Surface Diffusion Control Research Articles

Surface control vs. diffusion control during calcite dissolution: Dependence of step-edge velocity upon solution pH

The reaction of the (101̄4) calcite surface during dissolution was studied as a function of pH (HCl) by liquid-cell Atomic Force Microscopy (AFM) under ambient conditions of both temperature (22 °C) and partial pressure of carbon dioxide (PCO2). A flow through AFM liquid reaction cell was used, and solutions were renewed at a controlled flow rate and sampled for chemical analysis.

Surface diffusion control of the photocatalytic oxidation in air/TiO2 heterogeneous reactors

R. Tsekov, E. Evstatieva and P. G. Smirniotis, PhysChemComm, 2002, 5, 161 DOI: 10.1039/B207965H

A Film-Pore-Surface Diffusion Model for the Adsorption of Acid Dyes on Activated Carbon

The sorption of acid dyes from aqueous effluents onto activated carbon has been studied. The effects of initial dye concentration and activated carbon mass on the rate of Acid Blue 80, Acid Red 114 and Acid Yellow 117 removal have been investigated. A three-resistance mass transport model based on film, pore and surface diffusion control has been applied to model the concentration decay curves. The model incorporates an effective diffusion coefficient Deff, which is dependant on the equilibrium solid phase concentration or fractional surface coverage. The results of the film-pore-surface diffusion model are compared with the data obtained from the basic film-pore diffusion model. It has been found that the film-pore-surface diffusion model provides a major improvement over the data correlated by the film-pore diffusion model. Also, the relationship between surface diffusion and fractional surface coverage has been investigated for the adsorption of acid dyes on activated carbon.

On the correspondence between the homogeneous and heterogeneous theories of SHS

A comparison was conducted on the correspondence, and differences between the conventional homogeneous theory of flame propagation in self-propagating high-temperature synthesis (SHS) and the heterogeneous theory that properly accounts for the role of the high melting point particles in the mixture compact and the associated diffusion-limited reaction at the particle surface. By reformulating the governing equations for the bulk flame propagation in the condensed medium for the heterogeneous theory, it is demonstrated that they are of the same form as those for the homogeneous theory, except for the fact that the “reaction” term for the homogeneous theory is that of the empirical law of mass action with the temperature-sensitive Arrhenius kinetics, while that of the heterogeneous theory is the diffusion-controlled surface reaction with the temperature-sensitive Arrhenius liquid-phase mass-diffusion and a specific functional form for the concentration dependence. As such, the Arrhenius diffusion of the physically appropriate heterogeneous propagation was mimicked well by the Arrhenius kinetics of the homogeneous propagation in previous formulations. It is further shown that the particle size dependence of the “frequency factor” for the heterogeneous reaction term is the same as that previously inserted in the homogeneous reaction term in an ad hoc manner. The reformulated heterogeneous theory was then applied to the steady propagation of the planar flame in the doubly-infinite domain in the adiabatic limit to illustrate its utility.

Low-temperature cis to trans isomerization reaction-separation membranes using zeolite 13X polyethylacrylate

Zeolite–cobalt catalyst filled polyethylacrylate (PEA) reaction-separation membranes converted cis-piperylene to trans-piperylene in yields of more than 20% after 40 h. Pseudo-interpenetrating network (PIPN) membranes were tested by a single cell reactor at low temperatures (313–317 K). Proton nuclear magnetic resonance (NMR) was used to analyze the composition of the throughput and the feed in our experiment. The trans product did not contaminate the feed even after 40 h. Scanning electron microscopy (SEM) results used to analyze the membrane after a 40 h use indicated no cracks on the scale found previously in blend membrane. We also found the pseudo-first-order rate constant and its activation energy for the isomerization reaction in the membrane by using a phenomenological diffusion-reaction model. The latter values are consistent with surface diffusion control of the kinetics.

Low-temperature dehydrogenation reaction–separation membranes using zeolite 13X polyethylacrylate

We prepared blend and pseudo-interpenetrating network (PIPN) membranes containing zeolite 13X with the dehydrogenation catalyst (Ti or Ni) and polyethylacrylate (PEA). Membranes were tested by a single cell reactor using the dehydrogenation reaction of cyclohexane to benzene at low temperatures (323–360 K). Proton nuclear magnetic resonance (NMR) was used to analyze the composition of the throughput and the feed in our experiments. Using 2 wt% of Ti or Ni on 40 wt% of zeolite with 60 wt% PEA the conversion ratio of benzene to cyclohexane was about 4–8%. The feed did not contain measurable amounts of benzene, hence the separation was complete. Scanning electron microscopy (SEM) results showed that the blend membrane developed cracks considerably earlier than the PIPN membrane. We also find the pseudo-first-order rate constant and its activation energy for the dehydrogenation reaction in the membrane by using a phenomenological diffusion–reaction model. The latter values are consistent with surface diffusion control of the kinetics.

Solid-phase polymerization mechanism of poly(ethylene terephthalate) affected by gas flow velocity and particle size

Experimental studies on the solid-phase polymerization (SPP) of poly(ethylene terephthalate) (PET) for different particle sizes at temperatures of 190–220°C were carried out at different gas flow velocities. The SPP mechanism of PET changes under different operating conditions. At a given gas flow velocity, the SPP reaction mechanism for a large-sized sample changes from chemical reaction control to interior diffusion control with increasing temperature. At a given reaction temperature, the SPP reaction control mechanism for a small-sized sample changes from surface diffusion control to chemical reaction control with increasing gas flow velocity. At a given reaction temperature and gas flow velocity, the SPP reaction mechanism changes from interior diffusion control to surface diffusion control with decreasing particle size. The SPP reaction rate is not determined by a single control mechanism but by both diffusion and chemical reactions in the temperature range of 200–220°C. The primary control mechanism can be discerned based on the operating parameters.

Physicochemical and electrochemical characterization of active films of LaNiO 3 for use as anode in alkaline water electrolysis

Thin films of LaNiO 3 were prepared on Ni by the sequential coating method, and the effects of film preparation variables, such as concentration of the mixed metal nitrates solution, temperature and oxide loading, were examined for the electrocatalytic activity of the film regarding oxygen evolution in concentrated KOH solution. The oxide film with a loading of ~6 mg cm −2 was found to be the best electocatalyst among the electrodes prepared in situ. The activity of this film electrode was better than those prepared by othermethods, following sequential coatings of solution or mixed oxide coatings. Electrode kinetic parameters, such as Tafel slope, reaction order and activation energy, were found to be ~65 mV decade −1, ~1.2 and 18.4 kcal, respectively. Cyclic voltammetric studies, prior to the onset of oxygen evolution, exhibited two characteristic peaks corresponding to a diffusion-controlled surface redox process: Ni 2+ → Ni 3+. Based on these results, a probable mechanism for oxygen evolution on the oxide film electrode is suggested.

Parallel transport by surface and pore diffusion in a porous membrane

To investigate parallel transport by surface and pore diffusion within a porous material, we measured uptake curves and concentration profiles for adsorption of a direct dye on a cellulose membrane. A surface diffusion model, a pore diffusion model, and a homogeneous model each predicted well the uptake curves but not the concentration profiles, although the surface diffusion model gave a better agreement than the pore diffusion model. The surface diffusivities determined by assuming surface diffusion control, pore diffusivities assuming pore diffusion control, and the effective diffusivities for the homogeneous model (Deff) obtained from the uptake curves varied with the concentration of the dye and the stimulator (NaCl). The experimental concentration profiles were predicted well by the parallel surface and pore diffusion model. The surface diffusivities for the parallel diffusion model (Ds) were determined from the values of the intercepts of the plots of Deff[1 + (εpCo/qo)] vs εpCo/qo. The pore diffusivities (Dp) were obtained by matching the theoretical concentration profiles for the parallel diffusion model with the experimental data. The values of Ds and Dp were independent of the concentrations of the dye and the stimulator (NaCl), although the stimulator significantly increased the extent of adsorption. When qo/εpCo ⪢ 260, surface diffusion was the rate-controlling step. For lower qo/εpCo, the adsorption rate increased concomitantly because of the contribution of pore diffusion.

Surface reaction versus diffusion control of mineral dissolution and growth rates in geochemical processes

The kinetics of chemical reactions at mineral surfaces and the rates of diffusion of species in an aqueous phase are coupled in many geochemical systems. Analytical solutions to equations describing coupled mineral dissolution/growth and solute transport in both transient and steady-state systems are used to delimit regimes of pure reaction control, pure transport control and mixed kinetic control of mass-transfer rates. The relative significance of the two processes depends on the magnitudes of the diffusion coefficients and rate constants as functions of temperature, and the degree of disequilibrium in the system. In addition, the system geometry, the ratio of mineral surface area to diffusion cross-section, and the porosity and tortuosity of the medium through which aqueous species diffuse affect reaction vs. diffusion control. In general, diffusion control increases with increasing temperature and increasing distance over which diffusion occurs. Calculations for the mixed kinetic regime in transient systems demonstrate that the relative significance of diffusion and surface reaction varies with reaction progress, and approaches a limiting value as equilibrium is approached. This limiting value may be appropriate to natural water-rock interactions that occur at conditions that are close to equilibrium. This result permits extension of simple models for irreversible mass transfer in homogeneous systems to systems in which mass-transfer kinetics are controlled by coupled surface reactions and mass transport. Criteria are established for time and length scales and fluid velocity limits on the validity of the continuum hypothesis and the local equilibrium assumption in mass-transport modeling.

Shape instabilities of plate-like structures—II. Analysis

In this paper, a companion to the previous one, a susceptibility analysis which delineates the primary instability mode of a terminated plate as it depends on plate width to thickness (aspect) ratio and the energy of internal boundaries of plates is presented. The analysis is based on a simple averaging of Fick's first law, and thus is based on geometrical, yet physically plausible, approximations. The analysis is carried out for both volume diffusion and surface diffusion control of the instability process. Direct cylinderization of plates is favored when the plate aspect ratio is small and the energy of internal boundaries that may be present is low. Boundary induced splitting of plates is favored when the boundary energy is high, whereas edge spheroidization is the dominant instability mode for plates with large aspect ratios containing low energy internal boundaries. The results of the analysis can be succintly represented in terms of plate instability diagrams which define the dominant instability mode in terms of plate aspect ratio and internal boundary energy. Lines of constant instability times can be superimposed on the diagrams, thereby increasing their utility.

Surface diffusion of direct dyes in porous cellulose membranes

Adsorption of C.I. Direct Yellow 12 and C.I. Direct Blue 15 from aqueous solution onto cellulose membranes was carried out in an ultrafiltration-type cell. The dyeing process was analysed on the basis of the parallel transport mechanisms of surface and pore diffusion using Langmuir and Freundlich isotherms. The equilibrium isotherm was represented by Langmuir-type adsorption more accurately than Freundlich-type adsorption when the solution concentration of the dye was less than 0.3 mol m −3. The differences between the theoretical concentration profiles obtained on the assumption of surface diffusion control for the Langmuir and Freundlich isotherms was negligibly small. In contrast there is a difference between the theoretical concentration profiles of pore diffusion control for Langmuir and Freundlich isotherms. The experimental uptake curves and the concentration profiles showed better agreement with the theory for surface diffusion control than for pore diffusion control. The concentration of NACl influenced the equilibrium isotherm but had little effect on the surface d

Diffusion mechanism of direct dyes into a cellulose membrane: The structural effect of direct dyes on the adsorption rate

AbstractThe transport of three typical direct dyes, C.I. Direct Yellow 12, C.I. Direct Red 2, and C. I. Direct Blue 15, into a cellulose membrane has been studied at 55°C. Sodium chloride was used as a stimulator for dyeing. The effects of the concentration of the stimulator on the adsorption isotherms, the adsorption rate, and the concentration profiles in the membrane were tested. The experimental adsorption rates of three dyes were quite different. The diffusion mechanism of the dyes into a cellulose membrane was analyzed on the basis of the parallel transport equation of surface and pore diffusion as developed in our previous paper. The experimental uptake curves showed good agreement with the theoretical curves for surface diffusion control. Experimental concentration profiles also agreed reasonably well with the theoretical lines for surface diffusion control rather than pore diffusion control. The surface diffusivities of three dyes were quite different and nearly independent of the adsorbed phase concentration of the dye.

セルロース膜中における直接染料の表面拡散

The uptake curves and concentration profiles for C. I. Direct Yellow 12 (25°C) and C. I. Direct Blue 15 (55°C) in a cellulose membrane have been determined by a single membrane method. and a multi-membrane method, respectively. The adsorption rate was found to be approximately controlled by surface diffusion. The theoretical uptake curve and concentration profile could be calculated from a simplified analytical solution for surface diffusion control without complicated numerical analysis as presented in our previous paper. The experimental data agreed reasonably well with the analytical solution.

Short cycle time approximation of pressure swing adsorption with nonlinear adsorption isotherm.

A set of nonlinear partial differential equations of material balance on pressure swing adsorption (PSA) is expanded around a small value of cycle time to study the effects of nonlinearity of adsorption isotherm on PSA performance. Solution of the zeroth-order term is given by a quadrature to predict the time-averaged concentration C, and the solution of the first-order term is given by an ordinary linear differential equation to predict the concentration swing ΔC. In the case of surface diffusion control, a moderately favorable adsorption isotherm is advantageous in that the column length required to attain the desired level of product gas concentration is minimized. The relative concentration swing ΔC/C is almost independent of the type of adsorption isotherm. The present analysis may be a good approximation if cycle time is less than the reciprocal of the volumetric mass transfer coefficient based on driving force of the amount adsorbed per unit bed volume.

Short cycle time approximation and graphical solution of pressure swing adsorption.

A method of graphical solution of ordinary differential equations, derived on the basis of a short cycle time approximation, is proposed to evaluate the performance of pressure swing adsorption. The longitudinal distribution of the time-averaged concentration CA is obtained by graphical integration of the reciprocal of the effective driving force, which is found graphically by the construction of the operating line (which relates concentrations between the adsorption and desorption steps) and the tie lines (which relate bulk and surface values). The concentration swing ΔCA is solved as a function of CA by the isoclinal line method, in which the current coordinates are simply constructed to determine the direction of a tangent on a ΔCA - CA diagram. Simplified construction procedures are discussed for special cases of surface diffusion control, film diffusion control and linear isotherm. The usefulness of the proposed method is comfirmed in an illustrative solution.

Transport of direct dye into cellulose membrane

AbstractThe dyeing process for a cellulose membrane–direct dye system is analyzed based on a parallel transport mechanism of surface and pore diffusion with Freundlich isotherm. Numerical solutions were obtained in order to clarify how the surface and pore diffusion resistances affect the uptake curve. The numerical solutions were also compared with an analytical solution for surface diffusion control to establish the range where the analytical solution can be considered as an acceptable approximation. The uptake curves in the cellulose membrane‐chromophore (C.I. Direct Yellow 12) system in the presence of inorganic electrolyte were measured. The rate of adsorption and the maximum amount of adsorption increased with an increase in the concentration of those electrolytes. The rate of adsorption was approximately controlled by the surface diffusion rather than by pore diffusion. The surface diffusivities of the dye were little affected by either the concentration and or nature of the electrolyte.

The formation of water vapor bubbles in copper and their effect on intergranular creep fracture

Small, closely spaced water vapor bubbles are formed along grain boundaries in coarse grained copper by annealing first in air at 800°C and then in hydrogen at 600°C. Almost all of the cavities are formed at grain boundaries, primarily because oxygen strongly segregates to grain boundaries in copper. The average cavity diameter and planar spacing are found to be 0.8 and 3.2 μm, respectively. A study of the creep fracture properties of copper containing the above cavity microstructure indicates that intergranular cavity growth is controlled by the rate of self diffusion along the cavity surface in the manner first described by Chuang and Rice. The stress dependence of the rupture time is found to be of the form t r ~ σ −3. The temperature dependence for fracture is characterized by an activation energy of 92 kJ/mol, which is close to that for surface self diffusion. These properties, together with the absolute rupture times are in close agreement with the Chuang-Rice theory in the limit of surface diffusion control. The determination of the controlling fracture mechanism is supported by metallographic and fractographic evidence.

Sintering behavior of a reactively bonded thick film gold ink

The sintering behavior of thick film reactively bonded Au films was studied using electrical re-sistance measurement and scanning electron microscopy. Isothermal firings were conducted at 350‡ to 850‡C for times up to three hours. The sintering process consists of three portions: 1) Burnoff of the binding resin at 350‡ to 450‡C. 2) A second stage involving neck growth between the gold particles with an activation energy of ∼ 15 Kcal/mole and a time exponent of 5.5 to 6.5 corresponding to surface diffusion control and 3) a third stage of densificat ion by pore annihila-tion and grain growth. The activation energy in stage III of 35–45 Kcal/mole agrees closely with bulk diffusion control. Electrical resistance change appears to be a useful method for studying particularly the initial stages of sintering.

Boundary Layer Replenishment and Unsteady‐State Phenomena in Hydrogen‐Oxygen Fuel Cells

A one‐dimensional (for diffusion) platinum electrode immersed in either dilute potassium hydroxide or sulfuric acid solutions was investigated for startups and restarts after partial rest periods. The experimental results for both the cathode and anode of the hydrogen‐oxygen fuel cell were examined quantitatively to indicate the time periods for surface reaction control, diffusion control, and convection control.