RISM theory of polymer liquids: Analytical results for continuum models of melts and alloys

Correlations in Hard- and Soft-Core Generic Polymer Models

Generic polymer models capturing the chain connectivity and the non-bonded excluded-volume interactions between polymer segments can be classified into hard- and soft-core models depending on their non-bonded pair potential. Here we compared the correlation effects on the structural and thermodynamic properties of the hard- and soft-core models given by the polymer reference interaction site model (PRISM) theory, and found different behaviors of the soft-core models at large invariant degree of polymerization (IDP) depending on how IDP is varied. We also proposed an efficient numerical approach, which enables us to accurately solve the PRISM theory for chain lengths as large as 10⁶.

Coarse-graining simulation approaches for polymer melts: the effect of potential range on computational efficiency

The integral equation coarse-graining (IECG) approach is a promising high-level coarse-graining (CG) method for polymer melts, with variable resolution from soft spheres to multi CG sites, which preserves the structural and thermodynamical consistencies with the related atomistic simulations. When compared to the atomistic description, the procedure of coarse-graining results in smoother free energy surfaces, longer-ranged potentials, a decrease in the number of interaction sites for a given polymer, and more. Because these changes have competing effects on the computational efficiency of the CG model, care needs to be taken when studying the effect of coarse-graining on the computational speed-up in CG molecular dynamics simulations. For instance, treatment of long-range CG interactions requires the selection of cutoff distances that include the attractive part of the effective CG potential and force. In particular, we show how the complex nature of the range and curvature of the effective CG potential, the selection of a suitable CG timestep, the choice of the cutoff distance, the molecular dynamics algorithms, and the smoothness of the CG free energy surface affect the efficiency of IECG simulations. By direct comparison with the atomistic simulations of relatively short chain polymer melts, we find that the overall computational efficiency is highest for the highest level of CG (soft spheres), with an overall improvement of the computational efficiency being about 106-108 for various CG levels/resolutions. Therefore, the IECG method can have important applications in molecular dynamics simulations of polymeric systems. Finally, making use of the standard spatial decomposition algorithm, the parallel scalability of the IECG simulations for various levels of CG is presented. Optimal parallel scaling is observed for a reasonably large number of processors. Although this study is performed using the IECG approach, its results on the relation between the level of CG and the computational efficiency are general and apply to any properly-constructed CG model.

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.

Thermodynamic consistency in variable-level coarse graining of polymeric liquids

Numerically optimized reduced descriptions of macromolecular liquids often present thermodynamic inconsistency with atomistic level descriptions even if the total correlation function, i.e. the structure, appears to be in agreement. An analytical expression for the effective potential between a pair of coarse-grained units is derived starting from the first-principles Ornstein-Zernike equation, for a polymer liquid where each chain is represented as a collection of interpenetrating blobs, with a variable number of blobs, n(b), of size N(b). The potential is characterized by a long tail, slowly decaying with characteristic scaling exponent of N(b)(1/4). This general result applies to any coarse-grained model of polymer melts with units larger than the persistence length, highlighting the importance of the long, repulsive, potential tail for the model to correctly predict both structural and thermodynamic properties of the macromolecular liquid.

First-principle approach to rescale the dynamics of simulated coarse-grained macromolecular liquids

We present a detailed derivation and testing of our approach to rescale the dynamics of mesoscale simulations of coarse-grained polymer melts (I. Y. Lyubimov, J. McCarty, A. Clark, and M. G. Guenza, J. Chem. Phys. 132, 224903 (2010)). Starting from the first-principle Liouville equation and applying the Mori-Zwanzig projection operator technique, we derive the generalized Langevin equations (GLEs) for the coarse-grained representations of the liquid. The chosen slow variables in the projection operators define the length scale of coarse graining. Each polymer is represented at two levels of coarse graining: monomeric as a bead-and-spring model and molecular as a soft colloid. In the long-time regime where the center-of-mass follows Brownian motion and the internal dynamics is completely relaxed, the two descriptions must be equivalent. By enforcing this formal relation we derive from the GLEs the analytical rescaling factors to be applied to dynamical data in the coarse-grained representation to recover the monomeric description. Change in entropy and change in friction are the two corrections to be accounted for to compensate the effects of coarse graining on the polymer dynamics. The solution of the memory functions in the coarse-grained representations provides the dynamical rescaling of the friction coefficient. The calculation of the internal degrees of freedom provides the correction of the change in entropy due to coarse graining. The resulting rescaling formalism is a function of the coarse-grained model and thermodynamic parameters of the system simulated. The rescaled dynamics obtained from mesoscale simulations of polyethylene, represented as soft-colloidal particles, by applying our rescaling approach shows a good agreement with data of translational diffusion measured experimentally and from simulations. The proposed method is used to predict self-diffusion coefficients of new polyethylene samples.

Measurement of the interior structure of thin polymer films using grazing incidence diffuse x-ray scattering

A method is developed for calculating the small-angle x-ray scattering originating from within the interior of a thin film under grazing incidence illumination. This offers the possibility of using x-ray scattering to probe how the structure of polymers is modified by confinement. When the diffuse scattering from a thin film is measured over a range of incident angles, it is possible to separate the contributions to scattering from the interfaces and the contribution from the film interior. Using the distorted-wave Born approximation the structure factor, S(q), of the film interior can then be obtained. We apply this method to analyze density fluctuations from within the interior of a silicon supported molten polystyrene (PS) film. Measurements were made as a function of film thickness ranging from one to ten times the polymer radius of gyration (Rg). The compressibility, calculated by extrapolating the measured S(q) to q=0, agrees well with that of bulk PS for thick films, but thinner films exhibit a peak in S(q) near q=0. This peak, which grows with decreasing thickness, is attributed to a decreased interpenetration of chains and a consequent enhanced compressibility.

Thickness induced structural changes in polystyrene films

Changes to the structure of polystyrene melt films as measured through the spectrum of density fluctuations have been observed as a function of film thickness down to the polymer radius of gyration (Rg). Films thicker than 4Rg show bulklike density fluctuations. Thinner films exhibit a peak in S(q) near q=0 which grows with decreasing thickness. This peak is attributed to a decreased interpenetration of chains resulting in an enhanced compressibility. Measurements were made using small angle x-ray scattering in a standing wave geometry designed to enhance scattering from the interior of the film compared to interface scattering.

Theoretical coarse-graining approach to bridge length scales in diblock copolymer liquids

A microscopic theory for coarse graining diblock copolymers into dumbbells of interacting soft colloidal particles has been developed based on the solution of liquid-state integral equations. The Ornstein-Zernike equation is solved to provide a mesoscopic description of the diblock copolymer system at the level of block centers of mass, and at the level of polymer centers of mass. Analytical forms of the total correlation functions for block-block, block-monomer, and center-of-mass pairs are obtained for a liquid of structurally symmetric diblock copolymers as a function of temperature, density, chain length, and chain composition. The theory correctly predicts thermodynamically driven segregation of diblocks into microdomains as a function of temperature (chi parameter). The coarse-grained description contains contributions from density and concentration fluctuations, with the latter becoming dominant as temperature decreases. Numerical calculations for the block coarse-grained total correlation functions, as a function of the proximity of the system to its phase transition, are presented. Comparison with united atom molecular dynamics simulations are carried out in the athermal regime, where simulations and theory quantitatively agree with no need of adjustable parameters.

Wormlike lipid/DNA micelles in a non-polar solvent

The phase behavior of DOPE/DOTAP-DNA complexes in phase-separated oil(dodecane)/water mixtures was explored using Small Angle X-Ray Scattering (SAXS) and Fluorescence Correlation Spectroscopy (FCS). Inverse micelles of DNA with cationic-lipid coating were found in the oil phase. Varying the ratio between cationic and neutral lipids a transition from wormlike to spherical structures is observed for both long ( approximately 75000bp) and short (30-1246bp) DNA. In contrast to lipid/DNA complexes in the water phase, there is no indication of condensed liquid-crystalline structures in the non-polar phase. In fact, FCS measurements on short DNA oligomers complexed with cationic lipid in alkane give clear evidence for monomeric inverse micelles of DNA. Dilution series revealed a critical lower concentration of lipids and DNA for observing lipid/DNA micelles.

Prediction of the Phase Behaviour of Hydrogen-Bonded Polymer Blends

In the early 1990s your authors believed that they had essentially solved the problem of predicting the phase behaviour of hydrogen-bonded polymer blends. A text devoted to this subject, Specific Interactions and the Miscibility of Polymer Blends, was published and we thought that it was now time to look around for something else to do. This was before a colleague, Boris Veytsman, pointed out that there was a flaw in our derivation of the free energy of mixing equation. It has taken us some 15 years to correct the theory and match the predictions of the phase behaviour of hydrogen-bonded blends that we presented in our 1991 book. So we have come full circle. The subject has become far more complicated, but at the same time far more interesting. Along the way we have discovered that the phase behaviour of hydrogen-bonded polymer blends can be successfully predicted using equilibrium constants determined from appropriate low molecular weight analogues, if chain connectivity effects such as intermolecular screening and functional group accessibility are included.

Comparison of the Supramolecular Structures of Two Glyco Lipids with Chiral and Nonchiral Methyl-Branched Alkyl Chains from Natural Sources

Two alkyl glycosides with the same type of disaccharide headgroups (melibiose) and different methyl-branched alkyl chains, short chiral [(2R,4R,6R,8R)-2,4,6,8-tetramethyldecyl, extracted from an animal source] and long nonchiral (3,7,11,15-tetramethylhexadecyl, from a plant source), were synthesized. The supramolecular aggregate structure formed in dilute solutions was investigated by small-angle neutron scattering and surface tension measurements. The lyotropic phase diagram was studied by differential scanning calorimetry and water penetration scans. The thermotropic phase behavior was investigated by polarizing microscopy. The compounds showed unusual phase behavior: (i) The liquid-crystalline polymorphism is reduced to only form smectic A phases in the pure state; the formation of lyotropic phases such as hexagonal or lamellar phases was not observed. (ii) The compound with the longer nonchiral alkyl chain is more soluble in water than the one with the shorter chiral chain, most likely because of the different flexibilities of the chains. (iii) For the long-chain compound, the formation of micelles is observed, whereas the short-chain compound forms large disklike/bilayer aggregates. The method of methylation of the chain controls the self-assembly and can explain different biological functions for either plants (variable temperature) or animals (constant temperature).

Macromolecular theory of solvation and structure in mixtures of colloids and polymers

The structural and thermodynamic properties of mixtures of colloidal spheres and nonadsorbing polymer chains are studied within a general two-component macromolecular liquid state approach applicable for all size asymmetry ratios. The dilute limits, when one of the components is at infinite dilution but the other concentrated, are presented and compared to field theory and to models that replace polymer coils with spheres. Whereas the derived analytical results compare well, qualitatively and quantitatively, with mean-field scaling laws where available, important differences from "effective sphere" approaches are found for large polymer sizes or semidilute concentrations.

Intermolecular structure factors of macromolecules in solution: integral equation results

The intermolecular structure of semidilute polymer solutions is studied theoretically. The low-density limit of a generalized Ornstein-Zernicke integral equation approach to polymeric liquids is considered. Scaling laws for the dilute-to-semidilute crossover of the random-phase approximation (RPA)-like structure are derived for the intermolecular structure factor on large distances when intermolecular excluded volume is incorporated at the microscopic level. This leads to a nonlinear equation for the excluded volume interaction parameter. For macromolecular size-mass scaling exponents nu above a spatial-dimension dependent value, nu(c)=2/d, mean-field-like density scaling is recovered, but for nu<nu(c) the density scaling becomes nontrivial in agreement with field-theoretic results and justifying phenomenological extensions of the RPA. The structure of the polymer mesh in semidilute solutions is discussed in detail and comparisons with large-scale Monte Carlo simulations are added. Finally, a possibility to determine the correction to scaling exponent omega(12) is suggested.