252
J. Phys. Chem. 1985,89, 252-257
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In the first case, where Ps 1 according to eq 4.10a, eq 4.7 shows that for kDS/kD= we only require surface fractional coverage f 1 - Ps 1. Therefore, the second case of eq 4.10b should apply and low surface coverage of the ellipsoid results in a small rate constant relative to the full surface coverage rate.
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--
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and
The metric coefficients are
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Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research.
Appendix We present here the notation used in the text for prolate spheroidal coordinate^.^ The spheroid foci are a t the points x = y = 0 and z = *I/$, so the interfocal distance is a. The distances rl and r2 from (x,y,z) to the foci are rl = [ ( z f/2a)z x2 y 2 ] 1 / 2 r2 = [ ( z - Xu)' x2 y 2 ] 1 / 2 (AI) The coordinates t , q , and 4 are defined by 4 = tan-' ( y / x ) [ = (rl r 2 ) / a 7 = (rl - r 2 ) / a (A2)
+
+ + + +
+
The surface element du perpendicular to the ellipsoid defined by t = constant is dud = h,h, dq d4. The ranges of t , q, and 4 are 1 I5 I0 3 , -1 S 7
