Structure and thermodynamics of anisotropic polymer fluids

Ion-Concentration-Hopping Heterolayer Gel for Ultrahigh Gradient Energy Conversion

Conventional solid ion channel systems relying on single one- or two-dimensional confined nanochannels enabled selective and ultrafast convective ion transport. However, due to intrinsic solid channel stacking, these systems often face pore-pore polarization and ion concentration blockage, thereby restricting their efficiency in macroscale ion transport. Here, we constructed a soft heterolayer-gel system that integrated an ion-selective hydrogel layer with a water-barrier organogel layer, achieving ultrahigh cation selectivity and flux and effectively providing high-efficiency gradient energy conversion on a macroscale order of magnitude. Specifically, the hydrogel layer featured an unconfined 3D network, where the fluctuations of highly hydrated polyelectrolyte chains driven by thermal dynamics enhanced cation selectivity and mitigated transfer energy barriers. Such chain fluctuation mechanisms facilitated ion-cluster internal transmission, thereby enhancing ion concentration hopping for more efficient ion-selective transport. Compared to the existing rigid nanochannel-based gradient energy conversion systems, such a heterogel-based power generator exhibited a record power density of 192.90 and 1.07 W/m2 at the square micrometer scale and square centimeter scale, respectively (under a 500-fold artificial solution). We anticipate that such heterolayer gels would be a promising candidate for energy separation and storage applications.

Segmental dynamics in polymers: from cold melts to ageing and stressed glasses

Recent progress in developing statistical mechanical theories of supercooled polymer melts and glasses is reviewed. The focus is on those approaches that are either explicitly formulated for polymers, or are applications of more generic theories to interpret polymeric phenomena. These include two configurational entropy theories, a percolated free volume distribution model, and the activated barrier hopping nonlinear Langevin theory. Both chemically-specific and universal aspects are discussed. After a brief summary of classic phenomenological approaches, a discussion of the relevant length scales and key experimental phenomena in both the supercooled liquid and glassy solid state is presented including ageing and nonlinear mechanical response. The central concepts that underlie the theories in the molten state are then summarized and key predictions discussed, including the glass transition in oriented polymer liquids and deformed rubber networks. Physical ageing occurs in the nonequilibrium glass, and theories for its consequences on the alpha relaxation are discussed. Very recent progress in developing a segment scale theory for the dramatic effects of external stress on polymer glasses, including acceleration of relaxation, yielding, plastic flow and strain hardening, is summarized. The article concludes with a discussion of outstanding theoretical challenges.

Glassy dynamics and kinetic vitrification of isotropic suspensions of hard rods

A nonlinear Langevin equation (NLE) theory for the translational center-of-mass dynamics of hard nonspherical objects has been applied to isotropic fluids of rigid rods. The ideal kinetic glass transition volume fraction is predicted to be a monotonically decreasing function beyond an aspect ratio of two. The functional form of the decrease is weaker than the inverse aspect ratio. Vitrification occurs at lower volume fractions for corrugated tangent bead rods compared to their smooth spherocylinder analogs. The ideal glass transition signals a crossover to activated dynamics, which is estimated to be observable before the nematic phase boundary is encountered if the aspect ratio is less than roughly 25. Calculations of the glassy elastic shear modulus and absolute yield stress reveal a roughly exponential growth with volume fraction. The dependence of entropic barriers and mean barrier hopping times on concentration for rods of variable aspect ratios can be collapsed quite well based on a difference volume fraction variable that quantifies the distance from the ideal glass boundary. Full numerical solution of the NLE theory via stochastic trajectory simulation was performed for tangent bead rods, and the results were compared to their hard sphere analogs. With increasing shape anisotropy the characteristic length scales of the nonequilibrium free energy increase and the magnitude of the localization well and entropic barrier curvatures decreases. These changes result in a significant aspect ratio dependence of dynamical properties and time correlation functions including weaker intermediate time subdiffusive transport, stronger two-step decay of the incoherent dynamic structure factor, longer mean alpha relaxation time, and stronger wavevector-dependent decoupling of relaxation times and the self-diffusion constant. The theoretical results are potentially testable via computer simulation, confocal microscopy, and dynamic light scattering.

Orientational order and dynamics of the dendritic liquid crystal organo-siloxane tetrapodes determined using dielectric spectroscopy

The dielectric measurements have been carried out on the two zeroth generation dendrimers with four branched arms (called tetrapodes) based on the siloxane cores. The results are analyzed in the framework of the molecular theory of dielectric permittivity by Maier and Meier for nematogens. At least four molecular processes are resolved in the dielectric relaxation spectra in the nematic phase for each of the two tetrapodes. Three of them are assigned to the reorientation of the monomeric unit whereas the fourth is assigned to the rotation of the molecular segments in the individual arms of the monomeric unit around the long molecular axis. The dielectric relaxation strength of the low frequency process has been used to calculate the orientational order parameter. The dynamics of the resolved processes has been quantitatively analyzed using the results of the microscopic model of the rotational diffusion, given by Coffey and Kalmykov [W. T. Coffey and Yu. P. Kalmykov, Adv. Chem. Phys. 113, 487 (2000)] using the calculated order parameter. All molecular processes: the rotation around the short molecular axis (end-over-end rotation), precession around the director and the rotation around the long molecular axis (also called the spinning motion) are shown to have successfully been reproduced by the model. The anisotropy of the rotational diffusion coefficients gradually increases with a reduction in temperature, to a factor of 3 in the nematic phase relative to its isotropic phase.

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.