. Chem. Phys., 2015, 142, 054905) to the relative-entropy-based (RE-based) coarse graining of homopolymer melts. RE-based coarse graining provides a quantitative measure of the coarse-graining performance and can be used to select the appropriate analytic functional forms of the pair potentials between coarse-grained (CG) segments, which are more convenient to use than the tabulated (numerical) CG potentials obtained from structure-based coarse graining. In our general coarse-graining strategy for homopolymer melts using the RE framework proposed here, the bonding and non-bonded CG potentials are coupled and need to be solved simultaneously. Taking the hard-core Gaussian thread model (K. S. Schweizer and J. G. Curro, Chem. Phys., 1990, 149, 105) as the original system, we performed RE-based coarse graining using the polymer reference interaction site model theory under the assumption that the intrachain segment pair correlation functions of CG systems are the same as those in the original system, which de-couples the bonding and non-bonded CG potentials and simplifies our calculations (that is, we only calculated the latter). We compared the performance of various analytic functional forms of non-bonded CG pair potential and closures for CG systems in RE-based coarse graining, as well as the structural and thermodynamic properties of original and CG systems at various coarse-graining levels. Our results obtained from RE-based coarse graining are also compared with those from structure-based coarse graining.

Critical Casimir effect in a polymer chain in supercritical solvents

Density fluctuation effects on the conformation of a polymer chain in a supercritical solvent were investigated by performing a multiscale simulation based on the density-functional theory. We found (a) a universal swelling of the polymer chain near the critical point, irrespective of whether the polymer chain is solvophilic or solvophobic, and (b) a characteristic collapse of the polymer chain having a strong solvophilicity at a temperature slightly higher than the critical point, where the isothermal compressibility becomes less than the ideal one.

Interaction of cylindrical polymer brushes in dilute and semi-dilute solution

We present a systematic study of flexible cylindrical brush-shaped macromolecules in a good solvent by small-angle neutron scattering (SANS), static light scattering (SLS), and by dynamic light scattering (DLS) in dilute and semi-dilute solution. The SLS and SANS data extrapolated to infinite dilution lead to the shape of the polymer that can be modeled in terms of a worm-like chain with a contour length of 380 nm and a persistence length of 17.5 nm. SANS data taken at higher polymer concentration were evaluated by using the polymer reference interaction site model (PRISM). We find that the persistence length reduce from 17.5 nm at infinite dilution to 5.3 nm at the highest concentration (volume fraction 0.038). This is comparable with the decrease of the persistence length in semi-dilute concentration predicted theoretically for polyelectrolytes. This finding reveals a softening of stiffness of the polymer brushes caused by their mutual interaction.

Softening of the stiffness of bottle-brush polymers by mutual interaction

We study bottle-brush macromolecules in a good solvent by small-angle neutron scattering (SANS), static light scattering (SLS), and dynamic light scattering (DLS). These polymers consist of a linear backbone to which long side chains are chemically grafted. The backbone contains about 1600 monomer units (weight average) and every second monomer unit carries side chains with approximately 60 monomer units. The SLS and SANS data extrapolated to infinite dilution lead to the form factor of the polymer that can be described in terms of a wormlike chain with a contour length of 380 nm and a persistence length of 17.5 nm. An analysis of the DLS data confirms these model parameters. The scattering intensities taken at finite concentration can be modeled using the polymer reference interaction site model. It reveals a softening of the bottle-brush polymers caused by their mutual interaction. We demonstrate that the persistence decreases from 17.5 nm down to 5 nm upon increasing the concentration from dilute solution to the highest concentration (40.59 gl) under consideration. The observed softening of the chains is comparable to the theoretically predicted decrease of the electrostatic persistence length of linear polyelectrolyte chains at finite concentrations.

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.

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.

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.

Self-consistent molecular theory of polymers in melts and solutions

We propose a self-consistent molecular theory of conformational properties of flexible polymers in melts and solutions. The method employs the polymer reference interaction site model for the intermolecular correlations and the Green function technique for the intramolecular correlations. We demonstrate this method on n-alkane molecules in different environments: water, hexane, and in melt, corresponding to poor, good, and theta condition, respectively. The numerical results of the intramolecular correlation function, the radius of gyration, and the characteristic ratio of a polymer chain are indicative of conformational changes from one environment to another and are in agreement with other findings in the literature. Scaling laws for the chain size with respect to the number of monomers are discussed. We show results for the intra- and intermolecular correlation functions and the medium-induced potential. We also extract the Kuhn length and the characteristic ratio for the infinite chain limit for melts. The latter is compared to the experimental results and computer simulation. The conformational free energy per monomer in different solvents is calculated. Our treatment can be generalized readily to other polymer-solvent systems, for example, those containing branched copolymers and polar solvents.

Static properties of a simulated supercooled polymer melt: structure factors, monomer distributions relative to the center of mass, and triple correlation functions

We analyze structural and conformational properties in a simulated bead-spring model of a nonentangled, supercooled polymer melt. We explore the statics of the model via various structure factors, involving not only the monomers, but also the center of mass (CM). We find that the conformation of the chains and the CM-CM structure factor, which is well described by a recently proposed approximation [Europhys. Lett. 58, 53 (2002)]], remain essentially unchanged on cooling toward the critical glass transition temperature T(c) of mode-coupling theory. Spatial correlations between monomers on different chains, however, depend on temperature, albeit smoothly. This implies that the glassy behavior of our model cannot result from static intrachain or CM-CM correlations. It must be related to interchain correlations at the monomer level. Additionally, we study the dependence of interchain correlation functions on the position of the monomer along the chain backbone. We find that this site dependence can be well accounted for by a theory based on the polymer reference interaction site model. We also analyze triple correlations by means of the three-monomer structure factors for the melt and for the chains. These structure factors are compared with the convolution approximation that factorizes them into a product of two-monomer structure factors. For the chains this factorization works very well, indicating that chain connectivity does not introduce special triple correlations in our model. For the melt deviations are more pronounced, particularly at wave vectors close to the maximum of the static structure factor.