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

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.

Finite-size effects in the diffusion dynamics of a glass-forming binary mixture with large size ratio

Extensive molecular dynamics computer simulations of an equimolar, glass-forming AB mixture with a large size ratio are presented. While the large A particles show a glass transition around the critical density of mode-coupling theory ρ c, the small B particles remain mobile with a relatively weak decrease in their self-diffusion coefficient DB with increasing density. Surprisingly, around ρ c, the self-diffusion coefficient of species A, DA, also starts to show a rather weak dependence on density. We show that this is due to finite-size effects that can be understood from the analysis of the collective interdiffusion dynamics.

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.

Reconfiguring confined magnetic colloids with tunable fluid transport behavior

Collective dynamics of confined colloids are crucial in diverse scenarios such as self-assembly and phase behavior in materials science, microrobot swarms for drug delivery and microfluidic control. Yet, fine-tuning the dynamics of colloids in microscale confined spaces is still a formidable task due to the complexity of the dynamics of colloidal suspension and to the lack of methodology to probe colloids in confinement. Here, we show that the collective dynamics of confined magnetic colloids can be finely tuned by external magnetic fields. In particular, the mechanical properties of the confined colloidal suspension can be probed in real time and this strategy can be also used to tune microscale fluid transport. Our experimental and theoretical investigations reveal that the collective configuration characterized by the colloidal entropy is controlled by the colloidal concentration, confining ratio and external field strength and direction. Indeed, our results show that mechanical properties of the colloidal suspension as well as the transport of the solvent in microfluidic devices can be controlled upon tuning the entropy of the colloidal suspension. Our approach opens new avenues for the design and application of drug delivery, microfluidic logic, dynamic fluid control, chemical reaction and beyond.

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.

Tracer Transport Probes Relaxation and Structure of Attractive and Repulsive Glassy Liquids

Dynamic coupling of small penetrants to slow, cooperative relaxations within crowded cells, supercooled liquids, and polymer matrices has broad consequences for applications ranging from drug delivery to nanocomposite processing. Interactions between the constituents of these and other disordered media alter the cooperative relaxations, but their effect on penetrant dynamics remains incompletely understood. We use molecular dynamics simulations to show that the motions of hard-sphere tracer particles probe differences in local structure and cooperative relaxation processes in attractive and repulsive glassy liquid matrices with equal bulk packing fractions and long-time diffusivities. Coupling of the tracer dynamics to collective relaxations in each matrix affects the shape of tracer trajectories, which are fractal within the repulsive matrix and more compact in the attractive. These results reveal that the structure of relaxations controls penetrant transport and dispersion in cooperatively relaxing systems and provide insight into dynamical heterogeneity within glassy liquids.

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.

Investigating amorphous order in stable glasses by random pinning

We investigate stable glassy states that are found when glass-forming liquids are biased to lower than average dynamical activity. By pinning the positions of randomly chosen particles, we show that many-body correlations in these states are relatively strong and long ranged compared to equilibrium reference states. The presence of strong many-body correlations in these apparently disordered systems supports the idea that stable glassy states exhibit a kind of "amorphous order," which helps to explain their stability.

Dynamical correlations in a glass former with randomly pinned particles

The effects of randomly pinning particles in a model glass-forming fluid are studied, with a focus on the dynamically heterogeneous relaxation in the presence of pinning. We show how four-point dynamical correlations can be analyzed in real space, allowing direct extraction of a length scale that characterizes dynamical heterogeneity. In the presence of pinning, the relaxation time of the glassy system increases by up to two decades, but there is almost no increase in either the four-point correlation length or the strength of the four-point correlations. We discuss the implications of these results for theories of the glass transition.

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.

Anomalous transport in the crowded world of biological cells

A ubiquitous observation in cell biology is that the diffusive motion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarizing their densely packed and heterogeneous structures. The most familiar phenomenon is a sublinear, power-law increase of the mean-square displacement (MSD) as a function of the lag time, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations in time, non-Gaussian distributions of spatial displacements, heterogeneous diffusion and a fraction of immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarize some widely used theoretical models: Gaussian models like fractional Brownian motion and Langevin equations for visco-elastic media, the continuous-time random walk model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Particular emphasis is put on the spatio-temporal properties of the transport in terms of two-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even if the MSDs are identical. Then, we review the theory underlying commonly applied experimental techniques in the presence of anomalous transport like single-particle tracking, fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP). We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where a variety of model systems mimic physiological crowding conditions. Finally, computer simulations are discussed which play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.

Mixing normal and anomalous diffusion

In the densely filled biological cells often subdiffusion is observed, where the average squared displacement increases slower than linear with the length of the observation interval. One reason for such subdiffusive behavior is attractive interactions between the diffusing particles that lead to temporary complex formation. Here, we show that such transient binding is not an average state of the particles but that intervals of free diffusion alternate with slower displacement when bound to neighboring particles. The observed macroscopic behavior is then the weighted average of these two contributions. Interestingly, even at very high concentrations, the unbound fraction still exhibits essentially normal diffusion.

Microscopic models of mode-coupling theory: the F12 scenario

We provide extended evidence that mode-coupling theory (MCT) of supercooled liquids for the F(12) schematic model admits a microscopic realization based on facilitated spin models with tunable facilitation. Depending on the facilitation strength, one observes two distinct dynamical glass transition lines--continuous and discontinuous--merging at a dynamical tricritical-like point with critical decay exponents consistently related by MCT predictions. The mechanisms of dynamical arrest can be naturally interpreted in geometrical terms: the discontinuous and continuous transitions correspond to bootstrap and standard percolation processes, in which the incipient spanning cluster of frozen spins forms either a compact or a fractal structure, respectively. Our cooperative dynamical facilitation picture of glassy behavior is complementary to the one based on disordered systems and can account for higher-order singularity scenarios in the absence of a finite temperature thermodynamic glass transition. We briefly comment on the relevance of our results to finite spatial dimensions and to the F(13) schematic model.

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.