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Diffusion-controlled

Alternative approaches treat the adsorbed layer as an ideal solution or in terms of a Polanyi potential model (see Refs. 12-14 and Section XVII-7) a related approach has been presented by Myers and Sircar [15]. Adsorption rates have been modeled as diffusion controlled [16,17]. [Pg.394]

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... [Pg.722]

B) TRANSITION FROM GASEOUS TO LIQUID SOLVENT—ONSET OF DIFFUSION CONTROL... [Pg.845]

Collins F C and Kimball G E 1949 Diffusion-controlled rate processes J. Colloid Sol. 4 425... [Pg.865]

Adrian F J 1971 Theory of anomalous electron spin resonance spectra of free radicals in solution. Role of diffusion-controlled separation and reencounter of radical pairs J. Chem. Rhys. 54 3918-23... [Pg.1619]

This expression is the sum of a transient tenu and a steady-state tenu, where r is the radius of the sphere. At short times after the application of the potential step, the transient tenu dominates over the steady-state tenu, and the electrode is analogous to a plane, as the depletion layer is thin compared with the disc radius, and the current varies widi time according to the Cottrell equation. At long times, the transient cunent will decrease to a negligible value, the depletion layer is comparable to the electrode radius, spherical difhision controls the transport of reactant, and the cunent density reaches a steady-state value. At times intenuediate to the limiting conditions of Cottrell behaviour or diffusion control, both transient and steady-state tenus need to be considered and thus the fiill expression must be used. Flowever, many experiments involving microelectrodes are designed such that one of the simpler cunent expressions is valid. [Pg.1939]

Similarly to the response at hydrodynamic electrodes, linear and cyclic potential sweeps for simple electrode reactions will yield steady-state voltammograms with forward and reverse scans retracing one another, provided the scan rate is slow enough to maintain the steady state [28, 35, 36, 37 and 38]. The limiting current will be detemiined by the slowest step in the overall process, but if the kinetics are fast, then the current will be under diffusion control and hence obey the above equation for a disc. The slope of the wave in the absence of IR drop will, once again, depend on the degree of reversibility of the electrode process. [Pg.1940]

B) DIFFUSION CONTROL (SEE ALSO SECTION C2.11 OF THIS BOOK)... [Pg.2720]

Electrochemical processes can become diffusion controlled if the fonnation of the activated complex is fast compared with the diffusion of the reacting anion to the surface or dissolving cations from the surface. In aqueous... [Pg.2720]

Under diffusion controlled conditions tire reaction rate depends, tlien, only on tire supply of 02(g) to the surface which is detennined by Pick s law ... [Pg.2721]

In tlie polarization curve of figure C2.8.4 (solid line), tlie two regimes, activation control and diffusion control, are schematically shown. The anodic and catliodic plateau regions at high anodic and catliodic voltages, respectively, indicate diffusion control tlie current is independent of tlie applied voltage and7 is reached. [Pg.2721]

Figure C2.8.4. The solid line shows a typical semilogaritlimic polarization curve (logy against U) for an active electrode. Different stages of reaction control are shown in tlie anodic and catliodic regimes tlie linear slope according to an exponential law indicates activation control at high anodic and catliodic potentials tlie current becomes independent of applied voltage, indicating diffusion control. Figure C2.8.4. The solid line shows a typical semilogaritlimic polarization curve (logy against U) for an active electrode. Different stages of reaction control are shown in tlie anodic and catliodic regimes tlie linear slope according to an exponential law indicates activation control at high anodic and catliodic potentials tlie current becomes independent of applied voltage, indicating diffusion control.
Under diffusion-controlled dissolution conditions (in the anodic direction) the crystal orientation has no influence on the reaction rate as only the mass transport conditions in the solution detennine the process. In other words, the material is removed unifonnly and electropolishing of the surface takes place. [Pg.2722]

Caldin E F, de Forest L and Queen A 1990 Steric and repeated collision effects in diffusion-controlled reactions in solution J. Chem. See. Faraday Trans. 86 1549-54... [Pg.2850]

This determines the diffusion fluxes at the limit of bulk, diffusion control. [Pg.38]

This determines the total flux at the li/nic of viscous flow. Equations (5.18 and (5.19) therefore describe the limiting form of the dusty gas model for high pressure or large pore diameters -- the limit of bulk diffusion control and viscous flow,... [Pg.39]

Ac this point It is important to emphasize that, by changing a and p, it is not possible to pass to the limit of viscous flow without simultaneously passing to the limit of bulk diffusion control, and vice versa, since physical estimates of the relative magnitudes of the factors and B... [Pg.39]

It may seem curious that Knudsen diffusion coefficients still appear in equations (5.18) and (5.19), which supposedly give the flux relations at the limit of bulk diffusion control. However, inspection reveals that only ratios of these coefficients are effectively present, and from equation (2,11) it follows that... [Pg.41]

At the limit of bulk diffusion control this reduces to... [Pg.43]

Now when the pressure is high enough that bulk diffusion controls... [Pg.92]

Remick and Geankoplis made flux measurements for both species in the isobaric diffusion of nitrogen and helium through their tube bundle. Pressures spanned the interval from 0.444 nim, Hg to 300,2 ram Hg, which should cover the whole range between the limits of Knudsen streaming and bulk diffusion control. Then, since K and K, are known in this case, the form of the proposed flux relations could be tested immediately by plotting the left hand side of equation (10.15) against... [Pg.96]

In general, tests have tended to concentrate attention on the ability of a flux model to interpolate through the intermediate pressure range between Knudsen diffusion control and bulk diffusion control. What is also important, but seldom known at present, is whether a model predicts a composition dependence consistent with experiment for the matrix elements in equation (10.2). In multicomponent mixtures an enormous amount of experimental work would be needed to investigate this thoroughly, but it should be possible to supplement a systematic investigation of a flux model applied to binary systems with some limited experiments on particular multicomponent mixtures, as in the work of Hesse and Koder, and Remick and Geankoplia. Interpretation of such tests would be simplest and most direct if they were to be carried out with only small differences in composition between the two sides of the porous medium. Diffusion would then occur in a system of essentially uniform composition, so that flux measurements would provide values for the matrix elements in (10.2) at well-defined compositions. [Pg.101]

For an Isothermal pellet with pores sufficiently small that Knudsen diffusion controls, the flux relations are required to take the form (8.1), which can be written... [Pg.114]

At the opposite limit of bulk diffusion control and high permeability, all flux models are required to he consistent with the Stefan-Maxwell relations (8.3). Since only (n-1) of these are independent, they are insufficient to determine all the flux vectors, and they permit the problem to be formulated in closed form only when they can be supplemented by the stoichiometric relations (11.3). At this limit, therefore, attention must be restricted from the beginning to those simple pellet shapes for ich equations (11.3) have been justified. Furthermore, since the permeability tends to infininty, pressure gradients within the pellet tend to zero and... [Pg.115]


See other pages where Diffusion-controlled is mentioned: [Pg.48]    [Pg.115]    [Pg.542]    [Pg.843]    [Pg.843]    [Pg.846]    [Pg.1929]    [Pg.2421]    [Pg.2597]    [Pg.2721]    [Pg.2769]    [Pg.2946]    [Pg.2947]    [Pg.2953]    [Pg.1]    [Pg.24]    [Pg.49]    [Pg.54]    [Pg.68]    [Pg.78]    [Pg.102]    [Pg.105]    [Pg.108]    [Pg.110]    [Pg.111]    [Pg.114]   
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Achieving diffusion-controlled

Achieving diffusion-controlled transport conditions

Activation-diffusion control

Adsorption diffusion-controlled kinetics model

Adsorption diffusion-controlled, proteins

Adsorption electro-diffusion control

Adsorption kinetics model mixed diffusion-kinetic-controlled

Adsorption under diffusion control

Adsorption-diffusion control

Aggregate growth, diffusion-controlled

Aging diffusion controlled

Anodic diffusion control

Anthracene, diffusion control reactions

Ash diffusion control

Attachment reactions, diffusion controlled

Bed diffusion control

Bubble diffusion controlled

Bulk diffusion controlled process

Carbocations diffusion-controlled trapping

Cathodic diffusion control

Chain scission diffusion controlled

Characteristics of diffusion controlled polarographic waves

Chemical diffusion controlled

Chemical kinetics and diffusion control

Chemical reactions diffusion-controlled

Chemical vapor deposition diffusion control

Collision- and Diffusion-Controlled Models

Combustion diffusion-controlled

Conditions of diffusion control

Conformation change diffusion controlled substrate binding

Contact diffusion controlled reactions

Control Volume Alternative to the Theory of Diffusive Burning

Control of Curing by Chemical Reactivity or Diffusion

Control of Slow Release and Diffusion Processes

Controlled Release by Solute Diffusion

Controlled Release by Solvent Diffusion

Controlling Molecular Diffusion in the Fluidic Lipid Bilayer

Copolymerization diffusion control models

Coulombic interactions diffusion-controlled reactions

Criteria for diffusion control

Criteria for diffusion control of a catalytic reaction

Crystal diffusion control

Crystal dissolution diffusion-controlled

Crystal growth diffusion-controlled

Crystal growth volume-diffusion controlled

Cure reactions diffusion control

Deposition processes diffusion control

Devolatilization diffusion controlled

Diffusion Control of Crystallization

Diffusion Control of Reactions

Diffusion Controlled Interfacial Reaction

Diffusion Controlled Reactions Neutral Species

Diffusion Controlled Reactivity

Diffusion control

Diffusion control

Diffusion control and pre-association

Diffusion control cathodic reaction under

Diffusion control from excess catalyst

Diffusion control limit

Diffusion control of homogeneous reactions

Diffusion control passive oxidation

Diffusion control photolysis

Diffusion control rate equations

Diffusion control rates

Diffusion control, and kinetics

Diffusion control, azide trapping

Diffusion control, enzyme electrodes

Diffusion control, overall

Diffusion control, potential step methods

Diffusion control, solvents

Diffusion control, transport rate constant

Diffusion controlled adsorption mode

Diffusion controlled current density

Diffusion controlled currents methods

Diffusion controlled currents step methods

Diffusion controlled electrode process

Diffusion controlled electron transfer processes

Diffusion controlled encounter rates

Diffusion controlled free radical termination

Diffusion controlled homogeneous polymer reactions

Diffusion controlled hydrolysis

Diffusion controlled leveling

Diffusion controlled limit

Diffusion controlled limit, reaction

Diffusion controlled limiting current

Diffusion controlled mixtures

Diffusion controlled oxidation

Diffusion controlled polymerization

Diffusion controlled propagation

Diffusion controlled propagation reactions

Diffusion controlled rate constants

Diffusion controlled rate, triplet carbenes

Diffusion controlled reaction kinetics

Diffusion controlled reaction rates

Diffusion controlled reaction, transient effects

Diffusion controlled reactions collision frequencies

Diffusion controlled reactions encounters

Diffusion controlled reactions in polymer degradation

Diffusion controlled reactions with initially separated reactants

Diffusion controlled reactions, supercritical fluids

Diffusion controlled termination

Diffusion controlled uptake

Diffusion controlled-electrodeposition

Diffusion macropore control

Diffusion mass-transfer-controlled reactions

Diffusion processes, controlling kinetics

Diffusion rate controlled process

Diffusion rate controlling

Diffusion reaction control

Diffusion regime, control

Diffusion vs. Surface Controlled Deposition

Diffusion, coefficient controlled bimolecular reactions

Diffusion, coefficients controlled solution

Diffusion-Controlled Currents (DCC)

Diffusion-Controlled Fast Reactions

Diffusion-Controlled Fatigue Crack Growth

Diffusion-Controlled Rapid Reactions

Diffusion-Controlled Solid State Reactions. Andriy M. Gusak

Diffusion-control model

Diffusion-controlled SECM feedback

Diffusion-controlled adsorption mechanism

Diffusion-controlled behavior

Diffusion-controlled bimolecular association

Diffusion-controlled bimolecular rate constant

Diffusion-controlled bimolecular reaction

Diffusion-controlled case

Diffusion-controlled chain termination

Diffusion-controlled coagulation

Diffusion-controlled collision

Diffusion-controlled current

Diffusion-controlled dehydrations

Diffusion-controlled delivery systems

Diffusion-controlled deposition

Diffusion-controlled deprotonation

Diffusion-controlled dissolution

Diffusion-controlled drug delivery system

Diffusion-controlled entry

Diffusion-controlled evaporation

Diffusion-controlled fission product

Diffusion-controlled flocculation

Diffusion-controlled flocculation kinetics

Diffusion-controlled fluorescence

Diffusion-controlled grafting

Diffusion-controlled growth

Diffusion-controlled homogeneous reactions

Diffusion-controlled kinetics

Diffusion-controlled limit on reaction rate

Diffusion-controlled macromolecular reactions

Diffusion-controlled model

Diffusion-controlled model computer simulation results

Diffusion-controlled model concentration profiles

Diffusion-controlled model kinetic rate

Diffusion-controlled model kinetics

Diffusion-controlled morphology

Diffusion-controlled oxidation molecular models

Diffusion-controlled oxygen-reduction

Diffusion-controlled oxygen-reduction reaction

Diffusion-controlled particle aggregation under permanent source

Diffusion-controlled passive samplers

Diffusion-controlled polymer

Diffusion-controlled polymer reactions

Diffusion-controlled polymer release

Diffusion-controlled polymer termination reactions

Diffusion-controlled process

Diffusion-controlled processes theory

Diffusion-controlled processes, pressure effects

Diffusion-controlled protonation

Diffusion-controlled random termination

Diffusion-controlled rate

Diffusion-controlled rate constant determination

Diffusion-controlled rate constant general discussion

Diffusion-controlled rate constant reactivity

Diffusion-controlled reaction program

Diffusion-controlled reaction rate constant

Diffusion-controlled reactions

Diffusion-controlled reactions in solution, spin statistics

Diffusion-controlled reactions theory

Diffusion-controlled reactions, activation

Diffusion-controlled reactions, activation definition

Diffusion-controlled reactions. Black sphere model

Diffusion-controlled regime

Diffusion-controlled region

Diffusion-controlled release mechanisms

Diffusion-controlled release, oral drug delivery

Diffusion-controlled second-order

Diffusion-controlled systems

Diffusion-controlled systems, control delivery

Diffusion-controlled termination radical copolymerization

Diffusion-controlled termination radical polymerization

Diffusion-controlled trapping

Diffusion-controlled unimolecular

Diffusion-controlled void growth

Diffusion-controlled, bimolecular elementary

Diffusion-controlled-mechanism

Diffusive crystal growth diffusion-controlled

Diffusive flux controlling factors

Diffusivity mesopore-controlled process

Drug delivery diffusion-controlled

Drug delivery diffusion-controlled release

Drug release diffusion control

Electrochemical Nucleation with Diffusion-Controlled Growth

Electrodeposition of particles electrokinetic vs. diffusion control

Electron transfer diffusion control limit

Electron transfer, activation control diffusion limit

Encounter rate and diffusion control

Enzyme diffusion-controlled

Exchange is controlled by bulk diffusion into the support

Experimentation, effective diffusivity temperature control

External Mass Transfer and Intraparticle Diffusion Control

Fast (diffusion-controlled) coagulation

Flocculation diffusion control

Gas-solid kinetic processes diffusion control

Gasification reactions diffusion control

Grain Growth Controlled by Diffusion

Grain growth diffusion-controlled solution

Growth rate diffusion-controlled

Growth regime diffusion controlled

Hydrogen pure diffusion control

INDEX diffusion-controlled

Intermacromolecular diffusion controlled

Intermacromolecular diffusion controlled reaction

Ion exchange kinetics film diffusion control

Ion exchange kinetics particle diffusion control

Ionic reactions Diffusion control

Kinetic Parameters Diffusion Controlled Conditions

Kinetic rate equations, diffusion control

Kinetic-diffusion controlled

Kinetic-diffusion controlled growth

Kinetics of diffusion-controlled reactions

Macropore-micropore diffusion control

Macroscopic diffusion control

Mass transfer solid diffusion control

Mathematical models of diffusion-controlled oxidation

Microscopic diffusion control

Mixed diffusion and kinetic control

Mixed diffusion kinetic controlled

Models for diffusion-controlled, steady-state processes

Nucleation diffusion-controlled

Nucleation diffusion-controlled growth

Ohmic-diffusion control

Organic Reactions under Diffusion Control at Electrodes

Oxygen diffusion control

Parallel Pore and Solid Diffusion Control

Partially Diffusion Controlled

Partially Diffusion Controlled Reactions

Partially Diffusion Controlled Reactions Neutral Species

Particle diffusion control

Polymer crystallization diffusion-controlled mechanism

Polymer matrix diffusion-controlled

Polymer matrix diffusion-controlled drug

Polymer matrix diffusion-controlled drug delivery systems

Polymer matrix system diffusion-controlled release rate

Polymerization methyl methacrylate, diffusion-controlled kinetics

Pore Diffusion Control

Potential step methods diffusion controlled currents

Product layer diffusion control

Proton diffusion control

Proton dissociation, diffusion-controlled

Proton transfer diffusion controlled

Pure Diffusion Control

Quantitative models of diffusion-controlled adsorption

Quenching, diffusion controlled

Rate constant diffusion control

Rate constant diffusion-controlled, reactive

Rate constant for) diffusion controlled reactions

Rate constant, for diffusion controlled

Rate controlled process models pore diffusion

Rate-limiting diffusion control

Reaction diffusion control model

Reaction mechanism diffusion-controlled

Reaction rates, diffusion controlled limit

Reactive spheres diffusion-controlled rate

Region of Film Diffusion Control

Relaxation diffusion controlled

Relaxation-controlled transport diffusion

Release diffusion-controlled

Release, diffusion-controlled fission

Release, diffusion-controlled fission product

Reservoir devices/systems diffusion-controlled

Restructuring diffusion controlled

Reversible diffusion-controlled reactions

Scaled 2-Propanol Parameters Diffusion Controlled

Sensors diffusion controlled

Separation diffusion-controlled

Silylation diffusion-controlled

Slice Partially Diffusion Controlled Reactions

Smoluchowski equation, diffusion controlled reactions

Solid Diffusion Control

Specific Versus Overall Diffusion Control

Specific diffusion control, influence

Structure and diffusion-controlled processes in metallic systems

Subject diffusion controlled

Superoxide, diffusion-controlled

Surface Reaction and Diffusion-Controlled Crack Growth

Surface conditions, pure diffusion control

Surface diffusion rate controlled proces

The Implications of Using Diffusive or Convective Control

Theoretical models of diffusion-controlled adsorption kinetics

Theory diffusion-controlled SECM feedback

Transformation diffusion-controlled

Translational diffusion controlled

Translational diffusion controlled termination

Transport phenomena diffusion-controlled

Vapor-diffusion control

What is a Diffusion-Controlled Reaction

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