Nonequilibrium effects in diffusion of interacting particles on vicinal surfaces

We study the influence of nonequilibrium conditions on the collective diffusion of interacting particles on vicinal surfaces. To this end, we perform Monte Carlo simulations of a lattice-gas model of an ideal stepped surface, where adatoms have nearest-neighbor attractive or repulsive interactions. Applying the Boltzmann-Matano method to spreading density profiles of the adatoms allows the definition of an effective, time-dependent collective diffusion coefficient D(C) (t)(theta) for all coverages theta. In the case of diffusion across the steps and strong binding at lower step edges we observe three stages in the behavior of the corresponding D(xx,C) (t)(theta). At early times when the adatoms have not yet crossed the steps, D(xx,C) (t)(theta) is influenced by the presence of steps only weakly. At intermediate times, where the adatoms have crossed several steps, there are sharp peaks at coverages theta<1L and theta>1-1L, where L is the terrace width. These peaks are due to different rates of relaxation of the density at successive terraces. At late stages of spreading, these peaks vanish and D(xx,C) (t)(theta) crosses over to its equilibrium value, where for strong step edge binding there is a maximum at theta=1L. In the case of diffusion in direction along the steps the nonequilibrium effects in D(yy,C) (t)(theta) are much weaker, and are apparent only when diffusion along ledges is strongly suppressed or enhanced.     

Asymmetry of diffusion permeability of bi-layer membranes

To reveal the reason of asymmetry of the diffusion permeability of bi-layer electrodialysis membranes the following problems have been solved using the model of "homogeneous porous membrane": - diffusion of non-electrolyte solutions across a bi-layer membrane; - diffusion of electrolyte solutions across a non-charged bi-layer membrane; - diffusion of electrolyte solutions across a charged single layer membrane; - diffusion of electrolyte solutions across a charged bi-layer membrane. It is shown that the main factor responsible for the asymmetry is the difference between absolute values of densities of fixed charges (or so called "exchange capacities") of different layers of a membrane under investigation. Only in this case the ratio of the thickness of the membrane layers as well as the ratio of ion diffusivities contributes also to the asymmetry of the diffusion permeability. In the present review we survey and generalize our previous investigations and propose a new theory of asymmetry of diffusion permeability of bi-layer membranes. We have deduced explicit algebraic formulas for the degree of asymmetry of diffusion permeability of bi-layer membranes under consideration.     

Temperature dependence of metal-organic heteroepitaxy

The nucleation and growth of 2D layers of tetraphenyl porphyrin molecules on Ag(111) are studied with variable-temperature scanning tunneling microscopy. The organic/metal heteroepitaxy occurs by strict analogy to established principles for metal heteroepitaxy. A hierarchy of energy barriers for diffusion on terraces and along edges and around corners of adislands is established. The temperature is key to activating these barriers selectively, thus determining the shape of the organic aggregates, from a fractal shape at lower temperatures to a compact shape at higher temperatures. The energy barriers for the terrace diffusion of porpyrins and the molecule-molecule binding energy were determined to be 30 meV < E(terrace) < 60 and 130 meV < E(diss) < 160 meV, respectively, from measurements of island sizes as a function of temperature. This study provides an experimental verification of the validity of current models of epitaxy for the heteroepitaxy of organics and is thus expected to help establish design principles for complex metal-organic hybrid structures.     

A theory-based approach to thermal field-flow fractionation of polyacrylates

A theory-based approach is presented for the development of thermal field-flow fractionation (ThFFF) of polyacrylates. The use of ThFFF for polymer analysis has been limited by an incomplete understanding of the thermal diffusion which plays an important role in retention and separation. Hence, a tedious trial-and-error approach to method development has been the normal practice when analyzing new materials. In this work, thermal diffusion theories based on temperature dependent osmotic pressure gradient and polymer-solvent interaction parameters were used to estimate thermal diffusion coefficients (D(T)) and retention times (t(r)) for different polymer-solvent pairs. These calculations identified methyl ethyl ketone as a solvent that would cause significant retention of poly(n-butyl acrylate) (PBA) and poly(methyl acrylate) (PMA). Experiments confirmed retention of these two polymers that have not been previously analyzed by ThFFF. Theoretical and experimental D(T)s and t(r)s for PBA, PMA, and polystyrene in different solvents agreed to within 20% and demonstrate the feasibility of this theory-based approach.     

Permeation studies on transparent multiple hybrid SiO<Subscript>2</Subscript>-PMMA coatings-Al<Subscript>2</Subscript>O<Subscript>3</Subscript> barriers on PEN substrates

In this work we report the performance of permeation barriers based on organic/inorganic multilayer stacks. We have used PMMA-SiO₂ (poly methyl methacrylate-silica) hybrid films synthesized through a sol–gel route as organic–inorganic components, whereas Al₂O₃ thin films were used as the inorganic component. The hybrid layers were deposited by dip coating and the Al₂O₃ by atomic layer deposition (ALD), films were prepared on polyethylene naphthalene (PEN) substrates. The permeability of the films and stacks is evaluated using helium as the diffusion gas in a custom made ultra-high vacuum system. The results show that permeability for PEN is reduced from 5 × 10⁻³ g/m²-day to about 9 × 10⁻⁵ g/m²-day for the best multiple barrier evaluated. Increased barrier properties are due to the increasing in the path and hence the lag-time of the permeating gas. In particular, we report the surface roughness of the different layers and its impact on the barrier performance. The hybrid layers reduced notably the roughness of the bare PEN substrate improving the quality of the Al₂O₃ layer in the barrier. The optical transmittance of the barriers in the visible region is higher than 80% in all the studied cases.     

Pair diffusion, hydrodynamic interactions, and available volume in dense fluids

We calculate the pair diffusion coefficient D(r) as a function of the distance r between two hard sphere particles in a dense monodisperse fluid. The distance-dependent pair diffusion coefficient describes the hydrodynamic interactions between particles in a fluid that are central to theories of polymer and colloid dynamics. We determine D(r) from the propagators (Green's functions) of particle pairs obtained from molecular dynamics simulations. At distances exceeding ~3 molecular diameters, the calculated pair diffusion coefficients are in excellent agreement with predictions from exact macroscopic hydrodynamic theory for large Brownian particles suspended in a solvent bath, as well as the Oseen approximation. However, the asymptotic 1/r distance dependence of D(r) associated with hydrodynamic effects emerges only after the pair distance dynamics has been followed for relatively long times, indicating non-negligible memory effects in the pair diffusion at short times. Deviations of the calculated D(r) from the hydrodynamic models at short distances r reflect the underlying many-body fluid structure, and are found to be correlated to differences in the local available volume. The procedure used here to determine the pair diffusion coefficients can also be used for single-particle diffusion in confinement with spherical symmetry.     

Multiexponential decay autocorrelation function in dynamic light scattering in near-critical ternary liquid mixture

The dynamic structure factor of a ternary liquid mixture is calculated from the theory of thermodynamic fluctuations with the help of linearized hydrodynamic equations. The theoretical model allows evaluating and classifying the transport properties near a critical solution point of a ternary mixture. In the vicinity of the critical solution point, experimental dynamic light scattering measurements reveal two hydrodynamic relaxation modes with well-separated characteristic relaxation times. From the autocorrelation functions, we can determine two effective diffusivities D(1) and D(2). As theoretically predicted by a model developed in this work, one of these two modes can be associated with thermal diffusion and the other with mass diffusion. In the special case of an incompressible liquid mixture limit, D(1) and D(2) are decoupled, becoming thermodiffusion coefficient D(T) and mutual mass diffusion coefficient D(ij). A possible physical meaning of D(1) and D(2) for a ternary mixture is discussed.     

Permeability of the Perindopril Arginine under In Vitro Conditions across Caco-2 Monolayer and Biomimetic Phospholipid Membrane

Perindopril arginine (PA) as an angiotensin-converting enzyme (ACE) inhibitor is widely used in cardiovascular diseases, especially in systemic hypertension and heart failure. Although the pharmacokinetics of PA are well documented, there is no available detailed data on its permeation in in vitro conditions. The present study aimed to assess the transport of PA across both biological membranes and artificial biomimetic ones. For the determination of PA transport, the Caco-2 cell line was selected as a reliable in vitro model of gastrointestinal biological barriers. Additionally, a novel 96-well plate with phospholipid membrane PermeaPad was used to evaluate the transport of PA by passive diffusion. We confirmed that PA is relatively poorly permeable across the Caco-2 monolayer. The permeability results obtained from the non-cell-based model demonstrated higher transport of PA as compared to that of Caco-2. Thus, PA transport across the biological membranes might be suggested to be regulated by the membrane transporters.     

Diffusion of electrolytes of different natures through the cation-exchange membrane

Diffusion of different electrolytes through a negatively charged (cation-exchange) membrane into distilled water has been studied. It has been established theoretically (with no regard to the presence of diffusion layers) that the integral diffusion permeability coefficient of an electrolyte depends on the diffusion coefficients and the ratio between the charge numbers of a cation–anion pair, the ratio between the density of charges fixed in the membrane and electrolyte concentration, and the averaged coefficient of equilibrium distribution of cation?anion ion pairs in the membrane matrix. It has been found that, when co-ions have a higher mobility, the dependence of diffusion permeability on electrolyte concentration passes through a maximum. Derived equations have been compared with experimental dependences of the diffusion permeability of an MC-40 membrane with respect to different solutions of inorganic 1: 1 and 2: 1 electrolytes. The developed method has been shown to be applicable for describing diffusion of any electrolytes (including asymmetric ones) through arbitrary uniformly charged membranes.     

Time dependent diffusion in a disordered medium with partially absorbing walls: a perturbative approach

We present an analytical study of the time dependent diffusion coefficient in a dilute suspension of spheres with partially absorbing boundary condition. Following Kirkpatrick [J. Chem. Phys. 76, 4255 (1982)] we obtain a perturbative expansion for the time dependent particle density using volume fraction f of spheres as an expansion parameter. The exact single particle t operator for partially absorbing boundary condition is used to obtain a closed form time dependent diffusion coefficient D(t) accurate to first order in the volume fraction f. Short and long time limits of D(t) are checked against the known short time results for partially or fully absorbing boundary conditions and long time results for reflecting boundary conditions. For fully absorbing boundary condition the long time diffusion coefficient is found to be D(t)=5a(2)/(12fD(0)t)+O((D(0)t/a(2))(-2)) to the first order of perturbation theory. Here f is small but nonzero, D(0) the diffusion coefficient in the absence of spheres, and a the radius of the spheres. The validity of this perturbative result is discussed.     

Vapor Adsorption Measurements with Two-Dimensional Membranes

Two-dimensional (2D) membranes display extraordinary mass transfer properties, in particular for the permeation of gaseous substances. Their ultimate thickness not only ensures the shortest diffusion pathways, but also makes the membrane surface play a significant role in accommodating and guiding the permeating molecules. As saturated vapors of water and organic solvents are often observed to pass 2D membranes faster than inert gases, condensation is believed to be responsible for surface-mediated transport. Here, we present a spectroscopic experiment to probe adsorption of condensable species on 2D membranes under realistic conditions. Polarization-modulation infrared reflection absorption spectroscopy (PM IRAS) is coupled with a reaction chamber and a vacuum system to control the vaporous environments. The measurements are demonstrated to yield quantitative information on the amount of adsorbates onto supported 2D layers. As a case study, the azeotropic mixture of water and propanol is revealed to maintain its molar composition upon interaction with carbon nanomembranes.     

Aging correlation functions for blinking nanocrystals, and other on-off stochastic processes

Following recent experiments on power law blinking behavior of single nanocrystals, we calculate two-time intensity correlation functions I(t)I(t+t') for these systems. We use a simple two state (on and off) stochastic model to describe the dynamics. We classify possible behaviors of the correlation function and show that aging, e.g., dependence of the correlation function on age of process t, is obtained for classes of the on time and off time distributions relevant to experimental situation. Analytical asymptotic scaling behaviors of the intensity correlation in the double time t and t' domain are obtained. In the scaling limit I(t)I(t+t('))-->h(x), where four classes of behaviors are found: (i) finite averaged on and off times x=t' (standard behavior); (ii) on and off times with identical power law behaviors x=t/t' (case relevant for capped nanocrystals); (iii) exponential on times and power law off times x=tt' (case relevant for uncapped nanocrystals); (iv) for defected off time distribution we also find x=t+t'. Origin of aging behavior is explained based on simple diffusion model. We argue that the diffusion controlled reaction A+B <==>AB, when followed on a single particle level exhibits aging behavior.     

Grain morphology and trapping effects on electron transport in dye-sensitized nanocrystalline solar cells

We have examined the combined effects of grain morphology and electron trapping on the transient response of photoelectrons moving through the TiO2 grains in a dye-sensitized nanocrystalline solar cell using a multi-time-scale random walk Monte Carlo model. Our use of a multi-time-scale approach enables us to simulate transport for electrons moving through spherical connected grains in a three-dimensional (3D) voided network and look at the effect of the size of interparticle boundaries on carrier dynamics. We can also address similar times to those over which measurements are taken, namely, 0.1 ms. These times are long because of deep traps in the TiO2 grains. The grains have 2-fold connectivity in one dimension (linear chains) or 4-fold or 6-fold connectivity in three dimensions and traps with an exponential distribution of energies. Photoelectrons are generated by a light pulse of short duration. The spatial distribution of the photogenerated electron density from this pulse either has a uniform profile or is peaked on the electrolyte side. We show that the constrictions at the grain necks slow the electrons, making trapping more likely and hence further delaying their passage to the extracting electrode. By comparing our results for 4-fold and 6-fold coordinated particles on a cubic lattice with 2-fold coordinated particles on linear chains, we show that transport is slowed in the former case due to the additional paths available to the electrons in the 3D network. We also find that the charge and current transients cannot be fit to an analytical solution of the continuum equations with an effective diffusion coefficient even at long times. Therefore, caution must be exercised when attempting to fit experimental transient data with an effective diffusion coefficient.     

One sign ion mobile approximation

The electrical response of an electrolytic cell to an external excitation is discussed in the simple case where only one group of positive and negative ions is present. The particular case where the diffusion coefficients of the negative ions, D(m), is very small with respect to that of the positive ions, D(p), is considered. In this framework, it is discussed under what conditions the one mobile approximation, in which the negative ions are assumed fixed, works well. The analysis is performed by assuming that the external excitation is sinusoidal with circular frequency ω, as that used in the impedance spectroscopy technique. In this framework, we show that there exists a circular frequency, ω*, such that for ω > ω*, the one mobile ion approximation works well. We also show that for D(m) ? D(p), ω* is independent of D(m).     

Diffusion in linear porous media with periodic entropy barriers: A tube formed by contacting spheres

The problem of transport in quasi-one-dimensional periodic structures has been studied recently by several groups [D. Reguera et al., Phys. Rev. Lett.96, 130603 (2006); P. S. Burada et al., Phys. Rev. E75, 051111 (2007); B. Q. Ai and L. G. Liu, ibid.74, 051114 (2006); B. Q. Ai et al., ibid.75, 061126 (2007); B. Q. Ai and L. G. Liu, J. Chem. Phys.126, 204706 (2007); 128, 024706 (2008); E. Yariv and K. D. Dorfman, Phys. Fluids19, 037101 (2007); N. Laachi et al., Europhys. Lett.80, 50009 (2007); A. M. Berezhkovskii et al., J. Chem. Phys.118, 7146 (2003); 119, 6991 (2003)]. Using the concept of "entropy barrier" [R. Zwanzig, J. Phys. Chem.96, 3926 (1992)] one can classify such structures based on the height of the entropy barrier. Structures with high barriers are formed by chambers, which are weakly connected with each other because they are connected by small apertures. To escape from such a chamber a diffusing particle has to climb a high entropy barrier to find an exit that takes a lot of time [I. V. Grigoriev et al., J. Chem. Phys.116, 9574 (2002)]. As a consequence, the particle intrachamber lifetime tau(esc) is much larger than its intrachamber equilibration time, tau(rel), tau(esc)>tau(rel). When the aperture is not small enough, the intrachamber escape and relaxation times are of the same order and the hierarchy fails. This is the case of low entropy barriers. Transport in this case is analyzed in the works of Schmid and co-workers, Liu and co-workers, and Dorfman and co-workers, while the work of Berezhkovskii et al. is devoted to diffusion in the case of high entropy barriers.     

Some hydrodynamic boundary layer influences on mass transfer coefficients

As an initial approach to the quantitative understanding of the importance of various components of intestinal' contents as factors in mass transfer resistance, studies have been performed in diffusion cells containing polydimethylsiloxane membranes under circumstances sensitive to the boundary layers. (1) The effect of temperature change on permeability was measured. Under the conditions of the study, demonstration of a clear transition from membrane control to boundary control with rising temperature proved elusive. (2) When membrane thickness was systematically decreased, a gradual transition from membrane to boundary control was demonstrated, yet practical restrictions of the experimental conditions and system limited the degree to which either membrane or diffusion layers could be manipulated into a rate controlling role. (3) The effect of solution viscosity on mass transfer was also studied. Methylcellulose and sucrose were used as polymeric and low molecular weight viscosity inducing agents respectively. It was readily shown that viscosity has a much greater influence on the flux of a permeant through decreased diffusion coefficients than through increased boundary layer thicknesses, as is predicted by diffusional theories.     

Asymmetry of current–voltage characteristics: a bilayer model of a modified ion-exchange membrane

The asymmetry of the current–voltage characteristics of ion-exchange membranes is explained in terms of the model of a bilayer fine porous membrane with constant charge distributions over the thickness of layers. This model has previously been proposed for determining diffusion permeability of membranes. In the case of one uncharged (neutral) layer, a set of two implicit algebraic equations is derived for determining the total current–voltage characteristics (CVC) of a membrane. For the first time, implicit algebraic equations are obtained for calculating the limiting currents at different orientations of an anisotropic membrane in an electrodialysis cell and explicit expressions are derived for determining specific conductivity of the membrane from the slope of the ohmic region of a CVC under the approximation of “excluded coions.” The model may be successfully used for describing the CVCs of perfluorinated MF-4SC sulfonic cation-exchange membranes, the surface layers of which are modified with polyaniline or halloysite.     

Diffusion in multilayer media: transient behavior of the lateral diffusion coefficient

A general formalism for treating lateral diffusion in a multilayer medium is developed. The formalism is based on the relation between the lateral diffusion and the distribution of the cumulative residence time, which the diffusing particle spends in different layers. We exploit this fact to derive general expressions which give the global and local time-dependent diffusion coefficients in terms of the average cumulative times spent by the particle in different layers and the probabilities of finding the particle in different layers, respectively. These expressions are used to generalize two recently obtained results: (a) A solution for the short-time behavior of the lateral diffusion coefficient in two layers separated by a permeable membrane obtained by a perturbation theory is extended to the entire range of time. (b) A solution for the time-dependent diffusion coefficient of a ligand, which repeatedly dissociates and rebinds to sites on a planar surface, obtained under the assumption that the medium above the surface is infinite, is generalized to allow for the medium layer of finite thickness. For the latter problem we derive an expression for the Fourier-Laplace transform of the propagator in terms of the double Laplace transform of the probability density of the cumulative residence time spent by the ligand in the medium layer.     

Electrochemical characterization of polyelectrolyte/gold nanoparticle multilayers self-assembled on gold electrodes

Polyelectrolyte/gold nanoparticle multilayers composed of poly(l-lysine) (pLys) and mercaptosuccinic acid (MSA) stabilized gold nanoparticles (Au NPs) were built up using the electrostatic layer-by-layer self-assembly technique upon a gold electrode modified with a first layer of MSA. The assemblies were characterized using UV-vis absorption spectroscopy, cyclic and square-wave voltammetry, electrochemical impedance spectroscopy, and atomic force microscopy. Charge transport through the multilayer was studied experimentally as well as theoretically by using two different redox pairs [Fe(CN)(6)](3-/4-) and [Ru(NH(3))(6)](3+/2+). This paper reports a large sensitivity to the charge of the outermost layer for the permeability of these assemblies to the probe ions. With the former redox pair, dramatic changes in the impedance response were obtained for thin multilayers each time a new layer was deposited. In the latter case, the multilayer behaves as a conductor exhibiting a strikingly lower impedance response, the electric current being enhanced as more layers are added for Au NP terminated multilayers. These results are interpreted quite satisfactorily by means of a capillary membrane model that encompasses the wide variety of behaviors observed. It is concluded that nonlinear slow diffusion through defects (pinholes) in the multilayer is the governing mechanism for the [Fe(CN)(6)](3-/4-) species, whereas electron transfer through the Au NPs is the dominant mechanism in the case of the [Ru(NH(3))(6)](3+/2+) pair.     

Compartmental modeling of reversible intermolecular two-state excited-state processes coupled with rotational diffusion or with added quencher

Analysis of related time-resolved fluorescence measurements can possibly lead to the determination of the kinetic parameters of excited-state processes. A deterministic identifiability analysis on an error-free fluorescence decay data surface has to be executed to verify whether the parameters of a particular model can be determined and may point to the minimal experimental conditions under which this will become possible. In this work, similarity transformation is chosen as an identifiability analysis approach because it also gives the explicit relationships between the true and alternative model parameters. Results are presented for two kinetic models of a reversible intermolecular two-state excited-state process in isotropic environments: (a) with coupled species-dependent rotational diffusion described by Brownian reorientation and (b) with added quencher. For model a, both spherically and cylindrically symmetric rotors, with no change in the principal axes of rotation in the latter, are considered. The fluorescence delta-response functions I(parallel)(t) and I(perpendicular)(t), for fluorescence polarized respectively parallel and perpendicular to the electric vector of linearly polarized excitation, are used to define the sum S(t) = I( parallel)(t) + 2 I( perpendicular)(t) and the difference D(t) = I(parallel)(t) - I(perpendicular)(t) function. The identifiability analysis is carried out using the S(t) and D(t) functions. The analysis involving S(t) shows that two physically acceptable possible solutions for the overall rate constants of the excited-state process exist. Inclusion of information from polarized fluorescence measurements on the rotational kinetic behavior contained in D(t) results in the unique set of rate constants and rotational diffusion coefficients when the rotational diffusion coefficients are different. For model b, it is shown that addition of quencher plays formally the same role as rotational diffusion as far as the identification is concerned. When the quenching rate constants are different, the rate constants of a reversible intermolecular two-state excited-state process with added quencher can be uniquely determined.