Amplification of Molecular Traffic Control in catalytic grains with novel channel topology design

We investigate the conditions for reactivity enhancement of catalytic processes in porous solids by use of molecular traffic control (MTC). With dynamic Monte-Carlo simulations and continuous-time master equation theory applied to the high concentration regime we obtain a quantitative description of the MTC effect for a network of intersecting single-file channels in a wide range of grain parameters and for optimal external operating conditions. Implementing the concept of MTC in models with specially designed alternating bimodal channels we find the efficiency ratio (compared with a topologically and structurally similar reference system without MTC) to be enhanced with increasing grain diameter, a property verified for the first time for an MTC system. Even for short intersection channels, MTC leads to a reactivity enhancement of up to approximately 65%. This suggests that MTC may significantly enhance the efficiency of a catalytic process for small as well as large porous particles with a suitably chosen binary channel topology.Comment: 15 pages, 12 figure

Pore opening effects and transport diffusion in the Knudsen regime in comparison to self- (or tracer-) diffusion

We study molecular diffusion in linear nanopores with different types of roughness in the so-called Knudsen regime. Knudsen diffusion represents the limiting case of molecular diffusion in pores, where mutual encounters of the molecules within the free pore space may be neglected and the time of flight between subsequent collisions with the pore walls significantly exceeds the interaction time between the pore wall and the molecules. We present an extension of a commonly used procedure to calculate transport diffusion coefficients. Our results show that using this extension, the coefficients of self- and transport diffusion in the Knudsen regime are equal for all regarded systems, which improves previous literature data.Comment: 5 pages, 7 figure

Knudsen Diffusion in Silicon Nanochannels

Measurements on helium and argon gas flow through an array of parallel, linear channels of 12 nm diameter and 200 micrometer length in a single crystalline silicon membrane reveal a Knudsen diffusion type transport from 10^2 to 10^7 in Knudsen number Kn. The classic scaling prediction for the transport diffusion coefficient on temperature and mass of diffusing species,D_He ~ sqrt(T), is confirmed over a T range from 40 K to 300 K for He and for the ratio of D_He/D_Ar ~ sqrt(m_Ar/m_He). Deviations of the channels from a cylindrical form, resolved with transmission electron microscopy down to subnanometer scales, quantitatively account for a reduced diffusivity as compared to Knudsen diffusion in ideal tubular channels. The membrane permeation experiments are described over 10 orders of magnitude in Kn, encompassing the transition flow regime, by the unified flow model of Beskok and Karniadakis.Comment: 4 pages, 3 figure

Self-diffusion of polymers in cartilage as studied by pulsed field gradient NMR

Pulsed field gradient (PFG) nuclear magnetic resonance (NMR) was used to investigate the self-diffusion behaviour of polymers in cartilage. Polyethylene glycol and dextran with different molecular weights and in different concentrations were used as model compounds to mimic the diffusion behaviour of metabolites of cartilage. The polymer self-diffusion depends extremely on the observation time: The short-time self-diffusion coefficients (diffusion time Delta approximately 15 ms) are subjected to a rather non-specific obstruction effect that depends mainly on the molecular weights of the applied polymers as well as on the water content of the cartilage. The observed self-diffusion coefficients decrease with increasing molecular weights of the polymers and with a decreasing water content of the cartilage. In contrast, the long-time self-diffusion coefficients of the polymers in cartilage (diffusion time Delta approximately 600 ms) reflect the structural properties of the tissue. Measurements at different water contents, different molecular weights of the polymers and varying observation times suggest that primarily the collagenous network of cartilage but also the entanglements of the polymer chains themselves are responsible for the observed restricted diffusion. Additionally, anomalous restricted diffusion was shown to occur already in concentrated polymer solutions

Bulk-driven non-equilibrium phase transitions in a mesoscopic ring

We study a periodic one-dimensional exclusion process composed of a driven and a diffusive part. In a mesoscopic limit where both dynamics compete we identify bulk-driven phase transitions. We employ mean-field theory complemented by Monte-Carlo simulations to characterize the emerging non-equilibrium steady states. Monte-Carlo simulations reveal interesting correlation effects that we explain phenomenologically.Comment: 4 pages, 3 figure

Survival of interacting Brownian particles in crowded 1D environment

We investigate a diffusive motion of a system of interacting Brownian particles in quasi-one-dimensional micropores. In particular, we consider a semi-infinite 1D geometry with a partially absorbing boundary and the hard-core inter-particle interaction. Due to the absorbing boundary the number of particles in the pore gradually decreases. We present the exact analytical solution of the problem. Our procedure merely requires the knowledge of the corresponding single-particle problem. First, we calculate the simultaneous probability density of having still a definite number $N-k$ of surviving particles at definite coordinates. Focusing on an arbitrary tagged particle, we derive the exact probability density of its coordinate. Secondly, we present a complete probabilistic description of the emerging escape process. The survival probabilities for the individual particles are calculated, the first and the second moments of the exit times are discussed. Generally speaking, although the original inter-particle interaction possesses a point-like character, it induces entropic repulsive forces which, e.g., push the leftmost (rightmost) particle towards (opposite) the absorbing boundary thereby accelerating (decelerating) its escape. More importantly, as compared to the reference problem for the non-interacting particles, the interaction changes the dynamical exponents which characterize the long-time asymptotic dynamics. Interesting new insights emerge after we interpret our model in terms of a) diffusion of a single particle in a $N$-dimensional space, and b) order statistics defined on a system of $N$ independent, identically distributed random variables

Single-File Diffusion of Externally Driven Particles

We study 1-D diffusion of $N$ hard-core interacting Brownian particles driven by the space- and time-dependent external force. We give the exact solution of the $N$-particle Smoluchowski diffusion equation. In particular, we investigate the nonequilibrium energetics of two interacting particles under the time-periodic driving. The hard-core interaction induces entropic repulsion which differentiates the energetics of the two particles. We present exact time-asymptotic results which describe the mean energy, the accepted work and heat, and the entropy production of interacting particles and we contrast these quantities against the corresponding ones for the non-interacting particles

Asymmetry in shape causing absolute negative mobility

We propose a simple classical concept of nanodevices working in an absolute negative mobility (ANM) regime: The minimal spatial asymmetry required for ANM to occur is embedded in the geometry of the transported particle, rather than in the channel design. This allows for a tremendous simplification of device engineering, thus paving the way towards practical implementations of ANM. Operating conditions and performance of our model device are investigated, both numerically and analytically.Comment: 6 pages; accepted for publication in PR

Diffusion of Tagged Particle in an Exclusion Process

We study the diffusion of tagged hard core interacting particles under the influence of an external force field. Using the Jepsen line we map this many particle problem onto a single particle one. We obtain general equations for the distribution and the mean square displacement of the tagged center particle valid for rather general external force fields and initial conditions. A wide range of physical behaviors emerge which are very different than the classical single file sub-diffusion $ \sim t^{1/2}$ found for uniformly distributed particles in an infinite space and in the absence of force fields. For symmetric initial conditions and potential fields we find $ = {{\cal R} (1 - {\cal R})\over 2 N {\it r} ^2} $ where $2 N$ is the (large) number of particles in the system, ${\cal R}$ is a single particle reflection coefficient obtained from the single particle Green function and initial conditions, and $r$ its derivative. We show that this equation is related to the mathematical theory of order statistics and it can be used to find even when the motion between collision events is not Brownian (e.g. it might be ballistic, or anomalous diffusion). As an example we derive the Percus relation for non Gaussian diffusion