Simulation of a Hard-Sphere Fluid in Bicontinuous Random Media

Simulation of diffusion in a crowded environment

We performed extensive and systematic simulation studies of two-dimensional fluid motion in a complex crowded environment. In contrast to other studies we focused on cooperative phenomena that occurred if the motion of particles takes place in a dense crowded system, which can be considered as a crude model of a cellular membrane. Our main goal was to answer the following question: how do the fluid molecules move in an environment with a complex structure, taking into account the fact that motions of fluid molecules are highly correlated. The dynamic lattice liquid (DLL) model, which can work at the highest fluid density, was employed. Within the frame of the DLL model we considered cooperative motion of fluid particles in an environment that contained static obstacles. The dynamic properties of the system as a function of the concentration of obstacles were studied. The subdiffusive motion of particles was found in the crowded system. The influence of hydrodynamics on the motion was investigated via analysis of the displacement in closed cooperative loops. The simulation and the analysis emphasize the influence of the movement correlation between moving particles and obstacles.

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.

Diffusion within ultrathin, dense nanoporous silica films

In this work the origin of permselectivity in dense silica films which possess a pore structure with pore sizes commensurate with the molecular size of the diffusing gas species is investigated. Much of the recently reported work in this field has involved the development of composite membrane films, and while it is generally assumed that the transport process of the gas species within the selective layer of these films is activated in nature, there are anomalies with this simplified picture. In this paper a new model is developed which, for the first time, explains the permselective behavior of the thin selective coatings ubiquitous to membrane separation processes. The model involves the existence of two primary transport domains within the solid film, one of which rapidly conducts the permeating gas (under non-Fickian conditions), while the second domain involves a slow diffusion mode characterized by normal Fickian transport. To validate the model, molecular dynamics simulations are conducted for diffusion of a number of simple gases (He, N(2), and CO(2)) within silica glasses over a range of solid densities. The silica media employed in these studies are based on a novel approach developed in this work for the construction of three-dimensionally periodic atomistic structures of silica of arbitrary density in which network bond connectivity is ensured. The results obtained from this work are in qualitative agreement with experimental observations and confirm the existence of dual mode transport which is central to the interpretation of the permselectivity in composite membranes systems.

Atomistic simulation of the formation of nanoporous silica films via molecular chemical vapor deposition on nonporous substrates

To distinguish thin deposited film characteristics clearly from the influence of substrate morphological properties, the growth mechanism and the macroscale and nanoscale properties of nanoporous SiO(2) films deposited on nonporous silica (SiO(2)) substrates from chemical precursors Si(OH)(4) and TEOS (tetraethoxysilane) via low-pressure chemical vapor deposition are the primary targets of this study. This work employs a kinetic Monte Carlo (KMC) simulation method coupled to the Metropolis Monte Carlo method to relax the strained silica structure. The influence of the deposition temperature (473, 673, and 873 K) on the properties of the SiO(x) layers is addressed via analysis of the film growth rates, density profiles of the deposited thin films, pore size distributions, carbon depth profiles (with respect to TEOS), and voidage analysis for layers of different thicknesses (8-18 nm). A comparison of simulation with experimental results is also carried out.

Self-diffusion of non-interacting hard spheres in particle gels

Different kinds of particle gels were simulated using a process of random aggregation of hard spheres. The mean square displacement of Brownian spherical tracer particles through these rigid gels was monitored and the average diffusion coefficient, normalized with the free diffusion coefficient (D), was obtained. For each gel structure the effect of the gel volume fraction (φ) and size ratio of the tracer (d) on the relative diffusion coefficient was investigated systematically. The volume fraction that is accessible to the tracers (φ(a)) was determined in each case. D was found to be approximately the same if φ(a) was the same, independent of φ, d and the gel structure. However a different behaviour is found if the tracers can penetrate the strands of the gel. A state diagram of d versus φ is given that shows the critical values (d(c), φ(c)) at which all tracers become trapped. Different values are found for different gel structures. The dependence of D on φ/φ(c) is independent of d, while the dependence of D on d/d(c) is independent of φ.

The effect of matrix structure on the diffusion of fluids in porous media

The effect of matrix structure on the transport properties of adsorbed fluids is studied using computer simulations and percolation theory. The model system consists of a fluid of hard spheres diffusing in a matrix of hard spheres fixed in space. Three different arrangements of the fixed spheres, random, templated, and polymeric, are investigated. For a given matrix volume fraction the diffusion coefficient of the fluid, D, is sensitive to the manner in which the matrix is constructed, with large differences between the three types of matrices. The matrix is mapped onto an effective lattice composed of vertices and bonds using a Voronoi tessellation method where the connectivity of bonds is determined using a geometric criterion, i.e., a bond is connected if a fluid particle can pass directly between the two pores the bond connects, and disconnected otherwise. The percolation threshold is then determined from the connectivity of the bonds. D displays universal scaling behavior in the reduced volume fraction, i.e., D approximately (1-phi(m)phi(c))(gamma), where phi(m) is the matrix volume fraction and phi(c) is the matrix volume fraction at the percolation threshold. We find that gamma approximately 2.2, independent of matrix type, which is different from the result gamma approximately 1.53 for diffusion in lattice models, but similar to that for conduction in Swiss cheese models. Lattice simulations with biased hopping probabilities are consistent with the continuous-space simulations, and this shows that the universal behavior of diffusion is sensitive to details of local dynamics.

Crossover in the slow decay of dynamic correlations in the lorentz model

The long-time behavior of transport coefficients in a model for spatially heterogeneous media in two and three dimensions is investigated by molecular dynamics simulations. The behavior of the velocity autocorrelation function is rationalized in terms of a competition of the critical relaxation due to the underlying percolation transition and the hydrodynamic power-law anomalies. In two dimensions and in the absence of a diffusive mode, another power-law anomaly due to trapping is found with an exponent -3 instead of -2. Further, the logarithmic divergence of the Burnett coefficient is corroborated in the dilute limit; at finite density, however, it is dominated by stronger divergences.

Dual control cell reaction ensemble molecular dynamics: A method for simulations of reactions and adsorption in porous materials

We present a simulation tool to study fluid mixtures that are simultaneously chemically reacting and adsorbing in a porous material. The method is a combination of the reaction ensemble Monte Carlo method and the dual control volume grand canonical molecular dynamics technique. The method, termed the dual control cell reaction ensemble molecular dynamics method, allows for the calculation of both equilibrium and nonequilibrium transport properties in porous materials such as diffusion coefficients, permeability, and mass flux. Control cells, which are in direct physical contact with the porous solid, are used to maintain the desired reaction and flow conditions for the system. The simulation setup closely mimics an actual experimental system in which the thermodynamic and flow parameters are precisely controlled. We present an application of the method to the dry reforming of methane reaction within a nanoscale reactor model in the presence of a semipermeable membrane that was modeled as a porous material similar to silicalite. We studied the effects of the membrane structure and porosity on the reaction species permeability by considering three different membrane models. We also studied the effects of an imposed pressure gradient across the membrane on the mass flux of the reaction species. Conversion of syngas (H2/CO) increased significantly in all the nanoscale membrane reactor models considered. A brief discussion of further potential applications is also presented.