Impact of random obstacles on the dynamics of a dense colloidal fluid

Normal and anomalous diffusion in the disordered wind-tree model

Ehrenfests' wind-tree model (EWTM) refers to a two-dimensional system where noninteracting point tracer particles move through a random arrangement of overlapping or nonoverlapping square-shaped scatterers. Here, extensive event-driven molecular dynamics simulations of the EWTM at different reduced scatterer densities ρ are presented. For nonoverlapping scatterers, the asymptotic motion of the tracer particles is diffusive. We compare their diffusion coefficient D, as obtained from the simulation, with that predicted by kinetic theory where D^{-1} is expanded up to the second order in the scatterer density. While at low density quantitative agreement between theory and simulation is found, we show that beyond the low-density regime deviations to the theory are associated with the emergence of a maximum in the non-Gaussian parameter at intermediate times. For the case of overlapping scatterers, in agreement with a theoretical prediction, the asymptotic motion of the tracer particles is subdiffusive, i.e., the mean-squared displacement at long times t grows like t^{1-2ρ/3}. We propose a model of the van Hove correlation function that describes the density dependence of the tracer particles' asymptotic subdiffusive transport on a quantitative level.

Deformable hard particles confined in a disordered porous matrix

With suitably designed Monte Carlo simulations, we have investigated the properties of mobile, impenetrable, yet deformable particles that are immersed into a porous matrix, the latter one realized by a frozen configuration of spherical particles. By virtue of a model put forward by Batista and Miller [Phys. Rev. Lett. 105, 088305 (2010)], the fluid particles can change in their surroundings, formed by other fluid particles or the matrix particles, their shape within the class of ellipsoids of revolution; such a change in shape is related to a change in energy, which is fed into suitably defined selection rules in the deformation "moves" of the Monte Carlo simulations. This concept represents a simple yet powerful model of realistic, deformable molecules with complex internal structures (such as dendrimers or polymers). For the evaluation of the properties of the system, we have used the well-known quenched-annealed protocol (with its characteristic double average prescription) and have analyzed the simulation data in terms of static properties (the radial distribution function and aspect ratio distribution of the ellipsoids) and dynamic features (notably the mean squared displacement). Our data provide evidence that the degree of deformability of the fluid particles has a distinct impact on the aforementioned properties of the system.

Tracer diffusion in crowded solutions of sticky polymers

Macromolecular diffusion in strongly confined geometries and crowded environments is still to a large extent an open subject in soft matter physics and biology. In this paper, we employ large-scale Langevin dynamics simulations to investigate how the diffusion of a tracer is influenced by the combined action of excluded-volume and weak attractive crowder-tracer interactions. We consider two species of tracers, standard hard-core particles described by the Weeks-Chandler-Andersen (WCA) repulsive potential and core-softened (CS) particles, which model, e.g., globular proteins, charged colloids, and nanoparticles covered by polymeric brushes. These systems are characterized by the presence of two length scales in the interaction and can show waterlike anomalies in their diffusion, stemming from the inherent competition between different length scales. Here we report a comprehensive study of both diffusion and structure of these two tracer species in an environment crowded by quenched configurations of polymers at increasing density. We analyze in detail how the tracer-polymer affinity and the system density affect transport as compared to the emergence of specific static spatial correlations. In particular, we find that, while hardly any differences emerge in the diffusion properties of WCA and CS particles, the propensity to develop structural order for large crowding is strongly frustrated for CS particles. Surprisingly, for large enough affinity for the crowding matrix, the diffusion coefficient of WCA tracers display a nonmonotonic trend as their density is increased when compared to the zero affinity scenario. This waterlike anomaly turns out to be even larger than what observed for CS particle and appears to be rooted in a similar competition between excluded-volume and affinity effects.

Anomalous transport in the soft-sphere Lorentz model

The sensitivity of anomalous transport in crowded media to the form of the inter-particle interactions is investigated through computer simulations. We extend the highly simplified Lorentz model towards realistic natural systems by modeling the interactions between the tracer and the obstacles with a smooth potential. We find that the anomalous transport at the critical point happens to be governed by the same universal exponent as for hard exclusion interactions, although the mechanism of how narrow channels are probed is rather different. The scaling behavior of simulations close to the critical point confirm this exponent. Our result indicates that the simple Lorentz model may be applicable to describing the fundamental properties of long-range transport in real crowded environments.

Structure Dominates Localization of Tracers within Aging Nanoparticle Glasses

We investigate the transport and localization of tracer probes in a glassy matrix as a function of relative size using dynamic X-ray scattering experiments and molecular dynamics simulations. The quiescent relaxations of tracer particles evolve with increasing waiting time, t_w. The corresponding relaxation times increase exponentially at small t_w and then transition to a power-law behavior at longer t_w. As tracer size decreases, the aging behavior weakens and the particles become less localized within the matrix until they delocalize at a critical size ratio δ₀ ≈ 0.38. Localization does not vary with sample age even as the relaxations slow by approximately an order of magnitude, suggesting that matrix structure controls tracer localization.

Connect the Thermodynamics of Bulk and Confined Fluids: Confinement-Adsorption Scaling

A fluid (a gas or a liquid) adsorbed in a porous material can behave very differently from its bulk counterpart. The advent of various synthesized materials with nanopores and their wide applications have provided strong impetus for studying fluids in confinement because our current understanding is still incomplete. From a large number of Monte Carlo simulations, we found a scaling relation that allows for connecting some thermodynamic properties (chemical potential, free energy per particle, and grand potential per particle) of a confined fluid to the bulk ones. Upon rescaling the adsorbed fluid density, the adsorption isotherms for many different confining environments collapse to the corresponding bulk curve. We also reveal the intimate connection of the reported scaling relation to Gibbs theory of inhomogeneous fluids and morphological thermodynamics. The advance in our understanding of confined fluids, gained from this study, also opens attractive perspectives for circumventing experimental difficulty for directly measuring some fluid thermodynamic properties in nanoporous materials.

Nonergodicity parameters of confined hard-sphere glasses

Within a recently developed mode-coupling theory for fluids confined to a slit we elaborate numerical results for the long-time limits of suitably generalized intermediate scattering functions. The theory requires as input the density profile perpendicular to the plates, which we obtain from density functional theory within the fundamental-measure framework, as well as symmetry-adapted static structure factors, which can be calculated relying on the inhomogeneous Percus-Yevick closure. Our calculations for the nonergodicity parameters for both the collective as well as for the self motion are in qualitative agreement with our extensive event-driven molecular dynamics simulations for the intermediate scattering functions for slightly polydisperse hard-sphere systems at high packing fraction. We show that the variation of the nonergodicity parameters as a function of the wavenumber correlates with the in-plane static structure factors, while subtle effects become apparent in the structure factors and relaxation times of higher mode indices. A criterion to predict the multiple reentrant from the variation of the in-plane static structure is presented.

Dynamics of fluids in quenched-random potential energy landscapes: a mode-coupling theory approach

Motivated by a number of recent experimental and computational studies of the dynamics of fluids plunged in quenched-disordered external fields, we report on a theoretical investigation of this topic within the framework of the mode-coupling theory, based on the simple model of the hard-sphere fluid in a Gaussian random field. The possible dynamical arrest scenarios driven by an increase of the disorder strength and/or of the fluid density are mapped, and the corresponding evolutions of time-dependent quantities typically used for the characterization of anomalous self-diffusion are illustrated with detailed computations. Overall, a fairly reasonable picture of the dynamics of the system at hand is outlined, which in particular involves a non-monotonicity of the self-diffusion coefficient with fluid density at fixed disorder strength, in agreement with experiments. The disorder correlation length is shown to have a strong influence on the latter feature.

Fluids in porous media. IV. Quench effect on chemical potential

It appears to be a common sense to measure the crowdedness of a fluid system by the densities of the species constituting it. In the present work, we show that this ceases to be valid for confined fluids under some conditions. A quite thorough investigation is made for a hard sphere (HS) fluid adsorbed in a hard sphere matrix (a quench-annealed system) and its corresponding equilibrium binary mixture. When fluid particles are larger than matrix particles, the quench-annealed system can appear much more crowded than its corresponding equilibrium binary mixture, i.e., having a much higher fluid chemical potential, even when the density of each species is strictly the same in both systems, respectively. We believe that the insight gained from this study should be useful for the design of functionalized porous materials.

Dynamic heterogeneities and non-Gaussian behavior in two-dimensional randomly confined colloidal fluids

A binary mixture of superparamagnetic colloidal particles is confined between glass plates such that the large particles become fixed and provide a two-dimensional disordered matrix for the still mobile small particles, which form a fluid. By varying fluid and matrix area fractions and tuning the interactions between the superparamagnetic particles via an external magnetic field, different regions of the state diagram are explored. The mobile particles exhibit delocalized dynamics at small matrix area fractions and localized motion at high matrix area fractions, and the localization transition is rounded by the soft interactions [T. O. E. Skinner et al., Phys. Rev. Lett. 111, 128301 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.128301]. Expanding on previous work, we find the dynamics of the tracers to be strongly heterogeneous and show that molecular dynamics simulations of an ideal gas confined in a fixed matrix exhibit similar behavior. The simulations show how these soft interactions make the dynamics more heterogeneous compared to the disordered Lorentz gas and lead to strong non-Gaussian fluctuations.

Localization dynamics of fluids in random confinement

The dynamics of two-dimensional fluids confined within a random matrix of obstacles is investigated using both colloidal model experiments and molecular dynamics simulations. By varying fluid and matrix area fractions in the experiment, we find delocalized tracer particle dynamics at small matrix area fractions and localized motion of the tracers at high matrix area fractions. In the delocalized region, the dynamics is subdiffusive at intermediate times, and diffusive at long times, while in the localized regime, trapping in finite pockets of the matrix is observed. These observations are found to agree with the simulation of an ideal gas confined in a weakly correlated matrix. Our results show that Lorentz gas systems with soft interactions are exhibiting a smoothening of the critical dynamics and consequently a rounded delocalization-to-localization transition.

Simulation study of seemingly Fickian but heterogeneous dynamics of two dimensional colloids

A two-dimensional (2D) solid lacks long-range positional order and is diffusive by means of the cooperative motion of particles. We find from molecular dynamics simulations of hard discs that 2D colloids in solid and hexatic phases show seemingly Fickian but strongly heterogeneous dynamics. Beyond translational relaxation time, the mean-square displacement is linear with time, t, implying that discs would undergo Brownian diffusion and the self-part of the van Hove correlation function [G(s)(r,t)] might be Gaussian. But dynamics is still heterogeneous and G(s)(r,t) is exponential at large r and oscillatory with multiple peaks at intermediate length. We attribute the existence of several such peaks to the observation that there are several clusters of discs with discretized mobility. The cluster of marginally mobile discs grows with time and begins to percolate around translational relaxation time while clusters of fast discs emerge in the middle of the marginally mobile cluster.

Water confined in MCM-41: a mode coupling theory analysis

In this paper we analyze molecular dynamics simulation results on supercooled water in a MCM-41 pore in order to test the mode coupling theory. A layer analysis must be performed for water in the pore in order to exclude the contribution of water bound to the strongly hydrophilic surface. Upon supercooling a range of temperatures is reached where the liquid follows the mode coupling theory. From the power law behavior of the relaxation times extracted from the Kohlrausch-William-Watts fit to the self-intermediate scattering function, we obtain the crossover temperature T(C) and the γ exponent of the theory. The time-temperature superposition principle is also satisfied. A fit to the von Schweidler law yields a coefficient b from which all the other parameters of the theory have been calculated. In particular, we obtained the same value of γ as extracted from the power law fit to the relaxation times, in agreement with the requirements of the theory. For very low temperatures, the mode coupling theory no longer holds as hopping processes intervene and water turns its behavior to that of a strong liquid.

Mode-coupling theory predictions for the dynamical transitions of partly pinned fluid systems

The predictions of the mode-coupling theory (MCT) for the dynamical arrest scenarios in a partly pinned (PP) fluid system are reported. The corresponding dynamical phase diagram is found to be very similar to that of a related quenched-annealed (QA) system. The only significant qualitative difference lies in the shape of the diffusion-localization lines at high matrix densities, with a reentry phenomenon for the PP system but not for the QA model, in full agreement with recent computer simulation results. This finding clearly lends support to the predictive power of the MCT for fluid-matrix systems. In addition, the predictions of the MCT are shown to be in stark contrast with those of the random first-order transition theory. The PP systems are thus confirmed as very promising models for differentiating tests of theories of the glass transition.

Dynamic arrest of colloids in porous environments: disentangling crowding and confinement

Using numerical simulations we study the slow dynamics of a colloidal hard-sphere fluid adsorbed in a matrix of disordered hard-sphere obstacles. We calculate separately the contributions to the single-particle dynamic correlation functions due to free and trapped particles. The separation is based on a Delaunay tessellation to partition the space accessible to the centres of fluid particles into percolating and disconnected voids. We find that the trapping of particles into disconnected voids of the matrix is responsible for the appearance of a nonzero long-time plateau in the single-particle intermediate scattering functions of the full fluid. The subdiffusive exponent z, obtained from the logarithmic derivative of the mean squared displacement, is essentially unaffected by the motion of trapped particles: close to the percolation transition, we determined z approximately = 0.5 for both the full fluid and the particles moving in the percolating void. Notably, the same value of z is found in single-file diffusion and is also predicted by mode-coupling theory along the diffusion-localization line. We also reveal subtle effects of dynamic heterogeneity in both the free and the trapped component of the fluid particles, and discuss microscopic mechanisms that contribute to this phenomenon.

Anomalous transport of a tracer on percolating clusters

We investigate the dynamics of a single tracer exploring a course of fixed obstacles in the vicinity of the percolation transition for particles confined to the infinite cluster. The mean-square displacement displays anomalous transport, which extends to infinite times precisely at the critical obstacle density. The slowing down of the diffusion coefficient exhibits power-law behavior for densities close to the critical point and we show that the mean-square displacement fulfills a scaling hypothesis. Furthermore, we calculate the dynamic conductivity as a response to an alternating electric field. Last, we discuss the non-gaussian parameter as an indicator for heterogeneous dynamics.

Slow dynamics, dynamic heterogeneities, and fragility of supercooled liquids confined in random media

Using molecular dynamics simulations, we study the slow dynamics of supercooled liquids confined in a random matrix of immobile obstacles. We study the dynamical crossover from glass-like to Lorentz-gas-like behavior in terms of the density correlation function, the mean square displacement, the nonlinear dynamic susceptibility, the non-gaussian parameter, and the fragility. We find the cooperative and spatially heterogeneous dynamics to be suppressed as the obstacle density increases, leading to a more Arrhenius-like behavior in the temperature dependence of the relaxation time. Our findings are qualitatively consistent with the results of recent experimental and numerical studies for various classes of spatially heterogeneous systems. We also investigate the dependence of the dynamics of mobile particles on the protocol used to generate the random matrix. A re-entrant transition from the arrested phase to the liquid phase as the mobile particle density increases is observed for a class of protocols. This re-entrance is explained in terms of the distribution of the volume of the voids that are available to the mobile particles.