J. Phys. Chem. 1083, 87, 1583-1589
1583
Dependence on Scavenger Concentration of the Efficiency of Quenching Geminate-Ion Recombination Fluorescence of Saturated Hydrocarbon Liquids Hae Tak Chol, John A. Haglund,t and Sanford Llpsky' Department of Chamlstry, Unlversity of Minnesota, Mlnneapolis, Minnesota 55455 (Recelved: October 1 1, 1982; In Final Form: December 6, 1982)
The fluorescenceof liquid bicyclohexyl,decalin (cis and trans isomers),and cyclohexane excited by =Kr p particles has been studied as a function of the concentration of perfluorodecalin over a concentration range, cq: from to 0.03 M. By comparison with the effect of perfluorodecalin to quench the fluorescence of these liquids when excited with 165-nm light, it is possible to extract the probability, p t , that perfluorodecalin scavenges a geminate electron. This probability is found to be well represented by the function (ac,)O.'/[l + (ac,)O.'] over the entire concentration range studied with a = 66 (bicyclohexyl), 70 (decalin, mixed isomers), 124 (cis-decalin),58 (trans-decalin), and 102 (cyclohexane)M-I. The functional form of pt is found to be in good agreement with theoretical expectations.
-
Introduction The S1 So fluorescence that is observed during fast electron excitation of neat saturated hydrocarbon liquids derives largely from recombining geminate ion pairs.' Accordingly, the quenching of this fluorescence by the addition of a solute may be contributed to not only by an effect of the solute to nonradiatively depopulate the S1 state but also by its effect to inhibit the formation of S1 by scavenging of some member of the geminate pair. Under rather mild approximations, the probability, pf,for such scavenging can be determined from a comparison of the quenching efficiency when the solvent is excited optically (below the ionization threshold) and with fast electrons. Using perfluoro-n-hexane as an electron scavenger, we have recently demonstrated2 that the dependence of pf on scavenger concentration, cq, is better represented by the Stern-Volmer form (Le., a c q / ( l + acq)) than by a form initially suggested by Warman, Asmus, and Schuler3p4(WAS) (i.e., (cYc,)'/~/[~ + ( L Y C ~ a) t~least ~ ~ ]for ) cq from ~ 0 . 0 1to 0.2 M for cyclohexane and for cq from =0.004 to 0.05 M for decalin (mixed isomers). At somewhat lower concentrations, deviations from the SternVolmer form were observed and there was evidence for an approach of pt to the WAS form. However, the fluorescence was insufficiently quenched at these low concentrations to establish this with any confidence. The present investigation serves as a continuation of this earlier work. Using perfluorodecalin, a much more effective electron ~cavenger,~ we have now been able to reliably extend our previous measurements to substantially lower concentrations (=lX lo4 M) for the liquids bicyclohexyl, decalin, and cyclohexane. We find, over this expanded concentration range (Le., cq = 1 X 10-4-0.04 M), that the best representation of pt of the form (ac,)"/[l + (ac,)"] is obtained with n = 0.7. Also we demonstrate that this representation is quite consistent with theoretical predictions.
fluorodecalin studied ( ~ 0 . 0 4M) and any charge-transfer absorption makes negligible c~ntribution.~ The fluorescence was monitored at 226 (bicyclohexyl), 227 (transdecalin and mixed decalins), 240 (cis-decalin), and 205 (cyclohexane) nm. Stray light background, as determined with neat CC14 in the sample cell, was always much less than 1%. Fast electron excitation utilized the fl-ray spectrum of s5Kr (Ema= 0.67 MeV) after passage through two stainless-steel windows, each of 0.005-cm thickness. The fluorescence from cis-decalin and trans-decalin was monitored at 235 nm whereas for all other liquids, bicyclohexyl, decalin (mixed isomers), and cyclohexane, measurement was at 230 nm. The b$ckground intensity, which consists almost exclusively of Cerenkov radiation, was determined by using a solution of perfluorodecalin in isooctane (which itself is negligibly fluorescent).' To correct this for the effect on the Cerenkov intensity of differences between isooctane and the other liquids in refractive index and electron density, we also measured the luminescence intensity of all liquids at wavelengths sufficiently long (A > 325 nm) to ensure that only Cerenkov light (and not molecular fluorescence) was being radiated. Contribution from stray fluorescent light (and its second-order grating reflection) was removed by an appropriate cutoff filter at 300 nm. The ratios of intensities of luminescence from bicyclohexyl, decalin (cis, trans, and mixed isomers), and cyclohexaneto that of isooctane were thus determined to be 1.2, 1.2, and 1.0 for X ranging from ~ 3 2 to 5 475 nm. Over this range, the refractive indices of the liquids are essentially constant at ~ 1 . 4 (bicyclohexyl), 9 1.49 (decalin), 1.44 (cyclohexane), and 1.40 (isooctane) whereas, at the wavelengths where the fluorescence was monitored (230-235 nm), the refractive indices are significantly increased to 1.55 (bicyclohexyl), 1.55 (decalins), 1.4g5 (cyclohexane), and 1.46 To correct the relative
Experimental Section The equipment employed for measurement of the fluorescence has been previously described.'~~?~ Experiments involving optical excitation utilized the 165-nm line from a microwave discharge through CO. At this wavelength, the absorption is almost exclusively by the solvent even in the presence of the highest concentration of per-
(1) Walter, L.; Hirayama, F.; Lipsky, S. Int. J . Radiat. Phys. Chem. 1976, 8, 237.
'Lando Research Fellow, summer 1982.
(2) Choi, H. T.; Wu, K. C.; Lipsky, S. Znt. J. Radiat. Phys. Chem., in Dress. (3) Warman, J. M.; Asmus, K.-D.; Schuler, R. H. Adu. Chem. Ser. 1968, No. 82, 25. (4) Warman, J. M.; Asmus, K.-D.; Schuler, R. H. J . Phys. Chem. 1969, 7 .. -7,.931 - - -. (5) Choi, H. T.; Lipsky, S. J. Phys. Chem. 1981, 85, 4089. (6)Walter, L.; Lipsky, S. Int. J. Radiat. Phys. Chem. 1975, 7, 175. (7) Rothman, W.; Hirayama, F.; Lipsky, S. J. Chem. Phys. 1973,58, 1300.
0 1983 American Chemical Society
1584
Choi et al.
The Journal of Physical Chemistry, Vol. 87,No. 9, 7983
Cerenkov intensities at the long wavelengths to those at the monitoring wavelengths, the following procedure was employed. For a particle moving with velocity pc for a distpce, dr, in a medium of refractive index n,the number of Cerenkov photons radiated with frequency between w and w + dw is simply proportional to (1- l/(n2P2))dx dw.12 We now replace dx in this expression by mc2 /3 d@(dx/dE)/(l/32)3/2where E (=mc2/(1- p2)1/2)is the particle energy and dE/dx(the stopping power) equals -[2re4/mc2P2)]p;B(p) (where pz is the electron density and B(P) is a slowly varying function of @)13 and integrate over p from /3 = Po (its value at x = 0) to p = l / n with B(P) out of the integral. This gives the number of photons radiated into dw to be proportional to dw[(l - pO2)lI2+ (1- l / n 2 ) / ( l - po2)1/2 2(1- l/n2)’/3. Thus, the wavelength dependence of the intensity of Cerenkov light is obtained by now integrating this expression over that portion of the @ray spectrum that enters thtsample cell with a value of Po that exceeds l / n (i.e., the Cerenkov cutoff). This spectrum was deduced by using the Fermi di~tribution’~ shifted to lower values of Po by the amount of energy dissipated by each electron in its passage through 0.01 cm of stainless steel. This energy loss was calculated by integration and iteration of the stopping-power equation. The major assumption required by this procedure is that the energy lost in the stainless steel does not generate an appreciable number of secondary electrons with values of Po in excess of l / n (or, equivalently, for n < 1.55, with energy in excess of ~ 0 . 1 6MeV). As some measure of the validity of this procedure we find that the resultant electron energy spegtrum predicts reasonably well the spectral distribution of Cerenkov light from neat isooctane (from 400 to 225 nm). Applying it to our experimental ratios at long wavelengths, we calculate that, at the wavelength-at which the fluorescence was monitored, the ratios of Cerenkov intensity from bicyclohexyl, decalin, and cyclohexane to that of isooctane are all about 1.0 f 0.1. Thus, we require, at most, a 10% correction on the background intensity as measured with isooctane. In the case of bicyclohexyl and the decalin liquids, such a correction is of small influence since even the most strongly quenched solutions studied had fluorescence intensities about 2-3 times higher than that of isooctane and accordingly the correction is not expected to exceed 5% (for the highest cq) and to be less than 1% for the unquenched liquid. For the case of cyclohexane, however, a 10% correction would have a large effect, even on the unquenched liquid, since the intensity from neat cyclohexane is only about twice higher than that from isooctane. Therefore, for cyclohexanewe have used instead the following procedure for determining background. The luminescence intensity of isooctane at 230 nm was measured as a function of cq. The intensity declined linearly by about 8% at 0.2 M due to both increasing (8) These refractive indices were scaled to shorter wavelengths from their Na D values9 by using the reported wavelength dependence of the refractive index of n-hexane.1° The value for cyclohexane obtained via this procedure agrees (to the required accuracy) with that reported earlier by Sowers, Arakawa and Birkhoff.” (9) Riddick, J. A.; Bunger, W. B. “Organic Solvents”: Wiley-Interscience: New York, 1970; pp 77-105. (10) MacRae, R. A,; Arakawa, E. T.; Williams, M. W. J. Chem. Eng. Datn 1978, 23, 189. (11) Sowers, B. L.; Arakawa, E. T.; Birkhoff, R. D. J . Chem. Phys. 1971,54, 2319. (12) Jelley, J. V.“CerenkovRadiation and Its Applications”;Pergamon Press: New York. 1958: Chauter 2. (13) Bethe, H.A.;Askin, J.*In“Experimental Nuclear Physics“; SegrS, E., Ed.; Wiley: New York, 1953; Vol. I, part 11. (14)Fermi, E. “Nuclear Physics”, revised edition; University of Chicago Press: Chicago, 1950; Chapter IV.
61 I.
II
z . , - n-1.0
Flgure 1. Dependence of the experimental fluorescence ratio, Q, for bicyclohexylon perfluorodecalin concentration, cq,raised to the power 0.5 (A), 0.7 (B), and 1.0 (C). To convert the abscissas to c q n they , must be divided by the indicated scale factors N(n). ,The solid line for n = 0.7 (B) is the linear least-squares fit of Q to The solid lines for n = 0.5 (A) and n = 1.0 (C) are simply drawn smoothly through the indicated experimental data points.
~2.’.
3.
Q
2.
I.
2.
1.
0
.01
C:xN[nl
.02
,E
.04
(M”1
Flgure 2. Dependence of the experimental fluorescence ratio, 0 ,for decalin (mixed isomers) on perfluorodecalin concentration, c q, raised to the power 0.5 (A), 0.7 (B), and 1.0 (C). See caption of Figure 1.
electron density and decreasing refractive index. These intensities were then subtracted from those of the cyclohexane solutions, the differences plotted vs. cy1,and found to be concave upward. Assuming that there are no inflections between cq-l = 0 and c;l equal to its smallest experimental value (5 M-l) a linear extrapolation shows that the difference between the Cerenkov intensity from cyclohexane and that from isooctane must be in the interval from 1.5% to 2.2% of the isooctane intensity. A value of 1.9% was arbitrarily chosen and additionally subtracted from every cyclohexane solution. Spectroquality cyclohexane, isooctane, bicyclohexyl, and decalin were purified by repeated percolation through activated silica gel. Perfluoro-n-hexane (kindly donated to us by the 3M Co.), perfluorodecalin (Aldrich), and carbon tetrachloride (Fisher, spectroquality) were used
The Journal of Physical Chemistry, Vol. 87, No. 9, 1983 1585
Geminate-Ion Recombination Fluorescence 5.0
-----
2.5
5 . 0 " ! i i ~ I !
i
!
i
~
~
b
~
n = .7
Q
n = .7 2.
N= ,397
5.0
N=1.00
0
.01
.02
C:xN[nl
.03
[Vn
N~1.00
.04
I
Flgure 3. Dependence of the experimental fluorescence ratio, 0,for decalin (cis isomer) on perfluorodecalin concentration, cqraised to the power 0.5 (A), 0.7 (E), and 1.0 (C). See caption of Figure 1.
Figure 5. Dependence of the experimental fluorescence ratio, 0 ,for cyclohexane on perfiuorodecalinconcentration, cq,raised to the power 0.5 (A), 0.7 (B), and 1.0 (C). See caption of Figure 1
TABLE I: Least Squares Parameters A and B Obtained by ) ) A t BcqO.'for Perfluorodecalin Fitting Q ( = G & / ( G G ~to Quenching the Fluorescence of Some Saturated Hydrocarbon Liquids liquid A B, M-0.7
bicyclohexyl decalin (mixed isomers) cis-decalin
trans-decalin cyclohexane
Flgure 4. Dependence of the experimental fluorescence ratio, 0 ,for decalin (trans isomer) on perfluorodecalin concentration, c q, raised to the power 0.5 [A), 0.7 (B), and 1.0 (C). See caption of Figure 1.
without additional purification. All solvents were carefully deaerated by extensive purging with dry nitrogen and all solutions were prepared under nitrogen atmosphere.
Results We define Go/G and 40/4 to be the ratio of fluorescence intensity without quencher to that with quencher for excitation with fast electrons and 165-nm light, respectively. The ratio of these, i.e., Q E Go$/(G40) is shown plotted vs. cqn for n = 0.5,0.7, and 1.0 for bicyclohexyl, decalin (mixed isomers), cis-decalin, trans-decalin, and cyclohexane in Figures 1-5. As is apparent from these plots, Q can be well represented by a linear function on cq07 but not on cq1f2 nor on cq itself. The solid lines shown in each of the B figures is a nonweighted least-squares fit of Q to A + Bc 0.7. Attempts to fit Q to a linear regression on cqO6 or were always noticeably less successful than the n = 0.7 regression. The least-squares parameters A and B together with their 95% confidence intervals are listed in
~2%
i 0.01 1.01 i 0.02 0.96 f 0.02 0.97 f 0.02 1.00 f 0.02
0.99
18.8 19.6 29.2
+ 0.3 t 2
0.4 0.4
1 7 . 1 t 0.3 25.4
i
0.5
Table I. With the exception of cyclohexane, the maximum perfluorodecalin concentration employed was determined by solubility restrictions. For cyclohexane, a somewhat lower concentration (i.e., 0.0248 M) was used, since, at higher concent_rations,the emission intensity approaches too closely the Cerenkov background to make reliable their differences. Nevertheless, for all five liquids, their Q values, at the maximum concentrations, were all about the same ( ~ 3 - 4 ) . For bicyclohexyl, @o/4was found to be linear on cq over the entire range studied whereas for all other liquids, d0/4 vs. cq, although reasonably linear below cq = low3M, was concave upward thereaftere5 The limiting Stern-Volmer slopes of @o/4- 1vs. cq as cq 0 were found to be 33,38, 16, 48, and 54 M-l for bicyclohexyl, decalin (mixed isomers), cis-decalin, trans-decalin, and cyclohexane, respectively. The large disparity in the Stern-Volmer constant between cis- and trans-decalin is consistent with the longer lifetime15 and lower viscosityg of the trans isomer. For bicyclohexyl, at all cq, and for the other liquids at cq < M, Q was evaluated by using for $o/4 its value determined from the appropriate linear least-squares regression.
-
Discussion
A complete solution to the time-dependent Smoluchowski equation with a Coulomb potential, obtained recently by Hong and Noo1andi,l6 provides an analytic expression for the probability, F ( r , t ) , that two charged (15) Kataumura, Y.;Tabata, Y.; Tagawa, S. Radiat. Phys. Chem. 1982, 19, 267.
(16) Hong, K. M.;Noolandi, J. J. Chem. Phys. 1978,68,5163.
1586
The Journal of Physical Chemistty, Voi. 87, No. 9, 1983
Choi et al.
particles moving diffusively in their mutual Coulomb field will remain unrecombined at time t if initially separated by a distance r. By taking a Laplace time transform of F(r,t),Friauf, Noolandi, and Hong,17have developed an analytic expression for the probability, gsc(r,cq!, that one of the particles will ultimately be scavenged (in infinite time) by an arbitrary concentration, cq, of some homogeneously distributed scavenger. In Figure 1of their paper,17 they display the dependence of g,, on a dimensionless concentration variable s (k,r,2/4D)cq (where k, is the bimolecular rate constant for reaction of the scavenger with the particle, D is the particle’s diffusion constant, and r, is the Onsager radius) for various values of r ranging from 0.05rCto 2.5rC. These datal8 may be utilized to obtain a theoretical prediction of the dependence of the fluorescence parameter, Q, on the concentration of scavenger. To do this we have followed the procedure that is outlined below. As a radial probability density, f ( r ) ,for initial separation distances r , we have chosen
f ( r ) = (P3/2)e-Or
(1)
n
c
3.
, ,
n.1.0 , ,
2.
N-1.00
m. Of course, too, the disparity may merely be an indication of some inadequacy in our choice of f ( r ) . As this distribution is made more spatially compact, but maintained at the same pes!,Qtheor (eq 7 will tend to become more concave upward in its dependence on cqn and will require an increasingly large value of n to linearize. For example, we find, for a Gaussian radial probability density, i.e.
f(r) =
(4y3/&2)e9+
(8)
with yr, = 3.59 (which gives pee, = 0.0535), that a plot of Qtheorvs. is noticeably more linear (up to Qtheor= 2.9 with least-squares slope of 0.167 f 0.002 and intercept of 1.00 f 0.01) than the corresponding plot in Figure 6B using the exponential probability density with or, = 10 (which also gives pea,= 0.0535). From the connection between the dimensionless variable s and the scavenger concentration cq, it is clear that B‘ (=dQtheor/d~0.7) is related to B ( = d Q / d ~ , 0 .via ~) B = B’(k~,2/4D)~.~
(9)
Some measure of the validity of this relation is established by replacing k , / D by 4rRs (i.e., the diffusion-limited Smoluchowski rate) where R, is the contact distance at which reaction occurs with unit probability, i.e. B = B’(rR,rc2)0.7
(10)
Using this equation, one can estimate a value of R, from B and B! Taking Gfi = 0.15 for cyclohexanez4and assuming a total ion yield GT N 4,24gives an escape probability of -0.038 and from this can be calculated a value of B’ 0.09. With B = 25 M4.7 for cyclohexane (see Table I), eq 10 thus predicts that R, N 20 A. This value may be inflated somewhat due to the underestimation of k, by use of the Smoluchowski rate (which neglects the transient effects) or due to use of the exponential distribution (which (22) Lee, K.; Lipsky, S. J.Phys. Chem. 1982, 86, 1985. (23) Hummel, A. Adu. Radiat. Chem. 1973, 4 , 1. (24) Allen, A. 0. Natl. Stand. Ref. Data Ser. ( U S . , Natl. Bur. Stand.) 1976, No. 57.
1588
Choi et al.
The Journal of Physical Chemistry, Vol. 87, No. 9, 1983
,125
,100
3
,025
,050 [
,075
MO" I
Figure 10. Dependence of Rc:' on c C 7 for perfluorodecalin quenching of bcyclohexylfluorescence. The d i d line is a nonwelghted linear least-squares fit of Rc:' to c:'. The vertical bar associated with each experimental data point is the uncertainty in Rc,o.7 for a 2% Uncertainty in 0.
may be too spatially diffuse), but it is clearly of the right order of magnitude since, already, a value of 14 %, has been reported for interaction of perfluorodecalin with the lowest Rydberg state of c y ~ l o h e x a n e . ~For , ~ ~bicyclohexyl and for the decalins, values of Gfi are not reliably known but are probably not too disparate from that of cyclohexane. Accordingly, with the values of B listed in Table I, we would expect for these liquids similarly large values of R,. We return now to eq 6 and the assumption that 6 = 1. By a simple rearrangement, eq 6 can be written as R = 1/(6pt)
(11)
where R = Q/(Q - 1). Equation 11has the virtue that, if pt can be represented by Pt =
(CYCq)n/[l
+ (acJn1
(12)
then 6 is obtainable from the slope of the linear regression of Rcqnon cqn. For perfluoro-n-hexane as scavenger, we have previously reported2 that, over a relatively large concentration range, eq 12 works well with n = 1 (but not n = 0.5) and give 6 N 0.7-0.9. Although concave downward behavior of Rc, on c, was noted at low cq (e.g., 50.01 M in cyclohexane), the reliability of our data in this regime was generally considered too low for quantitative analysis.2 Indeed the present investigation, using the more effective scavenger, perfluorodecalin, was undertaken initially to more thoroughly investigate the form of pt at low c,. As we now realize from the theoretical results of Noolandi and c o - ~ o r k e r s , ~eq ~ J 1' 2 with n 0.7 generates a reasonably accurate representation of pt for the solutions that we have studied. Accordingly, 6 should be most logically extracted from a linear regression of Rc,~.'vs. c,0,'. An example of such a plot is shown in Figure 10 for bicyclohexyl. The fit is reasonably good from c9 N 3 X M to cq N 3 X M. The uncertainty bars indicate the sensitivity of Rc?' to an assumed 2% error in Q. The solid line shown in Figure 10 is a nonweighted least-squares fit with a slope and 95% confidence interval of 0.96 f 0.06. Similar plots for the other liquids covering about the same concentration range give slopes of 1.00 f 0.07 (decalin, mixed isomers), 0.91 f 0.05 (cis-decalin), 0.92 f 0.06 ( 2 5 ) Luthjens, L. H.; Codee, H. D. K.; DeLeng, H. C.; Hummel, A. Chem. Phys. Lett. 1981, 79,444.
J
Figure 11. Theoretical scavenging probability,p i , vs. s ' I 2 for o r , = 10 (A), or, = 15 (B),and pr, = 20 (C). The solid lines are extensions of the limiting slopes of p vs. s ' I 2 at s ' I 2 = 0.
(trans-decalin), and 0.99 f 0.05 (cyclohexane). Thus, we conclude that almost all solvents S1 states derive from ionic recombinations. Finally, we wish to comment briefly on the question, raised in a previous paper,2 as to whether or not there exists any significant difference between pt as determined by fluorescence quenching experiments (i.e., eq 12 with n = 0.7) and pt as determined via chemical scavenging over the same concentration range. In the latter case, Warman, Asmus, and Schuler3v4have concluded that, for a wide variety of chemical scavengers, the yield of some product of the scavenging reaction, G(P), can be represented as G(P) = Gfi + G,ipt
(13)
where Gfi and Ggi are free-ion and geminate-ion yields, respectively, and pt is given by eq 12 with n = 0.5. However, from the approximate magnitude of the parameters Gfi, Ggi, and CY which are required to fit G(P) over the concentration range usually studied ( = ~ l o - ~ - l O - ' M),3,4it can be shown that the quality of the fit with n = 0.5 depends significantly on the choice of Gfiand that to maintain a good fit as Gfiincreases requires generally that n be increased. Thus, for example, in the case of measurement of G(CH4)from CH&1 scavenging of electrons in cyclohexane, about equally good fits of eq 1 2 and 13 to G(P)26 can be obtained with n = 0.5 and Gfi = 0.12 as with n = 0.7 and Gfi = 0.19.24 The value of 0.12 was obtained by Warman, Asmus, and Schuler3s4from a low-concentration linear extrapolation of G(P)vs. c1i2. Although there is little doubt that pt will indeed approach c1f2as c 0,27328 this limiting form of pt is only expected to be achieved at concentrations very much inferior to the lowest concentrations usually studied. This point has been recently emphasized by Ende, Nyikos, Warman, and Hummela and was already implicit in the theoretical calculations of M ~ z u m d e r ,of ~ ' Magee and Taylor,29and, more recently, of Tachiya30and of Noolandi and c o - ~ o r k e r s . ~Indeed ~J~
-
(26) Using numerical data from ref 3 and 4 kindly supplied to us by Professor R. H. Schuler. (27) Mozumder, A. J . Chem. Phys. 1971,55, 3020. (28) van de Ende, C. A. M.; Nyikos, L.; Warman, J. M.; Hummel, A. Radiat. Phys. Chem. 1980, 15, 273. (29) Magee, J. L.; Taylor, A. B. J . Chem. Phys. 1972,56, 3061 (note misprint in eq 41 discussed by Tachiya30).
J. P h p . Chem. 1983, 87, 1589-1590
from our treatment of the results of Friauf, Noolandi, and Hong,17J8we find there to be already a 10% deviation of pt (for @rc= 15) from ita c~/: limiting behavior at s N 0.06, corresponding (with R rr, 20 A) to a c of -2 X M. This is illustrated in Figure 11, which &owLpt (=[h,(c ) - h,(0)1/[1- h,(0)1, from eq 4 plotted v8. s1/2 ( = ( T R ~ ? C ~ ) Q ~ for various values of pr,. Clearly, for liquids with Pr, 2 10 (i.e., pest 5 0.054), Gn cannot properly be obtained by cq1/2 extrapolations that utilize concentrations with cq 2 2 x 10-5 M. In the case of cyclohexane, application of the clearingfield method has yielded values for Ga of 0.15 and 0.19.% Although both of these values are indeed larger than 0.12 (as expected from the upward concavity exhibited in Figure ll),they are too disparate for reliable estimation of n in eq 12 and 13. For the other liquids, either clearing-field values of Gn are not reliably known (e.g., bicyclohexyl and decalin) or when they are (as in the case of n-hexane and i s o o ~ t a n e their ) ~ ~ comparison with reported values of Gn from cq1l2extrapolations is obscured by the large variations in these extrapolations from one scavenger to the next.24 Thus, the question of whether there is indeed any difference in the forms of pt for fluorescence quenching and for chemical scavenging still (30) Tachiya, M. J. Chem. Phys. 1978,70,238 (note misprint in eq 38 which should read a2 = -(5/36 - 7/6)].
1589
cannot be answered unequivocally. The good agreement that we find between the theoretically expected form of pt and that observed in fluorescence quenching (at least with perfluordecalin) makes it difficult to understand how the chemical scavenging results could be so different especially since the conditions for validity of the approximations in the theory are not expected to be more seriously violated for the chemical process (at least not in the direction required). Clearly the resolution of this problem would be assisted by a more definitive analysis of the concentration dependence of G(P) in some solvent for which there exists a reliable value of Gn. Acknowledgment. This research was supported in part by the US.Department of Energy, Division of Chemical Sciences, Office of Basic Energy Sciences. We are also very grateful to Mr. Kaidee Lee for his helpful comments and Mr. David B. Johnston and Ms. Diane Szaflarski for their technical assistance. Finally, we wish to acknowledge our gratitude to Dr. J. Noolandi for sending us tables of numerical values of g,, (r,c),to Professor R. H. Schuler for sending us the numerical values of G(CH4)for CH3Br and CH3Cl scavenging of electrons in cyclohexane, and to Professor A. Hummel for a stimulating correspondence. Registry No. Bicyclohexyl,92-51-3;decalin, 91-17-8;cis-decalin, 493-01-6;trans-decalin, 493-02-7;cyclohexane, 110-82-7; perfluorodecalin, 306-94-5.
Molecular Complexes. 6.' The Nuclear Magnetic Resonance Shift Difference Method and General Aspects in the Nuclear Magnetic Resonance Evaluation of Formation Constants of Weak Complexes As Exemplified by Some Benzene Complexest WlHrled Lamberty, Helmut Stamm, and Jiirgen Stafe Pharmazeutisch-Chemisches Institut der Universkiit HekMberg, I m Neuenheimer FeM 364, P6900 Heidelberg, federal Republic of Germany (Received: March 26, 1982; In final form: December 2, 1982)
The application of additional unspecific shielding (AUS) corrections during the evaluation of formation constants, K , of complexes is discussed for different methods used in referencing chemical shifts. The AUS effect may be nonlinear. Formation constants for the benzene complexes of p-nitrobenzaldehyde (NBA) and p-dinitrobenzene (DNB) are determined. The three proton signals of NBA provide the same K. The known AUS coefficients u2 are compared and analyzed. A partial AUS effect is described which lowers the AUS coefficient u2. By this particular AUS effect the aromatic a2 of DNB is distinctly smaller than u2of the structurally very similar aromatic NBA protons. The newly described shift difference method allows AUS corrections independent of the kind of shift referencing. Some applications of this method show that it can provide good results, if the measurements are accurate and employ a good range of saturation fraction and if the complex shift or its equivalent is distinctly different from zero. The strongly disturbing influence of large errors and low saturation fractions is demonstrated.
Introduction and General Aspects Determination of the equilibrium quotient K for the reaction A+DeAD by the NMR chemical shift is a standard method in this field, particularly if the donor is aromatic. The chemical shift Aobsd.iof an acceptor signal is measured in a series of 'Dedicated to Professor Milton Tamres on the occasion of his 60th birthday. 0022-3654/8312087-1589$0 1.5010
solutions i which contain a varying total (free and complexed) donor concentration [Doliand an (advantageously constant) total acceptor concentration [A,,]. These shifts are determined relative to the acceptor signal of a solution in which [Doliis zero (Le., relative to the signal of the free acceptor). Data reduction according to the linear equation 1, which is the Scatchard-Foster-Fyfe (ScFF) method,2
(1) H. Stamm and J. Stafe, 2.Naturforsch. B , 36, 1619 (1981),in English.
0 1983 American Chemical Society
