Kinetic rate-controlled regime

In the A sector (lower right), the deposition is controlled by surface-reaction kinetics as the rate-limiting step. In the B sector (upper left), the deposition is controlled by the mass-transport process and the growth rate is related linearly to the partial pressure of the silicon reactant in the carrier gas. Transition from one rate-control regime to the other is not sharp, but involves a transition zone where both are significant. The presence of a maximum in the curves in Area B would indicate the onset of gas-phase precipitation, where the substrate has become starved and the deposition rate decreased. 

Two fundamentally different regimes can exist 1) those characterized by transport-controlled reaction and 2) those characterized by kinetic rate-controlled reaction (2.)- In the case of transport-controlled reaction, the reaction rate constant is much faster than any of the transport processes involved so that the length scale over which a moving fluid comes to equilibrium is small. In this regime, therefore, the walls of a dissolution channel are essentially discontinuities in permeability while in the kinetic rate-controlled case, where equilibrium between the fluid and the reacting mineral occurs over some distance, the boundaries of a channel are blurred by a more gradual permeability change. 

It is rather straightforward to employ numerical methods and demonstrate that the effectiveness factor approaches unity in the reaction-rate-controlled regime, where A approaches zero. Analytical proof of this claim for first-order irreversible chemical kinetics in spherical catalysts requires algebraic manipulation of equation (20-57) and three applications of rHopital s rule to verify this universal trend for isothermal conditions in catalytic pellets of any shape. 

A regime of simultaneous dissolution has also been found for Cu—Ni alloys in acidic chloride solutions. Rotating ring-disk electrode studies revealed an apparent Tafel region of the alloy and component polarization curves with mixed mass transfer and kinetic rate control [44, 45]. For a CugoNiio alloy, the kinetic parameters again indicate a coupling of the copper and nickel partial currents under steady state conditions [44]. 

The equations of combiaed diffusion and reaction, and their solutions, are analogous to those for gas absorption (qv) (47). It has been shown how the concentration profiles and rate-controlling steps change as the rate constant iacreases (48). When the reaction is very slow and the B-rich phase is essentially saturated with C, the mass-transfer rate is governed by the kinetics within the bulk of the B-rich phase. This is defined as regime 1. 

Presently, the quantitative theory of irreversible polymeranalogous reactions proceeding in a kinetically-controlled regime is well along in development [ 16,17]. Particularly simple results are achieved in the framework of the ideal model, the only kinetic parameter of which is constant k of the rate of elementary reaction A + Z -> B. In this model the sequence distribution in macromolecules will be just the same as that in a random copolymer with parameters P(Mi ) = X =p and P(M2) = X2 = 1 - p where p is the conversion of functional group A that exponentially depends on time t and initial concen-... 

When considering the macrokinetics of PAR described by equations (Eq. 17), it is reasonable to focus on two limiting regimes. The first of these, the kinetically-controlled regime, takes place provided the rate of diffusion of molecules Z appreciably exceeds that of the chemical reaction. In this case, a uniform concentration Z = Ze should be established all over the globule after time interval t R2/D. Subsequently, during the interval t 1 /kZe, which is considerably larger than f[Pg.152]

Thus, th in a kinetically controlled regime is described by a dl law. Furthermore, th is found to be inversely proportional to pressure (for a first-order reaction) under kinetically controlled combustion, and in contrast, independent of pressure under diffusionally controlled combustion (since D P-1). In the kinetically controlled regime, the burning rate depends exponentially upon temperature. 

If Da = 1 is defined as the transition between diffusionally controlled and kinetically controlled regimes, an inverse relationship is observed between the particle diameter and the system pressure and temperature for a fixed Da. Thus, for a system to be kinetically controlled, combustion temperatures need to be low (or the particle size has to be very small, so that the diffusive time scales are short relative to the kinetic time scale). Often for small particle diameters, the particle loses so much heat, so rapidly, that extinction occurs. Thus, the particle temperature is nearly the same as the gas temperature and to maintain a steady-state burning rate in the kinetically controlled regime, the ambient temperatures need to be high enough to sustain reaction. The above equation also shows that large particles at high pressure likely experience diffusion-controlled combustion, and small particles at low pressures often lead to kinetically controlled combustion. 

Forster reported significantly different kinetic behavior in the neutral and ionic regimes. In the neutral regime reaction of Mel with [Ir(CO)3l] was relatively slow and inhibited by increased CO. In contrast, in the ionic regime the oxidative addition of Mel to [Ir(CO)2l2r to generate [IrMe(CO)2l3] was fast. The subsequent conversion of [IrMe(CO)2l3] to [Ir(C(0)Me)(C0)2l3] was rate controlling, favored by increased CO and powerfully inhibited by I . 

To ensure the system is probing reactions in a kinetically controlled regime, the reaction conditions must be calculated to determine the value of the Wiesz-Prater criterion. This criterion uses measured values of the rate of reaction to determine if internal dififusion has an influence. Internal mass transfer effects can be neglected for values of the dimensionless number lower than 0.1. For example, taking a measured CPOX rate of 5.9 x 10 molcH4 s g results... 

Aqueous lactose (40 wt-% in water) and xylose (50 wt-%) solutions were hydrogenated batchwise in a three-phase laboratory reactor (Parr Co.). Reactions with lactose were carried out at 120 °C and 5.0 MPa H2. Xylose hydrogenations were performed at 110 °C and 5.0 MPa. The stirring rate was 1800 rpm in all of the experiments to operate at the kinetically controlled regime. 

Regimes 2 and 3 - moderate reactions in the bulk (2) or in thefdm (3) and fast reactions in the bulk (3) For higher reaction rates and/or lower mass transfer rates, the ozone concentration decreases considerably inside the film. Both chemical kinetics and mass transfer are rate controlling. The reaction takes place inside and outside the film at a comparatively low rate. The ozone consumption rate within the film is lower than the ozone transfer rate due to convection and diffusion, resulting in the presence of dissolved ozone in the bulk liquid. The enhancement factor E is approximately one. This situation is so intermediate that it may occur in almost any application, except those where the concentration of M is in the micropollutant range. No methods exist to determine kLa or kD in this regime. 

Hydrodemetallation reactions require the diffusion of multiringed aromatic molecules into the pore structure of the catalyst prior to initiation of the sequential conversion mechanism. The observed diffusion rate may be influenced by adsorption interactions with the surface and a contribution from surface diffusion. Experiments with nickel and vanadyl porphyrins at typical hydroprocessing conditions have shown that the reaction rates are independent of particle diameter only for catalysts on the order of 100 /im and smaller (R < 50/im). Thus the kinetic-controlled regime, that is, where the diffusion rate DeU/R2 is larger than the intrinsic reaction rate k, is limited to small particles. This necessitates an understanding of the molecular diffusion process in porous material to interpret the diffusion-disguised kinetics observed with full-size (i -in.) commercial catalysts. 

On the other hand, if the kinetics of any of the reactions given by Eqs (5.8) and (5.9) are determined by the rate at which the activated complex is formed, the rate is said to proceed in the diffusional-controlled regime. In this case, the reaction rate may eventually depend on the sizes of the reacting species e.g., an epoxy group belonging to the monomer will diffuse at a faster rate than a similar epoxy group attached to the gel. However, the required diffusion must occur over a very short path (the necessary distance to approach both reactants to form the activated complex). Thus, diffu-... 

Initially, when the ApBq layer is very thin, the reactivity of the A surface is realised to the full extent because the supply of the B atoms is almost instantaneous due to the negligibly short diffusion path. In such a case, the condition kom kW]/x is satisfied. Therefore, if the surface area of contact of reacting phases A and ApBq remains constant, chemical reaction (1.1) takes place at an almost constant rate. In practice, this regime of layer growth is usually referred to as reaction controlled. The terms interface controlled regime and kinetic regime are also used, though less suited. 

However, when the view is restricted to simple, irreversible reactions obeying an nth order power rate law and, if additionally, isothermal conditions arc supposed, then—together with the results of Section 6.2.3—it can be easily understood how the effective activation energy and the effective reaction order will change during the transition from the kinetic regime to the diffusion controlled regime of the reaction. 

In both cases the effect of temperature on the initial reaction rates in the studied range was weak, while it became strong in the diffusion-controlled regime. Although thermodynamics predict the formation of some carbon for temperatures up to 973 K, this was not observed experimentally indicating that its formation is kinetically hindered in the studied temperature range. 

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