4040
TSUNETAKE FUJIYAMA AND BRYCE CRAWFORD, JR.
Vibrational Intensities.
XX.
Band Shapes of Some Fundamentals of Methyl Iodide-d, by Tsunetake Fujiyama and Bryce Crawford, Jr. Molecular Spectroscopy Laboratoru, Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 664666 (Received Nocember 13, 1968)
The refractive index, n, and extinction coefficient, k , have been measured by ATR techniques for the v g and vfl bands of CDJ, at 492 and 656 cm-’, respectively. The band-shape and intensity data are examined both in comparison with simple “collision-damped” models, and through the correlation-functionapproach, comparison being made with the corresponding branch of CHJ. The perpendicular band V6 of CHJ shows noticeable effects of inertial rotation; the other three bands show little, if any, such effects. A rather full discussion is given of the reliability of correlation functionsas calculated from spectroscopic data.
Introduction One of the more challenging problems in vibration spectroscopy is the measurement of absolute intensities of absorption bands and the understanding of band shapes in liquids. We have found attenuated total reflection (ATR) spectroscopy advantageous since we can by this method measure the absolute intensity of bands in the condensed phase without introducing certain kinds of systematic error such as the base-line correction and the effects of refractive index. The wing correction, however, is still a very important problem that remains to be solved; in this connection it would be valuable if we could establish some reasonable intensity distribution function as one which reproduces the shape of the absorption band. Recently, some authors have discussed absorption band shapes from the viewpoint of molecular motion in the liquid phase, and this seems to us a promising method of considering the problem quantitatively. In the present report we extend to the v3 and V6 bands of heavy methyl iodide the recent similar study on normal methyl iodide.‘ Our main interest is to decide whether and under what circumstances it is reasonable to use the Lorentzian function as a fairly general experimental function of the band shape. We also seek to derive quantitative information about the molecular motion itself from the band shape.
Determination of Optical Constants Experimental Conditions. The ATR spectrum of liquid methyl iodide-& was observed, using the spectrometer constructed in this laboratory2 for two fundamental bands, one the perpendicular e-type fundamental V6 a t 656 cm-l, and the other the a1 parallel fundamental v3 at 492 cm-’. These two bands were chosen because they are fairly well isolated from other bands and because the results obtained are directly comparable with the earlier results of methyl iodide.’ The spectrometer was used at a resolution of 3-5 cm-l at a temperature of about 27”. T h e Journal of Physical Chemistry
The optical constants for these two bands were obtained from the ATR spectrum by a slightly improved version of the techniques previously described, and the results obtained are given in Tables I and 11. The reliability of the optical constants is checked using the n(v’) is the refractive Kramer-Kronig e q ~ a t i o nwhere ,~ n(v’) - n’ = -
(1)
index at wave number v’ and n’ is the contribution to the refractive index arising from transitions other than those under consideration here. The refractive indices calculated from the equation agree with the observed ones within the standard estimates of error, a ( n ) , which are also given in Tables I and 11. Reduction to $‘True’’ B a n d Shape. In order to obtain parameters more amenable to theoretical interpretation, the effect of the dielectric field was eliminated by transforming the optical constant fi into the local SUSceptibility
e = C’ + iC”
(2)
using the Lorentz-Lorenz field.5 The imaginary part of the local susceptibility C”, after scaling, may be thought of as a f‘true” extinction coefficient, k0,6,7where IC,
=
2n4J”
(3)
To demonstrate the effect of the dielectric field on the (1) C. F. Favelukes, A. A. Clifford, and B. Crawford, Jr., J . Phya. Chem., 72, 962 (1968). (2) A. C. Gilby, J. Burr, Jr., and B. Crawford, Jr., ibid., 70, 1520
(1966). (3) A. C. Gilby, J. Burr, Jr., W. Krueger, and B. Crawford, Jr., ibid., 70, 1625 (1966). (4) For instance, W. K. H. Panofsky and M. Phillips, “Classical Electricity and Magnetism,” 2nd ed, Addison-Wesley, Reading, Mass., 1962. (5) A. A. Clifford and B. Crawford, Jr., J . Phys. Chem., 70, 1536 (1966). (6) N. G. Bakhshiev, 0. P. Girin, and V. S . Libov, Opt. Speclroac. (USSR) (EnglishTransl.), 15,225,336,395 (1963) ; 16,549 (1964). (7) W. C. Krueger, Ph.D. Thesis, University of Minnesota (1966).
VIBRATIONAL IKTENSITIES
4041
Table 11: Optical Constants for the 656-Cm-1 Band of Liquid Methyl Iodide-da
Table I: Optical Constants for the 492-Cm-' Band of Liquid Methyl Iodide-da v,
om-'
521.1 519.9 518.9 518.0 517.1 516.2 514.9 514.0 513.1 511.9 511.1 509.9 509.0 508.1 507.0 506.1 505.0 504.1 503.0 501.9 501.0 499.9 499.1 498.0 497.0 495.9 495.1 494.0 493 5 493.0 491.9 490.9 490.1 489.1 488.1 487.1 486.1 485.1 484.1 482.9 482.1 480.9 479.9 479.0 478.0 477.1 475.9 475.0 474.1 472.0 472.0 471.1 470.0 469.1 I
k
dk)
n
4)
0.0011 0,0013 0.0013 0.0012 0.0014 0.0017 0.0014 0.0016 0.0018 0.0018 0.0017 0.0022 0.0023 0.0028 0.0029 0.0030 0.0033 0.0035 0.0041 0.0052 0.0060 0.0072 0.0083 0,0109 0.0137 0.0194 0.0246 0.0300 0.0311 0.0315 0.0291 0.0240 0.0194 0.0147 0.0114 0.0085 0.0075 0.0056 0.0050 0.0042 0.0040 0.0032 0.0027 0.0027 0.0025 0.0022 0.0021 0.0017 0.0016 0.0016 0.0015 0.0016 0.0011 0.0009
0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005 0.0005 0.0006 0,0007 0.0009 0.0011 0.0013 0.0014 0.0015 0.0016 0.0015 0.0015 0.0014 0.0012 0.0011 0.0008 0.0008 0.0007 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003
1.5101 1.5099 1.5097 1.5096 1.5095 1.5093 1.5093 1.5090 1.5087 1,5081 1.5080 1.5076 1.5073 1,5065 1.5059 I . 5054 1.5046 1.5041 1.5022 1.4994 1.4974 1.4944 1.4920 1.4889 1.4910 1.4884 1,4879 1.4945 1.4999 1.5054 1.5148 1.5218 1.5260 1.5279 1.5271 1.5272 1.5235 1.5248 1.5244 1.5227 1.5213 1.5213 1.5210 1,5209 1.5211 1.5199 1.5182 1.5177 1.5178 1.5175 1.5167 1.5170 1.5173 1.5163
0.0014 0.0014 0.0014 0.0014 0.0014 0.0013 0.0014 0.0013 0.0013 0.0013 0.0013 0.0013 0.0013 0,0014 0.0014 0.0015 0,0016 0.0016 0,0019 0.0021 0.0022 0.0023 0.0023 0,0023 0.0025 0.0027 0.0029 0.0030 0.0031 0.0031 0.0031 0.0030 0.0029 0.0029 0,0027 0.0026 0.0024 0.0024 0.0024 0.0023 0.0022 0.0022 0.0022 0.0022 0.0022 0.0022 0.0021 0.0021 0,0021 0,0021 0.0020 0.0021 0.0021 0.0020
optical constants, we show both k and Lo, the continuous line and the broken line, respectively, in Figures l a and b. In general, the correction for dielectric effect causes not only a change in the magnitudes of k but also a shift of the absorption maximum and a change of band
v, om-1
740.5 734.8 730.2 724.7 720.3 715.1 710.0 705.1 700.2 694.7 690.1 684.8 680.4 678.2 676.0 673.9 671.8 669.7 668.4 666.3 664.3 662.3 660.3 658.3 656.4 653.8 651.9 650.0 648.1 645.7 643.9 642.0 639.7 637.9 636.1 634.4 632.1 629.8 624.8 620.1 615.2 609.9 604.8 600.2 595.3 590.1 585.0
IC
dk)
n
dn)
0.0003 0.0001 0.0002 0.0005 0.0007 0.0011 0.0018 0 0023 0.0027 0.0033 0.0041 0.0055 0.0063 0.0077 0.0084 0.0109 0.0122 0.01,50 0.0168 0.0194 0.0227 0.0261 0.0293 0.0320 0.0323 0.0285 0.0258 0.0216 0.0192 0.0131 0.0111 0.0098 0.0084 0.0075 0.0064 0.0053 0.0047 0.0037 0.0032 0.0034 0.0031 0.0022 0.0018 0.0015 0.0014 0.0009 0.0009
0.0002 0 0002 0.0002 0.0003 0.0003 0.0003 0.0003 0.0004 0.0004 0.0004 0.0005 0.0006 0 0006 0.0008 0.0008 0.0007 0.0007 0.0008 0.0009 0.0010 0.0011 0.0013 0.0015 0.0017 0,0018 0.0017 0.0016 0.0015 0.0013 0.0009 0.0009 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0008 0.0005 0.0004 0.0004 0.0003 0.0003 0.0003 0.0003 0.0003
1.5039 1.5035 1.5022 1.5017 1.5015 1.5009 1.5003 1.5000 1.4998 1,4993 1.4983 1.4974 1 4967 1.4935 1.4937 1.4903 1.4906 1.4890 1.4888 1.4890 1.4882 1,4895 1.4915 1.4959 1.5006 1.5097 1.5104 1.5163 1 5131 1.5166 1.5163 1.5160 1.5153 1.5150 1.5150 1.5147 1.5143 1.5139 1.5124 1.5151 1.5145 1.5134 1.5131 1.5128 1.5121 1.5109 1.5108
0.0022 0.0022 0 I0021 0.0021 0.0021 0.0021 0.0021 0.0021 0.0021 0.0021 0.0022 0.0023 0.0023 0,0028 0.0028 0.0026 0.0027 0,0028 0.0029 0.0031 0.0031 0.0034 0.0036 0.0038 0.0040 0.0041 0.0040 0.0042 0.0039 0.0027 0.0026 0.0025 0.0025 0.0024 0 0024 0.0024 0.0023 0.0023 0.0022 0.0024 0.0023 0.0023 0.0023 0.0017 0.0017 0.0017 0.0017
I
I
I
I
I
aIthough the effects are not so remarkable in the present case because of the weak bands a,ndlow polarity. The integrated intensities of the two bands are summarized in Table I11 for both normal and heavy methyl iodide, rk being obtained by the direct integration of the extinction coefficient, i.e. I'k = (4a/cm) J k ( v ) *do
(4)
(8) T. Fujiyama and B. Crawford, Jr., J. Phgs. Chem., 72, 2174 (1968).
Volume 78, Number 13 December 1969
4042
TSUNETAKE FUJIYAMA AND BRYCE CRAWFORD, JR. Coefficient
10-
ODserved
v3 of
4230,
CU31
I n Table 111, the parameters obtained are given together with the earlier results for methyl iodide. The intensity values rvvw, given by the relation
3a4''pl
0.03
rs = 8nav0(M/d)S
Y
(6 1
with M and d being molecular weight and density, respectively, are also included in the table. We remind the reader that the imaginary part of eq 5 reduces to the well-known Lorentzian shape function Y
C' ' = constant. (YO
Wavenuvber
In cm
- V I Z + Y2
if the ratio y / v o is small enough, and that the half-band width Avl/, by
1
y
(7) is related to
(8) It will be noted in Table I11 that the half-band widths of. the e-type bands are larger than those of the a-type bands and a remarkable decrease of half-band width is observed when passing from methyl iodide to methyl iodide-& for both v3 and V6 fundamentals. = (1/2)*Avi/,
Y6 41.7'
of
CD31
,
38.0'
0.03
Y
0.02
Table 111: Spectral Parameters for ~3 and Y O of Methyl Iodide and Methyl I o d i d e 4 CHnI
0.01
~3
0 Waverumber
in
cm-'
Figure 1 . Extinction coefficients for liquid C D J . (a) Parallel band, ~ 3 species , a; (b) perpendicular band, Y E , species e. Continuous lines, observed extinction coefficient, k; broken lines, corrected values, ko.
where cm is the molar concentration. I'pw is integrated intensity obtained from rk by the Polo-Wilson method and Yo'' is the integrated intensity resulting from direct integration of the imaginary part of the local susceptibilitye8
Y6
CDaI y3
vg
Comparison with Van Vleck and Weisskopf Theory and Spectral Parameters
(440-626 om-', 290 points) y o : 521.64 cm-l y: 5.168cm-l S: 0.608 K : 0.070 (750-1040 crn-l; 249 poiints) Y O : 884.16 y: 15.975 S: 1.016 K : 0.070
(430-530 cm-l; 243 points) Y O : 492.61 y : 3.376 S: 0.281 K : 0.072 (535-760 cm-l; 345 points) Y O : 666.11 y: 11.179 S: 0.599 K : 0.071
277.85 205.85 r c : 206.43 r v v w : 213.65 rk:
rp,;:
806.0 598.9 re": 600.8 rvvw: 607.03 rk:
rpw:
The observed local susceptibility, 6, was compared with the collision theory of Van Vleck and W e i ~ s k o p f . ~ * ~ The four parameters, namely, the damping constant y, the resonant frequency vo, the strength factor S, and It is also worth noting here, for discussion later, that the contribution K to the local susceptibility from the the band shape of V6 of methyl iodide is not well apoutside of the band, were obtained by the least-squares proximated by the Van Vleck-Weisskopf function, while method using the equation v3 of methyl iodide is well fitted to the function.
e=
+
vo - iy - v) - i,]
+ ir + + ir
vo +
(Yo
(5)
Y)
The calculated local susceptibilities are compared with the observed ones in Figures 2a and b, and they agree well within the experimental errors both for v3 and vg. The Journal of Physical Chemistry
Calculation of the Time-Correlation Function and the Estimation of Errors Time-correlation functions are calculated as the (9) J. H. Van Vleck and V. F. Weisskopf, Rev. Mod. Phys., 17, 227
(1946).
4043
VIBRATIONAL INTENSITIES 0 074
0006
T
a
'"
0004
during the present experiment, and hence the limit of reliability of our results is confined to times less than 1-2 psec. Numerical Procedure of Integration. This type of error is essentially systematic and sometimes leads to serious errors in the calculated absolute values because the integration is included in the denominator of eq 10. The magnitude of this error is easily estimated, and the effect is eliminated by choosing the proper numerical procedure and by taking enough data points. In this work about 300 points are used for each band. Thus the error is made negligibly small. Truncation Eflect. The calculated time-correlation functions are very sensitive to the actual extent of the region of integration which is indicated as band in eq 9. I n the actual procedure, we are compelled to truncate the region of integration because of the overlap of bands or the increase of random errors in the wing parts. The effects are clarified by numerical study using the Lorentzian
0,003m bi 'h ~0.070
1
520
,004
r
r
510
r
Y
500
-0.060 490
400
470
b 0.072
,003
0 071
"6 Of cD3'
Y(cM)-~
Figure 2 . Comparison of local susceptibilities with VVW calculation. Solid lines, C' and C" calcd; points, values from observation; vertical lines, standard errors, u(C') and u(C"). (a) parallel band, v 3 ; (b) perpendicular band, YO.
Fourier integral of the spectral density distribution functionlo
where I"(w) represents the normalized spectral density distribution function. We took the corrected C" as the spectral density. I n the actual numerical procedure we would use the summation
instead of eq 9. Several points regarding the reliability of time-correlation functions so calculated from infrared data seem worth discussion a t this point. Finite Resolution of Xpectrometer. Let the resolution of the spectrometer be Av; then one cannot obtain accurate information about phenomena which occur a t times greater than l / A v along the time axis, from the Fourier analysis of the observed phenomena along the frequency axis. This uncertainty is systematic in type. Our spectrometer is used a t a resolution of 3-5 cm-'
which closely represents the intensity distribution function of V6 of methyl iodide&. In Figure 3, we show several calculated correlation functions, curves A, B, C, D, and E corresponding to the range of integration being truncated at one, two, three, four, and eight times the half-band width (22 cm-I). The result of analytical integration (between ==I a ) is indicated by F in Figure 3. It is seen that the truncation causes an oscillation effect in the calculated correlation function and the periodicity of the oscillation is roughly inversely proportional to the range of the integration. As the correlation function is normalized for unity at t = 0, the amplitude increases as t increases. In addition, t,he amplitude of oscillation with respect to the line F increases as the range of integration is decreased. These results lead to the conclusion that the region of integration should be more than eight or ten times the halfband width to have a reliable correlation function for the time less than -2 psec. Baseline Eflect. The choice of baseline is also very critical. In order to investigate this effect, time-correlation functions were calculated by adding various constants to the function of eq 11. The effect of thus changing the baseline is demonstrated in Figure 4, where 1, 2, 3, and 4 correspond to the baselines being lowered 0, 0.0002, and 0.004 with respect to the original zero line, respectively; the region of integration is ten times the half-band width. We note that lowering the baseline 0.0002, which is about 0.5yoof the maximum value off (w), causes a remarkable error in the time-correlation function. Let f ( w ) be given by (10) R. G. Gordon, J. Chem. Phys., 43, 1307 (1966).
Volume 7 S , Number 18 December 1909
4044
TSUNEETAKE FUJIYAMA AND BRYCECRAWFORD, JR. 1.0
IO
2.0
(psec)
Then the ratio of f(u)to f(0)is expressed by the equation
If the region of integration is terminated at
=!=we corresponding to ten times the half-band width, f(w,) is about 1% of f(0)and the errors expected forf(we) should be less than ('lz)f(w,). Thus the effects of the truncation are safely eliminated when, and only when, the intensity distribution is measured over a frequency range at least ten times the half-band width and the intensity error of the wing parts is less than 50% of the absolute value of the wing intensity. It is difficult to satisfy this requirement for the usual infrared absorption bands and the common infrared absorption spectroscopy techniques. As the actual band shape does not always follow a Lorentzian function, the situation may be more complicated and the necessary condition needed to be able to ignore safely the truncation effect may have to be made more severe. The region of integration we used
1.0
1.c
2.0
(PSEC)
EFFECT OF INTEGRATION
Oal
0.0'
A AVq
12
8.
c: D E
" " I'
xz x3 x4
'' x 8 F algebraic
I
Figure 3. Effect of truncation of integration range on timecorrelation function (see text). Curves A, B, C, D, E, correspond to integration ranges 1, 2, 3, 4, and 8 times the half-band width; F is the algebraic result with no truncation. The JOuTnd of Physical Chemistry
0.1
0.01
Figure 4. Effect of baseline shift on time-correlation function (see text). Curve 1 corresponds to the unshifted baseline; curves 2,3, and 4 correspond to shifts of 0.0002, 0.003, and 0.004.
for each band is given in Table I11 together with the number of data points included in the integration. It must be emphasized here that the effect of truncation always occurs even in the region of short times but becomes worse as the time increases. These errors are systematic in type, and there is no way to eliminate them except to extend the observations of the wing intensity over a wider range of frequency with sufficiently high accuracy. Any mathematical techniques to eliminate the effect cause new systematic errors in the results. Random Errors. We estimated the effects of experimental random errors on the calculated time-correlation functions by propagating the standard errors of the parameters of the VVW functions, eq 5, fitted to the observed intensity. These standard errors of the VVW parameters themselves are calculated in the leastsquares procedure from the weight matrix determined by the ~ ( nand ) ~ ( k given ) in Tables I and 11. The effect of the VVW-parameter errors on the time-correlation function can be seen by noting that the simplified eq 7 would correspond to the time-correlation function expressed a(t) = exp(-pt)
(14)
If we express a ( t ) on the natural logarithmic scale, then
VIBRATIONAL INTENSITIES
4045
In [ ( ~ ( t )=] -Pt
(15)
and the standard error for In [ a ( t ) ]is estimated as a[ln ( ( ~ ( t ) )=] u(a)-t
(16)
This estimate depends, of course, on the appropriateness of the VVW function to describe the data. Results of Calculation. The calculated time-correlation functions are shown in Figure 5. The errors indicated by the vertical lines represent the contribution from the random errors only of the observed data, estimated as described above. We note that the systematic errors due to the truncation effect still remain clearly in all the results, and the systematic errors are at least comparable in magnitude with the random error.
Discussion of Results General. Although the time-correlation functions obtained are not accurate enough to support detailed quantitative interpretation, some interesting information can be obtained. The rotational motion of molecules having Cay symmetry is characterized by two types of rotation; one about the symmetry axis which we take as the x axis and one about one of the perpendicular axes (z or y). The rotational time-correlation function obtained from
t--3 0
1.0
(psec)
Y (a)
Figure 5. Time-correlation functions for the four bands studied. Vertical lines indicate estimates of random error effect as described in the text; D, curves for CDaI bands; H, curves for CHaI.
the al-type band corresponds to the decay of polarization parallel to the z axis, this being the direction of the transition-moment vector of the vibration; thus, the two equivalent rotations about the x and y axes enter into the analysis of this time-correlation function. Similarly, the two different rotations about the z and x axes affect the time-correlation function for the e-type band. Before discussing the actual results, let us consider what we might expect in the way of differences between the time-correlation functions for methyl iodide and methyl iodide-&. So far as the rotational motion is concerned, the chief differences between these two molecules are in the inertial rotational constants and in the position of the center of gravity along the z axis. The rotational constants reported for the gas phase are” A. = 5.119 and Bo = 0.2502 cm-1 for normal methyl iodide and A. = 2.586 and Bo = 0.2014 cm-1 for methyl iodide-&. Following the recent theoretical treatments of the subject10~12~13 we may distinguish two different limiting types of the decay process, one governed by a rotational diffusion and the other by inertial rotation. If the rotational motion of the molecules is essentially inertial and, hence, characterized by the rotational constants, then the behavior of the time-correlation function for an e-type band, involving both A. and Bo,should differ remarkably from methyl iodide to methyl iodide-&; that for an a-type band, involving only Bo, should be similar for both molecules. If, instead, the rotational motion is essentially a diffusion process, the time-correlation functions of al-type vibrations of the two molecules would be expected t o differ, since the change of the center of gravity would cause a change in the drag force and therefore a change in the diffusion constants. Time-Correlation Function. The time-correlation function should also reflect the nature of the decay process. A rotational diffusion mechanism should give an exponential decay, or logarithmic straight-line behavior for In a ( t ) ,as for any stochastic process.l* If, on the other hand, most of the molecules are rotating fairly freely and the rotation is inertial, logarithmic time-correlation function In a(t) deviates from a straight line, especially at short times. In fact, as Figure 5 shows, all four rotational correlation functions observed in the present experiment behave exponentially at long times; moreover, the limiting long-time exponential curves can be extrapolated back close to unity at time t = 0, the deviation from unity being most marked in the case of the rotational correlation function for the e-type band of normal methyl iodide. These results imply that the molecular rotation of methyl iodide or methyl iodide-& (11) E.W.Jones, R. J. L. Popplewell, and H. W. Thompson, Proc. Roy. Soc., A288,39,50 (1965). (12) H.Shimizu, J. Chem. Phys., 43,2453(1965). (13) H.Shimizu, Bull. Chem. SOC.Jup., 39, 2385 (1966). (14) “Investigations on the Theory of the Brownian Movement,” R. Furth, Ed., Dover Publications, New York, N. Y.,1956. Volume 73, Number 13 December 1969
4046
TSUNETAKE FUJIYAMA AND BRYCECRAWFORD, JR.
should be characterized essentially by a random reorientation process and the behavior of the rotationalcorrelation functions may be interpreted mainly by the diffusion equation. Favro'6 reports a general theory of rotational diffusion for the case of a rotational-correlation function which is governed by the stochastic process. If we adapt his formula to the case of the symmetric-top molecule, we obtain for the al-type band shape
and for the e-type
where D , and DEare the rotational diffusion constants with respect to the parallel and perpendicular axes, respectively, while A, and Ax represent the magnitude of the transition dipole moments along such axes. Thus the diffusion constants are related directly to the time derivative of the logarithmic correlation functions at long times. Since (17) and (18) are Lorentzian, we get
20, =
Pz
Dx 3- D,
=
and
Px
that is
Dx
L=
P5/2
and
Dz
=
Px
- (P&)
(19)
where p. and PX are the time derivatives of the logarithmic rotational correlation functions of 81- and etype bands, respectively. In Table IV, the diffusion constants thus observed are ~~~~~
~
~
Table IV: Diffusion Constants Obtained for Methyl Iodide and Methyl I o d i d e 4 CHaI
CDaI
1.94
1.71
0.48
0.33
given in units of psec-'. The results show that the magnitude of the diffusion constants about the symmetry axes are four to five times larger than those about the perpendicular axes. The diffusion constants about symmetry axes have nearly the same values for methyl iodide and methyl iodide-&, while those about perpendicular axes differ considerably. The results seem reasonable in terms of the expectations discussed above. The JOUTW~ of Physical Chemistry
We now turn to the behavior of the time-correlation functions at short times. As the perpendicular rotational constants Boof the two molecules are nearly equal, the behavior of the two rotational correlation functions concerned with the al-type vibrations should be very similar if the rotation of these molecules is inertial. Actually, it is seen from Figure 5 that the two v3 functions are quite different even at very short times. The change of a(t)of methyl iodide-& along the time axis is much slower than that of normal methyl iodide. From this we would conclude that the molecular rotations of these molecules in the liquid phase about their perpendicular axes must be strongly hindered, with the contribution of inertial rotation to the rotational-correlation function being very small. The rotational-correlation functions for the e-type vibration at short times are more complicated, since' both kinds of rotation, about parallel and perpendicular axes, contribute to them. From the present data we can draw no conclusion as to the contribution of inertial rotation to the short-time behavior of a(t). We can only conclude from the behavior of all four rotational correlation functions at short times, that the decay processes of methyl iodide and methyl iodide-& cannot be completely explained by the stochastic process, noting, however, that deviation from the random reorientation picture is marked only for V6 of normal methyl iodide. Band Shapes and Conclusion. As discussed above, the Van Vleck-Weisskopf theory and the diffusion theory lead essentially to the same band shape, the Lorcntzian, although their theoretical approaches are quite different, and if the band shape is approximated well by the Lorentz function, the logarithmic time-correlation function obtained from it will be a straight line. The conclusion we reached from comparison of the observed band shapes with the Van Vleck-Weisskopf function is that the band shapes of v3 and V6 of methyl iodide and of v3 of methyl iodide-& are approximated fairly well by a Lorentzian curve but not that of V 6 of methyl iodide; this is consistent with our discussion of the time-correlation functions, which show predominantly the logarithmic straight-line behavior reflecting diffusional rotation, although inertial rotation, or free rotation, affects all the time-correlation functions a little in the short-time region and most noticeably that for of CH3I. We SUSpect we can reasonably assume, from these and earlier results, that the Lorentz function is rather generally applicable to liquids composed of typical organic molecules, when proper allowance is made for the dielectric effect by correction to the local susceptibility, C" (or k~). From the molecular viewpoint, the factor dominating the shape of the infrared absorption band should be the drag force which the molecule experiences during rotation diffusion in the liquid phase. The effect of inertial
(16) L.D. Favro, Phys. Rev., 119,63 (1960).
SURFACE ORIENTATION IN ELECTROCAPILLARITY rotation perturbs the band shape, especially the wing parts, as is seen for Y6 of methyl iodide. I n concluding, we stress again that great care should be exercised in the calculation of time-correlation functions from observed band shapes, especially with regard to truncation effects. I n order to obtain a reliable time-correlation function, the extension of accurate ob-
4047 servations of the absorption coefficient to the wing region of the band is essential. Acknowledgments. We are grateful to the National Science Foundation for financial support of this research through Grant GP-3411. We are also grateful to Dr. Roger Frech for general help and Mrs. Charlotte Smith for assistance with the calculations.
Surface Orientation in Electrocapillarity by A. Sanfeld, A. Steinchen, and R. Defay Free University of Brussels (Faculty of Applied Sciences), Brussels, Belgium
(Received February 7,1969)
In the multilayer thermodynamic framework, the authors show the influence of the dipole orientation in electrocapillary systems. In the case of a low rate of orientation in the surface layer, the electrocapillarity equation of Lipmann must be modified. The new terms allow an approach of the electrocapillary phenomena when the orientation is delayed. Electrocapillary systems are usually treated as discontinuous media. I n this approach, the system is divided into well-defined spatial regions. I n each of these regions, electric and thermodynamic variables are continuous in space, but some of the intensive properties are discontinuous at the boundaries of the regions considered. This model has led to very good results in electrochemical kinetics, in colloid science, and in capillarity. It seems difficult, however, to describe quasi-microscopic discontinuous regions, as, for instance, interfacial layers with macroscopic variables. This difficulty disappears when the electrocapillary system is considered as a continuum, but the fundamental problem is then the mathematical formulation of the physical properties of this continuous system. If the layer is many molecules thick, its composition may vary with position within the layer; these circumstances make it physically consistent to use the multilayer model developed by Defay and colleagueslJa model one could call intermediate between the continuous and discontinuous models. The system is divided into uniform regions called phases. The nonuniform regions, such as the capillary layer, are subdivided into a number of laminae, each sufficiently thin to be considered homogeneous. Our purpose is to develop an electrocapillary theory based on the multilayer model with a view to deriving an explicit formulation of dipole orientation. Some results have been partially published in a previous papera4 I n fact, important properties of the interfacial layers
find their origin in this molecular orientation (ref 5-7). Excluding all microscopic fluctuation effects, this work deals only with systems for which orientation equilibrium occurs after the establishment of the diffusion equilibrium. All transport of matter from one region to another may be treated as a transfer of one or several components from one phase to another. The only entropy production sources are, on the one hand, the chemical reactions and the transport from one phase to another, and, on the other hand, the orientation of every component which occurs in the laminae. Thus, in addition to the classical electrochemical and transport affinities, we shall have orientation affinities. I n Defay’s work, l s 2 the orientation of the components is not treated as an independent variable. This means that the (1) R. Defay, I. Prigogine, and A. Bellemans, “Surface Tension and Adsorption,” D. H. Everett, trans., Longmans Green, New York, N. Y., 1966. (2) R.Defay, J. Chim. Phys., 46,375 (1949). (3) I. Prigogine and P. Mazur, Physica, 17,661 (1951);S. Nakajima, Proc. I n t . Conf. Theoret. Phys., Kyoto, Tokyo, Sept 1953. (4) A. Sanfeld, Koninkl. Vlaams, Acad. Wetenschap. Letter Schone Kunsten Belg. Colloq. Grenslaagverschijnselen Vloeistofllmen, 1966 (1966); “Introduction to Thermodynamics of Charged and Polarized Layers,” Monograph no. 10, “Statistical Physics,’’ I. Prigogine, Ed., Wiley Interscience, Dec 1968. (5) J. T. Davies and E. K. Rideal, “Interfacial Phenomena,” Academic Press, New York, N. Y., 1961. (6) J. Guastella, J. Chim. Phys., 44, 306 (1947); Mem. Sew. Chim. &at, (1947); J. Michel, ibid., 54,206 (1957). (7) A. N.Frumkin, ibid., 63, 786 (1966); B. B. Damaskin, Electrochim. Acta, 9,231 (1964). Volume 73, Number 18 December 1969
