Saik, Ostafin, and Lipsky: Recombination fluorescence in iso-octane
7357
Accordingly, the total singlet probability for arbitrary N,
hereafter referred to as Ps(x,t), can be written as
23 R. D. Levin and S. G. Lias, Natl. Stand. Ref. Data Sec. Natl. Bur. Stand.
71 ͑1982͒.
24 S. G. Lias, J. E. Bartmess, J. F. Liebman, J. L. Holmes, R. D. Levin, and
W. G. Mallard, J. Phys. Chem. Ref. Data 17, 1 ͑1988͒.
Nϩk
2
NϪk
25 M. Meot-Ner ͑Mautner͒, L. W. Sieck, and P. Ausloos, J. Am. Chem. Soc.
103, 5342 ͑1981͒; A. Ausloos, Radiat. Phys. Chem. 20, 87 ͑1982͒; S. G.
Lias, P. Ausloos, and Z. Harvath, Int. J. Chem. Kinet. 8, 725 ͑1976͒; R.
Mehnert, O. Brede, and W. Naumann, Radiat. Phys. Chem. 26, 499
͑1985͒; Ber. Bunsenges Phys. Chem. 89, 1031 ͑1985͒.
P x,t͒ϭ
!
!
͑
ͩ
ͪ ͩ
ͪ
s
2
N/2
2Iϩ1͒
͑
ϫ
p I,x,t͒,
͑
͚
N
N
Iϭk/2
26 W. Rothman, F. Hirayama, and S. Lipsky, J. Chem. Phys. 58, 1300 ͑1973͒.
27 Based on measured radiative rate constants of the order of 106–107 sϪ1 for
a variety of fluorescent saturated hydrocarbons ͑Ref. 28͒ a fluorescence
quantum yield of less than 5ϫ10Ϫ6 would imply a lifetime of excited
isooctane of less than 5 ps. Also, picosecond transient absorption spectros-
copy with excitation above the ionization threshold have indicated no
evidence for a state of iso-octane of lifetime longer than 10 ps ͓H. Mi-
yasaka, N. Mataga, Chem. Phys. Lett. 126, 219 ͑1986͔͒. These results
appear to be at variance with a lifetime of 38Ϯ12 ps that has been recently
reported in transient absorption measurements on iso-octane excited above
its ionization threshold ͓M. U. Sander, U. Brummund, K. Luther, and J.
Troe, J. Phys. Chem. 97, 8378 ͑1993͔͒ The origin of this discrepancy is
unknown, but recent measurements that we have made of the emission of
benzene from solutions of isooctane excited in the iso-octane absorption
system from 150 to 160 nm, provide a sensitization yield of only 0.02 at
1.0 M benzene, implying an iso-octane lifetime of less than 6 ps. ͓V. O.
Saik and S. Lipsky, J. Phys. Chem. 99, 10471 ͑1995͔͒. Accordingly, at 0.1
M hexafluorobenzene, we expect negligible ͑Ͻ0.2%͒ sensitization of
hexafluorobenzene by excited iso-octane.
ϩIϩ1 ! ϪI !
ͩ
ͪ ͩ
ͪ
2
2
͑A17͒
where k is 0 or 1 depending on whether N is even or odd and
where the coefficient of p(I,x,t) is simply the fraction of
states with a specified value of I. ͑e.g., for Nϭ6, this fraction
is 1/20, 5/20, 9/20, and 5/20 for Iϭ3,2,1, and 0 respectively͒.
For even N, Eq. ͑A17͒ assumes a much simpler form in the
two limiting cases of zero and infinite magnetic field
strength. For these two cases we obtain
Nϩ2
N
P 0,t͒ϭ
Ϫ
cosNϪ1 t/ប͒
͑
͑
ͫ
ͬ
ͫ
s
2 Nϩ1͒
͑
2
Nϩ2
Ϫ
cosNϩ1 t/ប͒
͑A18͒
͑
ͩ
ͪ
ͬ
28 R. Lyke Ph.D. thesis, University of Minnesota, 1984; R. Hermann and R.
Mehnert. J. Lumin. 33, 69 ͑1985͒; Y. Katsumura, Y. Yoshida, S. Tagawa,
and S. Tabata, Radiat. Phys. Chem. 21, 103 ͑1983͒.
Nϩ1
and
29 These considerations have been previously invoked to simplify the analy-
sis of the concentration dependence of the fluorescence of hexafluoroben-
zene in similar solvents excited with beta particles ͑Ref. 30͒.
30 D. W. Tweeten, K. Lee, and S. Lipsky, Radiat. Phys. Chem. 34, 771
͑1989͒.
1ϩcosN t/ប͒
͓
͑
͔
lim P x,t͒ϭ
.
͑
s
2
x→ϱ
31 D. V. Stass, B. M. Tadjikov, and Yu. N. Molin, Chem. Phys. Lett. 235, 511
͑1995͒. This paper came to our attention immediately after our manuscript
was submitted for publication.
1 B. S. Yakovlev and L. V. Lukin, Adv. Chem. Phys. 60, 99 ͑1985͒.
2 J. Casanovas, J. P. Guelfucci, and M. Terrisol, Radiat. Phys. Chem. 32,
361 ͑1988͒.
32 B. Brocklehurst, J. Chem. Soc. Faraday Trans. II 72, 1869 ͑1976͒.
33 H. T. Choi, J. A, Haglund, and S. Lipsky, J. Phys. Chem. 87, 1583 ͑1983͒.
34 L. F. Williams, M. B. Yim, and D. E. Wood, J. Am. Chem. Soc. 95, 6475
͑1973͒.
3 A. E. Ostafin and S. Lipsky, J. Chem. Phys. 98, 5408 ͑1993͒.
4 G. R. Freeman, Kinetics of Nonhomogeneous Processes, edited by G. R.
Freeman ͑Wiley, New York, 1987͒, Chap. 2.
5 J. M. Warman, The Study of Fast Processes and Transient Species by
Electron Pulse Radiolysis, edited by J. Baxendale and F. Busi ͑Reidel,
Dordrecht, 1982͒, p. 433.
35 M. B. Yim and D. E. Wood, J. Am. Chem. Soc. 98, 2053 ͑1975͒.
36 O. A. Anisimov and Yu. N. Molin, Khim. Vysok. Energ. 14, 307 ͑1980͒.
37 S. A. Sukhenko, P. A. Purtov, and K. M. Salikhov, Sov. J. Chem. Phys. 2,
29 ͑1985͒.
6 R. A. Holroyd and W. F. Schmidt, Annu. Rev. Phys. Chem. 40, 439
͑1989͒.
38 H. T. Choi, D. S. Sethi, and C. L. Braun, J. Chem. Phys. 77, 6027 ͑1982͒.
39 J. M. Jung, J. Klein, and R. Voltz, J. Chim. Phys. 88, 779 ͑1991͒.
40 The tracer diffusion constant of C6F6 in cyclohexane at 25 °C is
1.65ϫ10Ϫ5 cm2/s ͑Ref. 41͒. This was scaled to 1.91ϫ10Ϫ5 cm2/s in iso-
octane using the ratio of the viscosity of cyclohexane at 25 °C of 0.898 cp
to that of iso-octane at Ϫ10 °C of 0.777 cp ͑extrapolated from higher
7 J. M. Jung, J. Klein, and R. Voltz, J. Chem. Phys. 88, 779 ͑1991͒.
8 B. Brocklehurst, Nature 221, 921 ͑1969͒.
9 B. Brocklehurst, Int. Rev. Phys. Chem. 4, 279 ͑1985͒.
10 K. Schulten, H. Staerk, A. Weller, H.-J. Werner, and B. Nickel, Z. Phys.
Chem. N. F. 101, 371 ͑1976͒.
11 J. Klein and R. Voltz, Can. J. Chem. 55, 2102 ͑1977͒.
12 R. Z. Sagdeev, K. M. Salikhov, and Yu. M. Molin, Russ. Chem. Rev. 46,
297 ͑1977͒.
temperature
measurements
via
the
equation
ln ϭAϩB/T
ϩC ln TϩDTE͒ ͑Ref. 42͒. The self-diffusion constant of iso-octane, Di ,
at Ϫ10 °C was obtained via the semiempirical equation of Dullien ͓i.e.,
VmDi/RTϭ͑0.124ϫ10Ϫ16͒Vc2/3, where is the viscosity, Vm the molar
volume, Vc the critical volume, and all units are cgs͔ ͑Ref. 43͒ which
predicts the self-diffusion constants of 32 liquids with an average devia-
tion of ϳ4%. Using ϭ0.777 cp at Ϫ10 °C ͑Ref. 42͒, Vmϭ159 cm3 ͑in-
terpolated for Ϫ10 °C͒ ͑Ref. 42͒ and Vcϭ468 cm3, gives Diϭ1.27ϫ10Ϫ5
cm2/s. Adding this to the tracer diffusion constant of C6F6 provides us with
the value Dϭ3.18ϫ10Ϫ5 cm2/s in normal iso-octane. No isotope correc-
tion was attempted. The Onsager radius of 321 Å at Ϫ10 °C in iso-octane
was obtained using a NaD optical dielectric constant of ⑀ϭ1.98.
41 H. Weingartner and B. M. Braun, Ber. Bunsenges. Phys. Chem. 89, 906
͑1985͒.
13 K. M. Salikhov, Yu. N. Molin, R. Z. Sagdeev, and A. I. Buchachenko, Spin
Polarization and Magnetic Effects in Radical Reactions ͑Elsevier, Amster-
dam, 1984͒.
14 U. E. Steiner and T. Ulrich, Chem. Rev. 89, 51 ͑1989͒.
15 D. W. Werst, M. G. Bakker, and A. D. Trifunac, J. Am. Chem. Soc. 112, 40
͑1990͒.
16 O. A. Anisimov, Radical Ionic Systems, edited by A. Lund and M. Shiotani
͑Kluwer Academic, The Netherlands, 1991͒ p. 285.
17 M. Okazaki, Y. Tai, K. Nunome, K. Toriyama, and S. Nagakura, Chem.
Phys. 161, 177 ͑1992͒.
18 B. Brocklehurst, Z. Phys. Chem. 182, 217 ͑1993͒.
19 N. V. Shokhirev, A. A. Zharikov, and E. B. Krissinel, J. Chem. Phys. 99,
2643 ͑1993͒.
42 T. E. Daubert and R. R. Danner, Physical and Thermodynamic Properties
of Pure Compounds ͑U.S. GPO, Washington, D.C., 1989͒, Vol. 3.
43 F. A. L. Dullien, AIChE J. 18, 62 ͑1972͒.
20 O. Anisimov, V. M. Grigoryants, S. V. Kiyanov, K. M. Salikhov, S. A.
Sukhenko, and Yu. N. Molin, Theor. Exp. Chem. 18, 256 ͑1983͒.
21 K. M. Hong and J. Noolandi, J. Chem. Phys. 68, 5163 ͑1978͒.
22 J. Noolandi, Kinetics of Nonhomogeneous Processes, edited by G. R.
Freeman ͑Wiley, New York, 1987͒, p. 465.
44 The apparatus for determining the photocurrent is the same as has been
described in V. O. Saik and S. Lipsky, J. Phys. Chem. 98, 11 858 ͑1994͒.
45 K. Lee and S. Lipsky, J. Phys. Chem. 86, 1985 ͑1982͒.
J. Chem. Phys., Vol. 103, No. 17, 1 November 1995