Nonuniversal Behavior of the Thermodynamic Interaction Parameter in Blends of Star and Linear Polybutadiene

Thermodynamic Parameters of Crosslinked Elastomers (BR, SBR and NBR) and Their Blends

Herein, a methodology is employed based on the Flory-Rehner equation for estimating the Flory-Huggins interaction parameter (χ12*) of crosslinked elastomer blends. For this purpose, binary elastomer blends containing polybutadiene rubber (BR), styrene-butadiene rubber (SBR) and nitrile-butadiene rubber (NBR), were prepared in a mixing chamber at a temperature below the activation of the crosslinking agent. Swelling tests with benzene were employed to determine the crosslinked fraction, finding that after 20 min of thermal annealing, the BR and NBR were almost completely crosslinked, while the SBR only reached 60%. Additionally, the BR-SBR blend increased by 2-3 times its volume than its pure components; this could be explained based on the crosslink density. From the mechanical tests, a negative deviation from the rule of mixtures was observed, which suggested that the crosslinking was preferably carried out in the phases and not at the interface. Furthermore, tensile tests and swelling fraction (ϕsw) results were employed to determine the average molecular weight between two crosslinking points (Mc), and subsequently χ12*. Calculated χ12* values were slightly higher than those reported in the literature. The calculated thermodynamic parameters for the blends showed positive ΔGmix values and endothermic behavior, suggesting their immiscible nature.

Macromolecular 'size' and 'hardness' drives structure in solvent-swollen blends of linear, cyclic, and star polymers

In this paper, we apply molecular simulation and liquid state theory to uncover the structure and thermodynamics of homopolymer blends of the same chemistry and varying chain architecture in the presence of explicit solvent species. We use hybrid Monte Carlo (MC)/molecular dynamics (MD) simulations in the Gibbs ensemble to study the swelling of ∼12 000 g mol^-1 linear, cyclic, and 4-arm star polystyrene chains in toluene. Our simulations show that the macroscopic swelling response is indistinguishable between the various architectures and matches published experimental data for the solvent annealing of linear polystyrene by toluene vapor. We then use standard MD simulations in the NPT ensemble along with polymer reference interaction site model (PRISM) theory to calculate effective polymer-solvent and polymer-polymer Flory-Huggins interaction parameters (χ^eff) in these systems. As seen in the macroscopic swelling results, there are no significant differences in the polymer-solvent and polymer-polymer χ^eff between the various architectures. Despite similar macroscopic swelling and effective interaction parameters between various architectures, the pair correlation function between chain centers-of-mass indicates stronger correlations between cyclic or star chains in the linear-cyclic blends and linear-star blends, compared to linear chain-linear chain correlations. Furthermore, we note striking similarities in the chain-level correlations and the radius of gyration of cyclic and 4-arm star architectures of identical molecular weight. Our results indicate that the cyclic and star chains are 'smaller' and 'harder' than their linear counterparts, and through comparison with MD simulations of blends of soft spheres with varying hardness and size we suggest that these macromolecular characteristics are the source of the stronger cyclic-cyclic and star-star correlations.

Modeling intra- and intermolecular correlations for linear and branched polymers using a modified test-chain self-consistent field theory

A modified test-chain self-consistent field theory (SCFT) is presented to study the intra- and intermolecular correlations of linear and branched polymers in various solutions and melts. The key to the test-chain SCFT is to break the the translational symmetry by fixing a monomer at the origin of a coordinate. This theory successfully describes the crossover from self-avoiding walk at short distances to screened random walk at long distances in a semidilute solution or melt. The calculations indicated that branching enhances the swelling of polymers in melts and influences stretching at short distances. The test-chain SCFT calculations show good agreement with experiments and classic polymer theories. We highlight that the theory presented here provides a solution to interpret the polymer conformation and behavior under various conditions within the framework of one theory.

Entropic effects, shape, and size of mixed micelles formed by copolymers with complex architectures

The entropic effects in the comicellization behavior of amphiphilic AB copolymers differing in the chain size of solvophilic A parts were studied by means of molecular dynamics simulations. In particular, mixtures of miktoarm star copolymers differing in the molecular weight of solvophilic arms were investigated. We found that the critical micelle concentration values show a positive deviation from the analytical predictions of the molecular theory of comicellization for chemically identical copolymers. This can be attributed to the effective interactions between copolymers originated from the arm size asymmetry. The effective interactions induce a very small decrease in the aggregation number of preferential micelles triggering the nonrandom mixing between the solvophilic moieties in the corona. Additionally, in order to specify how the chain architecture affects the size distribution and the shape of mixed micelles we studied star-shaped, H-shaped, and homo-linked-rings-linear mixtures. In the first case the individual constituents form micelles with preferential and wide aggregation numbers and in the latter case the individual constituents form wormlike and spherical micelles.

Effective interaction parameter of linear/star polymer blends and comparison with that of linear/linear and star/star blends

The authors present a detailed study of the microscopic parameters, which control the miscibility in binary linear/star polymer blends. The effective interactions of linear/star polymer blends are studied by means of Monte Carlo simulations and comparison is made with linear/linear and star/star blends, which they also determined. Using the bond fluctuation model on a simple cubic lattice, the authors are able to simulate symmetric linear/linear, star/star, and, for the first time, linear/star blends with a moderate number of arms. The simulations were performed at a volume fraction of occupied lattice sites phi=0.5, which corresponds to dense polymer mixtures for this algorithm. In particular, we study star/star blends with 4, 8, and 12 arms and the respective linear/linear blends as well as linear/star blends, all having the same total number of units equal to 73 and 121. The authors find that linear/star blends are more miscible than the corresponding linear/linear blends, which is in agreement with recent experimental and theoretical results. They find that linear/star mixtures are less miscible than star/star blends, a result which is also verified by theoretical findings.

Influence of Acrylate Arm Topology on Phase Diagrams of Mixtures of Multiarm Acrylate Photocurative Monomers and Nematic Liquid Crystals

Phase equilibria of binary mixtures of liquid crystal and multiarm star acrylate derivatives have been established as a function of the number of acrylate arms by means of cloud point determination. Equilibrium phase diagrams of liquid crystal/multiarm acrylate derivatives have been calculated self-consistently in the framework of combined Flory-Huggins free energy of liquid-liquid demixing and Maier-Saupe free energy of nematic ordering. It was found experimentally that the phase diagram of the branched/star molecule/solvent shifts to elevated temperatures with an increasing number of acrylate arms. This movement of the coexistence line is attributed to the architectural effect contributing to the athermal entropic part of the chi interaction parameter. The present self-consistent solution has been tested satisfactorily with the observed phase diagrams of liquid crystal/acrylate systems.

Blends of POSS−PEO(n=4)8 and High Molecular Weight Poly(ethylene oxide) as Solid Polymer Electrolytes for Lithium Batteries

Solid polymer electrolyte blends were prepared with POSS-PEO(n=4)8 (3K), poly(ethylene oxide) (PEO(600K)), and LiClO4 at different salt concentrations (O/Li = 8/1, 12/1, and 16/1). POSS-PEO(n=4)8/LiClO4 is amorphous at all O/Li investigated, whereas PEO(600K) is amorphous only for O/Li = 8/1 and semicrystalline for O/Li = 12/1 and 16/1. The tendency of PEO(600K) to crystallize limited the amount of POSS-PEO(n=4)(8) that could be incorporated into the blends, so that the greatest incorporation of POSS-PEO(n=4)(8) occurred for O/Li = 8/1. Blends of POSS-PEO(n=4)(8)/PEO(600K)/LiClO4 (O/Li = 8/1 and 12/1) microphase separated into two amorphous phases, a low T(g) phase of composition 85% POSS-PEO(n=4)(8)/15% PEO(600K) and a high T(g) phase of composition 29% POSS-PEO(n=4)(8)/71% PEO(600K). For O/Li = 16/1, the blends contained crystalline (pure PEO(600K)), and two amorphous phases, one rich in POSS-PEO(n=4)(8) and one rich in PEO(600K). Microphase, rather than macrophase separation was believed to occur as a result of Li(+)/ether oxygen cross-link sites. The conductivity of the blends depended on their composition. As expected, crystallinity decreased the conductivity of the blends. For the amorphous blends, when the low T(g) (80/20) phase was the continuous phase, the conductivity was intermediate between that of pure PEO(600K) and POSS-PEO(n=4)(8). When the high T(g) (70/30, 50/50, 30/70, and 20/80) phase was the continuous phase, the conductivity of the blend and PEO(600K) were identical, and lower than that for the POSS-PEO(n=4)(8) over the whole temperature range (10-90 degrees C). This suggests that the motions of the POSS-PEO(n=4)(8) were slowed down by the dynamics of the long chain PEO(600K) and that the minor, low Tg phase was not interconnected and thus did not contribute to enhanced conductivity. At temperatures above T(m) of PEO(600K), addition of the POSS-PEO(n=4)(8) did not result in conductivity improvement. The highest RT conductivity, 8 x 10(-6) S/cm, was obtained for a 60% POSS-PEO(n=4)(8)/40% PEO(600K)/LiClO4 (O/Li = 12/1) blend.

Surface migration of branched molecules: Analysis of energetic and entropic factors

We have introduced energetic factors into the response theory developed by Wu and Fredrickson [Macromolecules 29, 7919 (1996)] to predict the enrichment of branched molecules due to architectural effects at surfaces. This development simultaneously increases the utility of the theory for guiding experimental investigations, and makes possible a rigorous assessment of theoretical predictions in careful studies of isotopically labeled linear/branched species binary blends at surfaces. For example, the introduction of energetic factors allows us to predict the existence of a crossover molecular weight, below which an energetically unfavorable species at a surface can be enriched entirely due to architecture. For binary blends of linear chains, the degree of polymerization (Kuhn) of the energetically unfavorable species at the crossover point is r(c) approximately =2U(e)/DeltaU(s). Here, U(e) is the attraction of chain ends towards the surface and DeltaU(s) is the difference in the interaction potential of main chain segments to the surface due to chemical differences and/or isotopic labeling. We also show that surface segregation of an additive in a host polymer due to architectural effects alone is significantly enhanced as the spinodal temperature of a branched/linear blend is approached. Detailed comparisons of the modified response theory with lattice simulations are used to evaluate the theory and to determine the limits of its applicability.

Surface enrichment of branched polymers in linear hosts: Effect of asymmetry in intersegmental interactions and density gradients

Variable density lattice treatment of surface enrichment of f-arm star-branched chains in star/linear polymer blends is compared with results of an analytical response theory proposed by Wu and Fredrickson [Macromolecules 29, 7919 (1996)]. We find that differences in treating the intersegmental interactions in the small interfacial region near a free surface lead to significant differences in the potentials by which polymer chain ends are attracted towards the surface. Consideration of an asymmetric relationship between segment potentials and density changes in polystyrene at 450 K and 0.1 MPa, for example, gives typically a threefold to fourfold enhancement in composition of star molecules at a vacuum interface. When contributions from gradients in density are included in the analysis even greater levels of surface enhancement (fivefold to sixfold increases) are observed. By appropriately estimating the attraction of chain ends and repulsion of branch points at a free surface, we show that concentration profiles of branched polymers predicted in the lattice model are consistent with results obtained in the analytical response theory.