Gas permeation through a polymer network (original) (raw)

Anomalous diffusion of ideal polymer networks

Physical Review E, 1997

Internal dynamics of swollen polymer arrays were investigated with Brownian dynamic techniques applied to regular Rouse networks. In all cases local or self-diffusion decayed as a power law with a power proportional to the given topological dimension. This behavior allows for the classification of three dynamic regimes: subcritical topologies accommodate power law anomalous diffusion; logarithmic anomalous diffusion occurs within the critical topological dimension d t ϭ2; and upper-critical topologies siege bounded anomalous diffusion. ͓S1063-651X͑97͒13206-8͔

Role of percolation in diffusion on random lattices

Physical Review E, 1995

Diffusion of single particles on lattices with random distributions of static barriers (randombarrier model) is investigated by Monte Carlo simulations and the time-dependent effective-medium approximation. The crossover from anomalous to linear diffusive behavior is discussed in terms of a percolation model. For a discrete distribution of barrier heights with a small concentration of "defect" barriers at the percolation threshold, an alternative kind of transition from bulk-controlled to defect-controlled diffusion is observed as the temperature decreases.

Diffusion of a polymer chain in random media

Macromolecules, 1989

Dynamic properties of a self-avoiding walk chain, which performs Brownian motion between randomly distributed impenetrable fixed obstacles, have been investigated by Monte Carlo simulations. Analogous to the case of a random walk chain in random media, the chain dynamics is found to be slower than even reptation demonstrated by a stronger inverse dependence of the chain diffusion coefficient on chain length. This phenomenon is attributed to the slowing down of the chain due to the presence of bottlenecks in the random medium. The bottlenecks squeeze the chain and reduce the chain entropy setting up entropic barriers at random locations. A scaling analysis is adopted to account for the effects of such entropic barriers on chain diffusion. The simulation data are consistent with the predictions of the scaling arguments demonstrating that chain diffusion in random media is controlled by the entropic barriers of the media.

Lattice Gas Automata Simulation of 2D Site-Percolation Diffusion: Configuration Dependence of the Theoretically Expected Crossover of Diffusion Regime

Lecture Notes in Computer Science, 2008

Theoretical analysis of random walk on percolation lattices has predicted that, at the occupied site concentrations of above the threshold value, a characteristic crossover between an initial sub-diffusion to a final classical diffusion behavior should occur. In this study, we have employed the lattice gas automata model to simulate random walk over a square 2D site-percolation lattice. Quite good result was obtained for the critical exponent of diffusion coefficient. The random walker was found to obey the anomalous sub-diffusion regime, with the exponent decreasing when the occupied site concentration decreases. The expected crossover between diffusion regimes was observed in a configuration-dependent manner, but the averaging over the ensemble of lattice configurations removed any manifestation of such crossovers. This may have been originated from the removal of short-scale inhomogeneities in percolation lattices occurring after ensemble averaging.

Monte carlo study of the percolation in two-dimensional polymer systems

Journal of Molecular Modeling, 2013

The structure of a two-dimensional film formed by adsorbed polymer chains was studied by means of Monte Carlo simulations. The polymer chains were represented by linear sequences of lattice beads and positions of these beads were restricted to vertices of a two-dimensional square lattice. Two different Monte Carlo methods were employed to determine the properties of the model system. The first was the random sequential adsorption (RSA) and the second one was based on Monte Carlo simulations with a Verdier-Stockmayer sampling algorithm. The methodology concerning the determination of the percolation thresholds for an infinite chain system was discussed. The influence of the chain length on both thresholds was presented and discussed. It was shown that the RSA method gave considerably lower thresholds for longer chains. This behavior can be explained by a different pool of chain conformations used in the calculations in both methods under consideration.

Bond percolation of polymers

Journal of Physics A-mathematical and General, 2004

We study bond percolation of NNN non-interacting Gaussian polymers of ell\ellell segments on a 2D square lattice of size LLL with reflecting boundaries. Through simulations, we find the fraction of configurations displaying {\em no} connected cluster which span from one edge to the opposite edge. From this fraction, we define a critical segment density rhocL(ell)\rho_{c}^L(\ell)rhocL(ell) and the associated critical fraction of occupied bonds pcL(ell)p_{c}^L(\ell)pcL(ell), so that they can be identified as the percolation threshold in the LtoinftyL \to \inftyLtoinfty limit. Whereas pcL(ell)p_{c}^L(\ell)pcL(ell) is found to decrease monotonically with ell\ellell for a wide range of polymer lengths, rhocL(ell)\rho_{c}^L(\ell)rhocL(ell) is non-monotonic. We give physical arguments for this intriguing behavior in terms of the competing effects of multiple bond occupancies and polymerization.

How proteins squeeze through polymer networks: A Cartesian lattice study

The Journal of Chemical Physics, 2009

In this paper a lattice model for the diffusional transport of particles in the interphase cell nucleus is proposed. The dynamical behaviour of single chains on the lattice is investigated and Rouse scaling is verified. Dynamical dense networks are created by a combined version of the bond fluctuation method and a Metropolis Monte Carlo algorithm. Semidilute behaviour of the dense chain networks is shown. By comparing diffusion of particles in a static and a dynamical chain network , we demonstrate that chain diffusion does not alter the diffusion process of small particles. However, we prove that a dynamical network facilitates the transport of large particles. By weighting the mean square displacement trajectories of particles in the static chain network data from the dynamical network can be reconstructed. Additionally, it is shown that subdiffusive behaviour of particles on short time scales results from trapping processes in the crowded environment of the chain network. In the presented model a protein with 30 nm diameter has an effective diffusion coefficient of 1.24 · 10 −11 m 2 /s in a chromatin fiber network.

Chappter 6. Diffusion of Gases in Amorphous Polymers: The Monte Carlo Void Method

We propose a method for studying diffusion in amorphous structures based on biased random walk in the free volume extracted from a polymer ("the Monte Carlo Void Method .") We analyze a number of simple free volume structures not derived from realistic polymers and show that the biased random walk method is offering intuitively realistic description of the particle motion and present a framework for computing diffusion coefficents.

Diffusion in a random medium: A Monte Carlo study

Physical Review E, 1993

We use lattices with randomly distributed site-barrier energies to study diffusion properties as a function of disorder and temperature. We study the case of "dynamic" disorder whereby the random environment is renewed at each successive jump of the hopping particle, and also the case of "static" disorder with frozen randomly distributed barriers. The transition characteristics are governed by Boltzmann statistics. We employ standard Monte Carlo techniques to monitor properties such as the mean-square displacement. The trends of the motion are shown to include local trapping at early times, allowing for the search of a crossover time to the conventional diffusive regime, (R)t, as a function of temperature. We find that the crossover time versus temperature dependence is of the Arrhenius type determined by an effective activation energy barrier for percolation in the case of static disorder. For a uniform distribution of the barriers, this activation barrier is shown to coincide with the threshold concentration for bond percolation, as simple arguments suggest. We also demonstrate that an increase in the degree of dynamic disorder leads to an increase in the particle mobility. Some relationships of the present model to several experimental systems are discussed.