Activated hopping and dynamical fluctuation effects in hard sphere suspensions and fluids

Single particle Brownian dynamics simulation methods are employed to establish the full trajectory level predictions of our nonlinear stochastic Langevin equation theory of activated hopping dynamics in glassy hard sphere suspensions and fluids. The consequences of thermal noise driven mobility fluctuations associated with the barrier hopping process are determined for various ensemble-averaged properties and their distributions. The predicted mean square displacements show classic signatures of transient trapping and anomalous diffusion on intermediate time and length scales. A crossover to a stronger volume fraction dependence of the apparent nondiffusive exponent occurs when the entropic barrier is of order the thermal energy. The volume fraction dependences of various mean relaxation times and rates can be fitted by empirical critical power laws with parameters consistent with ideal mode-coupling theory. However, the results of our divergence-free theory are largely a consequence of activated dynamics. The experimentally measurable alpha relaxation time is found to be very similar to the theoretically defined mean reaction time for escape from the barrier-dominated regime. Various measures of decoupling have been studied. For fluid states with small or nonexistent barriers, relaxation times obey a simple log-normal distribution, while for high volume fractions the relaxation time distributions become Poissonian. The product of the self-diffusion constant and mean alpha relaxation time increases roughly as a logarithmic function of the alpha relaxation time. The cage scale incoherent dynamic structure factor exhibits nonexponential decay with a modest degree of stretching. A nearly universal collapse of the different volume fraction results occurs if time is scaled by the mean alpha relaxation time. Hence, time-volume fraction superposition holds quite well, despite the presence of stretching and volume fraction dependent decoupling associated with the stochastic barrier hopping process. The relevance of other origins of dynamic heterogeneity (e.g., mesoscopic domains), and comparison of our results with experiments, simulations, and alternative theories, is discussed.     

Relationships between the single particle barrier hopping theory and thermodynamic, disordered media, elastic, and jamming models of glassy systems

The predictions of the ultralocal limit of the activated hopping theory of highly viscous simple fluids and colloidal suspensions [K. S. Schweizer and G. Yatsenko, J. Chem. Phys. 127, 164505 (2007), preceding paper] for the relaxation time and effective activation barrier are compared with those of diverse alternative theoretical approaches and computer simulation. A nonlinear connection between the barrier height and excess pressure as empirically suggested by simulations of polydisperse repulsive force fluids is identified. In the dense normal and weakly dynamical precursor regime, where entropic barriers of hard spheres are nonexistent or of order the thermal energy, agreement with an excess entropy ansatz is found. In the random close packing or jamming limit, the barrier hopping theory predicts an essential singularity stronger than the free volume model, which is in agreement with the simplest entropic droplet nucleation and replica field theoretic approaches. Upon further technical simplification of the theory, close connections with renormalization group and nonperturbative memory function based studies of activated transport of a Brownian particle in a disordered medium can been identified. Several analytic arguments suggest a qualitative consistency between the barrier hopping theory and solid-state elastic models based on the high frequency shear modulus and a molecular-sized apparent activation volume. Implications of the analysis for the often high degeneracy of conflicting explanations of glassy dynamics are discussed.     

Theory of nonlinear elasticity, stress-induced relaxation, and dynamic yielding in dense fluids of hard nonspherical colloids

We generalize the microscopic na?ve mode coupling and nonlinear Langevin equation theories of the coupled translation-rotation dynamics of dense suspensions of uniaxial colloids to treat the effect of applied stress on shear elasticity, cooperative cage escape, structural relaxation, and dynamic and static yielding. The key concept is a stress-dependent dynamic free energy surface that quantifies the center-of-mass force and torque on a moving colloid. The consequences of variable particle aspect ratio and volume fraction, and the role of plastic versus double glasses, are established in the context of dense, glass-forming suspensions of hard-core dicolloids. For low aspect ratios, the theory provides a microscopic basis for the recently observed phenomenon of double yielding as a consequence of stress-driven sequential unlocking of caging constraints via reduction of the distinct entropic barriers associated with the rotational and translational degrees of freedom. The existence, and breadth in volume fraction, of the double yielding phenomena is predicted to generally depend on both the degree of particle anisotropy and experimental probing frequency, and as a consequence typically occurs only over a window of (high) volume fractions where there is strong decoupling of rotational and translational activated relaxation. At high enough concentrations, a return to single yielding is predicted. For large aspect ratio dicolloids, rotation and translation are always strongly coupled in the activated barrier hopping event, and hence for all stresses only a single yielding process is predicted.     

Dynamic yielding, shear thinning, and stress rheology of polymer-particle suspensions and gels

The nonlinear rheological version of our barrier hopping theory for particle-polymer suspensions and gels has been employed to study the effect of steady shear and constant stress on the alpha relaxation time, yielding process, viscosity, and non-Newtonian flow curves. The role of particle volume fraction, polymer-particle size asymmetry ratio, and polymer concentration have been systematically explored. The dynamic yield stress decreases in a polymer-concentration- and volume-fraction-dependent manner that can be described as apparent power laws with effective exponents that monotonically increase with observation time. Stress- or shear-induced thinning of the viscosity becomes more abrupt with increasing magnitude of the quiescent viscosity. Flow curves show an intermediate shear rate dependence of an effective power-law form, becoming more solidlike with increasing depletion attraction. The influence of polymer concentration, particle volume fraction, and polymer-particle size asymmetry ratio on all properties is controlled to a first approximation by how far the system is from the gelation boundary of ideal mode-coupling theory (MCT). This emphasizes the importance of the MCT nonergodicity transition despite its ultimate destruction by activated barrier hopping processes. Comparison of the theoretical results with limited experimental studies is encouraging.     

The short-time self-diffusion coefficient of a sphere in a suspension of rigid rods

The short-time self-diffusion coefficient of a sphere in a suspension of rigid rods is calculated in first order in the rod volume fraction phi. For low rod concentrations, the correction to the Einstein diffusion constant of the sphere due to the presence of rods is a linear function of phi with the slope alpha proportional to the equilibrium averaged mobility diminution trace of the sphere interacting with a single freely translating and rotating rod. The two-body hydrodynamic interactions are calculated using the so-called bead model in which the rod of aspect ratio p is replaced by a stiff linear chain of touching spheres. The interactions between spheres are calculated using the multipole method with the accuracy controlled by a multipole truncation order and limited only by the computational power. A remarkable accuracy is obtained already for the lowest truncation order, which enables calculations for very long rods, up to p=1000. Additionally, the bead model is checked by filling the rod with smaller spheres. This procedure shows that for longer rods the basic model provides reasonable results varying less than 5% from the model with filling. An analytical expression for alpha as a function of p is derived in the limit of very long rods. The higher order corrections depending on the applied model are computed numerically. An approximate expression is provided, valid for a wide range of aspect ratios.     

Rheology of Dilute Suspensions of Hard Platelike Colloids

The concentration dependence of the viscosity is studied for suspensions of approximately hard, i.e., short-range repulsive, platelets. We combine rheological measurements on suspensions of sterically stabilized platelike colloids with dissipative particledynamics simulation for disks. This yields, for the first time, results for the intrinsic viscosity of (nearly) hard plate suspensions, as well as the second- and third-order φ (platelet volume fraction) coefficients in the viscosity. The intrinsic viscosity is used to calculate the number-average aspect ratio of the platelets, which is found to be 6.5 and 12 respectively for the two suspensions studied. The measured Huggins coefficients are intermediary between the theoretical value for hard spheres and hard rods. The combined results from viscosity measurements and simulations provide insight into the effect of Péclet number, particle model, and polydispersity on the viscosity of approximately hard platelet suspensions. Copyright 2001 Academic Press.     

Influence of static strain on dynamic mechanical behavior of amorphous networks prepared from aromatic polyesters

Dynamic mechanical experiments were performed between ?140 and 50°C on both poly(diethylene glycol isophthalate) and poly(triethylene glycol terephthalate) networks. Plots of loss tangent versus temperature show a well-defined α peak, associated with the transition from glasslike to rubberlike consistency, and two overlapping peaks (β₁ and β₂) in the glassy region. Dynamic deformations of small amplitude were superimposed on large static deformations. It was found that the position of the β₁ and β₂ peaks as well as their intensities are independent of the static elongation ratio. However, the intensity of the loss tangent associated with the glass–rubber transition tends to decrease with increasing static deformation. Moreover, the position of the maximum of the α peaks shifts to lower temperatures as the elongation ratio increases. This behavior suggests that for both networks the volume effects (shifting the α peaks to lower temperatures with increasing elongation ratio) overcome the entropic effects (shifting the α peaks to higher temperatures with decreasing entropy).     

Isotropic-nematic phase transition of nonaqueous suspensions of natural clay rods

A novel model system for studying the behavior of hard colloidal rods is presented, consisting of sterically stabilized particles of natural sepiolite clay. Electron microscopy and scattering results confirmed that the organophilic clay particles were individual, rigid rods when dispersed in organic solvents. With a length-to-diameter ratio of approximately 27, the particles showed nematic ordering for volume fractions phi > 0.06. Polarizing microscopy revealed that the phase separation process involved nucleation, growth, and coalescence of nematic domains. The phase volumes and particle concentrations in the coexisting phases were determined. The dependence of these quantities on the total concentration of the suspension agrees well with Onsager's [Ann. N. Y. Acad. Sci. 51, 627 (1949)] isotropic-nematic phase transition theory extended to bidisperse and polydisperse rod systems, and with previous experimental results for rigid rodlike particles. Particle size distributions were obtained by analyzing transmission electron microscopy images. A significant fractionation with respect to rod length (but not diameter) was observed in the coexisting isotropic and nematic phases. The relative polydispersity of both daughter phases was distinctly smaller than that of the parent suspension. The phase behavior of these daughter fractions agrees well with the predictions for hard spherocylinders of corresponding aspect ratios. An isotropic-nematic-nematic phase equilibrium was seen to develop in phase separated samples after 1 month standing and is ascribed to the effect of polydispersity and possibly gravity. The second nematic phase appearing is dominated by very long rods.     

Theory of relaxation and elasticity in polymer glasses

The recently developed activated barrier hopping theory of deeply supercooled polymer melts [K. S. Schweizer and E. J. Saltzman, J. Chem. Phys. 121, 1984 (2004)] is extended to the nonequilibrium glass state. Below the kinetic glass temperature T(g), the exact statistical mechanical relation between the dimensionless amplitude of long wavelength density fluctuations, S(0), and the thermodynamic compressibility breaks down. Proper extension of the theory requires knowledge of the nonequilibrium S(0) which x-ray scattering experiments find to consist of a material specific and temperature-independent quenched disorder contribution plus a vibrational contribution which varies roughly linearly with temperature. Motivated by these experiments and general landscape concepts, a simple model is proposed for S(0)(T). Deep in the glass state the form of the temperature dependence of the segmental relaxation time is found to depend sensitively on the magnitude of frozen in density fluctuations. At the (modest) sub-T(g) temperatures typically probed in experiment, an effective Arrhenius behavior is generically predicted which is of nonequilibrium origin. The change in apparent activation energy across the glass transition is determined by the amplitude of frozen density fluctuations. For values of the latter consistent with experiment, the theory predicts a ratio of effective activation energies in the range of 3-6, in agreement with multiple measurements. Calculations of the shear modulus for atactic polymethylmethacrylate above and below the glass transition temperature have also been performed. The present work provides a foundation for the formulation of predictive theories of physical aging, the influence of deformation on the alpha relaxation process, and rate-dependent nonlinear mechanical properties of thermoplastics.     

Molecular alignment of rigid rods in nonrigid spherical pores

We have investigated the orientation ordering of two shish-kebab chains confined by spherically harmonic potentials through Monte Carlo simulations and asymptotic analysis. The rigid rod is modeled as shish-kebab chains consisting of tangent hard spheres aligned in the same axis, and the harmonic potential is chosen to model nonrigid cavities. We first show that the interactions between a rod and the spherically harmonic potential are independent of chain orientation, indicating that the alignment of two confined rods arises from the excluded volume interactions alone. In the strong fields, the order parameter of two confined rods converges to different values, depending on the parity of chain length. From asymptotic order parameters, we find that the rods of odd-number beads rotate more freely even under the limiting strong confinement. However, the two rods of even-number beads are essentially trapped in a configuration of perpendicular alignment through intercalation of their central grooves. We attribute the dependence of the parity of chain length to the different locations of the center-of-mass in a rod for these two cases. Furthermore, we compare the shish-kebab chains with different rod models in the simulations, and utilize these models to explore the effect of the local rod smoothness on molecular alignment. Our findings suggest that increasing local rod smoothness enhances the rotational degree of freedom for confined rods, and the effect of local rod roughness emerges under strong enough applied potentials.     

Origin of de-swelling and dynamics of dense ionic microgel suspensions

A direct consequence of the finite compressibility of a swollen microgel is that it can shrink and deform in response to an external perturbation. As a result, concentrated suspensions of these particles exhibit relaxation dynamics and rheological properties which can be very different with respect to those of a hard sphere suspension or an emulsion. We study the reduction in size of ionic microgels in response to increasing number of particles to show that particle shrinkage originates primarily from steric compression, and that the effect of ion-induced de-swelling of the polymer network is negligible. With increasing particle concentration, the single particle dynamics switch from those typical of a liquid to those of a super-cooled liquid and finally to those of a glass. However, the transitions occur at volume fractions much higher than those characterizing a hard sphere system. In the super-cooled state, the distribution of displacements is non-gaussian and the dependence of the structural relaxation time on volume fraction is describable by a Volger-Fulcher-Tammann function.     

Effects of the strain rate and temperature in stress–strain tests: study of the glass transition of a polyamide-6

In this work new insights are presented on the measurement of the tangent and secant moduli from stress–strain curves in polymeric systems. Expressions for the strain-rate and strain dependence of both moduli are derived for systems characterised by a distribution of relaxation times. The equivalent frequency of the stress–strain experiments is shown to be dependent on the strain rate and on the strain at which the measurements are carried out. Such considerations enable using quasi-static tensile stress–strain tests to study relaxational processes in polymeric materials. The tensile behaviour of a 30% glass fibre reinforced polyamide 6 was characterised at different strain rates and temperatures, covering the glass transition region. A master curve of the tangent modulus as a function of strain rate was successfully constructed by simple horizontal shifting of the isothermal data. The temperature dependence of the shift factors was well described by the WLF equation. It was also possible to fit the master curve considering a polymeric system with a distribution of relaxation times, relevant parameters such as the KWW β parameter being extracted. The results were found to be consistent with dynamic mechanical analysis results.     

Dynamic Mechanical Relaxation in the Opaque and Transparent Poly(4-Methyl-1-Pentene) Films The glass transition zone

The thermomechanical properties of opaque and transparent polymer films of a solution of poly(4-methyl-1-pentene) (PMP) in cyclohexane and carbon tetrachloride obtained by casting on teflon and glass plates were investigated. The dynamic mechanical thermal analysis was applied in a frequency range from 0.01 to 100 Hz. The curves of loss tangent vs. temperature varied depending on the sample thermal history. The first part of these curves could relate to the backbone α relaxation into the unperturbed amorphous phase while the next relaxation could result from the backbone α relaxation into amorphous phase perturbed by the presence of the crystal domains. The Arrhenius plots of the first relaxation show a stronger curvature found in each of the transparent samples indicating strong dependency on specific volume. The second one in the case of transparent films and the first one for opaque samples might be approximate to straight lines. This revised version was published online in August 2006 with corrections to the Cover Date.     

Dichroism in dye-doped colloidal liquid crystals

Nematic liquid crystals were obtained in sterically stabilized suspensions of rodlike particles of sepiolite clay, with an average length up to 900 nm and aspect ratio up to 40. In agreement with computer simulations for hard spherocylinders, the isotropic-nematic transition shifted to lower volume fractions with increasing aspect ratio. However, the coexistence gap was broadened noticeably due to particle polydispersity. The sepiolite crystal structure includes channels filled with zeolitic water, which can be replaced by indigo dye molecules. The indigo molecules are constrained inside the zeolitic channels to be aligned along the long axes of the rods. As a result, the colloidal nematic phase showed a marked dichroism, with an order parameter up to 0.5 for magnetically aligned samples, similar to typical values for dye-doped thermotropic liquid crystals.     

Adhesive and mechanical properties of soft nanocomposites: Model studies with blended latex films

We used a unique approach based on contact mechanics to quantify the adhesive and linear viscoelastic properties of latex films approximately 100 μm thick. The latex films were formed from a mixture of two particle types and form stable films consisting of rigid and compliant regions. We used atomic force microscopy to verify that these regions remained well dispersed on the length scale of the original particle size. The properties of the films were determined by ?_h, the volume fraction of the stiffer component. For ?_h < 0.45, the films were quite adhesive, with viscoelastic properties determined by the compliant matrix material. Adhesive interactions between the film and indenter enabled us to oscillate the indenter in the direction normal to the film surface while maintaining a constant contact area, allowing us to determine the frequency dependence of the dynamic moduli of the films. Stiffer films with higher volume fractions of hard particles were characterized by indentation measurements, from which we were able to determine the time dependence of the relaxation modulus of the latex films. All results were consistent with a power‐law form of the relaxation modulus with an exponent of 0.25. The magnitude of the relaxation modulus increased by a factor of 3000 as the volume fraction of hard particles increased from 0 to 0.89. For low values of ?_h, the composition dependence of the film stiffness was similar to the concentration dependence of the viscosity of spherical particle suspensions. A much weaker concentration dependence was observed for the highest values of ?_h, where the properties of the films were dominated by the stiffer component. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 3090–3102, 2001     

On the dielectric glass relaxation process of polymers: Ball-like labels in polystyrene

Ball-like molecules with strong dipoles (labels) were mixed with technical polystyrene (PS168N) in low concentrations (<0.5% wt) and measured dielectrically in the frequency range 10^–2–10⁷ Hz, and the temperature range 100°–135°C (glass relaxation region). The measurements showed that these ball-like molecules relax cooperatively with the polymeric segments with relaxation times lying at the high-frequency tail of the glass process. The activation energy of the main label process is found to be very similar to that of the glass process of the polystyrene segments and also has the same temperature dependence. This finding implies the existence of an additional mode of relaxation in the dielectric spectrum of the glass process of polystyrene (compared to polyisoprene). Considering the different behavior of the ball-like molecules in polystyrene and polyisoprene and the temperature dependence of the half-width of dielectric loss peak in different polymers, we suggest that the polymers could be classified into three classes according to the available dielectric relaxation modes in the glass process. In addition, the label molecules showed a high-frequency local relaxation process. The relaxation strength ratio of the local process (X _local) to the total relaxation strength of the label was found to be dependent on the volume of the label. This phenomenon could supply a new method for the determination of the mean size of the holes (voids) representing the free volume of the host matrix.