2303
J. Phys. Chem. 1981, 85,2303-2304
In terms of our model, the difference between AGO at the p-f-H/W interface and the H/W interface of SDeS should then be given by RT In y where y is the activity coefficient of the decyl chain in perfluorohexane. To make such calculations, we have used the regular solution theory according to ~ h i ~ h ~ ~ s ~ ~ RT In yi = V,Aij (11)
where i signifies the ith component, Vi is the molar volume, A , is an interaction parameter, and y, is the activity coefficient at infinite dilution. Since fluorocarbon-hydrocarbon mixtures are known to deviate seriously from theories based on solubility parameter^,^'^^^ we have used experimental estimates of A , obtained from critical solution temperature data reported by Gilmour et al.31 Several values have had to be obtainsd by interpolation. Table I1 summarizes the G F data for several fluorocarbons in, hexane and several hydrocarbons_ in perfluorohexane at infinite dilution of the solute. G F varies linearly with chain length. The incremental change in G F of hydrocarbons in perfluorohexane due to an added -CHz- group is estimated to be 140 cal/mol. The $orresponding contribution of a -CF2- group to the G P of fluorocarbons in hexane is 100 cal/mol. From Figure 3, the change in adsorption free energy is estimated to be 130 cal/mol for a -CHz- group transferring from a H/W to a p-f-H/W interface and 70 cal/mol for a -CF2- group transferring from a p-f-H/W interface to a H / W interface. Considering all of the experimental and theoretical uncertainties, the agreement seems to be satisfactory. With respect to the total change in AGO of surfactants on transferring from one interface to the other, we note that AGO becomes more positive by 1780 cal/mol for SDeS when the interface changes from H/W to p-f-H/W. The calculated value of €,E in Table I1 for decane, 1460 cal/mol, is in fair agreement but is significantly lower. For SPFO, AGO increases by 1150 cal/mol when the interface ch-anges from p-f-H/W to H/W. The calculated value of GiE in Table I1 for perfluoroheptane is 1490 cal/mol, which is again in agreement in order of magnitude but seems to be significantly higher. These small differences can be caused by a number of possible factors related to the interactions of the head groups at the two interfacesz6as also limitations of the regular solution approach which are difficult to analyze quantitatively.
(31) J. B. Gilmour, J. 0. Zwicker, J. Katz, and R. L. Scott, J. Phys. Chen., 71, 3259 (1967).
Acknowledgment. This material is based on work supported by the National Science Foundation under Grant NO. ENG-78-16860.
The AAGO values at the A/W and H/W interfaces appear to be the same within experimental error. Nonideality of Mixing of Fluorocarbons and Hydrocarbons. While the interactions at the A/W interface are difficult to describe in molecular terms, the difference between the AGO values, and, particularly, AAGO values, a t the H/W and p-f-H/W interfaces are likely to be primarily due to the well-known nonideality of mixing of fluorocarbon and hydrocarbon l i q ~ i d s . ~It ~is,? therefore, ~~ of some interest to compare these changes in AGO and AAG” with estimates from molecular theories of solution. If the hydrocarbon chains in hexane and the fluorocarbon chains in perfluorohexane are considered to mix ideally, then the free energy difference produced by transferring the hydrocarbon chain of a surfactant from a H/W to a p-f-H/W interface may be ascribed to the excess free energy at the p-f-H/ W interface arising from nonideality effects. Similar considerations apply to the fluorocarbon chain of a surfactant transferred from a pf-H/W interface to a H/W interface. The excess free energy of a mixture can be expressed as GE = RT(xl In y1+ xz In yz)
(9)
where x1 and x 2 are the mole fractions of components 1 and 2 and y1 and yz are the activity coefficients.27 At infinite dilution of component 1,the partial molal excess free energy of component 1 is
GIE = RT In y1
(10)
COMMENTS Spin Selection Rules Concerning Intermolecular Energy Transfer. Comments on “Energy-Transfer Studies Using Doublet-State Acceptors”
ample of a process mediated by electron exchange is that of triplet-triplet energy t r a n ~ f e r : ~ , ~ , ~
Sir: When spin-orbit coupling is negligible, one can formulate spin correlation rules governing the interaction of two neighboring molecules, just as for two atoms.’iZ If an excited donor molecule D* is, or becomes, contiguous to an unexcited acceptor A, and if the total spin of the pair (D* A) equals that of the pair (D A*) or (D A), electron exchange between D* and A can be implicated in the quenching, if it occurs, of D* by A.3 A well-known ex-
Since, according to the fundamental theorem for the addition of angular rnomenta,’2 a triplet and a doublet can add up to a quartet or a doublet, and a singlet-doublet couple forms a doublet, triplet-doublet energy transfer, z(3D*2A) z(lD2A*), which is forbidden if the electron clouds of the donor and acceptor do not overlap, becomes allowed, by dint of electron exchange, when the clouds do overlap. A few years ago, it was claimed that, through
(1) G. Herzberg, “Spectra of Diatomic Molecules”, Van Noatrand, Princeton, NJ, 1950, pp 318-319. (2) F.Wilkinson, “Chemical Kinetics and Reaction Mechanisms”, Van Nostrand-Reinhold, New York, 1980, pp 277-279.
(3) G. J. Hoytink, Acc. Chem. Res., 2, 114 (1969). (4) A. Terenin and V. Ermolaev, Trans. Faraday SOC.,52,1942 (1956). (5) G . Porter and F. Wilkinson, Proc. R. SOC.London, Ser. A , 264, 1 (1961).
( D*1A)
electron exchange
3 3
3(1D3A*)
-
0022-3654181/2085-2303$01.25/00 1981 American Chemical Society
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The Journal of Physical Chemistry, Vol. 85, No. 15, 1981
electron exchange during an encounter, a triplet benzophenone molecule can hand over its electronic excitation to a doublet ketyl radical;'jt7this interpretation of the observation of fluorescence from a species which did not itself absorb the exciting light was at one with earlier work on triplet-doublet q u e n ~ h i n g . ~But, , ~ in a recent paper,1° Quan and Guzzo come to a different conclusion: "However it has been shown by Dexter'l that the probability of transfer via the exchange mechanism is proportional to a spin term of the form
Comments
t-t transfer matrix element (3@ilv13@f)
=
-K
t-s transfer matrix element (3@ilVll@f)
=0
s-t transfer matrix element (l@i(u(3@f) 5
0
t-d transfer matrix element
1
sA*(1) S D ( ~SA@) ) dT1 d72
J-
From this we conclude that we have nonzero transfer probability if the spins of ground-state donor and acceptor are the same and if the excited states are the same. This is clearly the case with triplet-triplet transfer but is not the case here. Triplet-doublet transfer would require a spin flip, and thus should be forbidden". As noted previously by Steel and myself,12 though Dexter's visualization of the exchange interaction was altogether sound, his exposition of the theme left some room for improvement. To clarify the situation, I reconsider various cases of multiplet-multiplet energy transfer, taking into account, as before,12 both coulomb and exchange mechanisms; other manifestations of the latter mechanism have been discussed by Hoytink3 and by Chiu.13 Suppose the two species, donor and acceptor, have molecular orbitals 4 and 0; let the subscripts 0 and 1refer to the highest occupied and lowest vacant orbitals. Then, with the usual nomenclature,14 we may employ the following f u n ~ t i o n s : ' ~ J ~
z*1@i(2*1D* + IA) = (1/21/2)[140~Oo&lf I;bo4100$l]
+
2*1@f(1D 2*1A*)= (1/21/2)[140&190&l f Iq50&$$ll]
[email protected](3D* + 'A) = (1/31/2)[l~o~i&l + I40600l+ l&4i~0lI 2ai(3D* + 2A)
I 2a1 =
(1/61'2)[21404i&I - IdoZOoI - I&&ifloII '@i('D*
+ 2A)
I 2@pz
'@f(lD
= (1/21~2)[J40~1901 - l$&Ool]
+ 'A*)
=
I&&I911
In what follows, the letters s, d, and t will represent respectively singlet, doublet, and triplet; v will denote the energy of interaction between the donor and the acceptor. Making the usual assumption that 40, &, Bo, and fll are orth~normal,'~ and using the symbols J and K for twoelectron coulomb and exchange integrals,14 we find the following matrix elements (the first three of which have already been given by other authors15J6): s-s transfer matrix element (l@il~ll@f)
(6) K. Razi Naqvi and
= 2J-K
U.P. Wild, Chem. Phys. Lett., 41, 570 (1976).
(7) K. Razi Naqvi, H. Staerk, and T. Gillbro, Chern. Phys. Lett., 49, 160 (1977). (8) G. Porter and M. R. Wright, Discuss. Faraday Soc., 27, 18 (1959).
(9) G. J. Hoytink, "Chemiluminescence and Bioluminescence", M. J. Cormier, D. M. Hercules, and J. Lee, Ed., Plenum, New York, 1972, pp 147-168.
(10)N. N. Quan and A. V. Guzzo, J. Phys. Chem., 85, 140 (1981). (11) D. L. Dexter, J. Chem. Phys., 21, 836 (1953). (12) K. Razi Naqvi and C. Steel, Chem. Phys. Lett., 6, 29 (1970). (13) Y.-N. Chiu, J. Chem. Phys., 56, 4882 (1972). (14) R. Daudel, R. Lefebvre, and C. Maser, "Quantum chemistry", Interscience, New York, 1959, pp 439, 471.
(4@p,Iv(2@f)
(2@11v12@f)
0
= -(3/2)'/2K
s-d transfer matrix element (2@21~12@f)
= (1/2)1/2(2J - K )
A process is allowed or forbidden by the coulomb (exchange) interaction according as the coulomb (exchange) integral appears or does not appear in the matrix element connecting the initial and final states of the donor-acceptor pair. The coulomb integral vanishes if the radiative transition D* D or A* A is spin forbidden; the other integral, when the total spin of the (D*A) pair differs from that of the (DA*) pair. So long as the spin-orbit interaction remains weak, its inclusion does not invalidate the foregoing selection rule concerning exchange-mediated energy transfer; but, as emphasized by Forster," a transfer process formally forbidden by the coulomb interaction may nonetheless occur, on account of spin-orbit coupling, provided that the quantum yield of the D* D radiative transition is high and the transition A* A is dipole allowed. Tripletsinglet transfer can therefore take place only in media (such as rigid solutions) which are conducive to phosphorescence emission.l8 Among the processes listed above, t-d transfer is thus unique, in sharing the characteristics of t-t transfer on the one hand and of t-s transfer on the other hand; accordingly, it may operate through one interaction or However, the experimental conditions can always be so arranged as to favor one mechanism over the other: for example, Lisvoskaya, Plotnikov, and Alfimov,l9who are apparently the first to report Forster-type s-d and t-d transfer, effectively eliminated the exchange interaction by using frozen solutions and low acceptor concentrations (thereby keeping most donors and acceptors far apart); conversely, the work reported in ref 6 and 7 was conducted in fluid solutions, where phosphorescence yield of the donor was extremely low and electron exchange was efficiently brought about by the diffusive transport of 3D* and 2A. Though Quan and GuzzolO employed rigid solutions, acceptor concentrations were unfortunately so high that the participation of the exchange mechanism in the t-d transfer observed by them cannot be ruled out.
-
-
--
Dr. Guzzo has indicated to the Editors his agreement with the comment. (15) R. E. Merrifield, J. Chem. Phys., 23, 402 (1955). (16) S. H. Lin, Mol. Phys., 21, 853 (1971). The final state for trip-
let-triplet transfer is incorrectly identified in this paper. (17) Th. Forster, Discuss. Faraday Soc , 27, 7 (1959). (18) R. G. Bennett, R. P. Schwenker, and R. E. Kellogg, J . Chern. Phys., 41, 3040 (1964); R. E. Kellogg, ibid., 47, 3403 (1967). (19) I. A. Lisvoskaya, V. G. Plotnikov, and M. V. Alfimov, Opt. Spectrosc., 35, 1091 (1973). Institute of Physics University of Trondheim-NLHT N-7055 Dragvoll, Norway Received: April 6, 198 1
K. Razi Naqvl
