Reactive Diffusion Rate

The usual etherifying agents are the alkyl chlorides or sulfates. The advantage, usually found in organic reactions, of using the alkyl iodides and bromides because of their greater reactivity as compared to the chlorides is overshadowed by their much slower diffusion rate, lower solubility in the alkali and greater rate of saponification. The sulfates are relatively costly. Alkyl sulfites have also been proposed ... 

Like H202, HO passes easily through membranes and cannot be kept out of cells. Hydroxyl radical damage is diffusion rate-limited . This highly reactive radical can... 

High crosslink densities may severely depress polymer reactivity as a result of large decreases in swelling and diffusion rate within the polymer. Diffusion control in a polymer reaction can be detected by the inverse dependence of rate on polymer particle size (radius for spherical particle, thickness for film or sheet) [Imre et al., 1976 Sherrington, 1988]. 

At one extreme diffusivity may be so low that chemical reaction takes place only at suface active sites. In that case p is equal to the fraction of active sites on the surface of the catalyst. Such a polymer-supported phase transfer catalyst would have extremely low activity. At the other extreme when diffusion is much faster than chemical reaction p = 1. In that case the observed reaction rate equals the intrinsic reaction rate. Between the extremes a combination of intraparticle diffusion rates and intrinsic rates controls the observed reaction rates as shown in Fig. 2, which profiles the reactant concentration as a function of distance from the center of a spherical catalyst particle located at the right axis, When both diffusion and intrinsic reactivity control overall reaction rates, there is a gradient of reactant concentration from CAS at the surface, to a lower concentration at the center of the particle. The reactant is consumed as it diffuses into the particle. With diffusional limitations the active sites nearest the surface have the highest turnover numbers. The overall process of simultaneous diffusion and chemical reaction in a spherical particle has been described mathematically for the cases of ion exchange catalysis,63 65) and catalysis by enzymes immobilized in gels 66-67). Many experimental parameters influence the balance between intraparticle diffusional and intrinsic reactivity control of reaction rates with polymer-supported phase transfer catalysts, as shown in Fig. 1. 

Spacer chains affect intrinsic reactivity as well as intraparticle diffusion. Rates for Br-I exchange reactions with spacer-modified catalyst 41 were larger than those with catalyst 35 containing no spacer (Fig. 11). An aliphatic spacer makes the catalyst more lipophilic and the intrinsic reactivity of the active site larger, though the intraparticle diffusity of an inorganic reagent is reduced. It is not known at this time how intrinsic reactivity contributes to the rate increase. 

Recently, Steiger and Keizer [259b] have discussed the theory of reactions between anisotropically reactive species in considerable detail. They illustrated their analysis by using a diffusion equation approach to solve for the rate coefficient for reaction between species which displayed dipolar reactivity. The rate coefficient was reduced by approximately 15% from the Smoluchowski value [eqn. (19)]. Berdnikov and Doktorov [259c] have also analysed the rate of reactions between a spherical reactant having a reactive site, which is a spherical shell of semi-angle 60, and a spherical symmetric reactant. Again, these reactants were not allowed to rotate. Approximate analytic expressions were obtained for the rate coefficient, which was a factor feit less than the Collins and Kimball expression, where... 

Hasinoff noted that the rate coefficient of formation of encounters pairs, fcD, was smaller than predicted from the Smoluchowski—Stokes—Einstein rate coefficient [eqn. (29)]. In aqueous glycerol, this reduction was by 0.14 times, in aqueous polyethylene glycol by 0.30 times, and in aqueous ethylene glycol by 0.11 times. Hasinoff compared these reductions in rate of diffusive rate of formation of encounter pairs with three theories of anisotropic reactivity due to Weller [262], Schmitz and Schurr [257] and... 

An example of a very low diffusion rate of D = 0.1 is shown in Fig. 9.13. For this case the phase transition at y vanishes. Because of the very small reactivity of the H atoms large cluster structures of particles are formed. This allows the simultaneous appearance of H and N atoms on the surface. 

If we enlarge the diffusion rate of the H atoms up to D = 10 as shown in Fig. 9.15, the value of the phase transition point y and the coverages of N, NH and NH2 are almost unaffected by this change, only the concentration of H atoms drops more rapidly for j/n > 2/i- This behaviour shows increased reactivity of H atoms which are now more mobile. The coverages of the other particles depend only on the concentration of the activated sites of the surface but not on the reactivity of the H atoms. 

For the case 5=1 and D = 1 the results of the stochastic model are in good agreement with the CA model y = 0.262). This is understandable because the different definition of the reaction which leads to a difference in the blocking of activated sites cannot play significant role because all sites are activated. The diffusion rate of D = 10 leads nearly to the same reactivity as if we define the reaction between the nearest-neighbour particles. If the diffusion rate is considerably lowered (D = 0.1), the behaviour of the system changes completely because of the decrease of the reaction probability. This leads to the disappearance of the kinetic phase transition at y because different types of particles may reside on the surface as the nearest neighbours without reaction, a case which does not occur at all in the CA approach. 

We have also performed calculations for higher diffusion rates (D = 100) and for the triangular lattice (coordination number z — 6). The qualitative behaviour is in complete agreement with the calculation presented here. For the case S = 1 the increase of the diffusion rate or change of the lattice structure leads to a very small shift of the phase transition point y to higher values of j/n- This trend is clear because the reactivity of the H atoms is increased by the larger mobility. For S < 1 nearly no effect is observed which means that the system s behaviour is mainly dominated by the number of activated sites. The correlation of the adsorbed particles are rather small as expected for S < 1. 

Pentanol reacts much faster than 3-pentanol. The ratio of reactivities calculated from data at 50% H202 conversion is 12 1. Because in term of diffusion rates and chemical behavior these two alcohols are similar to each other, the results are explained by restricted transition-state selectivity, a steric influence of the catalyst pores. Cyclohexanol is oxidized at a very low rate, and this is best... 

One further reason for the development of residual stresses should be mentioned. This is the heterogeneity of the final state of a material which may occur even if the initial reactive mixture was homogeneous. This phenomenon is related to the differing diffusion rates of the various components of the reactive mass during a chemical reaction. This localized distribution of concentrations can be frozen upon solidification of the material. 

Ryu et al. (37) and Xanthos et al. (38) prepared thin films of sintered PP, 200-300 micron diameter, precoated at room temperature with POX E . The films were allowed to react in a constant-temperature oven and samples were withdrawn and analyzed to determine Mw and MWD. It was found that the reduction rates of the M v and MWD became essentially zero after six to seven half-lives of POX E as measured in dodecane. The conclusion is, since there is no mixing during reaction, the diffusion rate of the POX coating onto the PP particulates is not rate controlling, that is, CR-PP for those coated 200-300-pm PP powder particulates is not diffusion controlled. In reactive processing one should strive for process conditions and reaction kinetics where the reactive polymer processing environment is uniform, resulting in uniform product. We discuss this in Sections 11.2 and 11.3. 

The rate of aggregation of fully renneted micelles is very sensitive to temperature. At room temperature it is appreciably less than the diffusional collision rate, which led Payens (1977) to consider the possibility that only a fraction of the surface is reactive (so-called hot spots). The idea of hot spots is consistent with the low fractal dimension of micelle clusters formed during renneting and leads to only a proportion of all encounters between fully renneted micelles being successful. In effect, a statistical prefactor is included in the reaction kernel to reduce the diffusion rate to a level comparable with experiment. However, Payens developed the idea of hot spots only within his theory of the aggregation of fully renneted micelles. 

There are reports that the surface chemistry of Li alloys is indeed largely modified, compared with Li metal electrodes [303], It appears that they are less reactive with solution species, as is expected. The morphology of Li deposition on Li alloys may also be largely modified and smooth, compared with Li deposition on Li substrates [302,304], A critical point in the use of Li alloys as battery anodes is the lithium diffusion rates into the alloys. Typical values of Li diffusion coefficient into alloys are 3-LiAl —> 7 16 9 cm2/s [305], Li44Sn —> 2 10 9 cm2/s [306], LiCd and LiZn —> 1010 cm2/s [307], It should be emphasized that it is very difficult to obtain reliable values of Li diffusion coefficient into Li alloys, and thus the above values provide only a rough approximation for diffusion rates of Li into alloys. However, it is clear that Li diffusion into Li alloys is a slow process, and thus is the rate-limiting process of these electrodes. Li deposition of rates above that of Li diffusion leads to the formation of a bulk metallic lithium layer on the alloy s surface which may be accompanied by mas-... 

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