14 research outputs found
Single-particle motion in colloids: force-induced diffusion
We study the fluctuating motion of a Brownian-sized probe particle as it is dragged by a constant external force through a colloidal dispersion. In this nonlinear-microrheology problem, collisions between the probe and the background bath particles, in addition to thermal fluctuations of the solvent, drive a long-time diffusive spread of the probe's trajectory. The influence of the former is determined by the spatial configuration of the bath particles and the force with which the probe perturbs it. With no external forcing the probe and bath particles form an equilibrium microstructure that fluctuates thermally with the solvent. Probe motion through the dispersion distorts the microstructure; the character of this deformation, and hence its influence on the probe's motion, depends on the strength with which the probe is forced, F^(ext), compared to thermal forces, kT/b, defining a Péclet number, Pe = F^(ext)/(kT/b), where kT is the thermal energy and b the bath particle size. It is shown that the long-time mean-square fluctuational motion of the probe is diffusive and the effective diffusivity of the forced probe is determined for the full range of Péclet number. At small Pe Brownian motion dominates and the diffusive behaviour of the probe characteristic of passive microrheology is recovered, but with an incremental flow-induced ‘microdiffusivity’ that scales as D^(micro) ~ D_aPe^2φ_b, where φ_b is the volume fraction of bath particles and D_a is the self-diffusivity of an isolated probe. At the other extreme of high Péclet number the fluctuational motion is still diffusive, and the diffusivity becomes primarily force induced, scaling as (F^(ext)/η)φ_b, where η is the viscosity of the solvent. The force-induced microdiffusivity is anisotropic, with diffusion longitudinal to the direction of forcing larger in both limits compared to transverse diffusion, but more strongly so in the high-Pe limit. The diffusivity is computed for all Pe for a probe of size a in a bath of colloidal particles, all of size b, for arbitrary size ratio a/b, neglecting hydrodynamic interactions. The results are compared with the force-induced diffusion measured by Brownian dynamics simulation. The theory is also compared to the analogous shear-induced diffusion of macrorheology, as well as to experimental results for macroscopic falling-ball rheometry. The results of this analysis may also be applied to the diffusive motion of self-propelled particles
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Vitrification is a spontaneous non-equilibrium transition driven by osmotic pressure.
Persistent dynamics in colloidal glasses suggest the existence of a non-equilibrium driving force for structural relaxation during glassy aging. But the implicit assumption in the literature that colloidal glasses form within the metastable state bypasses the search for a driving force for vitrification and glassy aging and its connection with a metastable state. The natural relation of osmotic pressure to number-density gradients motivates us to investigate the osmotic pressure as this driving force. We use dynamic simulation to quench a polydisperse hard-sphere colloidal liquid into the putative glass region while monitoring structural relaxation and osmotic pressure. Following quenches to various depths in volume fractionϕ(whereϕRCP≈ 0.678 for 7% polydispersity), the osmotic pressure overshoots its metastable value, then decreases with age toward the metastable pressure, driving redistribution of coordination number and interparticle voids that smooths structural heterogeneity with age. For quenches to 0.56 ⩽ϕ⩽ 0.58, accessible post-quench volume redistributes with age, allowing the glass to relax into a strong supercooled liquid and easily reach a metastable state. At higher volume fractions, 0.59 ⩽ϕ< 0.64, this redistribution encounters a barrier that is subsequently overcome by osmotic pressure, allowing the system to relax toward the metastable state. But forϕ⩾ 0.64, the overshoot is small compared to the high metastable pressure; redistribution of volume stops as particles acquire contacts and get stuck, freezing the system far from the metastable state. Overall, the osmotic pressure drives structural rearrangements responsible for both vitrification and glassy age-relaxation. The connection of energy, pressure, and structure identifies the glass transition, 0.63 <ϕg⩽ 0.64. We leverage the connection of osmotic pressure to energy density to put forth the mechanistic view that relaxation of structural heterogeneity in colloidal glasses occurs via individual particle motion driven by osmotic pressure, and is a spontaneous energy minimization process that drives the glass off and back to the metastable state
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Vitrification is a spontaneous non-equilibrium transition driven by osmotic pressure.
Persistent dynamics in colloidal glasses suggest the existence of a non-equilibrium driving force for structural relaxation during glassy aging. But the implicit assumption in the literature that colloidal glasses form within the metastable state bypasses the search for a driving force for vitrification and glassy aging and its connection with a metastable state. The natural relation of osmotic pressure to number-density gradients motivates us to investigate the osmotic pressure as this driving force. We use dynamic simulation to quench a polydisperse hard-sphere colloidal liquid into the putative glass region while monitoring structural relaxation and osmotic pressure. Following quenches to various depths in volume fractionϕ(whereϕRCP≈ 0.678 for 7% polydispersity), the osmotic pressure overshoots its metastable value, then decreases with age toward the metastable pressure, driving redistribution of coordination number and interparticle voids that smooths structural heterogeneity with age. For quenches to 0.56 ⩽ϕ⩽ 0.58, accessible post-quench volume redistributes with age, allowing the glass to relax into a strong supercooled liquid and easily reach a metastable state. At higher volume fractions, 0.59 ⩽ϕ< 0.64, this redistribution encounters a barrier that is subsequently overcome by osmotic pressure, allowing the system to relax toward the metastable state. But forϕ⩾ 0.64, the overshoot is small compared to the high metastable pressure; redistribution of volume stops as particles acquire contacts and get stuck, freezing the system far from the metastable state. Overall, the osmotic pressure drives structural rearrangements responsible for both vitrification and glassy age-relaxation. The connection of energy, pressure, and structure identifies the glass transition, 0.63 <ϕg⩽ 0.64. We leverage the connection of osmotic pressure to energy density to put forth the mechanistic view that relaxation of structural heterogeneity in colloidal glasses occurs via individual particle motion driven by osmotic pressure, and is a spontaneous energy minimization process that drives the glass off and back to the metastable state
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"Dense diffusion" in colloidal glasses: short-ranged long-time self-diffusion as a mechanistic model for relaxation dynamics.
Despite decades of exploration of the colloidal glass transition, mechanistic explanation of glassy relaxation processes has remained murky. State-of-the-art theoretical models of the colloidal glass transition such as random first order transition theory, active barrier hopping theory, and non-equilibrium self-consistent generalized Langevin theory assert that relaxation reported at volume fractions above the ideal mode coupling theory prediction φg,MCT requires some sort of activated process, and that cooperative motion plays a central role. However, discrepancies between predicted and measured values of φg and ambiguity in the role of cooperative dynamics persist. Underlying both issues is the challenge of conducting deep concentration quenches without flow and the difficulty in accessing particle-scale dynamics. These two challenges have led to widespread use of fitting methods to identify divergence, but most a priori assume divergent behavior; and without access to detailed particle dynamics, it is challenging to produce evidence of collective dynamics. We address these limitations by conducting dynamic simulations accompanied by experiments to quench a colloidal liquid into the putative glass by triggering an increase in particle size, and thus volume fraction, at constant particle number density. Quenches are performed from the liquid to final volume fractions 0.56 ≤ φ ≤ 0.63. The glass is allowed to age for long times, and relaxation dynamics are monitored throughout the simulation. Overall, correlated motion acts to release dynamics from the glassy plateau - but only over length scales much smaller than a particle size - allowing self-diffusion to re-emerge; self-diffusion then relaxes the glass into an intransient diffusive state, which persists for φ < 0.60. We observe similar relaxation dynamics up to φ = 0.63 before achieving the intransient state. We find that this long-time self-diffusion is short-ranged: analysis of mean-square displacement reveals a glassy cage size a fraction of a particle size that shrinks with quench depth, i.e. increasing volume fraction. Thus the equivalence between cage size and particle size found in the liquid breaks down in the glass, which we confirm by examining the self-intermediate scattering function over a range of wave numbers. The colloidal glass transition can hence be viewed mechanistically as a shift in the long-time self-diffusion from long-ranged to short-ranged exploration of configurations. This shift takes place without diverging dynamics: there is a smooth transition as particle mobility decreases dramatically with concomitant emergence of a dense local configuration space that permits sampling of many configurations via local particle motion
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Exploring the validity of time-concentration superposition in glassy colloids: Experiments and simulations
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