Handbook of Solvents - George Wypych - ChemTech - Ventech!

682 Tai-ichi Shibuya
cule in its interior and Scholte’s
extension 12 of the cavity field and the
reaction field in the
Onsager-B�ttcher theory 13,14 to an ellipsoidal
cavity. Buckingham’s formula
involves the polarizability of
the solute molecule and appears
quite different from Eq. [11.2.2]. It
was shown 6 that the Buckingham
formula reduces to Eq. [11.2.2].
11.2.3 DIELECTRIC SOLVENT
EFFECT ON THE
RADIATIVE RATE
CONSTANT
The radiative rate constant is related
to the absorption intensity of the transition from the ground state to the excited state under
consideration. The application of Eq. [11.2.2] leads 15 Figure 11.2.2. Plots of y = nf ′ / fc′ vs.x=n
to
2 - 1 for the π → π *
absorption bands of β-carotene (crosses) and the n →π* absorption
bands of pyrazine (solid circles). [After reference 6]
2 [ ( ) ]
k′′ / k = n s n − 1 + 1 [11.2.4]
r r
2
where:
k r′
apparent radiative rate constant of the solute molecule measured in a solvent of the
refractive index n
kr radiative rate constant of the molecule in its isolated state
Note that the local-field correction factor n[s(n 2 -1)+1] 2 varies from n to n 5 as s varies
from 0 to 1. For 9,10-diphenylanthracene (DPA), the correction factor was given 15 as
n[(0.128)(n 2 -1)+1] 2 , which lies between n and n 2 . This agrees with the observed data 16 of
fluorescence lifetimes of DPA in various solvents.
REFERENCES
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2 G. Kort�m, Z. Phys. Chem., B33, 243 (1936).
3 (a) V. Henri and L. W. Pickett, J. Chem. Phys., 7, 439 (1939); (b) L. W. Pickett, E. Paddock, and E. Sackter,
J. Am. Chem. Soc., 63, 1073 (1941).
4 L. E. Jacobs and J. R. Platt, J. Chem. Phys., 16, 1137 (1948).
5 S. R. Polo and M. K. Wilson, J. Chem. Phys., 23, 2376 (1955).
6 T. Shibuya, J. Chem. Phys., 78, 5176 (1983).
7 C. Kittel, Introduction to Solid State Physics, 4th Ed., Wiley, New York, 1971, Chap. 13.
8 A. B. Myers and R. R. Birge, J. Chem. Phys., 73, 5314 (1980).
9 T. Shibuya, Bull. Chem. Soc. Jpn. , 57, 2991 (1984).
10 A. D. Buckingham, Proc. Roy. Soc. (London), A248, 169 (1958); A255, 32 (1960).
11 J. G. Kirkwood, J. Chem. Phys., 7, 911 (1939).
12 T. G. Scholte, Physica (Utrecht), 15, 437 (1949).
13 L. Onsager, J. Am. Chem. Soc., 58, 1486 (1936).
14 C. J. F. B�ttcher, (a) Physica (Utrecht), 9, 937, 945 (1942); (b) Theory of Electric Polarization, Elsevier,
New York, 1952; 2nd Ed., 1973, Vol. I.
15 T. Shibuya, Chem. Phys. Lett., 103, 46 (1983).
16 R. A. Lampert, S. R. Meech, J. Metcalfe, D. Phillips, A. P. Schaap, Chem. Phys. Lett., 94, 137 (1983).