Interpretation of diffusion coefficients in nanostructured materials from random walk numerical simulation

We make use of the numerical simulation random walk (RWNS) method to compute the "jump" diffusion coefficient of electrons in nanostructured materials via mean-square displacement. First, a summary of analytical results is given that relates the diffusion coefficient obtained from RWNS to those in the multiple-trapping (MT) and hopping models. Simulations are performed in a three-dimensional lattice of trap sites with energies distributed according to an exponential distribution and with a step-function distribution centered at the Fermi level. It is observed that once the stationary state is reached, the ensemble of particles follow Fermi-Dirac statistics with a well-defined Fermi level. In this stationary situation the diffusion coefficient obeys the theoretical predictions so that RWNS effectively reproduces the MT model. Mobilities can be also computed when an electrical bias is applied and they are observed to comply with the Einstein relation when compared with steady-state diffusion coefficients. The evolution of the system towards the stationary situation is also studied. When the diffusion coefficients are monitored along simulation time a transition from anomalous to trap-limited transport is observed. The nature of this transition is discussed in terms of the evolution of electron distribution and the Fermi level. All these results will facilitate the use of RW simulation and related methods to interpret steady-state as well as transient experimental techniques.     

Time-dependent yield stress materials

Time-dependent yield stress materials abound in nature and in industrial processes. Examples include clays, light metal alloys, paints and inks, adhesives, gelled waxy crude oils, drilling muds, fresh cement pastes, food products, biological fluids, ferrofluids, some lubricants, gypsum paste, and many other slurries, emulsions, suspensions, and foams. In this article, we describe the main features of time-dependent yield stress materials, present recent developments and applications, and discuss a number of important issues regarding the physics that govern the mechanical behavior of these complex materials. Finally, we discuss some recently developed experimental methods that are suitable to the rheological characterization of time-dependent yield stress materials.     

Calculation of diffusion coefficients for cylindrical granule of an adsorbent with a bidisperse porous structure

Conclusions Theoretical equations were obtained for the first two statistical moments of the kinetic curve in the case of a cylindrical granule of an adsorbent with a bidisperse porous structure, with either an impermeable side surface or impermeable faces. The indicated equations can be used to determine the internal diffusion coefficients from the experimental kinetic curves.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 7, pp. 1653–1655, July, 1974.The author expresses his deep gratitude to P. P. Zolotarev and A. M. Voloshchuk for discussing the work and valuable advice.     

Time-dependent ion selectivity in capacitive charging of porous electrodes

In a combined experimental and theoretical study, we show that capacitive charging of porous electrodes in multicomponent electrolytes may lead to the phenomenon of time-dependent ion selectivity of the electrical double layers (EDLs) in the electrodes. This effect is found in experiments on capacitive deionization of water containing NaCl/CaCl(2) mixtures, when the concentration of Na(+) ions in the water is five times the Ca(2+)-ion concentration. In this experiment, after applying a voltage difference between two porous carbon electrodes, first the majority monovalent Na(+) cations are preferentially adsorbed in the EDLs, and later, they are gradually replaced by the minority, divalent Ca(2+) cations. In a process where this ion adsorption step is followed by washing the electrode with freshwater under open-circuit conditions, and subsequent release of the ions while the cell is short-circuited, a product stream is obtained which is significantly enriched in divalent ions. Repeating this process three times by taking the product concentrations of one run as the feed concentrations for the next, a final increase in the Ca(2+)/Na(+)-ratio of a factor of 300 is achieved. The phenomenon of time-dependent ion selectivity of EDLs cannot be explained by linear response theory. Therefore, a nonlinear time-dependent analysis of capacitive charging is performed for both porous and flat electrodes. Both models attribute time-dependent ion selectivity to the interplay between the transport resistance for the ions in the aqueous solution outside the EDL, and the voltage-dependent ion adsorption capacity of the EDLs. Exact analytical expressions are presented for the excess ion adsorption in planar EDLs (Gouy-Chapman theory) for mixtures containing both monovalent and divalent cations.     

Electroosmosis in porous materials

Electroosmosis is the phenomenon of fluid flow induced by an applied electric field. This paper is concerned with electroosmosis in a porous material composed of closely-packed spheres immersed in a general electrolyte. A formula is obtained for the electroosmotic flow rate in the case when the double layer is much thinner than the particle radius. By combining this formula with electroosmosis measurements it is possible to determine the particle ζ potential. To test the validity of the model which underlies this, and most other electrokinetic calculations, ζ potentials obtained from Van der Put and Bijsterbosch's (J. Colloid Interface Sci. 92, 499, 1983) electroosmosis measurements are compared with potentials obtained from their conductivity and electrophoresis measurements.     

Time-dependent rate coefficients for diffusion-influenced reactions with centrosymmetric potentials

Simple closed-form expressions are presented for the time-dependent rate coefficients of diffusion-influenced reactions in the presence of spherically symmetric potentials. For diffusion-controlled contact reactions, our expression reproduces the first two terms in both the short- and long-time expansions of the rate coefficient. At intermediate times, agreement with numerical results for the Debye-Hückel potential is found to be within a few percent for a wide range of parameters. For diffusion-influenced contact reactions (described by the radiation boundary condition), the agreement is even better. When the reactivity depends on the distance between the reactants (e.g., exponentially), our analytic result is less accurate, because it reproduces the two terms in the long-time expansion only to the linear order of the reciprocal of the diffusion coefficient. Our results should prove useful in the analysis of experimental data for diffusion-influenced reactions with centrosymmetric interaction potentials.     

Time-dependent coupled-cluster calculations of polarizabilities and dispersion energy coefficients

Time-dependent coupled cluster theory, with unrestricted electron spins and full treatment of orbital rotation, is used to calculate polarizabilities at imaginary frequencies for Li, Ar, HCl, CO, N(2), O(2), and H(2)O, and to obtain dispersion energy coefficients for their pair interactions. Results obtained with augmented quadruple-zeta basis sets agree well with the best literature values of the C(6) dispersion energy coefficients. Time-dependent coupled cluster with single and double excitations theory will be useful as a benchmark for evaluating more approximate theories. (c) 2007 Wiley Periodicals, Inc. J Comput Chem, 2008.     

Positronium chemistry in porous materials

Porous materials have fascinated positron and positronium chemists for over decades. In the early 1970s it was already known that ortho-positronium (o-Ps) exhibits characteristic long lifetimes in silica gels, porous glass and zeolites. Since then, our understanding of Ps formation, diffusion and annihilation has been drastically deepened. Ps is now well recognized as a powerful porosimetric and chemical probe to study the average pore size, pore size distribution, pore connectivity and surface properties of various porous materials including thin films. In this paper, developments of Ps chemistry in porous materials undertaken in the past some 40 yr are surveyed and problems to be addressed in future are briefly discussed.     

Hydrodynamic approximation for distinct diffusion coefficients

The distinct diffusion coefficient is a measure of the coupling of the diffusive motions of two particles. It is given as the integral over a velocity cross correlation rather than the velocity self correlation that determines the self-diffusion coefficient. A hydrodynamic approximation for the distinct diffusion coefficient is proposed and then tested by comparison with data for a wide range of non-ionic binary mixtures. The hydrodynamic approximation gives negative distinct diffusion coefficients and is in qualitative agreement with most of the data. In many cases, deviations from the model results can be explained in terms of interactions which are not accurately treated by the model.     

Measurement of diffusion coefficients by radioanalysis

Radioanalysis, more particularly the use of radiotracers, enables measurement of coefficients of mass- and self-diffusion by simple benchtop experiments. They are related to environmental inquiries and materials science mainly Current procedures are surveyed here.     

The effect of diffusion on nanoaerosol filtration through porous materials with allowance for desorption processes

The effects of the finite residence time of aerosol particles in the bound state and their detachment due to thermal fluctuations on the filtration efficiency of porous and fibrous materials have been investigated with allowance for longitudinal diffusion in a flow. It has been shown that the desorption of particles affects the filtration efficiency even at times shorter than residence time τ_d of the particles in the bound state, while, at t ? τ_d, filtration stops. Allowance for the diffusion of aerosol particles in the flow leads to a decrease in the filtration efficiency as compared with the calculations performed without taking into account the longitudinal diffusion.     

Time-dependent control of hole-opening degree of porous ZnO hollow microspheres

Well-designed, monodispersed porous ZnO hollow microspheres with controlled hole-opening were successfully synthesized by a facile two-step solution route at low temperature. The hollow microspheres having average diameter of 3-4 μm showed time-dependent hole-opening, i.e. 4-100% for 15-75 min. The hole-opening percentage increases linearly with time until complete opening. The ZnO hollow microspheres also exhibited a high surface area (34 m(2) g(-1)), a large pore volume (0.19 cm(3) g(-1)) and an average pore diameter of 3.8 nm. A plausible growth mechanism for the formation of ZnO hollow microspheres was also proposed.     

Determination of diffusion coefficients by gas chromatography

Gas chromatography (GC), apart from the qualitative and quantitative analysis of gaseous mixtures, offers many possibilities for physicochemical measurements, among which the most important is the determination of diffusion coefficients of gases in gases and liquids and on solids. The gas chromatographic techniques used for the measurement of diffusion coefficients, namely the methods based on the broadening of the chromatographic elution peaks, and those based on the perturbation of the carrier gas flow-rate, are reviewed from the GC viewpoint, considering their running though the history, the experimental arrangement and procedure, the appropriate mathematical analysis and the main results with brief discussions. The experimental data on diffusion coefficients, determined by the various gas chromatographic techniques, are compared with those quoted in the literature or estimated by the known empirical equations predicting diffusion coefficients. This comparison permits the calculation of the precision and accuracy of the techniques applied to the measurement of diffusion coefficients.     

Measurement of diffusion coefficients for diffusion-controlled reactions

The Taylor dispersion technique has been used to measure the diffusion coefficients of nine compounds in dilute solution in isopropanol at 300 K. These compounds correspond, by the difference of a single hydrogen atom, to nine free radicals, for which the rate constants for bimolecular (termination) reactions have been previously measured under the same conditions by e.s.r. Comparison of the two sets of results show the termination reactions to be essentially diffusion-controlled, and, assuming no activation-energy effect, interaction parameters for the termination reactions are calculated and discussed.     

Form of multicomponent Fickian diffusion coefficients matrix

The form of multicomponent Fickian diffusion coefficients matrix in thermodynamically stable mixtures is established based on the form of phenomenological coefficients and thermodynamic factors. While phenomenological coefficients form a symmetric positive definite matrix, the determinant of thermodynamic factors matrix is positive. As a result, the Fickian diffusion coefficients matrix has a positive determinant, but its elements — including diagonal elements — can be negative. Comprehensive survey of reported diffusion coefficients data for ternary and quaternary mixtures, confirms that invariably the determinant of the Fickian diffusion coefficients matrix is positive.     

On measurement of thermal diffusion coefficients in multicomponent mixtures

We investigate the steady-state separation of the individual components of an incompressible multicomponent liquid mixture in a narrow two-dimensional thermogravitational column. Analytic working equations for measuring thermal diffusion coefficients analogous to the existing equations for a binary mixture are derived. Similar to the binary results, we find that when compositional variation has negligible effect on fluid density and vertical diffusive flux can be ignored, molecular diffusion does not affect steady-state separation. However, when compositional effects on density are taken into account, molecular diffusion does affect the bulk convective flow and the steady-state separation of the components. There may be also two distinct trends in the velocity and separation profiles. With one or more negative thermal diffusion coefficients, there may be more than one convection cell resulting in oscillatory behavior of separation. The working equations presented can be used to measure thermal diffusion coefficients of multicomponent mixtures. Such measurements have not yet been reported in the literature.