Chapter 8
Cage Pair Intermediates and Activation Parameters 1
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Downloaded by CALIFORNIA INST OF TECHNOLOGY on March 30, 2017 | http://pubs.acs.org Publication Date: June 25, 1990 | doi: 10.1021/bk-1990-0428.ch008
T. Koenig , T. W. Scott , and James A. Franz 1
Department of Chemistry, University of Oregon, Eugene, OR 97403 Corporate Research Laboratories, Exxon Research and Engineering Company, Clinton Township, Route 22 East, Annandale, NJ 08801 Pacific Northwest Laboratories, P.O. Box 999, Richland, WA 99352
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Equations that describe the effect of cage pair intermediates on apparent activation parameters for bond homolysis and recombination are presented. These equations demonstrate the curvature that is present in ln(k/T) versus l/T relationships which depends on the activation parameters for the recombination and diffusive separation reactions of the cage pair intermediates. Recent results on laser photolysis of diphenyl disulfide in decalin solution are analyzed in terms of a simple chemical model and the radiation boundary hydrodynamic model for the cage effect. The resulting activation parameters suggest that the effective activation enthalpy for diffusive separation of the thermal cage pair is equal to that for diffusion of the free radical intermediates. This result is used to illustrate the predicted curvature for self-termination of the phenylthiyl free radicals and for the reactions of reactive free radicals with trapping agents. Curvature effects for reversible bond homolyses, as determined by observed rate constants for disappearance of organometallic precursors in the presence of the appropriate excess of free radical trapping agent, are also discussed.
A description of a bond thermolysis i n s o l u t i o n requires at l e a s t two elementary steps. This i s due to the f a c t that the immediate product of the bond cleavage step i s a p a i r of r a d i c a l s which are i n i t i a l l y r e s t r i c t e d to remain as neighbors by the surrounding solvent molecules. We follow Rabinowitch and Wood and term t h i s reactive species the cage p a i r intermediate Scheme 1 depicts a simple chemical model f o r t h i s k i n e t i c sequence. Subsequent to the 0097-6156/90/0428-0113$06.00/0 © 1990 American Chemical Society
Marks; Bonding Energetics in Organometallic Compounds ACS Symposium Series; American Chemical Society: Washington, DC, 1990.
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BONDING ENERGETICS IN ORGANOMETALLIC COMPOUNDS
k R-R
h
k
d
2k
D
» [R* -R] «
4
*
c
k Precursor
c
Cage Pair Collisional
SCHEME 1
Chemical Model
2 [R-] Free Radicals
C o l l i s i o n a l Cage Pair
homolysis step (k^, Scheme 1), the c o l l i s i o n a l cage p a i r of Scheme 1 ([R* *R] ) can be p a r t i t i o n e d by the competition between the reformation of the covalent precursor ( k , Scheme 1) and d i f f u s i v e separation (kradiation boundary (RBM), (+) Chemical model.
0.0025
0.0027
0.0029
0.0031
0.0033
0.0035
0.0037
0.0039
0.0041
0.0043
1/TEMPERATURE
Figure 4. Trapping of 5-hexenyl r a d i c a l with Beckwith n i t r o x i d e i n cyclohexane. (•) F - 1, (+) Scheme 4. c
Marks; Bonding Energetics in Organometallic Compounds ACS Symposium Series; American Chemical Society: Washington, DC, 1990.
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BONDING ENERGETICS IN ORGANOMETALLIC COMPOUNDS
Table I I I * * AH xfapp AS xfapp
R */Trap
a
* * ΔΗ χη AS χη
26
AH*
AS* x b p Fx c A O
c
Tc
c
NBUyc H SH 1.04 -13.1 .02 1.04 -18.32 2.00^ -5.23 5-HE*/BEN -.50 -12.1 .42 0.26 -16.29 2.90 -5.77 CPM'/BEN -.50 -12.1 .30 2.526 -6.60 a) Enthalpies i n k c a l mole-1, Entropies i n c a l / mole-Κ. b) * T d - A H * AS* 0 Addition of the same constant to both * T c and A S * f f t Tc or k obs. c) 25 C. d) Nonane solvent, e) No cage s i n g l e t / t r i p l e t spin s e l e c t i o n , f ) Cyclohexane solvent, g) Hexafluorobenzene solvent. F i n a l l y , we should note that the rate constants f o r the cage pair trapping^reaction £kxp i ) i n Scheme 3 are also determined by values f o r ΔΗ x and AS χ such as those of Table I I I . The form of the k x p ^ rate constant d i f f e r s from that of k f i n that i t applies to r e l a t i v e l y high trap concentrations where the trapping agent can be one of the 4-8 molecules that make up the cage w a l l . A d i f f u s i v e step need not be involved i n the k x i process i n t h i s concentration range. The cage p a i r trapping reaction rate constant could be approximated as the sum of a d i f f u s i o n a l path and a nond i f f u s i o n a l cage w a l l path. The a c t i v a t i o n parameters f o r the ^ chemical cage reaction f o r reactive r a d i c a l / t r a p cage pairs (AH , AS x , Table I I I ) are the fundamental values that govern both of these cage p a i r trapping processes. The cage p a i r trapping reaction i s experimentally accessible through c a r e f u l measurements of the rate constants of Scheme 3 homolyses i n the 0.1M - 1M trap concentration region. The temperature dépendance of those r e s u l t s can y i e l d the a c t i v a t i o n enthalpy differences f o r the cage recombination (AH , k , Scheme 3) and cage p a i r trapping ( k x p ^ , Scheme 3) processes. Values f o r AH are the most important unknown i n the s o l u t i o n phase equations f o r bond d i s s o c i a t i o n energies of organometallic systems. 6
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AH
TD)
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AS
F
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Td d o e s
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Bond Homolysis reactions.--We have previously reported an approximate version of the present formalism as i t pertains to the a c t i v a t i o n parameters f o r disappearance of an organometallic precursor through reaction with a suitable free r a d i c a l trapping agent (Scheme 3). That preliminary account was incomplete and d i d not make the d i s t i n c t i o n between apparent a c t i v a t i o n parameters and what we term "observed" a c t i v a t i o n parameters. This d i s t i n c t i o n i s necessary, i n p r i n c i p l e , f o r the rate constants observed f o r homolytic decay of R-M of Scheme 3 (k obs) at scavenger concentrations such that a l l free r a d i c a l s and no cage pairs are being trapped. As discussed above f o r free r a d i c a l s e l f termination, we use the subscript "obs" to denote the a c t i v a t i o n parameters that give the observed rate constants at any temperature i n the i n t e r v a l of observation. These values should be^ distinguished from apparent a c t i v a t i o n parameters (AH app, AS app) derived from l i n e a r regression of ln(k obs/T) against 1/T. The l a t t e r values w i l l give approximate values f o r k obs which d i f f e r from the true ones by the extent of the curvature. n
n
n
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Marks; Bonding Energetics in Organometallic Compounds ACS Symposium Series; American Chemical Society: Washington, DC, 1990.
8.
KOENIGETAL.
Cage Pair Intermediates and Activation Parameters
Equations (17) and (18) below give the a c t i v a t i o n parameters which correspond to the observed rate constants [k obs, equation (16)] f o r a bond homolysis leading to reaction of reactive r a d i c a l s with a trapping agent at the free radical stage (Scheme 4). n
k obs - [1 - F ( T ) ] ' k h
c
(16)
h
AH* (T)obs - ΔΗ* + F (T)[AH* -AH* ] h
η
c
d
c
AS* (T)obs - A s V F ( T ) [ ( A H * - A H * ) / ( T ) ] + R l n [ l - F ( T ) ] Downloaded by CALIFORNIA INST OF TECHNOLOGY on March 30, 2017 | http://pubs.acs.org Publication Date: June 25, 1990 | doi: 10.1021/bk-1990-0428.ch008
h
c
d
c
(18)
c
anc
Figure 6 i l l u s t r a t e s the d i s t i n c t i o n between ΔΗ , ΔΗ h W o b s * ΔΗ app f o r a hypothetical M-R and solvent with the a c t i v a t i o n parameters shown. The l i n e corresponding to ΔΗ P P generated by l i n e a r regression of ln(k obs/T) against 1/T at the three highest temperatures and extended to the (experimentally inaccessible) low temperature region. The curved l i n e i s the r a t i o of the rate constants calculated from the apparent a c t i v a t i o n parameters (k app) to those calculated from equations (17) and (18) with an added graphical multiple (-15) to allow the display of the k app/k obs measure of the curvature on the same scale as the Eyring p l o t s . The curvature e f f e c t i s present but of much less importance than that shown i n Figure 3^above f o r free r a d i c a l s e l f termination. The difference between ΔΗ app and ΔΗ obs i s not s i g n i f i c a n t f o r rate constants of ordinary accuracy over ordinary temperature ranges. n
η
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I f d i f f e r e n t i a l solvation e f f e c t s are ignored , then the bond d i s s o c i a t i o n energy f o r the R-M bond can be approximated as i n equation (19). The example shown i n Figure 6 corresponds to a case where F (T) approaches unity. Equation (19) shows that, C
BDE - AH *app + [1 - F ( T ) ] [AH* -AH* ] - ΔΗ* h
C
d
c
(19)
η
i n the F (T) - 1 l i m i t , the BDE i s simply the difference between ΔΗ app (34.80 kcal/mole i n Figure 6) and ΔΗ η (5 kcal/mole i n Figure 6 i f ΔΗ η — ΔΗ ) . For the example of Figure 6, t h i s difference i s 29.80 kcal/mole which compares favorably with the actual (30 kcal/mole) value. This procedure i s equivalent to the one put f o r t h by Halpern and the present r e s u l t s show that i t can give quite good r e s u l t s i f F (T) i s close to one. C
η
d
C
The Halpern procedure becomes less accurate when the f r a c t i o n a l cage e f f i c i e n c y i s not so close to one. A system with the a c t i v a t i o n parameters of Figure 6, except f o r a reduction of ΔΗ , models a more f l u i d solvent. D i f f u s i v e escape becomes f a s t e r , r e l a t i v e to cage combination, and t h i s leads to reduced values of F ( T ) . A reduction of the value of ΔΗ to 2.6 kcal/mole gives F (T) as 0.2 at the mean of the temperature range that would apply to a ΔΗ app value of 30.6 kcal/mole. The Halpern procedure leads to an estimated 28 kcal/mole f o r the BDE i n t h i s case, somewhat less than the actual 30 kcal/mole value. The value of F ( T ) , the d
C
d
C
η
C
Marks; Bonding Energetics in Organometallic Compounds ACS Symposium Series; American Chemical Society: Washington, DC, 1990.
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BONDING ENERGETICS IN ORGANOMETALLIC COMPOUNDS 32 η 30 28 26 -
Eyrina
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Arrhenius
24 -
E (i) 7.13±.08 log Ai 13.25±.17 a
a
AH* 6.73±.08 AS*| 0.76±.76
22 -
a
b
CPM
Downloaded by CALIFORNIA INST OF TECHNOLOGY on March 30, 2017 | http://pubs.acs.org Publication Date: June 25, 1990 | doi: 10.1021/bk-1990-0428.ch008
20 18 -
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a) Kcal mole*
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b) Cal mole* K' 1
1
12 10 8 6 4 20
ι
ι 0.002
ι
r 0.004
ι
• Τ 0.006
Γ 0.008
1Λ(Κ)
Figure 5. Eyring p l o t f o r the r i n g opening isomerization (k£) o f cyclopropylmethyl free r a d i c a l .
