NOTES
3374 20,'O was measured as 46.6 Hz and was conveniently independent of temperature. The rate constants for internal rotation are set out in Table I which also lists the kinetic parameters extracted from the Arrhenius plot (Figure 1) in the usual manner.*t3 Selected line shape fits are presented in Figure 2, where the continuous lines are computed line shapes and the data points from normalized experimental spectra are superimposed. The average spectral intensity deviation in all the line shape fits was less than 1.8%. In the table the value of AX* is satisfactorily close to zero. The contribution in simple amides of structure I b which represents the 7r character of the C-N bond in the ground state is larger for thioamides than for amides because of the less efficient overlap of S 3p and C 2p orbitals.
x=o,s
Ib
la
The expected trend in urea compounds is analogous, but here the overall barrier is further lowered because of the sharing of 7r character between two C-N bonds, as shown by structures IIb and c. X =O,S,Se 0
X
X
I1a
Ilb
IIC
The previous study of thioureas was performed using coalescence temperatures in unsymmetrical ureas6 and possibly on reexamination some downward adjustment of AG* = 14 kcal mol-l would be expected.
Hologram Interferometry for Isothermal
Diffusion Measurements
by Julius G. Becsey," Nathaniel R. Jackson, and James A. Bierlein Aerospace Research Laboratories, Wright-Patterson A i r Force Base, Ohio 464SS (Received March 18, 1971) Publication costs assisted by the Aerospace Research Laboratories
I n this paper we report the use of hologram interferometryl for the study of isothermal diffusion from a boundary. The principal advantage of the method, aside from the simplicity of the optics, is that there is T h e Journal of Physical Chemistry, Vol. 76, N o . 81, 1971
no need for optical-quality windows in the diffusion cell. Since the base hologram can be taken with the cell filled with a homogeneous solution, the real-time interferogram is formed between the reconstructed homogeneous cell image and the cell image with the diffusion in progress. Thus, all contributions due to optical retardation in the test zone are nulled out except those produced by the diffusion process. Traditional interferometric techniques such as R a ~ l e i g h , ~Nach-~ Zehnder,5 and wave-front shearing6-" do not possess this valuable characteristic. Our finite fringe hologram interferometer is essentially the same as described b e f ~ r e ' ~with * l ~ the exception of the laser (in this work we used a 15-mW CW He/Ne laser), collimator lenses (f.1. = 36 cm), recording camera (35-mm model, f.1. = 135 mm), and base hologram plate holder. To eliminate inevitable shrinkage due to atmospheric humidity changes, a wet-gate plate holder was used (Jodon Engineering Associates) which affords excellent fringe stability over long periods. The base holograms were recorded on Agfa Scientia 8E75 and 10E75 plates (about '/IO to 1/50-sec exposures). The real-time interferograms were recorded on Kodak Pan-X film (about 1/500-sec exposures). To minimize the skewness of the interferograms due to higher order aberrations in the cell, the recording camera was focused at a plane located within the cell at one-third of the cell length measured from the exit window. l 4 The magnification of the recording camera was also determined at this plane. The measurements were taken in a flowing-junction cell5 about 8 cm high, length 7.95 cm, width 0.8 cm. The beam deflector was adjusted so that five finite fringes appeared in the image of the cell. To interpret the finite fringe interferograms, we need to know the optical path P in a free-diffusion cell at any distance 2 measured upward from the initial boundary (eq 1). (1) L. 0. Heflinger, R. F. Wuerker, and R. E. Brooks, J . A p p l . Phys., 37, 642 (1966). (2) J. StL. Philpot and G. H. Cook, Reoearch (London), 1, 234 (1948). (3) L. G. Longsworth, J . A m e r . Chem. SOC.,74, 4155 (1952). (4) H. Svensson, Acta Chem. Scand., 4, 399, 1329 (1950); 5, 72, 1301 (1951). (5) C. S. Caldwell, J. R. Hall, and A. L. Babb, Rea. Sci. Instrum., 28, 816 (1957). (6) E. J. Ingelstam, J . Opt. Soc. Amer., 47, 536 (1957). (7) 0. Bryngdahl, Acta Chem. Scand., 11, 1017 (1957). (8) 0. Bryngdahl and S. J. Ljunggren, J . P h y s . Chem., 64, 1264 (1962). (9) 0. Bryngdahl, J . Opt. SOC.Amer., 53, 571 (1963). (10) W. J. Thomas and McK. Nicholl, A p p l . Opt., 4, 823 (1965). (11) C. N. Pepela, B. J. Steel, and P. J. Dunlop, J . Amer. Chem. Soc., 92, 6743 (1970). (12) G. E. Maddux and J. G. Becsey, Re%. Sci. Instrum., 41, 880 (1970). (13) J. G. Becsey, G. E. Maddux, N. R. Jackson, and J. A. Bierlein, J . P h y s . Chem., 74, 1401 (1970). (14) H. Svensson, Opt. Acta, 1, 25 (1954).
NOTES
3375
P(t,s) = L p ( t , x ) = ~p
+ ( L A ~ / z )erf(x/Zv'Di)
Here t is the time since the start of the experiment, L is the geometric length of the cell, p is the instantaneous refractive index a t any vertical distance x, p is the mean of the initial refractive indices of the diffusing solutions, Ap is their difference, and D is the isothermal diffusivity. A fringe number j can be assigned to a selected fringe if one counts (in the direction of decreasing x) the number of the fringes intercepting the continuation of the vertical and straight portion of any fringe until the selected fringe is reached. Since the distance between the adjacent fringes corresponds to a path difference of one wavelength, the fringe number j can be expressed as a function t and x
- P(t,x)/X = (LA~/ZX) [I - e r f ( x / Z a t ) I
I
(1)
i-
lCrn
I.
."
I I
i,mm
00
208
441
673
837
1375
Figure 1. Finite fringe real-time hologrmn interferogram. Aqueous KCI (0.03M )diffusinginto pure water at 25.0'.
j(t,z) e P(t,x + -)/A
=
( L A ~ / Z Xcerf(z/Zv'B) )
(2)
We index each interferogram serially in time by the subscript m = 1,2, etc., and each fringe number on the interferogram by n = 1,2, etc. I n practice it is necessary to introduce a zero-time correction to (applicable to all &,) and a base-line correction E,,, (peculiar to each interferogram) to account for error in locating the straight portion of the fringes. Hence eq 2 becomes
j(trn,zmJ= Ln= (LAd2X) For each interferogram taken a t time t, the value of x+,,,~was measured for each j,,n; the parameters D, to, LAp/ZX, and a set of E , were calculated by the minimization of the function
Figure 2. Wave-front reconstruction by holograms and analysis with wave-front shearing interferometer.
Table I: Isothermal Diffusivities of Vmious Aqueous Solutions at 25.0' Measured by Hologram Inferferometry
where (jca~o&,n is given by eq 3. A grid-search type nonlinear least-squares method was applied in the data reduction process.13 The interferogram obtained during the interdiffusion of water and 0.03 M aqueous KC1 solution are shown in Figure 1. Table I summarizes our results for several different systems. i V is the mean of the initial molal concentrations and AM is the initial concentration difference between the interdiffusing solutions. The errors given are the standard errors of the mean obtained from independent measurements. The zerotime corrections ranged between 0 and 90 sec; the values of B, were of the same magnitude as the average fringe number errors (about 0.08). All measurements were made a t 25.0". The experimental values are in reasonable agreement with other determinations.I8-'* It is also possible to record the entire refractive field in the freedifiusion cell by taking holograms during the diffusion process. If these holograms are reconstrncted by a collimated laser beam (incident from the same angle as the original reference beam), the re-
-D AWe0"B aoluti0n
KCI
Da CdIn a
X I@,cm%eo---
a
AM
This work
0.0150 0.9973 0.4923 0.4674
0.0300 1.9946 0.9845 0.0287
1.872+0.012 2.242i0.014 2.284 + 0.014 0.808 + 0.006
{
References 16 and 17.
Liters t"re
1.876. 2.264L 2.268*
...
Reference 18.
called real object beam can be studied by different optical methods. Figure 2 shows an interferogram obtained from a hologram (0.005 M aqueous KCl/ water at 25.0", t = 10.3 min) with a wave-front shearing Thus, the actual refractive (15)J. G.Beosey, L. Berke, and J. R. C d a n , J . CAm. Edw., 45, 728 (1968). (16) H. S. Hsmed and L. R.Nuttdl, J . Amer. Chem. Soc., 71.1460 (1949). (17)H. S.Hssned and L. R. Nuttdl, ibid., 69, '736 (1947). (18)L. G. Longsworth, J . Phya. C h m . , 54, 1914 (1960). The Jouml of Phwical Chemishy, Vol. 76,N o . 81. 1971
NOTES
3376 index field can be recorded and reconstructed at any time for evaluation by various optical methods chosen at convenience.
Vibrational Deexcitation of Highly Excited Polyatomic Molecules.
T h e Amount of
Energy Transferred per Collision'" by B. S. Rabinovitch,*lb H. F. J. D. Rynbrandt, J. H. Georgakakos, Department of Chemistry, Unisersity of Washington, Seattle, Washington 98106
B. A. Thrush, and R. Atkinson Department of Physical Chemistry, University of Cambridge, Cambridge, CB2 I E P , United Kingdom (Received J u n e I , 1971) Publication costs assisted by the A i r Force Ofice of Scientific Research
The purpose of this note is to clarify the conclusions from some recent studies of collisional energy transfer involving highly vibrationally excited polyatomic molecules. A study of the collisional quenching of vibrationally excited, ground electronic state cycloheptatriene (CHT), and of its deuterated analog CHT-ds, has been reported by Atkinson and Thrush2 (AT). From their treatment of the data, AT concluded that the average amount of energy removed from CHT per collision ((AE)) by various bath gases is (kJ mol-'): CHT, 17.5; toluene, 11.5; SFe, 5.9; COz, 3.8; He, 0.6. These magnitudes agree with earlier estimates based on fluorescence quenching experiments with p-naphthylamine.3 However, they are much smaller than the clown-jump steps reported at room temperature by Kohlmaier and Rabinovitch4 (KR) from chemical activation studies of vibrationally excited see-butyl radicals (kJ mol-'): SFs, 2 3 7 ; C4Hs, 237; COz, 16.7; He, 2 3 . 3 . The values of AT are smaller yet than those deduced for vibrationally excited, cyclopropanes5 chemically activated by methylene radical reaction. Atkinson and Thrush suggested that their results w-ould be better reconciled with those of KR if the latter's values had been incorrectly deduced: they proposed that an error by KR of a factor of 2 in the calculated magnitudes of the decomposition rate constants, JCE, could have led t o an error of more than a factor of 2 in the deduced ( A E ) quantities. In addition, they proposed that while k~ values were known accurately in the cyclopropane work, an incorrect value of AHfO(CH,) had caused an error in the assumed energy and treatment of cyclopropane; with use of the original data, but with a current value of AHfo(CH2),AT presented drastically revised (AE) quantities for the cyclopropane T h e Journal of Physical Chemistry, Vol. 76,N o . 81, 1971
system (kJ mol-'): He, 0.6; Ar, 1.6; Nz, 1.9; C2H4,2.5. The value so obtained for He is in striking agreement with the like quantity for CHT. It is evident that some disagreements in interpretations and conclusions exist between the data treatment and results of the Washington and Cambridge groups. ~ called attention recently to a differSetser, et U I ? . , have ence in interpretation between their recent results on halogenated ethanes and that of AT. We wish here to examine these matters in some depth, albeit with brevity. The data of AT were analyzed by them in terms of Stern-Volmer plots with multistep quenching, and with the assumption that a constant amount of energy was removed from CHT on each collision. We first wish to demonstrate that the discrepancy between the work of the Washington and Cambridge groups is not as large as 1% as originally stated-especially for less efficient bath gases. We have applied the stochastic method of data treatment4r7j8t o the He-CHT data. Theoretical values of JCE were similar to those used previously.2 Two sets of weak collider calculations were made-one for a stepladder, and the other for an exponential distribution of down-transition probabilities. On the basis of a stepladder model, which was employed by AT, the average energy amount transferred per down-step from CHT is 1.9 kJ mol-'. This quantity is three times larger than the original value of AT. The increase is due mainly to the fact that AT (as well as the earlier workers with P-na~hthylamine~) neglected up-transitions; these have a probability relative t o down-transitions which is governed by detailed balance. The correction is smaller for more efficient gases; thus, the original value of 3.8 kJ for Cot is raised t o 5.0 kJ, while the values for toluene and CHT are essentially unchanged. Nonetheless, the values of (AE) found for down-steps for He and COzfrom the CHT work are now only tx-o to three times smaller than those of KR, and any discrepancy is substantially reduced. Some discrepancy still remains and depends, in part, on the relative magnitudes of the collision cross sections used by (1) (a) This work was supported by the Air Force Office of Scientific Research, Directorate of Chemical Sciences, under Contract No. F 44620-70-C-0012; (b) on leave, 1971; (c) on leave from Kingsborough Community College, The City University of New York, City University Research Fellow. (2) R. Atkinson and B. A. Thrush, Proc. Roy. Soc., Ser. A, 316, 131 (1970). (3) M. Boudart and J. T . Dubois, J . Chem. Phys., 23, 223 (1955). (4) G. Kohlmaier and B. S. Rabinovitch, ibad., 38, 1692, 1709 (1963). (5) J. W. Simons, B. S. Rabinovitch, and D. W. Setser, ibid., 41, 800 (1964); D. W. Setser, B. S. Rabinovitch, and J. W. Simons, ib@, 40, 1751 (1964). (6) W.G. Clark, D. W.Setser, and E. E. Siefert, J. P h y s . Chem., 74, 1670 (1970). (7) J. H. Georgakakos, B. S. Rabinovitch, and E. J. McAlduff, J . Chem. Phys., 52, 2143 (1970); J. D. Rynbrandt and B. S. Rabinovitch, J . P h y s . Chern., 74, 1679 (1970). (8) Y . N. Lin and B. S. Rabinovitch, ibid., 72,1726 (1968).
