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95% ethanol as described by Patai and Rappaport.17 The compounds were then repeatedly recrystallized from propanol to give a constant melting point. The INDO program was obtained from the Quantum Chemical Program Exchange (QCPE). Acknowledgment. We are grateful to the National Institute of Health for support of this work. The NIH support was from Grant No. RR-8102 of the Division of Research Resources. We also wish to thank Dr. Ira Goldberg for pointing out to us that the coupling constants reported in ref 8 are in error. G.R.S. is grateful to the sabatical leave host (Stanford University) where part of this report was prepared.
References and Notes (1) B. 8. Corson and R. W. Stoughton, J. Am. Chem. SOC.,5 0 , 2835 (1928). (2) D. H. Finn, M. A. Hogg, and D.Richton, British Patent, 967600 (1964); G. T. White and L. R. Rothstein, US. Patent, 3314835 (1967); P. J. R. Bryant, A. R. Owen, and F. S. Scanes, US. Patent 3391 036 (1968).
For example, see F. E. Stewart and M. Eisner, MOL Phys., 12, 173 (1967). G. N. R. Jones and M. J. Israel, Nature(London),228, 1315 (1970). W. A. Pryor, Chem. Eng. News, 34 (June 7, 1971). N. L. Petrakis, H. R. Bierman, and M. B. Shimkin, Cancer Res., 12, 573 (1952). E. M. Gal, F. H. Fung, and D. M. Greengerg, Cancer Res., 12, 565 (1962). F. J. Smentowski and G. R. Stevenson, J. Phys. Chem., 74,2525 (1970). R. Chang and R. D. Allendoerfer, J Phys Chem., 76, 3384 (1972). P. H. Rieger and G. K. Fraenkel, J. Chem. Phys., 37,2811 (1967). J. A. Pople and D. Beverldge, “Approximate Molecular Orbital Theory”, McGraw-Hill, New York, N.Y., 1971. G. R. Stevenson, A. E. Alegrh, and A. M. Block, J. A n Chem Soc., 97,4859 (1975). G. R. Stevenson, M. Colon, I. Ocasio, J. G. Concepcion, and A. M. Block, J. Phys. Chem., 79, 1685 (1975). L. E. Sutton, Ed., “Tables of Interatomic Distances and Configuration in Molecules and Ions”, The Chemical Society, London, Burlington House, W. l., 1958. M. J. S. Dewar and N. C. Baird, Quantum Chemical Program Exchange, Department of Chemistry, Indiana University, Bloomington, Ind. L. Pauling, “The Nature of the Chemical Bond”, Corneil University Press, Ithica, N.Y., 1960. S. Patai and 2. Rappaport, J. Chem. Soc., 383 (1962).
Efdects of Solvent and Concentration on the Diffusion of Triplet Anthracene R. D. Burkhart Deparfment of Chemistry, University of Nevada, Reno, Nevada 89557 (Received October 28, 1976) Publication costs assisted by the U.S. Energy Research and Development Administration
The delayed fluorescence spectrometer used to measure triplet diffusion by the space intermittency method has been modified to augment the intensity of emission signals and to facilitate data handling by computer methods. As a result a significant improvement in precision has been achieved. Measurements of triplet anthracene diffusion have been carried out in methylcyclohexane and cyclooctane at 25 “C. A decrease in measured diffusion coefficient with increasing concentration has been observed, the effect being greater in the less viscous solvent. At the lowest concentrations used D (in methylcyclohexane) = 2.67(*0.18) X 10” cm2/s and D (in cyclooctane) is 1.42(f0.14) X cmz/s.
ftittdwtion During the past few years several published studies have appeared on the solution-phase or liquid-phase mobility of aromatic Most of these studies utilize annihilation or, P-type, delayed fluorescence to monitor the spatial distribution of triplets following an irradiation pulse which produces triplets in a spatially intermittent array. Noyes and co-workers applied a somewhat similar method to the measurement of free-radical diffusion coefficients.6 Triplet exciton migration in anthracene crystals also was studied using this technique.? Part of our motivation for studying triplet migration is to try to characterize the physical state in which these species exist in solution. It is hoped that this can be accomplished by comparing observed mobilities with those which would be expected either from Stokes-Einstein behavior or from measured mobilities of the corresponding ground state species. An additional motivation is provided by the realization that accurate diffusion data for molecules in fluid media which mimic the characteristics of biological cells can provide very useful information about the hydrodynamics of the cell e n v i r ~ n m e n t . It ~ ,is ~ difficult to apply conventional diffusion techniques in such studies. None of these hoped-for objectives will be realized unless the execution of the experiments can be reduced to a fairly The Journal of Physical Chemistry, Vol. 8 1, No. 4, 1977
simple procedure which is known to give reliable results with good precision. The purpose of this paper is to describe some modifications of the earlier experimental setup, including methods of data handling, which have led to a significant improvement in the precision of diffusion results. In addition, some new data have been obtained on the solvent dependence and concentration dependence of triplet anthracene diffusion which will be useful in characterizing the general properties of the translational motion of triplets in solution.
Experimental Section Both methylcyclohexane and cyclooctane were treated with concentrated H2S04,neutralizing base, and several water washes before being dried and then doubly distilled. The anthracene sample is 99.999% pure material purchased from James Hinton of Columbia, S.C. The optical system is very similar to that previously describedlO with the following modifications. The light source is a Hg-Xe lamp which has a variable power output from about 250 to 1000 W. Patterns consisting of opaque and transluscent strips of equal width are inserted in the light beam and, using the optical system described earlier, the sample is irradiated with a reduced image of these patterns. Since the optical path through the sample is only
Diffusion of Triplet Anthracene
37 1
1 mm, the pattern image stays in focus during its passage through the solution. A major modification of the optical system is that the photomulitplier has been moved into a position which is in-line with the excitation beam rather than at 90”. This has made a considerable improvement in the signal level obtained with very little sacrifice in the stray light level. The excitation light is filtered using a Corning CS 7-60 filter which has a fairly sharp cutoff at 400 nm transmitting only at wavelengths shorter than this. The emission signal is chopped at 30 Hz and is picked up by the photomultiplier after passing through a cutoff filter transmitting above 400 nm. Each delayed fluorescence decay pulse is sent to a Nicolet 1072 multichannel analyzer and, after a signal level sufficient for analysis has been accumulated, the data are punched out on tape and then stored on the computer. Curve fitting procedures are then applied (vide infra) to extract the desired information. All solutions are degassed on a high vacuum system. Enough freeze-pump-thaw cycles are used so that residual gas causes a pressure jump of less than 3 X Torr, as measured on a Penning gauge at the beginning of a pumping stage. The solutions are sealed off under vacuum with the frozen solution open to the vacuum pump during seal off. Solutions prepared in this way gave constant delayed fluorescence lifetimes over periods of many weeks.
Experimental Results In the limit of sufficiently small triplet concentrations such that second-order processes for their removal have a negligible rate compared with first order processes, one may write
a T/a t = $ q ( X ,
t ) + DV’T - T/r
(1)
In this equation & ( x , t ) is the time-dependent and spatially-dependent rate of triplet formation; 4 being the triplet quantum yield and q ( x , t ) being the rate of light absorption. The triplet diffusion coefficient is symbolized by D, 7 is the triplet lifetime, and T i s meant to represent the concentration of triplets. The diffusion term is important because the spatially intermittent formation of triplets leads to delayed fluorescence intensities which are dependent upon diffusion rates. The solutions are irradiated through a pattern consisting of parallel light and dark strips and we symbolize the width of a light plus dark strip, or repeat distance as Xo. In these particular patterns the light and dark strips have equal width so the window-to-period ratio, r, is 0.5. The solution to eq 1for delayed fluorescence decay isL1
@ N ( t=) {exp(-2/3t) + TA1exp[-2(1 + a ’12)P t I} /N(a1
(2)
where a = 2n(Dr)”2/Xo A l = 2 sin- (17rr)/rz7rzL2(l+ l’a’)’
(3) (4)
and
N ( u )= 1 + XAi 1
(5)
In these equations @ = 1 / and ~ d N ( t ) is the delayed fluorescence intensity normalized to unity at t = 0. To measure a diffusion coefficient it is necessary, first of all, to determine the triplet lifetime under conditions of homogeneous illumination. The delayed fluorescence decay is collected by storing several thousand decay events on the multichannel analyzer. The data are transferred to the computer and a weighted least-squares program is
TABLE I: Lifetimes and Diffusion Coefficients of Triplet Anthracene in Two Different Solvents and Different Concentrations at 25 C [ Anthra-
cene], M x 10’ 0.99 2.0 4.9 12.4 0.94 1.89 4.72
T
Solvent Methylcyclohexane Methylcyclohexane Methylcyclohexane Methylcyclohexane Cyclooctane Cyclooctane Cyclooctane
,
ms 8.19 3.22 5.75 3.15 4.81 3.76 1.82
~
D cm’/s x 105 2.67 1.52 1.24
