Viscosity barrier crossing rate

Figure 15. Calculated values of the transmission coefficient k plotted as a function of the solvent viscosity rf for four barrier frequencies a>b at 7 = 0.85. The squares denote the calculated results for to = 3 x 1012 s I, the asterisks denote results for to = 5 x 1012 s-1, the triangles denote results for to = 1013 s I and the circles denote results for a>b = 2 x 1013 s l. The solid lines are the best-fit curves with exponents a 0.72 for wb = 3 x 1012s l, a 0.58 for wb = 5 x 1012 s-1,a 0.22 for wb = 1013 s l, and a 0.045 for cob = 2 x 10I3s-. Note here that the barrier crossing rate becomes completely decoupled from the viscosity of the solvent at wb = 2 x 10l3s-1. The transmission coefficient k is obtained by using Eq. (326). Note here that the viscosity is calculated using the procedure given in Section X and is scaled by a2/ /mkBT, and a>b is scaled by t -1. For discussion, see the text. This figure has been taken from Ref. 170.

As can be seen from the numbers, the exponent a is clearly a function of barrier frequency (cob) and its value is decreasing with increase in a>b- For cob — 2 x 1013 s-1, its value almost goes to zero (a < 0.05), which clearly indicates that beyond this frequency the barrier crossing rate is entirely decoupled from solvent viscosity so that one recovers the well-known TST result that neglects the dynamic solvent effects. 

In the limit of very large viscosity, such as the one observed near the glass transition temperature, it is expected that rate of isomerization will ultimately go to zero. It is shown here that in this limit the barrier crossing dynamics itself becomes irrelevant and the Grote-Hynes theory continues to give a rate close to the transition theory result. However, there is no paradox or difficulty here. The existing theories already predict an interpolation scheme that can explain the crossover to inverse viscosity dependence of the rate... 

Fig.2 summarizes the general friction (or viscosity) dependence expected for the rate constant of activated barrier crossing reactions. 

The dynamics of tiie photoinduced conformational change shown in Figure 11.14 allows us to explore the role of flie solvent in barrier crossing. The measured rate for isomerization of 1,1 bmaphtyl as a function of solvent viscosity is shown... 

The rate constants of diffusion-controlled reactions are proportional to the diffusion rates of both reaction components. They are therefore a function of solvent viscosity inversely proportional to it according to Einstein [54]. Except in extreme cases, propagation is not diffusion-controlled. Monomer addition to the radical requires the crossing of an energy barrier of about 10 kJ mol and larger the steric factor of this reaction is 10 and less. Therefore the rate constant of propagation does not decrease even at medium conversion at considerably increased viscosity (see Chap. 4, Tables 3 and 4). 

Thus it appears that a turn-over can be esqpected for the rate constants measured at low viscosity (Kramers turn-over). Furthermore, due to repeated crossing and recrossing of the barrier under the influence of the solvent, the rate constant is always lower than the transition - state value. Finally, at high viscosities, in the Smoluchowski limit, the pree qponential factor is proportional to... 

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