J. Phys. Chem. 1983,87,3606-3610
3600
ARTICLES Picosecond Kinetics by Exchange Broadening in the Infrared and Raman. 1. 1,P-Dichloroethane Benyamln Cohen and Shmuel Weiss' Department of Chemistry, Ben-Gurion University, Beer-Sheva 84 105, Israel (Received: September 7, 1982; In Final Form: February 23, 1983)
Spectra of 1,2-dichloroethane,as neat liquid, in solution, and in the solid, were recorded over a wide temperature range. Variation of line shape with temperature was interpreted as due to exchange broadening, caused by interconversion of rotamers, and the Bloch equation could indeed be fitted to the spectra. Spectra of 1,2dichloroethylene and of l,l,l-trichloroethane taken as controls showed only slight temperature dependence. Rate constants, in the 1012-s-'range, and, from them, activation energies and entropies were determined. These were consistent with thermodynamic functions and of reasonable magnitudes.
Introduction Although the study of chemical kinetics by exchange broadening in NMR and ESR is a well-established technique, for a long time now this has not been so in the infrared and Raman. The basic difference is in the time domain. The NMR technique is centered around the convenient and long familiar millisecond range. In the infrared and Raman 1-cm-' change in width corresponds to 5 X 10-l2s so that one finds himself in the picosecond and subpicosecond range which has come only recently into the focus of interest. The possbility of observing exchange broadening in the infrared has been noted by Eigen' and by others2 and a number of instances in which observation of kinetic line broadening has been claimed have indeed been reported in the l i t e r a t ~ r e . ~Most - ~ of these claims, however, must be considered tentative for failure to exclude alternative line broadening mechanisms. We believe that in a case recently reported by us exchange broadening has indeed been proven.'O Alternative experimental approaches to the study of picosecond reactions of ground-state molecules in solution are few. Most of our information on such reactions derives from dielectric relaxation measurements. Laser pulse methods are sometimes useful for following reactions of ground-state molecules in the wake of reactions of excited molecules. Thus, the scarcity of alternatives and its experimental simplicity make infrared and Raman line (1) M. Eigen, Angew. Chem., Int. Ed. Engl., 3, 1 (1964). (2) W. H. Flygare, "Molecular Structure and Dynamics", PrenticeHall, Englewood Cliff, NJ, 1978, Chapter 7. (3) M. M. Kreevoy and C. A. Mead, J . Am. Chem. SOC.,84, 4596 (1962). (4) M. M. Kreevoy and C. A. Mead, Discuss. Faraday SOC.,39, 166, 176 (1965). (5) A. K. Covington, M. J. Tait, and Lord Wynne-Jones, Discuss. Faraday SOC.,39, 172 (1965). (6) J. A. Williams and M. M. Kreevoy, J . Am. Chem. SOC., 89, 5499 (1967). (7) A. K. Covington, J. G. Freeman, and T. H. Lilley, J. Phys. Chem., 74. 3773 (1970). '(8)J. Husar and M. M. Kreevoy, J . Am. Chem. SOC., 94, 2902 (1972). (9) J. G. David, Spectrochim. Acta, Part A, 28, 977 (1972). (10) B. Cohen and S. Weiss, J. Chem. Phys., 72,6804 (1980). See also a comment by R. Weston, J . Chem. Phys., 74, 3634 (1981), and our reply, ibid., 74, 3635 (1981).
0022-3654/83/2087-3606$0 1.50/0
broadening a very attractive technique well worth exploring. Before we can carry over the Bloch equations formalism from the NMR and ESR to the infrared or Raman we need to consider two questions: first, whether the Bloch equations developed for magnetization apply to electric polarization as well and, second, whether assumptions used to deal with reactions in the millisecond range or its vicinity still hold in the picosecond range. Now Flygare and Schmalz have shown'l how phenomenological equations may be set up for the electric polarization which are analogous to the Bloch equations for the magnetic case. The solutions to these equations are likewise similar and the authors concluded that "all the phenomena observed in the electric resonance case have their analogs in the magnetic resonance case". In this sense it might be sufficient for our purpose to simply carry over the Bloch equations as modified by Gutowsky, McCall, and Slichter12 to include the effects of chemical exchange. There remains one small difference between the NMR case and that of the I R and Raman. In NMR the magnetic dipole retains its magnitude whether in state A or B. This is not so in the infrared, or Raman, where the electric dipole or (dp/dq)6q may have quite different values in the two states. This simply means that a given vibration, for example, may give rise to different absorption intensities depending on whether the molecule is in state A or B. This problem has been dealt with recently by MacPhail, Snyder, and Strauss,13who give a line-shape equation suitable for the case when the intrinsic intensities are unequal. As for the differences in time scales, the assumption which might be affected is that the duration of the jump between the reactant and product states-or vice versais short relative to the states lifetimes. Now the average (11) W. H. Flygare and T. G. Schmalz, Acc. Chem. Res., 9,385 (1976). (12) See, e.g., J. A. Pople, W. G. Schneider, and H. J. Bernstein in "High Resolution Nuclear Magnetic Resonance", McGraw-Hill, 1959, pp 218-24. Note that there is an error in their eq 10-14 which should read
(13) R. A. MacPhail, R. G. Snyder, and H. L. Strauss, J . Am. Chem. SOC.,102, 3976 (1980).
0 1983 American Chemical Society
Picosecond Kinetics by Exchange Broadening
duration of "jumps" is proportional to the concentration of molecules which, at a given time, are in the process of "jumping". If, as a crude estimate, we take that concentration as the concentration of molecules near the top of the barrier, we will find that for barriers of the order of a few kcal/mol and reasonable temperatures (our case in the present article) this concentration does not amount to more than a few percent of the total number of molecules. The jump duration is then smaller than the lifetimes of the states by at least 1 order of magnitude. For very low barriers this may no longer be true. Various categories of reactions might qualify as possible candidates for study by infrared and Raman line broadening: the formation and dissociation of charge-transfer complexes, the formation and dissociation of hydrogen bonds, proton transfer, association of un-ionized molecules to ion pairs and vice versa, and conformationaltransitions. It is clear that all intermolecular processes will have to be studied in fairly concentrated solutions as otherwise the diffusion-controlled limit will place the kinetics outside the picosecond range. In the present article we report on the kinetics of the conformational transition in 1,2-dichloroethane which has the advantage of being a well-studied phenomenon14 so that a t least some of our results may be compared with results obtained by other techniques. In subsequent articles we shall report on the kinetics of some other reactions belonging to different categories. 1,2-Dichloroethaneexists as a mixture of two rotational isomers: a nonpolar trans form of symmetry C 2 h in which the chlorine atoms are as far from one another as possible and a gauche form of symmetry Cz in which the CH2Cl groups are rotated relative to one another from their position in the trans form. It was customary in the literature to assume that the angle of rotation is 120° but electron diffraction work15 has established a value of 106'. The trans from has the lower energy of the two and the energy difference between the rotamers has been determined from the temperature dependence of the intensities of spectral features attributed to the two isomers16as well as from the temperature dependence of the dielectric constant.16 Using this information together with the measured torsional frequencies Mizushima et al.17 have calculated the potential energy as a function of the angle of internal rotation as well as the positions of the torsional levels. The height of the energy barrier separating the trans and gauche forms, in the isolated molecule, is thus known. Each of the two rotamers has 18 normal mdoes of vibration. All of these give rise to both IR and Raman bands for the gauche form whereas the spectrum of the trans, which has a center of symmetry, consists of nine IR and nine Raman fundamental bands. The vibrations of the two rotamers, though occurring in different structures, can be paired (as, e.g., C-C stretch or CCCl deformation in both rotamers). Pair separations are mostly in the 0100-cm-' range. Experimental Section Spectra were taken on a Perkin-Elmer 225 infrared spectrometer using a resolution of 0.6-0.7 cm-'. Samples were contained in a RIIC variable-temperature cell. The (14)The literature is well summarized in "Internal Rotation in Molecules", W. J. Orville-Thomas, Ed., Wiley, New York, 1974. (15)K. Kveseth, Acta Chem. Scand., Ser. A., 28,482,(1974). (16)S.Mizushima, "Structure of Molecules and Internal Rotation", Academic Press, New York, 1954. (17)S.Mizushima, T. Shimanouchi, I. Harada, Y. Abe, and H. Takeuchi, Can. J. Phys., 53, 2085 (1975).
The Journal of Physical Chemistry, Vol. 87, No. 19, 1983
3607
L
1100
1125
1150
1175
cm-'
Figure 1. Spectra of liquid 1,2-dichloroethane. The ordinate is absorbance in arbitrary units. A fit by two Lorentzians, (dashed line) is shown for the spectrum at 70 'C.
temperature range employed in this study was -110 to +280 OC. Low temperatures were measured with the aid of a thermistor and the higher ones with a thermocouple. At temperatures above the normal boiling point of 1,2dichloroethane the samples were kept under nitrogen pressure (up to 80 atm) in a cell equipped with KBr windows and sealed in Teflon gaskets. Solid samples were prepared by simple freezing of the liquid. Optical paths were 0.02-0.05 mm for samples of pure 1,2-dichloroethane and 1 mm for solutions. Results are reported as absorbances. Results and Discussion Liquid Phase. Both the neat liquid and dilute solutions in CS2 (4% v/v) were studied. The choice of bands to be studied was governed mostly by experimental and occasionally by interpretative considerations. Thus, bands in the far-infrared are inconvenient to study and normal modes involving chlorine atoms pose difficulties in data evaluation because of the band structure brought about by the existence of two chlorine isotopes. The most common consideration, however, against the choice of a given band was its excessive intensity which dictated optical paths too small to realize conveniently when the cell had to be pressurized. In solution work it was, of course, also necessary to avoid overlap with solvent bands. On the basis of these considerations the bands at 1124 (trans) and 1144 (gauche) cm-l were chosen for detailed study. A number of other bands were also studied, in less detail, to check if their behavior corresponded to that of the above two bands (see below). The bands at 1124 and 1144 cm-' are both described as CH2twist by Mizushima et al.17 and are sufficiently separated to be described independently with the aid of Lorentzians. Representative spectra are reproduced in Figures 1and 2 along with the Lorentzians fitted to some of the spectra. The fitting was accomplished through a least-squares procedure.
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Cohen and Weiss
The Journal of Physical Chemistry, Vol. 87, No. 19, 1983
TABLE I : Activation Energies and Entropies and Thermodynamic Functions for 1,2-Dichloroethanein the Liquid AH," AH,^ Ema cal/mot AS+,^ eu cal/mol cal/mol AS,a eu Neat Liquid
trans guache
2300 t 1 2 0 1 7 0 0 ~100
1.0 f 0.2 -0.3 f 0.2
trans
24805 1 7 0
gauche
2180+-140
4.0 F 1.0
1280 F 220
3 10
1.0
} 6 2 0 ~50
830
1.6 F 0.2
f
0.2
Solution in CS, a
3.0
+_
0.5
This work. Uncertainties quoted are standard deviations determined from the experimental scatter.
Literature values
(ref 14).
A
1100
1120
1140
1160
cm-'
Figure 2. Spectra of 1,28chloroethane in CS, (4% v h ) . The ordinate is absorbance in arbitrary units; optical path, 1 mm. A fit by two Lorentzians (dashed line) is shown for the spectrum at +27 OC.
The lines owe their widths to both the kinetic broadening and the natural line width. In our analysis we have assumed all of the temperature-dependent width to be of kinetic origin. To test this assumption we also ran spectra of 1,Zdichloroethylene( C l H W H C 1 ) in which the barrier to internal rotation is sufficiently high to effectively preclude rapid interconversion at our temperatures, and of l,l,l-trichloroethane in which rotational conformers are equivalent. The results, reproduced in Figure 3, show that in the absence of internal rotation or of nonequivalent rotational isomers line-shape variation over a considerable temperature range is indeed slight. The line widths of each band were then assumed to be sums of a constant natural width and a temperature-dependent width of kinetic origin. The natural width was therefore treated as an adjustable parameter to be determined by yielding the closest fit to a straight line when In k is plotted vs. 1/T. (The rate constants are related to the half-width at half-height by k = 2aAvlI2). The rate constants obtained were in the range of (0.6-2.3) X 10l2s-l. The natural half-width of the trans line was 4.1 cm-' in the neat liquid and 2.6 cm-' in solution, and that of the gauche line was 3.2 cm-l in the neat liquid
I150
I200
1250
I300
I350
cm-' Figure 3. (A) Spectra of liquid 1,2dichloroethylene (mixture of trans and cis forms). The peaks or shoulders at 1295 and 1215 cm-' belong to the cis form and those at 1275, 1200, and 1165 cm-' to the trans form (seeH. J. Bemstein and D. A. Ramsay, J . Chem. Phys., 17, 556 (1949)). (B)Spectra of 1,1,l-trichloroethane. The ordinate is absorbance in arbitrary units.
and 2.3 cm-' in solution. Plots of In k vs. 1/T are reproduced in Figures 4 and 5. From these plots activation energies were calculated. Also, calculating AG* from k , = (kT/h)exp(-AG*/RT) and plotting it vs. T, one obtains values of A S . All of these are collected in Table I. In this table we also show values of AH and AS, for the difference between the two rotamers, determined from the ratio of the intensities of trans and gauche lines at different temperatures. Attention is drawn to the agreement, within experimental uncertainty, between differences in activation energies and corresponding AH values. AH values for 1,2-dichloroethane have been determined before, both for the neat liquid and for solution in CSp14 These are quoted in Table I and are in reasonable agreement with the values determined by us. The only sources
The Journal of Physical Chemistty, Vol. 87, No. 19, 1983
Picosecond Kinetics by Exchange Broadening
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TABLE 11: Temperature Variation of Some Bands in the Neat Liquid
ink
I 29.0 t
half-width, cm-'
band position, cm"
band assignmenta
1124 1144 1232 1285 1314 1430 1450
CH, twist, trans CH, twist, gauche CH, wag, trans CH, wag, gauche CH,wag,gauche CH, sciss, gauche CH, sciss, gauche
at at 30 "C 100 "C 6.2 6.5 7.7 6.5 11 7.5 6.7
8.6 8.7 10 8.5 13 9.7 8.7
variation, cm-' 2.4 2.2 2.3 2.0 2.0 2.2 2.0
Reference 17.
I
2751
*7.01 I
1.8
2.3
28
Flgwe 4. Plot of in k vs. 1 / T for the trans (t) and gauche (9) rotamers in the pure liquid.
I Ink 27.6
I
3.3
3.8
4.3
4.8
*
B
a
t
i.103
5.3
Flgure 5. Plot of In k vs. 1/ T for the trans (t) and gauche (g) rotamers in C S p solution (4% v/v).
of kinetic measurements in the literature are dielectric loss determinations. Dielectric relaxation times in the range
1.21-4.53 ps were measured in various solvents (CS2none of them) with the higher values pertaining to aromatic solvents where special factors lengthen the relaxation times. However, the contribution of overall rotation of the molecule could not be separated from that of the internal rotation. Our relaxation time, calculated as 7 = (k,+ kJ1, would be 1.08 ps at 20 "C. Barrier heights for the isolated molecule-measured from the lowest torsional level in each rotamer-were determined by Mizushima et al." from the IR and Raman spectra and are 4270 cal/mol for the trans isomer and 3120 cal/mol for the gauche. The activation energies of both ratomers are lowered in the liquid relative to the values calculated for the isolated molecule" (see table I). It has been remarked that the energy of the polar gauche form would be lowered in dielectric media whereas the energy of the nonpolar trans would remain unaffected.16 This has been cited as explanation for the very low AH value found for the neat liquid. If it is assumed that the eclipsed transition state (C1 opposite H atom) is highly polar-due to changes beyond internal rotation-then the lowering of the activation energies in the liquid might be similarly explained. Finally, if our assumption that the width of each line is made up of a constant natural width and a temperature-dependent kinetic contribution is correct, then the widths of all lines should vary by the same amount over the same temperature range (as long as they are sufficienly separated from their counterparts to be approximated by two Lorentzians). As a test we therefore measured the widths of five more lines (of the neat liquid) at 30 and 100 "C. The results are collected in Table I1 and bear out our assumption. Solid Phase. It is generally accepted, on the basis of the disappearance of the spectral features of the gauche form upon solidification, that the solid is all trans.16 X-ray diffraction work too supports this view.18 The various bands tend to split in the solid and this splitting has been explained by Mizushima et al. as crystal field splitting.16 We have studied this splitting and found that it occurred in exactly the same way when solutions of dichloroethane in benzene and in CCll were studied as it did in pure dichloroethane (see Figure 6). It would therefore seem that the splitting is not due to crystal field splitting. Moreover, the relative intensity of the components varies with temperature as do their widths. We also note that on solidification the dielectric constant remains fairly high (4.8 at -40 "C, 5 "C below the melting point).Ig These various findings could be explained if it were assumed that in the solid too, at the higher temperatures, two forms of dichloroethane exist. These might be a nonpolar trans form and a polar form not much different from the trans (18) M. E. Milberg and W. N. Lipscomb, Acta Crystallogr., 4, 369 (1951); T. B. Reed and W. N. Lipscomb, ibid., 6, 45 (1953). (19) A. H. White and S.0. Morgan, J . Chem. Phys., 5, 655 (1937).
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The Journal of Physical Chemistry, Vol. 87, No. 19, 1983
Cohen and Weiss Ink
1
27.51
. 9
i
1420
1430 1440 1450 1460 1470
1480
t
cm-'
Figure 6. Spectra of solid 1,2dichloroethane. The ordinate is absorbance in arbitrary units. I n the inset is reproduced a spectrum of 1,2dichloroethane in solM benzene. A fit of the bloch equation (dashed line) is shown for the spectrum at -78 'C.
Flgure 7. Plot of In k vs. 1I T for the trans (t) and gauche (9) rotamers
form. Pending more concrete identification we shall simply label these forms as form A and form B. For the actual study the lines at 1460 cm-' (form A) and 1447 cm-l (form B) (CH2~cissors'~) were used. The kinetics of the interconversion of forms A and B can be studied in a fashion similar to that used for the trans + gauche transition in the liquid. However, at the higher temperature considerable coalescence occurs and it was therefore felt that the full Bloch equation might be more appropriate for the analysis of these spectra. To do this the spectra were again decomposed into two Lorentzians, as before, and tentative natural lifetimes and exchange lifetimes determined. Tentative rate constants determined in this way yield an equilibrium constant through K = k A / kB. Another expression for the equilibrium constant is obtained from the integrated intensities of the two components K = (tA/tg)(IB/IA) where tA and E B are the molar absorption coefficients of forms A and B, respectively. Comparison of the two expressions allows t A / t g , which is necessary for the application of the Bloch equation,13to be estimated. All of these parameters were then fed into the Bloch equation and it was found that they required only little adjustment. A typical fit is reproduced in Figure 6. The t A / e B value was 0.87. Rate constants, determined as before, in the range (0.08-0.8) X 10l2s-l were obtained. Plots of In k vs. 1/T are reproduced in Figure 7 and activation energies and
TABLE 111: Activation Energies and Entropies and Thermodynamic Functions for 1 ,a-Dichloroethane in the Solid
in the solid.
Ema cal/mol
AS*,^
eu
AH,^ cal/mol
AS,^ eu
solid ...
form A 4200 2 500 13.0 t 1.9} 850 formB 3 3 0 0 + 290 9 . 5 2 1.0
180 3.4
~
o.4
a Uncertainties quoted are standard deviations determined from the experimental scatter.
entropies as well as thermodynamic functions are collected in Table 111. The close resemblance of the activation energies to the barrier heights in the isolated molecule is remarkable but we are unable, at this stage, to further comment on it. It could be fortuitous. The relatively high entropies of activation indicate that the transition between the two forms involves a number of neighbors. This further strengthens our view that we are dealing with a real transformation between two distinct forms. Acknowledgment. This work was supported by a grant from the Fund for Basic Research administered by the Israel Academy of Sciences and Humanities. Registry No. 1,2-Dichloroethane, 107-06-2; 1,Z-dichloroethylene, 540-59-0; l,l,l-trichloroethylene,71-55-6.
