Liquid-state theory of anisotropic flexible polymer fluids

Orientational ordering transitions of semiflexible polymers in thin films: a Monte Carlo simulation

Athermal solutions (from dilute to concentrated) of semiflexible macromolecules confined in a film of thickness D between two hard walls are studied by means of grand-canonical lattice Monte Carlo simulation using the bond fluctuation model. This system exhibits two phase transitions as a function of the thickness of the film and polymer volume fraction. One of them is the bulk isotropic-nematic first-order transition, which ends in a critical point on decreasing the film thickness. The chemical potential at this transition decreases with decreasing film thickness ("capillary nematization"). The other transition is a continuous (or very weakly first-order) transition in the layers adjacent to the hard planar walls from the disordered phase, where the bond vectors of the macromolecules show local ordering (i.e., "preferential orientation" along the x or y axes of the simple cubic lattice, but no long-range orientational order occurs), to a quasi-two-dimensional nematic phase (with the director at each wall being oriented along either the x or y axis), while the bulk of the film is still disordered. When the chemical potential or monomer density increase, respectively, the thickness of these surface-induced nematic layers grows, causing the disappearance of the disordered region in the center of the film.

Theory of glassy dynamics in conformationally anisotropic polymer systems

A mode coupling theory for the ideal glass transition temperature, or crossover temperature to highly activated dynamics in the deeply supercooled regime, T(c), has been developed for anisotropic polymer liquids. A generalization of a simplified mode coupling approach at the coarse-grained segment level is employed which utilizes structural and thermodynamic information from the anisotropic polymer reference interaction site model theory. Conformational alignment or/and coil deformation modifies equilibrium properties and constraining interchain forces thereby inducing anisotropic segmental dynamics. For liquid-crystalline polymers a small suppression of T(c) with increasing nematic or discotic orientational order is predicted. The underlying mechanism is reduction of the degree of coil interpenetration and intermolecular repulsive contacts due to segmental alignment. For rubber networks chain deformation results in an enhanced bulk modulus and a modest elevation of T(c) is predicted. The theory can also be qualitatively applied to systems that undergo nonuniversal local deformation and alignment, such as polymer thin films and grafted brush layers, and large elevations or depressions of T(c) are possible. Extension to treat directionally dependent collective barrier formation and activated hopping is possible.

Thermodynamics, Orientational Order and Elasticity of Strained Liquid Crystalline Melts and Elastomers

A microscopic polymer liquid-state theory has been developed for the structure, thermodynamics and mechanical properties of strained liquid crystalline elastomers. The theory captures the experimentally observed phenomenon of spontaneous distortion and establishes a direct correlation between it and the nematic order parameter. Strain induced softening of the elastic modulus is predicted to emerge due to coupling of the induced orientational order and anisotropic interchain excluded volume interactions. Comparison of our results with limited experiments shows good qualitative and sometimes quantitative agreement. The theory predicts that deformation in the liquid crystalline state results in an increase of the amplitude of density fluctuations (compressibility) which becomes more pronounced as chain degree of polymerization and/or segmental density are decreased.

Microscopic theory of rubber elasticity

A microscopic integral equation theory of elasticity in polymer liquids and networks is developed which addresses the nonclassical problem of the consequences of interchain repulsive interactions and packing correlations on mechanical response. The theory predicts strain induced softening, and a nonclassical intermolecular contribution to the linear modulus. The latter is of the same magnitude as the classical single chain entropy contribution at low polymer concentrations, but becomes much more important in the melt state, and dominant as the isotropic-nematic liquid crystal phase transition is approached. Comparison of the calculated stress-strain curve and induced nematic order parameter with computer simulations show good agreement. A nearly quadratic dependence of the linear elastic modulus on segmental concentration is found, as well as a novel fractional power law dependence on degree of polymerization. Quantitative comparison of the theory with experiments on polydimethylsiloxane networks are presented and good agreement is found. However, a nonzero modulus in the long chain limit is not predicted since quenched chemical crosslinks and trapped entanglements are not explicitly taken into account. The theory is generalizable to treat the structure, thermodynamics and mechanical response of nematic elastomers.

Microscopic theory of orientational order, structure and thermodynamics in strained polymer liquids and networks

A microscopic integral equation theory of the segmental orientational order parameter, structural correlations and thermodynamics of strained polymer solutions, melts and networks has been developed. The nonclassical problem of the consequences of intermolecular excluded volume repulsions and chain connectivity is addressed. The theory makes several novel predictions, including effective power law dependences of the orientational order parameter on monomer concentration and chain degree of polymerization, and strain hardening of the bulk modulus. The predictions of a nearly classical strain dependence, and supralinear scaling with segment concentration, of the strain-induced nematic order parameter is in agreement with nuclear magnetic resonance experiments. The absolute magnitudes of the a priori calculated orientational order parameter agree with simulations and experiments to within a factor of 2. The possible complicating influence of "trapped entanglements" in crosslinked networks is discussed. Extensions of the theory are possible to treat the mechanical response of flexible polymer liquids and rubbers, and the structure, thermodynamics, and mechanical properties of strained liquid crystal forming polymers.

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.