Isomerization rate, solvent viscosity

As is inversely proportional to solvent viscosity, in sufficiently viscous solvents the rate constant k becomes equal to k y. This concerns, for example, reactions such as isomerizations involving significant rotation around single or double bonds, or dissociations requiring separation of fragments, altiiough it may be difficult to experimentally distinguish between effects due to local solvent structure and solvent friction. 

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 dynamic RIS model developed for investigating local chain dynamics is further improved and applied to POE. A set of eigenvalues characterizes the dynamic behaviour of a given segment of N motional bonds, with v isomeric states available to each bond. The rates of transitions between isomeric states are assumed to be inversely proportional to solvent viscosity. Predictions are in satisfactory agreement with the isotropic correlation times and spin-lattice relaxation times from 13C and 1H NMR experiments for POE. 

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. 

The rate constant for the isomerization of /ra/i.v-stilbene in the S, state is also affected by solvent viscosity and has served as a favorite prototype for the investigation of solvent dynamics in fast monomolecular kinetic processes (Saltiel and Sun, 1990). 

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). 

Photochemical isomerization provides a practical testing ground for the above theory. Time resolved spectroscopy has been used to study the isomerization, i.e. a Icurge amplitude structural change, in different molecules Which are listed in Table I. In these molecules, the rate of isomerization was measured as a function of temperature, pressure amd solvent viscosity. 

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 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. 

Recently much attention has been aroused on solution reactions whose rates decrease as the viscosity Tj of solvents increases. These reactions cannot be rationalized in the framework of the transition state theory. To describe them, two currents of theories have been developed by extending the Kramers theory. One was initiated by Grote and Hynes, while the other by Sumi and Marcus. Recent data on thermal Z/E isomerization of substituted azobenzenes and A/ -benzyU-deneanilines confirms the applicability of the latter for 77 variation over 10 times under pressure. 

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. 

Usually, X is proportional to the viscosity of the solvent, t]. In many kinds of solution reactions, the rate constant decreases with an increase in t] [32]. These reactions cover not only elementary reactions such as electron-, excitation-, atom-group-transfer reactions, and isomerization reactions, but also composite reactions such as biological ones, including enzymatic reactions. The general formula for rates of solution reactions has not been clarified fully yet, in spite of solution reactions being one of the most central subjects in chemistry. 

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. 

The objective of this paper is to demonstrate the importance of phase and reaction equilibria considerations in the rational development of SCF reaction schemes. Theoretical analysis of phase and reaction equilibria are presented for two relatively simple reactions, viz., the isomerizations of n-hexane and 1-hexene. Our simulated conversion and yield plots compare well with experimental results reported in the literature for n-hexane isomerization (4) and obtained by us for 1-hexene isomerization. Based on our analysis, the choice of an appropriate SCF reaction medium for each of these reactions is discussed. Properties such as viscosity, surface tension and polarity can affect transport and kinetic behavior and hence should also be considered for complete evaluation of SCF solvents. These rate effects are not considered in our equilibrium study. 

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