Caging efficiency

For structure H, however, the shape of the large guest molecule is of considerable importance, perhaps because it is important to fill the available large cage efficiently. Ripmeester and Ratcliffe (1990a) indicate that, unlike si and sll,... 

AS obs) with those for the elementary processes of Scheme 1. The fractional cage efficiency factor [Fq(T)] is temperature dependent to the extent that k /k j is temperature dependent. ... 

The variables of equation (9) are the ratio (K) of the initial separation distance (d j) to the sum of the hard sphere collision radii (s), the ratio (L) of the proportionality constant for the combination reaction (k ) to the second order rate constant for pair diffusion (k(j2) ind the ratio (r) of the time elapsed since pair formation to the diffusive time constant (s /D). The fractional cage efficiency is the complement to the pair... 

Our present focus is on the values of F (T) that are contained in the convoluted fits to equation (9) obtained in cis-decalin over the temperature range from 237 K to 429 K. These results give cage efficiencies for the photochemical case directly and predict those for the corresponding collisional case where K may be set equal to one. The viscosity of this solvent has been characterized (Table I) and fits the Andrade equation (6) with an of 3685 cal/mole and a pre-exponential constant (Aj ) of 6.45X10 cP. These results are summarized in Table I and Figure 2. 

Free Radical Self-Termination. The cage efficiencies and activation parameters for the phenylthiyl collisional cage pair provide the basis for illustrating some of the important features of equations (3)-(5) and for predicting the observed rates of self-termination of phenylthiyl free radicals. Application of the SW procedure to the completely diffusion controlled step of Scheme 1 (kj) ) for phenylthiyl free radicals in cis-decalin can be expressed by the transition state equation with a AH d of 3448 cal/mole and a AS d of -4.3 cal/mole-K. The corresponding activation enthalpy (AH d) from the Stokes-Einstein-Schmoluchowski relationship is 3685 cal/mole for cis-decalin) so that the a of equation (8) is 0.94. The micro-frictional multiplier (mf, equation 8 above), which is incorporated into the SW activation entropy (AS j)), is 2.4. The SW activation entropy for a truly diffusion controlled self-termination of phenylthiyl free radicals (2k obs -2kj), - 1 at... 

The relationships corresponding to equations (l)-(5) above are as follows The obse ed rate constants (kjfobs) and activation parameters (AH xfobs AS -pfobs) for disappearance of R by reaction with T depend on the second order rate constant for diffusive collision to form the cage pair (k pj), equation 12) and the fractional cage efficiency (Fjc equation 11). The latter is determined by the first order rate constants for the chemical reaction (kjc) and diffusive (re)separation (kj j) of the T/R collisional cage pair. The associated activation parameters are given by equations (13) and (14). 

In cases where the fractional cage efficiency is this low (< 0.1), equation (14) can be replaced with the more intuitive approximate form shown as equation (14a). This equation together with the value of AS xD used to obtain the value of AS xc... 

The Halpern procedure becomes less accurate when the fractional cage efficiency is not so close to one. A system with the activation parameters of Figure 6, except for a reduction of AH (i, models a more fluid solvent. Diffusive escape becomes faster, relative to cage combination, and this leads to reduced values of F (T). A reduction of the value of AH to 2.6 kcal/mole gives Fq(T) as 0.2 at the mean of the temperature range that would apply to a AH app value of 30.6 kcal/mole. The Halpern procedure leads to an estimated 28 kcal/mole for the BDE in this case, somewhat less than the actual 30 kcal/mole value. The value of Fq(T), the... 

Professor C. B. Harris has informed us that he has found quite similar cage efficiencies for diphenyl disulfide photolysis using his ultrashort pulse system in which convolution is less important. 

The cage efficiency predominantly depends on the stability of the R radical that determines the barrier of the cage reaction. Comparing the cage efficiency observed for various substrates such as cyclohexane [17], toluene [19], and ethylbenzene [16] confirms a systematic trend and readily explains the difference in alcohol-to-ketone ratio for those substrates (see Figure 1.4). 

Figure 1.4 Effect of the substrate on the solvent-cage efficiency and alcohol-to-ketone ratio.

For all dUialogens examined, there is a strong increase of caging efficiency with increasing cluster size n. Complete caging is observed once a single solvation shell is completed. Results for I2 (C02) are shown in Figure 11.11 and compared with dynamical simulations. 

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