Interplay Of Diffusion Research Articles

Non-Markovian Diffusion and Adsorption-Desorption Dynamics: Analytical and Numerical Results.

The interplay of diffusion with phenomena like stochastic adsorption-desorption, absorption, and reaction-diffusion is essential for life and manifests in diverse natural contexts. Many factors must be considered, including geometry, dimensionality, and the interplay of diffusion across bulk and surfaces. To address this complexity, we investigate the diffusion process in heterogeneous media, focusing on non-Markovian diffusion. This process is limited by a surface interaction with the bulk, described by a specific boundary condition relevant to systems such as living cells and biomaterials. The surface can adsorb and desorb particles, and the adsorbed particles may undergo lateral diffusion before returning to the bulk. Different behaviors of the system are identified through analytical and numerical approaches.

(Invited) Second-Layer Growth Kinetics As a Decisive Factor for Non-Equilibrium Thin-Film Morphologies

Understanding and control of cluster growth on solid surfaces is a subject of intensive research to develop materials with new properties. Of particular interest is the self-organized structure formation by deposition of atoms and molecules on surfaces, where the interplay of diffusion, nucleation, aggregation, segregation and superlattice ordering yields a rich variety of growth phenomena [1]. The resulting structures are often frozen-in non-equilibrium structures with properties distinctly different from the equilibrium bulk phases. Here I will discuss the role of second layer nucleation for three-dimensional cluster formation and its influence on cluster morphologies.[1] M. Einax, W. Dieterich, P. Maass, Rev. Mod. Phys. 85, 921 (2013).

The interplay of diffusion and heterogeneity in nucleation of the networked Ising model

Nucleation underlies the dynamics of most first-order phase transitions in natural and man-made systems. However, most of the systems of interest are out of equilibrium. Little is known on the effect of nonequilibrium factors on the dynamics of nucleation. Here, we use the forward flux sampling method to investigate the effect of nonequilibrium diffusion on nucleation in small-world Ising networks, wherein spins can be exchanged between nearest-neighboring nodes. We introduce a parameter α to quantify the difference of nucleation rate with and without diffusion. We find that α shows a nonmonotonic dependence on the rewiring probability p of small-world networks. In particular, for different diffusion probability D, a crossover happens at p ≃ 0.17, below which the nucleation rate decreases as D increases, suggesting that the diffusion is against nucleation; while above which the nucleation rate increases with D, indicating that the diffusion is in favor of nucleation. By identifying the distinct features of nucleating clusters along the pathways for different randomness of networks, we reveal the underlying mechanism of such a nontrivial dependence.

Kinetics of transfer of volatile amphiphiles (fragrances) from vapors to aqueous drops and vice versa: Interplay of diffusion and barrier mechanisms

Subject of this work is to investigate the kinetics of mass transfer of volatile amphiphiles from their vapors to aqueous drops, and from the saturated aqueous drop solutions to air. The used amphiphiles are benzyl acetate, linalool, and citronellol, all of which have low saturated vapor pressures, appreciable solubility in water, and well pronounced surface activity. The adequate theoretical processing of the equilibrium surface tension, σ, isotherms is applied to construct the two-dimensional equation of state, which relates σ to the adsorption, Γ, at the interface. The measured surface tension relaxations with time t in the regimes of adsorption from vapor and evaporation from drop combined with the equations of state provide quantitative information on the change of adsorption because of the volatile amphiphile mass transfer across the surface. The theoretical analysis of the diffusion and barrier mechanisms in the case of adsorption from vapor to the aqueous drop shows that the mixed barrier-diffusion control in the vapor and diffusion control in the drop describe experimental data. The obtained values of the adsorption rate constants are six orders of magnitude larger than those for hexane and cyclohexane reported in the literature. The regime of evaporation from aqueous amphiphile solution drop follows the convection-enhanced adsorption mechanism with desorption rate constant in the vapor affected by the simultaneous water evaporation and amphiphile desorption. The water evaporation suppresses the evaporation of linalool and accelerates desorption of benzyl acetate and citronellol. From viewpoint of applications, the obtained physicochemical parameters of the studied three fragrances can help for better understanding of their performance in shampoo systems and perfumes. From theoretical viewpoint, the result show that by introducing an effective amphiphile desorption rate constant it is possible to quantify the complex volatile amphiphile desorption accompanied with the water evaporation.

Getting around the cell: physical transport in the intracellular world

Eukaryotic cells face the challenging task of transporting a variety of particles through the complex intracellular milieu in order to deliver, distribute, and mix the many components that support cell function. In this review, we explore the biological objectives and physical mechanisms of intracellular transport. Our focus is on cytoplasmic and intra-organelle transport at the whole-cell scale. We outline several key biological functions that depend on physically transporting components across the cell, including the delivery of secreted proteins, support of cell growth and repair, propagation of intracellular signals, establishment of organelle contacts, and spatial organization of metabolic gradients. We then review the three primary physical modes of transport in eukaryotic cells: diffusive motion, motor-driven transport, and advection by cytoplasmic flow. For each mechanism, we identify the main factors that determine speed and directionality. We also highlight the efficiency of each transport mode in fulfilling various key objectives of transport, such as particle mixing, directed delivery, and rapid target search. Taken together, the interplay of diffusion, molecular motors, and flows supports the intracellular transport needs that underlie a broad variety of biological phenomena.

Diffusion coefficients in nanoporous solids derived from membrane permeation measurements

Based on the molecular understanding of the interplay of diffusion and adsorption, new membrane materials can be developed and the operational conditions of gas separation membranes can be optimized. Therefore, numerous diffusion and adsorption studies are conducted to optimize membrane materials. However, in an opposite way, transport or Fickian diffusion coefficients DT can be derived from membrane permeation studies with surprising accuracy. From measuring the gas transport through nanoporous supported thin-layer membranes or through mixed matrix membranes with nanoporous fillers in a polymer matrix, the transport diffusion coefficients DT of gases in novel nanoporous materials such as zeolites, MOFs, COFs… can be estimated.

Chemical reaction and diffusion kinetics during laser-induced submillisecond heating for lithographic applications

Reactions in solid-state chemistry are controlled by both underlying chemical reaction rates and temperature-dependent diffusion of reactants and products. Due to distinctly different activation energies, the relative rates of reaction and diffusion may shift dramatically with temperature. In this work, the acid catalyzed deprotection of acid labile groups of model chemically amplified photopolymers was studied to understand the effects of temperature on diffusion-coupled reactions. In these systems, strong acids form during exposure of photoacid generators (PAGs) to ultraviolet radiation and then diffuse and catalyze deprotection reactions. By using very short duration laser-induced heating for the postexposure bake step, the potential reaction temperature range is extended by several hundred degrees compared to traditional thermal processing temperatures. Thermal degradation at these temperatures is avoided by simultaneously reducing the heating time from minutes to submilliseconds. Both diffusion and reaction rates were measured in this high temperature region for three different photoresists combined with two different PAGs, with activation energies of the key processes determined. The interplay of diffusion and reaction rates was also examined by comparing results of high-resolution pattern formation. The best image formation at high temperature was achieved using photoresists with high deprotection rates combined with PAGs exhibiting low diffusivity.

Anti-diffusion in continuous opinion dynamics

Considerable effort using techniques developed in statistical physics has been aimed at numerical simulations of agent-based opinion models and analysis of their results. Such work has elucidated how various rules for interacting agents can give rise to steady state behaviors in the agent populations that vary between consensus and fragmentation. At the macroscopic population level, analysis has been limited due to the lack of an analytically tractable governing macro-equation for the continuous population state. We use the integro-differential equation that governs opinion dynamics for the continuous probability distribution function of agent opinions to develop a novel nonlinear partial differential equation for the evolution of opinion distributions. The highly nonlinear equation allows for the generation of a system of approximations. We consider three initial population distributions and determine their small-time behavior. Our analysis reveals how the generation of clusters results from the interplay of diffusion and anti-diffusion and how initial instabilities arise in different regions of the population distribution.

A Thermodynamically Consistent Approach to Phase-Separating Viscous Fluids

Abstract The de-mixing properties of heterogeneous viscous fluids are determined by an interplay of diffusion, surface tension and a superposed velocity field. In this contribution a variational model of the decomposition, based on the Navier–Stokes equations for incompressible laminar flow and the extended Korteweg–Cahn–Hilliard equations, is formulated. An exemplary numerical simulation using C 1 {C}^{1} -continuous finite elements demonstrates the capability of this model to compute phase decomposition and coarsening of the moving fluid.

The Interplay of Diffusion, Motor-Driven Walks, and Tethering in Intracellular Transport

The Interplay of Diffusion, Motor-Driven Walks, and Tethering in Intracellular Transport

Size Effects in Nanoparticle Catalysis at Nanoparticle Modified Electrodes: The Interplay of Diffusion and Chemical Reactions

Electron transfer reactions mediated via nanoparticles immobilized on an electrode surface are considered in respect of catalytic processes in which solution phase species are either oxidized or reduced to form products exclusively via electron transfer with negligible reaction at the underlying supporting electrode. Specifically simulation is used to explore the effect of the nanoparticle size for individual nanoparticles as well as ensembles of nanoparticles, and a kinetic diagram is developed. For a single nanoparticle its size controls the rates of diffusion of species to and from the particle so that the relative extent of the catalysis is reduced for larger particles. For an array of nanoparticles the response of the whole is sensitive not only to the particle size but also to the particle coverage since the interparticle distance influences the extent, or otherwise, of the local overlap of the diffusion layers of neighboring particles and hence also the extent of the catalysis. Both particle size a...

Controllable Synthesis of Silver Dendrites via an Interplay of Chemical Diffusion and Reaction

Here we report a study on the role of chemical diffusion and reaction on the morphology evolution of silver particles. Electrochemical reaction is employed to synthesize silver particles. The reaction rate is regulated by current density while the diffusion rate of silver ions is regulated by the viscosity of solution. Silver dendritic particles are largely synthesized at various diffusion and reaction conditions. At a high reaction rate, silver dendrites are formed at the medium diffusion rates of silver ions while the dendritic structures are only formed at an extremely low diffusion rate of silver ions when the reaction proceeds slowly. Therefore, the interplay of diffusion and reaction plays a key role on the structure development of dendrites because the interplay determines the chemical distribution on the growth front of crystals. Once a chemical concentration gradient is established at the growth front, the dendritic structures is triggered.

Quantitatively Relating Diffusion and Reaction for Shaping Particles

Chemical diffusion and reaction rates are two general kinetic factors involved in the formation of materials. They play an important role in the structure development of materials. In most cases, chemical diffusion and reaction are coupled each other, which makes it difficult to differentiate their effects in shaping materials. Here we propose to quantify diffusion and reaction by the Damkohler number (Da) and to elucidate their roles in shaping particles. Silver particles are synthesized by electrodeposition approach at different reaction and diffusion conditions. Both diffusion efficiency and reaction rate constants are quantified, and the Damkohler number is calculated. If chemical diffusion or reaction is the rate-determining step in the formation of materials, simple structures, such as polyhedrons and irregular particles, are usually formed. When the interplay of diffusion and reaction dominates the structure development, complex structures, such as dendrites, are generated. The formation of each st...

General Einstein relation model in disordered organic semiconductors under quasiequilibrium

In this work, the Einstein relation between the diffusivity and mobility of charge carriers for disordered organic semiconductors is analyzed. We formulate an analytic theory that allows predicting the Einstein relation for charge carrier hopping in disordered organic semiconductors with Gaussian density of states distribution as a function of disorder, temperature, bias field, and Fermi level, i.e., concentration of occupied states of the DOS under the condition of quasiequilibrium. By scanning the Fermi across the DOS, we calculate the charge carrier mobility and diffusivity as well the $qD/\ensuremath{\mu}{k}_{B}T$ ratio. We are thus able to identify the role of mobile and localized states on the interplay of diffusion and drift and can determine under which condition Einstein relation is valid or not.

Interplay of diffusion and phase transformations in microstructural evolution of the interaction zone between U–9 wt.% Mo and Zr–1 wt.% Nb alloys

Metallurgical interaction between U–9 wt.% Mo metallic fuel alloy and Zr–1 wt.% Nb clad material has been assessed. Interdiffusion of constituent elements across their interface, together with the phase reactions occurring at high temperature and during subsequent cooling, resulted in development of a layered interaction zone where coexistence of a bcc solid solution phase with varying compositions, along with α-U, α-Zr and Mo2Zr phases could be noticed.

Modeling and analysis of hydrodynamic and physico-chemical effects in bacterial deposition on surfaces

The parallel-plate flow chamber (PFC) is often used for characterizing the propensity of microorganisms to attachment to surfaces. The model presented quantitatively analyzes the complex interplay of diffusion, convection, inertial lift, buoyancy, and surface forces in the PFC, which make it difficult to separate the surface- and microorganism-specific effects from the hydrodynamics. An empirical dimensionless factor K entering the boundary condition expresses enhancement of adhesion diffusion of microorganisms across a thin fluid layer adjacent to the surface by adhesion forces. The model examines the role of various factors (eg shear rate, size of bacterium, and strength of adhesion) on the rate of bacterial deposition. Using no adjustable parameter for strongly adhesive surfaces and K as the only adjustable parameter for repulsive or weakly adhesive surfaces, the model explains the observed decrease in deposition flux at high flow rates and compares reasonably with reported experimental results. The results suggest that the fitted value of K may be used for ‘rating’ the propensity of bacteria to deposit on surfaces and separating this from hydrodynamic effects.

DNA Capture and Translocation through Nanoscale Pores—a Fine Balance of Electrophoresis and Electroosmosis

DNA Capture and Translocation through Nanoscale Pores—a Fine Balance of Electrophoresis and Electroosmosis

DNA capture into a nanopore: Interplay of diffusion and electrohydrodynamics

We present a detailed analysis of the process of voltage driven capture of DNA molecules by nanopores. We show that ionic current generates a nonuniform electric field that acts on both the DNA and on its counterions and that the response of DNA to the electric field is affected by its electroosmotic coupling to the mobile counterions. We calculate the voltage and molecular mass dependence of the radius of capture and of the capture rate in the diffusion limited regime. We argue that electroosmotic flow through the DNA coil is suppressed in the vicinity of the pore and present a tentative estimate of the capture rate in the barrier limited regime.

Comment on: “From pore scale to wellbore scale: Impact of geometry on wormhole growth in carbonate acidization by C.E. Cohen et al. [Chemical Engineering Science 63, 3088–3099, 2008

During the dissolution of porous rock, positive feedback between fluid transport and mineral dissolution leads to the spontaneous formation of pronounced wormhole-like channels. In a recent paper, Cohen et al. (2008) analyzed wormhole growth and competition in a dissolving porous rock, using a Darcy-scale numerical model developed by Golfier et al. (2002). In particular, they analyzed the competition between wormholes, which hinders the growth of shorter channels and leads to the emergence of a hierarchical structure, with many short wormholes, and only a few long ones. By analyzing the distribution of wormhole lengths (reproduced in Fig. 1) they found evidence for the existence of a characteristic length d ≈ 5cm, at which a change in slope occurs. They concluded that the wormhole competition process is not completely scale invariant. The length scale d was interpreted as marking a transition to a regime where the interplay of diffusion and convection of reactant within a wormhole plays a decisive role in its growth.

Interplay of diffusion and dissociation mechanisms during hydrogen absorption in metals

Kinetic measurements of gas-solid reactions, in particular hydrogen-sorption kinetics, are usually interpreted according to single rate-limiting step models. However, recent studies gave clear evidence for the interdependence of fundamentally different steps involved in hydrogen sorption. This interdependence is explored in a one-dimensional continuum model in order to estimate the time, temperature, and pressure dependences of the sorption kinetics and the relevance of several materials parameters involved in the process. Quantitative descriptions of the extraction of physical parameters for various scenarios are given. The model is successfully tested for several experimental cases, ranging from model systems (thin films) to practical systems (${\text{LaNi}}_{5}{\text{H}}_{x}$ and ${\text{MgH}}_{2}$ powder samples).