Communications to the Editor
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chiometric salts. This may partially account for the observed spectral modification. In Figure '7 the molalities of the saturated rare earth perchlorate solutions are shown and the numerical values of these concentrations can be found in Table IV. It should be noted that saturation occurs when approximateain for each rare earth perchlorate unit.
Acknowledgments. The authors would like to thank Mr. J. L. Defer and Dr. A. Habenschuss for assistance with the computer programming, and Mr. L. E. Shiers for preparing the conductivity water and for furnishing the density polynomial fits. Some of the saturated solution analyses were performed by Drs. J. L. Baker and J. P. Walters in the course of their own research. Thanks are due to Dr. J. E. Powell's group for preparing the rare earth oxides and do Mr. P . Palmer for providing the rare earth metals used as EDTA standards. The authors also thank Dr. A. Habenschuss for a critical. reading of the manuscript.
Supplemeniary Material Available. Tables I and 11, listings of the density coefficients and conductance data will appear following these pages in the microfilm edition of this volume OS the journal. Photocopies of the supplementary material from this paper only or microfiche (105 X 148 mm, 24X reduction, negatives) containing all of the supplementary material for the papers in this issue may be obtained from the Journals Department, American Chemical Society, 1155 16th St., N.W., Washington, D. C. 20036. Remit check or money order for $4.00 for photocopy or $2.00 for microfiche, referring to code number JPC-74-1435. This paper is based. in part, on the Ph.D. Dissertation of J. A. Rard, Iowa State University, Ames. Iowa, Feb 1973. F. H. Spedding. P. E. Porter, and J. M. Wright, J. Amer. Chem. Soc., 74, 2781 1.1952). F H. Spedding and G. Atkinson in "The Structure of Electrolytic Solutions," W. J. Hamer, Ed.. Reinhold, New York, N. Y., 1959, Chaoter 22 V . W. Saeger and F. H. Spedding, IS-338, unclassified AEC report, Ames Laboratory. Ames. Iowa, 1960. F. H. Spedding, M. J. Pikal, and B. 0. Ayers, J. Phys. Chem., 70, 2440 (1966)
(6) F. H. Spedding and K. C. Jones, J. Phys. Chem., 70,2450 (1966). (7) J. P, Walters and F. ti. Spedding, IS-1988. unclassified AEC report, Ames Laboratory, Ames. Iowa, 1968. (8) F. H. Spedding, P. E. Porter, and J. M. Wright, J. Amer. Chem. SOC., 74, 2778 (1952). (9) F. H. Spedding and S. Jaffe, J. Amer. Chem. Soc., 76, 884 (1954). (10) F. H. Spedding and J. L. Dye, J , Amer. Chem. Soc.. 76, 879 (1954). (11) F. H. Spedding and M. J. Pikal, J. Phys. Chem., 7 0 , 2430 (1966). (12) W. E. Lewis, J. A. Jackson, J. F. Lemons, and H. Taube, J . Chem. Phys., 36, 694 (1962). (13) L. 0. Morgan. J. Chem. Phys., 38, 2788 (1963) (14) D. G . Karraker, lnorg. Chem., 7, 473 (1968). (15) K. Nakamura and K. Kawamura, Bull. Chem. Scc. Jap., 44, 330 (1971). (16) L. Gutierrez, W . C. Mundy, and F. H. Spedding, d. Chem. Phys., accepted for publication. (17) F. H. Spedding and L. L. Martin, unpublished X-ray diffraction data. (18) A. R . Olson and T.R. Simonson, J. Chem. Phys , ? 7 , 1322 (1949). (19) J. Sutton, Nature (London), 169, 71 (1952). (20) L. J. Heidt and J . Berestecki, J , Amer. Chem. Soc., 77, 2049 (1955). (21) .L H. Sutcliffe and J. R . Weber, Trans. Faraday SOC., 52, 2225 (1956). (22) M. M. Jones, E. A. Jones, D. F. Harmon, and R. T. Semmes, J. Amer. Chem. Scc., 83, 2038 (1961). (23) M. Alei, Jr., Inorg. Chem., 3, 44 (1964). (24) 2. Libus and T. Sadowska, J. Phys. Chem.. 73, 3229 (1969). (25) G . Brink and M. Falk. Can. J . Chem.. 48, 3019 (1970). (26) F. H. Spedding. P. F. Cullen, and A. Habenschuss, J. Phys. Chem., 78, 1106 (1974). (27) P. H. Dike, Rev. Sci. Instrum., 2, 379 (1937). (28) G . Jones and G. M. Bollinger, J. Amer. Chem. SOC., 53, 411 (1931). (29) G. Jones and D. Bollinger, J. Amer. Chem. Soc,, 57,280 (1935). (30) G. Jones and M. J. Prendergast, J. Arrrer Chem. SOC., 59, 731 (1937). Dsrer, D. L. Swan(31) F. H. Spedding, L. E. Shiers, M. A. Brown, J. i. son, and A. Habenschuss, unpublished density data. (32) See paragraph at end of paper regarding supplementary material. (33) F. H. Spedding, J. A. Rard, and V. W, Saeger, J. Chem. Eng. Data, to be submitted for publication. (34) F. H. Spedding, L. E. Shiers. and J. A. Rard, unpublished viscosity data. (35) F. H. Spedding and H. 0. Weber, unpublished activity data. (36) P. Dryjanski and 2. Kecki, Rocz. Chem., 43, 1053 (1969): 44, 1141 (1970). (37) F. M . Spedding, J . A . Rard, H. 0 . Weber, and L. E. Shiers, unpublished activity data. (38) R. A. Robinson and C. K. Lim.J. Chem. Soc.. 1840 (1951). (39) W. H. Beck, J. Caudle, A. K. Covingion, and LV. F. K. WynneJones, Proc. Chem. Soc., (London), 110 (1963). (40) R. G. Bates. "Determination of pH Theory and Practice," 2nd ed, Wiley, New York, N. Y.. 1973. (41) R. A. Robinson and R . H. Stokes, "Electrolyte Solutions," 2nd ed, revised, Butterworths, London, 1965.
ATIONS TO THE EDITOR Dielectric Response by Real Time Analysis of Time Domain Spectroscopy Data Publicat!on costs assisted by lhe Materials Science Program Brown! University with scipoori frcm the National Science Foundation
Sir: Considerable interest has developed recently in use of time domain spectroscopy (TDS) for study of dielectric relaxation processes in the time range 10-7 to sec. One observes reflected or transmitted signals as a function of time after incidence of a voltage pulse on a dielectric The Journal of Physical Chemistry. Vol. 78, No. 14. 1974
sample, but in most methods1 the dielectric response function can be determined only by numerical Fourier analysis and other transformations. An exception is Fellner-Feldegg's thin sample method,2 which yields the derivative of the response function directly, but as van Gemert3 has shown is inaccurate unless the sample thickness and, as a result, the observed signal are very small. We present here some of the results of an analysis which is much less restricted and gives the response function without specific assumptions as to its form by simple numerical methods.
Communicationsto the Editor 20
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L+, P"~I
This result requires only simple numerical integration of R ( t ) and its self convolution to obtain q ( t ) ,and has been found to work very well. As an example, the observed response for a 7%" sample of 1-butanol at 22" is shown as the upper curve in Figure 1, and the two lower curves are the results for ( t , - 1) O ( t ) from the thin sample formula and from the present analysis. Although both the latter are well fitted by Debye functions @ ( t )= (60 - c,)[l - exp(-t/r)], the time constant r from the sec), some uncorrected curve is 720 psec (1 psec = 40% larger than values in the range 500-540 psec from transform analysis and steady-state results. The present analysis gives r = 530 psec in much better agreement. This value is essentially the same as that given by an approximate formula derived by van Gemert assuming Debye relaxation; his formula can be obtained as a special case of eq 3. The static permittivity €0 = 17.2 in the limit t ---* m and the high-frequency value t , = 3.2 from analysis of short time response also agree well with other results. The advantages of the present treatment are that the response function \ P ( t ) can be obtained with satisfactory accuracy for a considerable range of sample thickness and other parameters without specific assumptions about its form and without numerical Fourier transformations. The analysis has been generalized to take account of finite ohmic sample conductivity and finite rise times; similar methods have also been developed for a finite dielectric sample terminating a coaxial line. These will be presented in detail later.
+
0
500
1000
0
500
I000
Figure 1 . Upper graphic shows reflected voltage R ( t ) from a 7.8." sample of I-butanol at 22" for a 240-mV applied step voltage, using a Wewlett-Packard Type 181 TDR system with 40-psec rise time Lower trace shows ( A ) dielectric response function calculated from thin sample formula (integral of eq 2) and ( B ) response function from finite sample formula (eq 3). For a dielectric sample of thickness d placed in a coaxial line terminated in its characteristic impedance, solution of the propagation equations through terms of order dz relates the dielectric response function t, * ( t )to the incident voltage pulse Vo(t) and reflection - R ( t ) , t > 0, bY
+
Acknowledgments. This work was supported by the Brown University Materials Science Program and the National Science Foundation. I am indebted to T. G. Copeland for the computer program for numerical integrations, and to Dr. M. J. C. van Gemert for a copy of his paper3 on analysis of the thin cell method in advance of publicat ion. References and Notes
where c is the speed of propagation in the empty, loss free line and 8 ( t ) is the Dirac delta function for a n instantaneous response e - 1. If R ( t ) is neglected in comparison to Vo(t)and dR(t)/dt compared to c R ( t ) / d , then for a step voltage Vo(t)= Vo, t > 0, one obtains Fellner-Feldegg's first-order result
(1) For a review and further references, see A Suggett in 'Dielectric and Related Molecular Processes," Vol 1, Chemical Society London, 1972, p 100. (2) H. Fellner-Feldegg, J. Phys. Chem., 7 6 , 2116 (1972). (3) M. J. C. van Gemert, J. Chem. Phys., submitted for publication.
Chemistry Department Brown University Providence. Rhode I s l a n d 02912
Robert H. Cole
Received Aprii 1, 1974
The observed response can only approximate the impulse ( e m - 1)6(t) at short times because of the finite reflection tiine 2dd7Jc in the sample, but more serious a t longer times is the error from assuming that the sample voltage is Vo(t) rather than Vo(t) - R ( t ) . For a considerable range of sample lengths and other parameters, this error can be satisfactorily corrected by using eq 2 as an approximation In the correction term of eq 1. For a step voltage, this gives on integration
Comments on the Paper, "Flash Photolysis of Aromatic Sulfur Molecules," by F. C. Thyrion Publication costs assisted by the American Cyanamid Company
Sir: In his above-mentioned paper,l Thyrion reports transient absorptions with maxima around 300 nm upon flash photolysis of aromatic thiols, disulfides, and sulfoxides in ethanol and cyclohexane solutions. The author correctly assigns these transients to RS. radicals. He fails to mention, however, that similar results The Journal of Physical Chemistry. Voi. 78, No 74. 1974
