Simon K. Schnyder

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.

Rounding of the localization transition in model porous media

The generic mechanisms of anomalous transport in porous media are investigated by computer simulations of two-dimensional model systems. In order to bridge the gap between the strongly idealized Lorentz model and realistic models of porous media, two models of increasing complexity are considered: a cherry-pit model with hard-core correlations as well as a soft-potential model. An ideal gas of tracer particles inserted into these structures is found to exhibit anomalous transport which extends up to several decades in time. Also, the self-diffusion of the tracers becomes suppressed upon increasing the density of the systems. These phenomena are attributed to an underlying percolation transition. In the soft potential model the transition is rounded, since each tracer encounters its own critical density according to its energy. Therefore, the rounding of the transition is a generic occurrence in realistic, soft systems.

Dynamic arrest in model porous media — intermediate scattering functions

Heterogeneous media constitute random disordered environments where transport is drastically hindered. Employing extensive molecular dynamics simulations, we investigate the spatio-temporal dynamics of tracer particles in the Lorentz model in the vicinity of the localization transition. There transport becomes anomalous and non-gaussian due to the presence of self-similar spatial structures, and dynamic scaling behavior is anticipated. The interplay of different time and length scales is revealed by the intermediate scattering functions, which are sensitive both to the underlying spatial fractal as well as the anomalous transport. We compare our numerical results in the transition regime to a mode-coupling approach, and find that certain aspects are surprisingly well predicted.

Long-wavelength anomalies in the asymptotic behavior of mode-coupling theory

We discuss the dynamic behavior of a tagged particle close to a classical localization transition in the framework of the mode-coupling theory of the glass transition. Asymptotic results are derived for the order parameter as well as the dynamic correlation functions and the mean-squared displacement close to the transition. The influence of an infrared cutoff is discussed.

Classical Liquids in Fractal Dimension

We introduce fractal liquids by generalizing classical liquids of integer dimensions d=1,2,3 to a noninteger dimension dl. The particles composing the liquid are fractal objects and their configuration space is also fractal, with the same dimension. Realizations of our generic model system include microphase separated binary liquids in porous media, and highly branched liquid droplets confined to a fractal polymer backbone in a gel. Here, we study the thermodynamics and pair correlations of fractal liquids by computer simulation and semianalytical statistical mechanics. Our results are based on a model where fractal hard spheres move on a near-critical percolating lattice cluster. The predictions of the fractal Percus-Yevick liquid integral equation compare well with our simulation results.

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.

Collective motion of cells crawling on a substrate: roles of cell shape and contact inhibition

Contact inhibition plays a crucial role in cell motility, wound healing, and tumour formation. By mimicking the mechanical motion of cells crawling on a substrate, we constructed a minimal model of migrating cells that naturally gives rise to contact inhibition of locomotion (CIL). The model cell consists of two disks, a front disk (a pseudopod) and a back disk (cell body), which are connected by a finite extensible spring. Despite the simplicity of the model, the collective behaviour of the cells is highly non-trivial and depends on both the shape of the cells and whether CIL is enabled. Cells with a small front disk (i.e., a narrow pseudopod) form immobile colonies. In contrast, cells with a large front disk (e.g., a lamellipodium) exhibit coherent migration without any explicit alignment mechanism in the model. This result suggests that crawling cells often exhibit broad fronts because this helps facilitate alignment. After increasing the density, the cells develop density waves that propagate against the direction of cell migration and finally stop at higher densities.

Structure factors in a two-dimensional binary colloidal hard sphere system

ABSTRACT Hard disks are one of the simplest interacting many-body model system in two dimensions (2D). Here, we present a comprehensive set of measurements of the static structure factors for quasi-2D monodisperse fluids and two different binary colloidal hard sphere mixtures: a small size ratio (SSR) system with a negligibly small negative non-additivity and a large size ratio system with a significantly larger non-additivity. We compare the experimental results for the monodisperse and SSR systems to those calculated using density functional theory (DFT) for additive mixtures. Furthermore, we determine the zero-wavevector limits of the static structure factors for the monodisperse and binary hard sphere fluids directly from an analysis of number and concentration fluctuations. For the monodisperse case, this leads to the isothermal compressibility, which agrees very well with DFT, and is consistent with the scaled particle theory equation of state for hard disks. For the binary fluids, the partial static structure factors are used to calculate the Bhatia–Thornton structure factors, and we find qualitative agreement with DFT for the SSR mixture. Finally, the zero-wavevector limits of the Bhatia–Thornton structure factors are determined and directly related to the thermodynamic factor, the dilatation factor and the isothermal compressibility. GRAPHICAL ABSTRACT