Isomerization rate, solvent viscosity dependence

From stochastic molecnlar dynamics calcnlations on the same system, in the viscosity regime covered by the experiment, it appears that intra- and intennolecnlar energy flow occur on comparable time scales, which leads to the conclnsion that cyclohexane isomerization in liquid CS2 is an activated process [99]. Classical molecnlar dynamics calcnlations [104] also reprodnce the observed non-monotonic viscosity dependence of ic. Furthennore, they also yield a solvent contribntion to the free energy of activation for tlie isomerization reaction which in liquid CS, increases by abont 0.4 kJ moC when the solvent density is increased from 1.3 to 1.5 g cm T Tims the molecnlar dynamics calcnlations support the conclnsion that the high-pressure limit of this unimolecular reaction is not attained in liquid solntion at ambient pressure. It has to be remembered, though, that the analysis of the measnred isomerization rates depends critically on the estimated valne of... 

The E,Z-photoisomerization of previtamin D to tachysterol has also received recent attention. Jacobs and coworkers examined the process in various solvents at 92 K and found evidence for the formation of a triene intermediate which converts thermally (Ea ca 6.5 kcal mol 1) to the more stable tEc rotamer of tachysterol (tEc-T equation 58)230. The rate of this conversion is viscosity dependent. They identified this intermediate as the cEc rotamer, produced by selective excitation of the cZc rotamer of previtamin D. In a re-examination of the low temperature ,Z-photoisomerization of previtamin D as a function of excitation wavelength, Fuss and coworkers have suggested an alternative mechanism, in which tEc-1 is produced directly from cZc-P and cEc-T directly from tZc-P (equation 59)103. This mechanism involves isomerization about both the central double bond and one of its associated single bonds—the hula-twist mechanism of Liu and Browne101 — and involves a smaller volume change than the conventional mechanism for ,Z-isomerization. The vitamin D system has also been the subject of recent theoretical study by Bemardi, Robb and Olivucci and their co workers232. 

The pressure dependence of obtained above was converted to its dependence on the solvent viscosity t] determined at each pressure. It is shown in Fig.6. We see therein that ib has indeed the 7) dependence of eq.(6) and it is satisfied for t) variation extending over 10 times. We see thus that thermal isomerization of substituted azobenzenes andiV-benzylideneanilines in solvents has rate constants which can well be rationalized in the framework of the Sumi-Marcus model which gives eqs.(5) and (6). More detailed discussions can be found in Ref. 14. 

It has been reported by many groups that the rate of isomerization at the Si state is inversely proportional to a fractional power of the solvent viscosity [39]. Those measurements were almost certainly performed at TST-invalid viscosities. Therefore, the observed rate constant would have been fluctuation limited. This consideration suggests a similar viscosity dependence of our kf (Eq. 3.9). 

The observed pressure dependence of the rate constant kgi, for thermal isomerization of DBNA in TFB and DNAB in GTA is shown respectively in parts (a) and (b) of Fig.4. Detailed experimental setup for the measurement was described in Refs. 13 and 14. The viscosity Tj of these solvents was determined also in Refs. 13 and 14 by best fitting of t] values measured at several pressures P with a formula of log Tj oc /> since they met this formula in the whole P region used. The solvents remained transparent in this region without any indication of phase change. 

If we assume that the HT form is excited mainly with the 530-nm pulse, there are three possible candidates for the mechanism that governs the decay rate of the fast component (1) intersystem crossing from the excited singlet state of HT to HT triplet (2) trans-cis isomerization and (3) internal conversion to the ground state. The first possibility is excluded, based on the absence of a reasonable yield of phosphorescence, even at low temperatures. Possibility 3 is not very plausible because of the existence of the additional long component and the strong dependence on the viscosity of the solvent. Trans-cis isomerization is the most reasonable possibility. 

Fig. 14.8 The dependence of the activation energy of the frani-stilbene isomerization reaction on solvent (w-hexane) viscosity, t], and polarity expressed in terms of the refractive index n as shown. The input for this graph is obtained from rate, viscosity, and refraction index data over a wide range of temperature and pressure. (From J. Schroeder, J. Troe, and P. Vohringer, Chem. Phys. Lett. 203, 255 (1993)).

One of the features of stilbene photochemistry is its essentially strong dependence on medium polarity and temperature the competition between fluorescence and trans-cis isomerization has been shown to be extremely sensitive to medium viscosity. Solvent polarity can affect both the dynamics and the pathway of the reaction. The dipolar character of asymmetrically substituted stilbenes and polarizability of the traws-stilbene transition state can explain the sensitivity of the photoisomerization rate to medium polarity [5, 6, 12, 31, 66-69]. 

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