Glassy dynamics and mechanical response in dense fluids of soft repulsive spheres. I. Activated relaxation, kinetic vitrification, and fragility

The microscopic nonlinear Langevin equation theory of activated glassy dynamics is applied to dense fluids of spherical particles that interact via a finite range Hertzian contact soft repulsion. The activation barrier and mean alpha relaxation time are predicted to be rich functions of volume fraction and particle stiffness, exhibiting a non-monotonic variation with concentration at high volume fractions. The latter is due to a structural "soft jamming" crossover where the real space local cage order weakens when soft particles significantly overlap. The highly variable dependences of the relaxation time on temperature and volume fraction are reasonably well collapsed onto two distinct master curves that are qualitatively consistent with a recent scaling ansatz and computer simulation study. A kinetic vitrification diagram is constructed and compared to its dynamic crossover analog. Intersection of the dynamic crossover and soft jamming threshold boundaries occurs for particles that are sufficiently soft, implying the nonexistence of a clear activated dynamics regime or kinetic arrest transition for such particles. The isothermal dynamic fragility is predicted to vary over a wide range as a function of particle stiffness, and soft particles behave as strong glasses. Qualitative comparisons with simulations and microgel experiments reveal good agreement.     

Glassy dynamics and mechanical response in dense fluids of soft repulsive spheres. II. Shear modulus, relaxation-elasticity connections, and rheology

We apply the quiescent and mechanically driven versions of nonlinear Langevin equation theory to study how particle softness influences the shear modulus, the connection between shear elasticity and activated relaxation, and nonlinear rheology of the repulsive Hertzian contact model of dense soft sphere fluids. Below the soft jamming threshold, the shear modulus follows a power law dependence on volume fraction over a narrow interval with an apparent exponent that grows with particle stiffness. To a first approximation, the elastic modulus and transient localization length are controlled by a single coupling constant determined by local fluid structure. In contrast to the behavior of hard spheres, an approximately linear relation between the shear modulus and activation barrier is predicted. This connection has recently been observed for microgel suspensions and provides a microscopic realization of the elastic shoving model. Yielding, shear and stress thinning of the alpha relaxation time and viscosity, and flow curves are also studied. Yield strains are relatively weakly dependent on volume fraction and particle stiffness. Shear thinning commences at values of the effective Peclet number far less than unity, a signature of stress-assisted activated relaxation when barriers are high. Apparent power law reduction of the viscosity with shear rate is predicted with a thinning exponent less than unity. In the vicinity of the soft jamming threshold, a power law flow curve occurs over an intermediate reduced shear rate range with an apparent exponent that decreases as fluid volume fraction and/or repulsion strength increase.     

Determination of static microstructure of dilute and concentrated suspensions of anisotropic particles by ultra-small-angle X-ray scattering

Ultra-small-angle X-ray scattering was performed on suspensions of anisotropic polystyrene particles of varying degrees of anisotropy. The wave vector dependence of particle form factors is well described by a model developed by Debye for the scattering from fused spheres. As volume fraction is raised, all suspensions undergo a disorder/order phase transition. The scattering from disordered and ordered suspensions of anisotropic particles is the same as that of spheres up to volume fractions of 0.45, suggesting that, in the dilute crystalline phase, the anisotropic particles order into a rotator or plastic crystal phase, where the particle centers of mass are ordered, but the particle directors are randomly distributed. Further increase in particle volume fraction leads to differences in scattering between homonuclear dicolloids and spheres, implying that the homonuclear dicolloids form a body-centered tetragonal phase with both positional and directional order. This conclusion is supported by real-space imaging of dried films of the particles.     

Communication: effects of stress on the tube confinement potential and dynamics of topologically entangled rod fluids

A microscopic theory for the effect of applied stress on the transverse topological confinement potential and slow dynamics of heavily entangled rigid rods is presented. The confining entanglement force localizing a polymer in a tube is predicted to have a finite strength. As a consequence, three regimes of terminal relaxation behavior are predicted with increasing stress: accelerated reptation due to tube widening (dilation), relaxation via deformation-assisted activated transverse barrier hopping, and complete destruction of the lateral tube constraints corresponding to microscopic yielding or a disentanglement transition.     

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.     

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.     

Rotational and translational self-diffusion in concentrated suspensions of permeable particles

In our recent work on concentrated suspensions of uniformly porous colloidal spheres with excluded volume interactions, a variety of short-time dynamic properties were calculated, except for the rotational self-diffusion coefficient. This missing quantity is included in the present paper. Using a precise hydrodynamic force multipole simulation method, the rotational self-diffusion coefficient is evaluated for concentrated suspensions of permeable particles. Results are presented for particle volume fractions up to 45% and for a wide range of permeability values. From the simulation results and earlier results for the first-order virial coefficient, we find that the rotational self-diffusion coefficient of permeable spheres can be scaled to the corresponding coefficient of impermeable particles of the same size. We also show that a similar scaling applies to the translational self-diffusion coefficient considered earlier. From the scaling relations, accurate analytic approximations for the rotational and translational self-diffusion coefficients in concentrated systems are obtained, useful to the experimental analysis of permeable-particle diffusion. The simulation results for rotational diffusion of permeable particles are used to show that a generalized Stokes-Einstein-Debye relation between rotational self-diffusion coefficient and high-frequency viscosity is not satisfied.     

Collisions, caging, thermodynamics, and jamming in the barrier hopping theory of glassy hard sphere fluids

An ultralocal limit of the microscopic single particle barrier hopping theory of glassy dynamics is proposed which allows explicit analytic expressions for the characteristic length scales, energy scales, and nonequilibrium free energy to be derived. All properties are shown to be controlled by a single coupling constant determined by the fluid density and contact value of the radial distribution function. This parameter quantifies an effective mean square force exerted on a tagged particle due to collisions with its surroundings. The analysis suggests a conceptual basis for previous surprising findings of multiple inter-relationships between characteristics of the transient localized state, the early stages of cage escape, non-Gaussian or dynamic heterogeneity effects, and the barrier hopping process that defines the alpha relaxation event. The underlying physical picture is also relevant to fluids of nonspherical molecules and sticky colloidal suspensions. The possibility of a unified view of liquid dynamics is suggested spanning the range from dense gases to the zero mobility jammed state.     

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.     

Predicting NMR Relaxation Rates in Anisotropically Tumbling Proteins through Networks of Coupled Rotators

We show that the prediction of ¹⁵N relaxation rates in proteins can be extended to systems with anisotropic global rotational diffusion by using a network of coupled rotators (NCR), starting from a three‐dimensional structure. The relaxation rates predicted by this method are confronted in several examples with experiments performed by other groups. The NCR spectral density functions are compared with the results obtained from reduced spectral density mapping. The consequence of the timescales of internal motions on the predicted relaxation rates and the effects of the predicted local anisotropy—present only in the case of anisotropic overall tumbling—on dynamic parameters, are discussed.     

Dielectric relaxation behavior of colloidal suspensions of palladium nanoparticle chains dispersed in PVP/EG solution

Dielectric measurements were carried out on colloidal suspensions of palladium nanoparticle chains dispersed in poly(vinyl pyrrolidone)/ethylene glycol (PVP/EG) solution with different particle volume fractions, and dielectric relaxation with relaxation time distribution and small relaxation amplitude was observed in the frequency range from 10(5) to 10(7) Hz. By means of the method based on logarithmic derivative of the dielectric constant and a numerical Kramers-Kronig transform method, two dielectric relaxations were confirmed and dielectric parameters were determined from the dielectric spectra. The dielectric parameters showed a strong dependence on the volume fraction of palladium nanoparticle chain. Through analyzing limiting conductivity at low frequency, the authors found the conductance percolation phenomenon of the suspensions, and the threshold volume fraction is about 0.18. It was concluded from analyzing the dielectric parameters that the high frequency dielectric relaxation results from interfacial polarization and the low frequency dielectric relaxation is a consequence of counterion polarization. They also found that the dispersion state of the palladium nanoparticle chain in PVP/EG solution is dependent on the particle volume fraction, and this may shed some light on a better application of this kind of materials.     

Colloid Vibration Potential in a Concentrated Suspension of Spherical Colloidal Particles

A relation between the dynamic electrophoretic mobility of spherical colloidal particles in a concentrated suspension and the colloid vibration potential (CVP) generated in the suspension by a sound wave is obtained from the analogy with the corresponding Onsager relation between electrophoretic mobility and sedimentation potential in concentrated suspensions previously derived on the basis of Kuwabara's cell model. The obtained expression for CVP is applicable to the case where the particle zeta potential is low, the particle relative permittivity is very small, and the overlapping of the electrical double layers of adjacent particles is negligible. It is found that CVP shows much stronger dependence on the particle volume fraction φ than predicted from the φ dependence of the dynamic electrophoretic mobility. It is also suggested that the same relation holds between the electrokinetic sonic amplitude of a concentrated suspension of spherical colloidal particles and the dynamic electrophoretic mobility. Copyright 1999 Academic Press.     

Dielectric response of a concentrated colloidal suspension in a salt-free medium

In this paper the complex dielectric constant of a concentrated colloidal suspension in a salt-free medium is theoretically evaluated using a cell model approximation. To our knowledge this is the first cell model in the literature addressing the dielectric response of a salt-free concentrated suspension. For this reason, we extensively study the influence of all the parameters relevant for such a dielectric response: the particle surface charge, radius, and volume fraction, the counterion properties, and the frequency of the applied electric field (subgigahertz range). Our results display the so-called counterion condensation effect for high particle charge, previously described in the literature for the electrophoretic mobility, and also the relaxation processes occurring in a wide frequency range and their consequences on the complex electric dipole moment induced on the particles by the oscillating electric field. As we already pointed out in a recent paper regarding the dynamic electrophoretic mobility of a colloidal particle in a salt-free concentrated suspension, the competition between these relaxation processes is decisive for the dielectric response throughout the frequency range of interest. Finally, we examine the dielectric response of highly charged particles in more depth, because some singular electrokinetic behaviors of salt-free suspensions have been reported for such cases that have not been predicted for salt-containing suspensions.     

Anomalous nonlinear dielectric and Kerr effect relaxation steady state responses in superimposed ac and dc electric fields

It is shown how the rotational diffusion model of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended to anomalous nonlinear dielectric relaxation and the dynamic Kerr effect by using a fractional kinetic equation. This fractional kinetic equation (obtained via a generalization of the noninertial kinetic equation of conventional rotational diffusion to fractional kinetics to include anomalous relaxation) is solved using matrix continued fractions yielding the complex nonlinear dielectric susceptibility and the Kerr function of an assembly of rigid dipolar particles acted on by external superimposed dc E0 and ac E1(t)=E1 cos omegat electric fields of arbitrary strengths. In the weak field limit, analytic equations for nonlinear response functions are also derived.     

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.     

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.     

Anisotropic dynamics of dipolar liquids in narrow slit pores

We report molecular dynamics simulation results for Stockmayer fluids confined to narrow slitlike pores with structureless, nonconducting walls. The translational and rotational dynamics of the dipolar particles have been investigated by calculating autocorrelation functions, diffusion coefficients, and relaxation times for various pore widths (five or less particle diameters) and directions parallel and perpendicular to the walls. The dynamic properties of the confined systems are compared to bulk properties, where corresponding bulk and pore states at the same temperature and chemical potential are determined in parallel grand canonical Monte Carlo simulations. We find that the dynamic behavior inside the pore depends on the distance from the walls and can be strongly anisotropic even in globally isotropic systems. This concerns especially the particles in the surface layers close to the walls, where the single particle and collective dipolar relaxation resemble that of true two-dimensional dipolar fluids with different in-plane and out-of-plane relaxations. On the other hand, bulklike relaxation is observed in the pore center of sufficiently wide pores.     

Electrokinetics of concentrated suspensions of spherical colloidal particles with surface conductance, arbitrary zeta potential, and double-layer thickness in static electric fields

In this paper the electrophoretic mobility and the electrical conductivity of concentrated suspensions of spherical colloidal particles have been numerically studied under arbitrary conditions including zeta potential, particle volume fraction, double-layer thickness (overlapping of double layers is allowed), surface conductance by a dynamic Stern layer model (DSL), and ionic properties of the solution. We present an extensive set of numerical data of both the electrophoretic mobility and the electrical conductivity versus zeta potential and particle volume fraction, for different electrolyte concentrations. The treatment is based on the use of a cell model to account for hydrodynamic and electrical interactions between particles. Other theoretical approaches have also been considered for comparison. Furthermore, the study includes the possibility of adsorption and lateral motion of ions in the inner region of the double layers (DSL model), according to the theory developed by C. S. Mangelsdorf and L. R. White (J. Chem. Soc. Faraday Trans.86, 2859 (1990)). The results show that the correct limiting cases of low zeta potentials and thin double layers for dilute suspensions are fulfilled by our conductivity formula. Moreover, the presence of a DSL causes very important changes, even dramatic, on the values of both the electrophoretic mobility and the electrical conductivity for a great range of volume fractions and zeta potentials, specially when double layers of adjacent cells overlap, in comparison with the standard case (no Stern layer present). It can be concluded that in general the presence of a dynamic Stern layer causes the electrophoretic mobility to decrease and the electrical conductivity to increase in comparison with the standard case for every volume fraction, zeta potential, and double-layer thickness.     

Structural relaxation and glass transition behavior of binary hard-ellipse mixtures

Structural relaxation and glass transition in binary hard-spherical particle mixtures have been reported to exhibit unusual features depending on the size disparity and composition. However, the mechanism by which the mixing effects lead to these features and whether these features are universal for particles with anisotropic geometries remains unclear. Here, we employ event-driven molecular dynamics simulation to investigate the dynamical and structural properties of binary two-dimensional hard-ellipse mixtures. We find that the relaxation dynamics for translational degrees of freedom exhibit equivalent trends as those observed in binary hard-spherical mixtures. However, the glass transition densities for translational and rotational degrees of freedom present different dependencies on size disparity and composition. Furthermore, we propose a mechanism based on structural properties that explain the observed mixing effects and decoupling behavior between translational and rotational motions in binary hard-ellipse systems.     

Electro-optic characteristics of optically interacting beta-FeOOH particles

In this article the influence of multiple light scattering on the basic electro-optic parameters of optically dense colloidal particles is analyzed. The model system is an aqueous suspension of monodisperse ellipsoidal beta-FeOOH particles that displays large electric light scattering variations, including sign reversal, at very low particle volume fractions (two orders of magnitude below the critical concentration of particle electric interactions). The scaling method permits the relative variations in particle electric polarizability to be followed and its relaxation frequency to be determined. Particle rotational relaxation frequency and the phase shift of the responses at this frequency are obtained by the alternating component of the effects. Characteristic field intensity curves in the low-frequency range are used to follow the relative changes induced by the slow electrokinetic effect. The experimental results show that, despite the drastic variations in the effects with volume fraction, the basic electro-optic parameters are independent of multiple scattering and can be adequately determined for any particle concentration, excluding a narrow range in the vicinity of the electro-optic sign reversal. The investigation demonstrates that the dependence of the frequency behavior of aqueous beta-FeOOH on particle volume fraction reported in the literature is due not to optical interactions but to variation of particle surface electric state in the process of dilution.