Kenneth Schweizer - Academia.edu (original) (raw)

Papers by Kenneth Schweizer

ACS applied materials & interfaces, Jan 6, 2015

We report a three-dimensional (3D) porous carbon electrode containing both nanoscale and microsca... more We report a three-dimensional (3D) porous carbon electrode containing both nanoscale and microscale porosity, which has been hierarchically organized to provide efficient ion and electron transport. The electrode organization is provided via the colloidal self-assembly of monodisperse starburst carbon spheres (MSCSs). The periodic close-packing of the MSCSs provides continuous pores inside the 3D structure that facilitate ion and electron transport (electrode electrical conductivity ∼0.35 S m(-1)), and the internal meso- and micropores of the MSCS provide a good specific capacitance. The capacitance of the 3D-ordered porous MSCS electrode is ∼58 F g(-1) at 0.58 A g(-1), 48% larger than that of disordered MSCS electrode at the same rate. At 1 A g(-1) the capacitance of the ordered electrode is 57 F g(-1) (95% of the 0.24 A g(-1) value), which is 64% greater than the capacitance of the disordered electrode at the same rate. The ordered electrode preserves 95% of its initial capacitanc...

Journal of Physics-condensed Matter - J PHYS-CONDENS MATTER, 2006

Weak depletion gels with particle radii of ∼200–500 nm have been reported to display a time-depen... more Weak depletion gels with particle radii of ∼200–500 nm have been reported to display a time-dependent settling behaviour where an initially space spanning gel displays a catastrophic collapse after a characteristic period of time, defined as the delay time. Several experiments suggest that thermally activated particle rearrangements promote macroscopic gel coarsening, which ultimately triggers the rapid collapse. The delay time is found to be a sensitive function of the colloid volume fraction and polymer concentration. We have performed systematic experiments on the silica–decalin–polystyrene depletion system to explore how colloid volume fraction, polymer concentration, particle radius and ratio of polymer radius of gyration to particle radius influence the delayed collapse time of transient gels. We employ a recently developed activated barrier-hopping theory to make predictions of the timescales over which colloids can escape localized states as a function of system parameters. ...

The Journal of Physical Chemistry B, 2005

A microscopic polymer liquid-state theory has been developed for the structure, thermodynamics an... more 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.

Physical Review E, 2008

The coupled activated dynamics in dense mixtures of repulsive and sticky hard spheres is studied ... more The coupled activated dynamics in dense mixtures of repulsive and sticky hard spheres is studied using stochastic nonlinear Langevin equation theory. The effective free energy surface, barriers, saddle point trajectories, and mean first passage times depend in a rich manner on mixture composition, (high) total volume fraction, and attractive interaction strength. In general, there are three types of saddle point trajectories or relaxation pathways: a pure sticky or pure repulsive particle displacement keeping the other species localized, and a cooperative motion involving repulsive and attractive particle displacements. The barrier for activated hopping usually increases with the ratio of sticky to repulsive particle displacement. However, at intermediate values of the displacement ratio it can attain a broad plateau value, and can even exhibit a local maximum, and hence nonmonotonic behavior, at high sticky particle mixture compositions if the attraction strength is modest. The mean first passage, or hopping, times are computed using multidimensional Kramers theory. In most cases the hopping time trends reflect the behavior of the barrier height, especially as the sticky particle attraction strengths become large. However, there are dramatic exceptions associated with cooperative repulsive and attractive particle trajectories where the barriers are high but a greatly enhanced number of such trajectories exist near the saddle point.

Physical Review E, 2008

A statistical segment scale theory for the physical aging of polymer glasses is proposed and appl... more A statistical segment scale theory for the physical aging of polymer glasses is proposed and applied. The approach is based on a nonlinear stochastic Langevin equation of motion and the concept of an effective free energy which quantifies temporary localization, collective barriers, and the activated segment hopping process. The key collective structural variable that plays the role of the dynamic order parameter for aging is the experimentally measurable nanometer and longer wavelength amplitude of density fluctuations, S0 . The degree of local cooperativity, and the bare activation energy of the high-temperature Arrhenius process, are determined in the molten state by utilizing experimental measurements of the glass temperature and dynamic crossover time, respectively. A first-order kinetic equation with a time varying rate is proposed for the temporal evolution of S0 which is self-consistently and nonlinearly coupled with the mean segmental relaxation time. The theory has been applied to study physical aging of the alpha relaxation time, shear relaxation modulus, amplitude of density fluctuations, cohesive energy, absolute yield stress, and fictive temperature of polymethylmethacrylate and other glasses over a range of temperatures. Temperature-dependent logarithmic and effective power-law aging is predicted at intermediate times. Time-aging time superposition is found for the mechanical relaxation function. A strongly asymmetric aging response is predicted for up and down temperature jump experiments. Comparison of the approach with the classic phenomenological model is presented.

Macromolecules, 1990

Polymer RISM (reference interaction site model) theory is used to examine the intermolecular radi... more Polymer RISM (reference interaction site model) theory is used to examine the intermolecular radial distribution function and isothermal compressibility of semiflexible polymer melts. Chains are modeled as a series of linked, hard sites with a local bending energy proportional to the cosine of the bond angle. Chain stiffness is controlled by a single parameter, the persistence length, which may be matched to the material of interest. Comparisons of the predicted intermolecular radial distribution functions to the molecular dynamics results of Grest and Kremer for chains of 50, 100, and 150 sites show very good agreement on all length scales. Parametric studies as a function of chain length and chain stiffness reveal that as the characteristic stiffness is increased beyond three bond lengths, the radial distribution function and isothermal compressibility saturate, becoming relatively insensitive to chain length or stiffness. At low densities the local structure is dominated by a correlation hole, indicating a relative absence of intermolecular neighbors, while at high densities the pair correlation function shows a peak and valley structure, qualitatively similar to that of monatomic fluids.

Macromolecules, 2013

We combine polymer integral equation theory and computational chemistry methods to study the inte... more We combine polymer integral equation theory and computational chemistry methods to study the interfacial structure, effective interactions, miscibility and spatial dispersion mechanism of fullerenes dissolved in specific random AB copolymer melts characterized by strong noncovalent electron donor–acceptor interactions with the nanofiller. A statistical mechanical basis is developed for designing random copolymers to optimize fullerene dispersion at intermediate copolymer compositions. Pair correlation calculations reveal a strong sensitivity of interfacial packing near the fullerene to copolymer composition and adsorption energy mismatch. The potential of mean force between fullerenes displays rich trends, often nonmonotonic with copolymer composition, reflecting a nonadditive competition between direct filler attractions and polymer-mediated bridging and steric stabilization. The spinodal phase diagrams are in qualitative agreement with recent solubility limit experimental observations on three systems, ...

Macromolecules, 1993

Microscopic equations-of-state are developed for n-alkanes and polyethylene based on the polymer ... more Microscopic equations-of-state are developed for n-alkanes and polyethylene based on the polymer reference interaction site model (PRISM) integral equation theory and a generalized Flory approach. The molecules are modeled as a series of overlapping spheres (methylene groups) with constant bond length and bond angles; internal rotations are accounted for by the rotational isomeric state approximation. The interaction between sites on different molecules is taken to be of the Lennard-Jones form. The thermodynamic properties of the fluid are obtained via standard perturbation theory in which the potential is divided into a repulsive reference system and an attractive perturbation. The reference system is approximated by a hard-core repulsion in which the hard-sphere diameter d(T) is estimated for polyethylene from wide-angle X-ray scattering experiments. The PRISM theory is used to calculate the hard-sphere chain contribution to the equation-of-state by three different thermodynamic routes: (1) integrating the compressibility, (2) evaluating the density profile at a hard wall, and (3) using a hard-sphere 'charging" method analogous to the virial approach in monatomic liquids. The generalized Flory dimer (GFD) theory is used to obtain a fourth equation-of-state for the hard-sphere chains. The attractive perturbation is treated with first-order perturbation theory, making use of the radial distribution functiongo(r) of the reference system. The various equations-of-state presented differ in the route to the hard-chain pressure; PRISM is used in all cases to treat the attractions. Excellent agreement for the equation-of-state is found between the hybrid GFD/PRISM calculations and molecular dynamics simulations of n-butane and experimental pressure-volume-temperature (PVT) measurements on polyethylene melts. The compressibility and charging routes predict pressures which are too low and too high, respectively, for polyethylene. The wall route yields pressures in good agreement at experimental densities but predicts a melt which is too compressible.

The Journal of Chemical Physics, 2000

We apply an anisotropic version of the polymer reference interaction site model ͑PRISM͒ integral ... more We apply an anisotropic version of the polymer reference interaction site model ͑PRISM͒ integral equation description of flexible polymers to analyze athermal liquid crystallinity. The polymers are characterized by a statistical segment length, o , and by a physical hard-core thickness, d, that prevents the overlap of monomers on different chains. At small segment densities, , the microscopic length scale d is irrelevant ͑as it must be in the universal semidilute regime͒, but becomes important in concentrated solutions and melts. Under the influence of the excluded volume interactions alone, the chains undergo a lyotropic, first-order isotropic-nematic transition at a concentration dependent upon the dimensionless ''aspect ratio,'' o /d. The transition becomes weaker as d→0, becoming second order, as has been previously shown. We extend the theory to describe the transition of rigid, thin rods, and discuss the evolution of the anisotropic liquid structure in the ordered phase.

The Journal of Chemical Physics, 2005

A recently proposed microscopic activated barrier hopping theory [K. S. Schweizer and E. J. Saltz... more A recently proposed microscopic activated barrier hopping theory [K. S. Schweizer and E. J. Saltzman, J. Chem. Phys. 119, 1181 (2003)] of slow single-particle dynamics in glassy liquids, suspensions, and gels is derived using nonequilibrium statistical mechanics. Fundamental elements underlying the stochastic nonlinear Langevin equation description include an inhomogeneous liquid or locally solid-state perspective, dynamic density-functional theory (DDFT), a local equilibrium closure, and a coarse-grained free-energy functional. A dynamic Gaussian approximation is not adopted which is the key for avoiding a kinetic ideal glass transition. The relevant excess free energy is of a nonequilibrium origin and is related to dynamic force correlations in the fluid. The simplicity of the approach allows external perturbations to be rather easily incorporated. Dynamic heterogeneity enters naturally via mobility fluctuations associated with the stochastic barrier-hopping process. The derivation both identifies the limitations of the theory and suggests new avenues for its systematic improvement. Comparisons with ideal mode-coupling theory, alternative DDFT approaches and a field theoretic path-integral formulation are presented.

The Journal of Chemical Physics, 2004

A microscopic integral equation theory of elasticity in polymer liquids and networks is developed... more 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.

The Journal of Chemical Physics, 2008

Naive mode coupling theory ͑NMCT͒ and the nonlinear stochastic Langevin equation theory of activa... more Naive mode coupling theory ͑NMCT͒ and the nonlinear stochastic Langevin equation theory of activated dynamics have been generalized to mixtures of spherical particles. Two types of ideal nonergodicity transitions are predicted corresponding to localization of both, or only one, species. The NMCT transition signals a dynamical crossover to activated barrier hopping dynamics. For binary mixtures of equal diameter hard and attractive spheres, a mixture composition sensitive "glass-melting" type of phenomenon is predicted at high total packing fractions and weak attractions. As the total packing fraction decreases, a transition to partial localization occurs corresponding to the coexistence of a tightly localized sticky species in a gel-like state with a fluid of hard spheres. Complex behavior of the localization lengths and shear moduli exist because of the competition between excluded volume caging forces and attraction-induced physical bond formation between sticky particles. Beyond the NMCT transition, a two-dimensional nonequilibrium free energy surface emerges, which quantifies cooperative activated motions. The barrier locations and heights are sensitive to the relative amplitude of the cooperative displacements of the different species.

Integral equation theory for atactic polystyrene nanocomposite melts with a multi-site model

The microscopic Polymer Reference Interaction Site Model theory is employed to study, for the fir... more The microscopic Polymer Reference Interaction Site Model theory is employed to study, for the first time, the effective interactions, spatial organization, and miscibility of dilute spherical nanoparticles in non-microphase separating, chemically heterogeneous, compositionally symmetric AB multiblock copolymer melts of varying monomer sequence or architecture. The dependence of nanoparticle wettability on copolymer sequence and chemistry results in interparticle potentials-ofmean force that are qualitatively different from homopolymers. An important prediction is the ability to improve nanoparticle dispersion via judicious choice of block length and monomer adsorption-strengths which control both local surface segregation and chain connectivity induced packing constraints and frustration. The degree of dispersion also depends strongly on nanoparticle diameter relative to the block contour length. Small particles in copolymers with longer block lengths experience a more homopolymer-like environment which renders them relatively insensitive to copolymer chemical heterogeneity and hinders dispersion. Larger particles (sufficiently larger than the monomer diameter) in copolymers of relatively short block lengths provide better dispersion than either a homopolymer or random copolymer. The theory also predicts a novel widening of the miscibility window for large particles upon increasing the overall molecular weight of copolymers composed of relatively long blocks.

ACS applied materials & interfaces, Jan 6, 2015

We report a three-dimensional (3D) porous carbon electrode containing both nanoscale and microsca... more We report a three-dimensional (3D) porous carbon electrode containing both nanoscale and microscale porosity, which has been hierarchically organized to provide efficient ion and electron transport. The electrode organization is provided via the colloidal self-assembly of monodisperse starburst carbon spheres (MSCSs). The periodic close-packing of the MSCSs provides continuous pores inside the 3D structure that facilitate ion and electron transport (electrode electrical conductivity ∼0.35 S m(-1)), and the internal meso- and micropores of the MSCS provide a good specific capacitance. The capacitance of the 3D-ordered porous MSCS electrode is ∼58 F g(-1) at 0.58 A g(-1), 48% larger than that of disordered MSCS electrode at the same rate. At 1 A g(-1) the capacitance of the ordered electrode is 57 F g(-1) (95% of the 0.24 A g(-1) value), which is 64% greater than the capacitance of the disordered electrode at the same rate. The ordered electrode preserves 95% of its initial capacitanc...

Physical review letters, Jan 14, 2014

Replica and effective-medium theory methods are employed to elucidate how to massively reconfigur... more Replica and effective-medium theory methods are employed to elucidate how to massively reconfigure a colloidal assembly to achieve globally homogeneous, strongly clustered, and percolated equilibrium states of high electrical conductivity at low physical volume fractions. A key idea is to employ a quench-disordered, large-mesh rigid-rod network as a templating internal field. By exploiting bulk phase separation frustration and the tunable competing processes of colloid adsorption on the low-dimensional network and fluctuation-driven colloid clustering in the pore spaces, two distinct spatial organizations of greatly enhanced particle contacts can be achieved. As a result, a continuous, but very abrupt, transition from an insulating to metallic-like state can be realized via a small change of either the colloid-template or colloid-colloid attraction strength. The approach is generalizable to more complicated template or colloidal architectures.

The Journal of chemical physics, Jan 28, 2014

Two decades of experimental research indicate that spatial confinement of glass-forming molecular... more Two decades of experimental research indicate that spatial confinement of glass-forming molecular and polymeric liquids results in major changes of their slow dynamics beginning at large confinement distances. A fundamental understanding remains elusive given the generic complexity of activated relaxation in supercooled liquids and the major complications of geometric confinement, interfacial effects, and spatial inhomogeneity. We construct a predictive, quantitative, force-level theory of relaxation in free-standing films for the central question of the nature of the spatial mobility gradient. The key new idea is that vapor interfaces speed up barrier hopping in two distinct, but coupled, ways by reducing near surface local caging constraints and spatially long range collective elastic distortion. Effective vitrification temperatures, dynamic length scales, and mobile layer thicknesses naturally follow. Our results provide a unified basis for central observations of dynamic and pse...

The Journal of chemical physics, Jan 21, 2014

We generalize the force-level nonlinear Langevin equation theory of single particle hopping to in... more We generalize the force-level nonlinear Langevin equation theory of single particle hopping to include collective effects associated with long range elastic distortion of the liquid. The activated alpha relaxation event is of a mixed spatial character, involving two distinct, but inter-related, local and collective barriers. There are no divergences at volume fractions below jamming or temperatures above zero Kelvin. The ideas are first developed and implemented analytically and numerically in the context of hard sphere fluids. In an intermediate volume fraction crossover regime, the local cage process is dominant in a manner consistent with an apparent Arrhenius behavior. The super-Arrhenius collective barrier is more strongly dependent on volume fraction, dominates the highly viscous regime, and is well described by a nonsingular law below jamming. The increase of the collective barrier is determined by the amplitude of thermal density fluctuations, dynamic shear modulus or transi...

Journal of the Chemical Society, Faraday Transactions, 1992

ABSTRACT

ACS applied materials & interfaces, Jan 6, 2015

We report a three-dimensional (3D) porous carbon electrode containing both nanoscale and microsca... more We report a three-dimensional (3D) porous carbon electrode containing both nanoscale and microscale porosity, which has been hierarchically organized to provide efficient ion and electron transport. The electrode organization is provided via the colloidal self-assembly of monodisperse starburst carbon spheres (MSCSs). The periodic close-packing of the MSCSs provides continuous pores inside the 3D structure that facilitate ion and electron transport (electrode electrical conductivity ∼0.35 S m(-1)), and the internal meso- and micropores of the MSCS provide a good specific capacitance. The capacitance of the 3D-ordered porous MSCS electrode is ∼58 F g(-1) at 0.58 A g(-1), 48% larger than that of disordered MSCS electrode at the same rate. At 1 A g(-1) the capacitance of the ordered electrode is 57 F g(-1) (95% of the 0.24 A g(-1) value), which is 64% greater than the capacitance of the disordered electrode at the same rate. The ordered electrode preserves 95% of its initial capacitanc...

Journal of Physics-condensed Matter - J PHYS-CONDENS MATTER, 2006

Weak depletion gels with particle radii of ∼200–500 nm have been reported to display a time-depen... more Weak depletion gels with particle radii of ∼200–500 nm have been reported to display a time-dependent settling behaviour where an initially space spanning gel displays a catastrophic collapse after a characteristic period of time, defined as the delay time. Several experiments suggest that thermally activated particle rearrangements promote macroscopic gel coarsening, which ultimately triggers the rapid collapse. The delay time is found to be a sensitive function of the colloid volume fraction and polymer concentration. We have performed systematic experiments on the silica–decalin–polystyrene depletion system to explore how colloid volume fraction, polymer concentration, particle radius and ratio of polymer radius of gyration to particle radius influence the delayed collapse time of transient gels. We employ a recently developed activated barrier-hopping theory to make predictions of the timescales over which colloids can escape localized states as a function of system parameters. ...

The Journal of Physical Chemistry B, 2005

A microscopic polymer liquid-state theory has been developed for the structure, thermodynamics an... more 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.

Physical Review E, 2008

The coupled activated dynamics in dense mixtures of repulsive and sticky hard spheres is studied ... more The coupled activated dynamics in dense mixtures of repulsive and sticky hard spheres is studied using stochastic nonlinear Langevin equation theory. The effective free energy surface, barriers, saddle point trajectories, and mean first passage times depend in a rich manner on mixture composition, (high) total volume fraction, and attractive interaction strength. In general, there are three types of saddle point trajectories or relaxation pathways: a pure sticky or pure repulsive particle displacement keeping the other species localized, and a cooperative motion involving repulsive and attractive particle displacements. The barrier for activated hopping usually increases with the ratio of sticky to repulsive particle displacement. However, at intermediate values of the displacement ratio it can attain a broad plateau value, and can even exhibit a local maximum, and hence nonmonotonic behavior, at high sticky particle mixture compositions if the attraction strength is modest. The mean first passage, or hopping, times are computed using multidimensional Kramers theory. In most cases the hopping time trends reflect the behavior of the barrier height, especially as the sticky particle attraction strengths become large. However, there are dramatic exceptions associated with cooperative repulsive and attractive particle trajectories where the barriers are high but a greatly enhanced number of such trajectories exist near the saddle point.

Physical Review E, 2008

A statistical segment scale theory for the physical aging of polymer glasses is proposed and appl... more A statistical segment scale theory for the physical aging of polymer glasses is proposed and applied. The approach is based on a nonlinear stochastic Langevin equation of motion and the concept of an effective free energy which quantifies temporary localization, collective barriers, and the activated segment hopping process. The key collective structural variable that plays the role of the dynamic order parameter for aging is the experimentally measurable nanometer and longer wavelength amplitude of density fluctuations, S0 . The degree of local cooperativity, and the bare activation energy of the high-temperature Arrhenius process, are determined in the molten state by utilizing experimental measurements of the glass temperature and dynamic crossover time, respectively. A first-order kinetic equation with a time varying rate is proposed for the temporal evolution of S0 which is self-consistently and nonlinearly coupled with the mean segmental relaxation time. The theory has been applied to study physical aging of the alpha relaxation time, shear relaxation modulus, amplitude of density fluctuations, cohesive energy, absolute yield stress, and fictive temperature of polymethylmethacrylate and other glasses over a range of temperatures. Temperature-dependent logarithmic and effective power-law aging is predicted at intermediate times. Time-aging time superposition is found for the mechanical relaxation function. A strongly asymmetric aging response is predicted for up and down temperature jump experiments. Comparison of the approach with the classic phenomenological model is presented.

Macromolecules, 1990

Polymer RISM (reference interaction site model) theory is used to examine the intermolecular radi... more Polymer RISM (reference interaction site model) theory is used to examine the intermolecular radial distribution function and isothermal compressibility of semiflexible polymer melts. Chains are modeled as a series of linked, hard sites with a local bending energy proportional to the cosine of the bond angle. Chain stiffness is controlled by a single parameter, the persistence length, which may be matched to the material of interest. Comparisons of the predicted intermolecular radial distribution functions to the molecular dynamics results of Grest and Kremer for chains of 50, 100, and 150 sites show very good agreement on all length scales. Parametric studies as a function of chain length and chain stiffness reveal that as the characteristic stiffness is increased beyond three bond lengths, the radial distribution function and isothermal compressibility saturate, becoming relatively insensitive to chain length or stiffness. At low densities the local structure is dominated by a correlation hole, indicating a relative absence of intermolecular neighbors, while at high densities the pair correlation function shows a peak and valley structure, qualitatively similar to that of monatomic fluids.

Macromolecules, 2013

We combine polymer integral equation theory and computational chemistry methods to study the inte... more We combine polymer integral equation theory and computational chemistry methods to study the interfacial structure, effective interactions, miscibility and spatial dispersion mechanism of fullerenes dissolved in specific random AB copolymer melts characterized by strong noncovalent electron donor–acceptor interactions with the nanofiller. A statistical mechanical basis is developed for designing random copolymers to optimize fullerene dispersion at intermediate copolymer compositions. Pair correlation calculations reveal a strong sensitivity of interfacial packing near the fullerene to copolymer composition and adsorption energy mismatch. The potential of mean force between fullerenes displays rich trends, often nonmonotonic with copolymer composition, reflecting a nonadditive competition between direct filler attractions and polymer-mediated bridging and steric stabilization. The spinodal phase diagrams are in qualitative agreement with recent solubility limit experimental observations on three systems, ...

Macromolecules, 1993

Microscopic equations-of-state are developed for n-alkanes and polyethylene based on the polymer ... more Microscopic equations-of-state are developed for n-alkanes and polyethylene based on the polymer reference interaction site model (PRISM) integral equation theory and a generalized Flory approach. The molecules are modeled as a series of overlapping spheres (methylene groups) with constant bond length and bond angles; internal rotations are accounted for by the rotational isomeric state approximation. The interaction between sites on different molecules is taken to be of the Lennard-Jones form. The thermodynamic properties of the fluid are obtained via standard perturbation theory in which the potential is divided into a repulsive reference system and an attractive perturbation. The reference system is approximated by a hard-core repulsion in which the hard-sphere diameter d(T) is estimated for polyethylene from wide-angle X-ray scattering experiments. The PRISM theory is used to calculate the hard-sphere chain contribution to the equation-of-state by three different thermodynamic routes: (1) integrating the compressibility, (2) evaluating the density profile at a hard wall, and (3) using a hard-sphere 'charging" method analogous to the virial approach in monatomic liquids. The generalized Flory dimer (GFD) theory is used to obtain a fourth equation-of-state for the hard-sphere chains. The attractive perturbation is treated with first-order perturbation theory, making use of the radial distribution functiongo(r) of the reference system. The various equations-of-state presented differ in the route to the hard-chain pressure; PRISM is used in all cases to treat the attractions. Excellent agreement for the equation-of-state is found between the hybrid GFD/PRISM calculations and molecular dynamics simulations of n-butane and experimental pressure-volume-temperature (PVT) measurements on polyethylene melts. The compressibility and charging routes predict pressures which are too low and too high, respectively, for polyethylene. The wall route yields pressures in good agreement at experimental densities but predicts a melt which is too compressible.

The Journal of Chemical Physics, 2000

We apply an anisotropic version of the polymer reference interaction site model ͑PRISM͒ integral ... more We apply an anisotropic version of the polymer reference interaction site model ͑PRISM͒ integral equation description of flexible polymers to analyze athermal liquid crystallinity. The polymers are characterized by a statistical segment length, o , and by a physical hard-core thickness, d, that prevents the overlap of monomers on different chains. At small segment densities, , the microscopic length scale d is irrelevant ͑as it must be in the universal semidilute regime͒, but becomes important in concentrated solutions and melts. Under the influence of the excluded volume interactions alone, the chains undergo a lyotropic, first-order isotropic-nematic transition at a concentration dependent upon the dimensionless ''aspect ratio,'' o /d. The transition becomes weaker as d→0, becoming second order, as has been previously shown. We extend the theory to describe the transition of rigid, thin rods, and discuss the evolution of the anisotropic liquid structure in the ordered phase.

The Journal of Chemical Physics, 2005

A recently proposed microscopic activated barrier hopping theory [K. S. Schweizer and E. J. Saltz... more A recently proposed microscopic activated barrier hopping theory [K. S. Schweizer and E. J. Saltzman, J. Chem. Phys. 119, 1181 (2003)] of slow single-particle dynamics in glassy liquids, suspensions, and gels is derived using nonequilibrium statistical mechanics. Fundamental elements underlying the stochastic nonlinear Langevin equation description include an inhomogeneous liquid or locally solid-state perspective, dynamic density-functional theory (DDFT), a local equilibrium closure, and a coarse-grained free-energy functional. A dynamic Gaussian approximation is not adopted which is the key for avoiding a kinetic ideal glass transition. The relevant excess free energy is of a nonequilibrium origin and is related to dynamic force correlations in the fluid. The simplicity of the approach allows external perturbations to be rather easily incorporated. Dynamic heterogeneity enters naturally via mobility fluctuations associated with the stochastic barrier-hopping process. The derivation both identifies the limitations of the theory and suggests new avenues for its systematic improvement. Comparisons with ideal mode-coupling theory, alternative DDFT approaches and a field theoretic path-integral formulation are presented.

The Journal of Chemical Physics, 2004

A microscopic integral equation theory of elasticity in polymer liquids and networks is developed... more 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.

The Journal of Chemical Physics, 2008

Naive mode coupling theory ͑NMCT͒ and the nonlinear stochastic Langevin equation theory of activa... more Naive mode coupling theory ͑NMCT͒ and the nonlinear stochastic Langevin equation theory of activated dynamics have been generalized to mixtures of spherical particles. Two types of ideal nonergodicity transitions are predicted corresponding to localization of both, or only one, species. The NMCT transition signals a dynamical crossover to activated barrier hopping dynamics. For binary mixtures of equal diameter hard and attractive spheres, a mixture composition sensitive "glass-melting" type of phenomenon is predicted at high total packing fractions and weak attractions. As the total packing fraction decreases, a transition to partial localization occurs corresponding to the coexistence of a tightly localized sticky species in a gel-like state with a fluid of hard spheres. Complex behavior of the localization lengths and shear moduli exist because of the competition between excluded volume caging forces and attraction-induced physical bond formation between sticky particles. Beyond the NMCT transition, a two-dimensional nonequilibrium free energy surface emerges, which quantifies cooperative activated motions. The barrier locations and heights are sensitive to the relative amplitude of the cooperative displacements of the different species.

Integral equation theory for atactic polystyrene nanocomposite melts with a multi-site model

The microscopic Polymer Reference Interaction Site Model theory is employed to study, for the fir... more The microscopic Polymer Reference Interaction Site Model theory is employed to study, for the first time, the effective interactions, spatial organization, and miscibility of dilute spherical nanoparticles in non-microphase separating, chemically heterogeneous, compositionally symmetric AB multiblock copolymer melts of varying monomer sequence or architecture. The dependence of nanoparticle wettability on copolymer sequence and chemistry results in interparticle potentials-ofmean force that are qualitatively different from homopolymers. An important prediction is the ability to improve nanoparticle dispersion via judicious choice of block length and monomer adsorption-strengths which control both local surface segregation and chain connectivity induced packing constraints and frustration. The degree of dispersion also depends strongly on nanoparticle diameter relative to the block contour length. Small particles in copolymers with longer block lengths experience a more homopolymer-like environment which renders them relatively insensitive to copolymer chemical heterogeneity and hinders dispersion. Larger particles (sufficiently larger than the monomer diameter) in copolymers of relatively short block lengths provide better dispersion than either a homopolymer or random copolymer. The theory also predicts a novel widening of the miscibility window for large particles upon increasing the overall molecular weight of copolymers composed of relatively long blocks.

ACS applied materials & interfaces, Jan 6, 2015

We report a three-dimensional (3D) porous carbon electrode containing both nanoscale and microsca... more We report a three-dimensional (3D) porous carbon electrode containing both nanoscale and microscale porosity, which has been hierarchically organized to provide efficient ion and electron transport. The electrode organization is provided via the colloidal self-assembly of monodisperse starburst carbon spheres (MSCSs). The periodic close-packing of the MSCSs provides continuous pores inside the 3D structure that facilitate ion and electron transport (electrode electrical conductivity ∼0.35 S m(-1)), and the internal meso- and micropores of the MSCS provide a good specific capacitance. The capacitance of the 3D-ordered porous MSCS electrode is ∼58 F g(-1) at 0.58 A g(-1), 48% larger than that of disordered MSCS electrode at the same rate. At 1 A g(-1) the capacitance of the ordered electrode is 57 F g(-1) (95% of the 0.24 A g(-1) value), which is 64% greater than the capacitance of the disordered electrode at the same rate. The ordered electrode preserves 95% of its initial capacitanc...

Physical review letters, Jan 14, 2014

Replica and effective-medium theory methods are employed to elucidate how to massively reconfigur... more Replica and effective-medium theory methods are employed to elucidate how to massively reconfigure a colloidal assembly to achieve globally homogeneous, strongly clustered, and percolated equilibrium states of high electrical conductivity at low physical volume fractions. A key idea is to employ a quench-disordered, large-mesh rigid-rod network as a templating internal field. By exploiting bulk phase separation frustration and the tunable competing processes of colloid adsorption on the low-dimensional network and fluctuation-driven colloid clustering in the pore spaces, two distinct spatial organizations of greatly enhanced particle contacts can be achieved. As a result, a continuous, but very abrupt, transition from an insulating to metallic-like state can be realized via a small change of either the colloid-template or colloid-colloid attraction strength. The approach is generalizable to more complicated template or colloidal architectures.

The Journal of chemical physics, Jan 28, 2014

Two decades of experimental research indicate that spatial confinement of glass-forming molecular... more Two decades of experimental research indicate that spatial confinement of glass-forming molecular and polymeric liquids results in major changes of their slow dynamics beginning at large confinement distances. A fundamental understanding remains elusive given the generic complexity of activated relaxation in supercooled liquids and the major complications of geometric confinement, interfacial effects, and spatial inhomogeneity. We construct a predictive, quantitative, force-level theory of relaxation in free-standing films for the central question of the nature of the spatial mobility gradient. The key new idea is that vapor interfaces speed up barrier hopping in two distinct, but coupled, ways by reducing near surface local caging constraints and spatially long range collective elastic distortion. Effective vitrification temperatures, dynamic length scales, and mobile layer thicknesses naturally follow. Our results provide a unified basis for central observations of dynamic and pse...

The Journal of chemical physics, Jan 21, 2014

We generalize the force-level nonlinear Langevin equation theory of single particle hopping to in... more We generalize the force-level nonlinear Langevin equation theory of single particle hopping to include collective effects associated with long range elastic distortion of the liquid. The activated alpha relaxation event is of a mixed spatial character, involving two distinct, but inter-related, local and collective barriers. There are no divergences at volume fractions below jamming or temperatures above zero Kelvin. The ideas are first developed and implemented analytically and numerically in the context of hard sphere fluids. In an intermediate volume fraction crossover regime, the local cage process is dominant in a manner consistent with an apparent Arrhenius behavior. The super-Arrhenius collective barrier is more strongly dependent on volume fraction, dominates the highly viscous regime, and is well described by a nonsingular law below jamming. The increase of the collective barrier is determined by the amplitude of thermal density fluctuations, dynamic shear modulus or transi...

Journal of the Chemical Society, Faraday Transactions, 1992

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