J. Chem. SOC., Furaday Trans. I , 1989, 85(4), 957-967 Study of the Conformational Equilibrium between Rotational Isomers using Ultrasonic Relaxation and Raman Spectroscopy Part 3.-1 -Bromo-2-chloroethane Shinobu Koda, Hirohito Matsui and Hiroyasu Nomura" Department of Chemical Engineering, School of Engineering, Nagoya University, Chikusa-ku, Nagoya-shi 464, Japan The rotational isomerism of 1 -bromo-2-chloroethane has been studied by Raman and ultrasonic spectroscopy. Ultrasonic relaxation spectra have been measured in the wide frequency range from 10 MHz to GHz, using the pulse, high-resolution Bragg reflection and Brillouin scattering methods. The enthalpy and volume differences between trans and gauche forms have been obtained from the temperature and pressure dependences of Raman bands, respectively.Combining the ultrasonic and Raman data, the entropy difference between two conformers has been estimated. The enthalpy difference of 1-bromo-2-chloroethane is almost the same as that of 1,2- dichloroethane, but the volume difference and entropy difference are small, in comparison with those of 172-dichloroethane and 1,2-dibromoethane. These results are interpreted in terms of the differences in the intermolecular interaction and packing state in the dihalogenoalkane molecules. In our series of the rotational isomerism of several halogenoalkanes in liquid and dissolved states was investigated by means of the ultrasonic relaxation and Raman spectroscopy. In the previous paper,4 we pointed out that a linear relationship between the ultrasonic relaxation time for the rotational isomerism and the molecular weight holds for most part of chloro- and bromo-homologues, but the relaxation times of 1,2-dichroloethane and 1,2-dibrornethane were abnormally short and deviated largely from the values expected from their respective homologues.However, dihalogenoethanes are still typical samples for conformational equilibrium between trans and gauche forms in a molecule. In order to elucidate more clearly the rotational isomerism of the dihalogenoethanes, we studied the conformational equilibrium of 1 -bromo-2-chloroethane in liquid state by means of ultrasonic relaxation and Raman spectroscopy. Earlier works on dihal~genoethanes~. suggested that the ultrasonic relaxation due to the rotational isomerism of 1-bromo-2-chloroethane was to be in the frequency range above a few hundred MHz.For measurements of the ultrasonic velocities and absorptions in the frequency ranges from one hundred to several hundred MHz, the high-resolution Bragg reflection method proposed and developed by Takagi and co-workers5~ is particularly useful. In this work, an apparatus based on the high-resolution Bragg reflection method was constructed and used. Since the thermodynamic and kinetic parameters related to the rotational isomerism of 1 -bromo-2-chloroethane have been determined completely, these values will be discussed in comparing with those of 1,2-di~hloroethane~ and 1,2-dibr0moethane.~958 Rotational Isomers of 1 -Bromo-2-chloroethane 9 10 11 ,2 n 7 3 1 analyser - e3 Lock- in A+, recorder I I Fig.1. Block diagram of HRB method. 1, He-Ne laser; 2, light chopper; 3, 28 MHz oscillator; 4, diffraction cell; 5, rotary table; 6, sample cell; 7, differential transformer; 8, signal generator; 9, half-mirror ; 10, lens ; 1 1, photodiode ; 12, pre-amplifier ; 13, spectrum analyser ; 14, lock-in amplifier ; 15, X- Y recorder. Experiment a1 Sample The sample, 1 -bromo-2-chloroethane, was purchased from Tokyo Kasei Kogyou Co. Ltd, and was fractionally distilled before use. Raman Spectroscopy The characteristic bands of the C-X (X = halogen) sensitive stretching mode of I-bromo-2-chloroethane are as follows; for trans conformer, 724 and 631 cm-l for C-CI and C-Br stretching modes, respectively, and for the gauche form, 664 and 568 cm-l for C-CI and C-Br stretching modes, respectively.The Raman spectra under high pressure and the temperature dependence of Raman spectra were recorded using the same laser Raman spectrometer, apparatus, and attachments as used in our previous The operating pressure was up to 2500 x Pa. Detailed experimental procedure and data analysis are described el~ewhere,~ The accuracy of the integrated intensities was within 3 O/O. Ultrasonic Measurements ( I ) Below 100 MHz, the ultrasonic absorption coefficients were measured by the usual pulse method. Several different types of measurement cells were used depending on the measuring frequencies. The error in the ultrasonic absorption coefficient was within ca. 3 % on the a/f x lo1’ Np s2 cm-l scale. (2) In order to measure accurately the ultrasonic absorption coefficient and velocity in the frequency range higher than 100 MHz, we constructed an apparatus based on the high-resolution Bragg reflection (HRB) method, in which the optical heterodyne system was set up.* The experimental arrangement is schematically shown in fig.1. The laser beam (He-Ne Laser of NEC, GLG5800) is expanded to 6 mm# in diameter. The parallel light incident on the sample cell is scattered by the continuous sound wave of frequency,S. Koda, H . Matsui and H. Nomura 959 c 28 MHz 1 I I I I I I 1 I Cb 19634' 33' 32' 31' 193' 59' 58' 57' 56' 55' Fig. 2. Typical beat spectra obtained for water at 351 MHz at 25 "C. The beat signals at 28 and 379 MHz correspond to the incident and scattered radiation, respectively.f, under the condition of Bragg reflection. The sound wave comes from a quartz buffer rod, to which a ZnO film transducer with a fundamental frequency of 500 MHz is deposited. Part of the parallel light is modulated by an ultrasonic light modulator at a frequency of 28 MHz and is used as a reference light. In practice, the light reflected under Bragg's condition is superimposed with the reference light on a half-mirror. The intensity of the beat signal is detected with a pinphoto-diode (HP4220) and a Spectrum- Analyzer (Takeda Riken TR4113AL). In order to obtain the intensity spectrum of the beat signal around the Bragg angle, the direction of sound beam is changed by rotating the rotary table. A typical recorder chart obtained for water at f = 35 1 MHz is shown in fig.2. This shows the Lorentzian distribution with an angular width proportional to the ultrasonic absorption (a =q cos @,A@, where q is the wavenumber and a,, the Bragg reflection angle). After the beat signal at f+28 MHz is recorded, the table is rotated until a sharp beat note at 28 MHz is detected. The difference between the two peak points gives directly half of the scattering angle, 0,. The sound velocity can be determined as U = nf/(q sin 0,). Velocities of water determined by HRB method in the frequency range 26MOO MHz are listed in table 1. The temperature of water was controlled within kO.1 "C. The accuracy of velocity measurement was better than kO.05 O/O. Also given in table 1, are the sound velocities that Greenspan and Tschiegg measured at 3 MHz' and the ultrasonic absorptions measured by Mukhopadhyay. lo Agreement is satisfactory.(3) The sound velocity in the GHz region was measured by the Brillouin scattering method. The details of the apparatus and experimental procedures are given elsewhere. l1 The accuracy in the sound velocity was within 1 %. Results and Data Analysis Raman Spectroscopy Fig. 3 shows the typical Raman spectra of C-X sensitive stretching vibrational mode of the sample, together with those of 1,2-dichloroethane and 1,2-dibromoethane (hereafter abbreviated as 1,2-DCE and 1 ,2-DBE, respectively). For assignment, the960 Rotational Isomers of 1 -Bromo-2-chloroethane Table 1. Ultrasonic absorption coefficient and sound velocity of water obtained from the high- resolution Bragg Reflection technique (at 25 "C) f/MHz U/m s-' lO"a/fZNp s2 cm-' 1497.00" 22.2b 26 1 1498.57 21.8 351 1497.45 22.5 457 1497.77 22.9 56 1 1496.09 22.5 " Ref.(9). Ref. (10). I 1 I 1 1 I I 550 600 650 700 750 800 v/m- dibromoethane in the liquid state and 1-bromo-2-chloroethane in the solid state. Fig. 3. Raman spectra of (a) l-bromo-2-chloroethane, (b) 1,2-dichloroethane and (c) 1,2- Raman spectrum of 1-bromo-2-chloroethane (1,2-BCE) in solid state is also shown in fig. 3. The assignment is complete and the frequencies of their characteristic C-X sensitive stretching vibrational modes of each conformer are given in fig. 3. The vibrational frequencies used were independent of temperature and pressure ranges concerned in this work. Assuming that the ratio i2,/SZ, (where SZ is the absolute scattering cross-section of Raman scattering of each mode) is independent of pressure and temperature in the whole range of measurements, the volume and enthalpy differences between the twoS.Koda, H. Matsui and H. Nomura -1.7- -1.8 -1.9- 96 1 0 - a a - - - a - - - I I I I I conformers, that is, trans and gauche forms, can be estimated from the Arrhenius and van’t Hoff equations : where I refers to the Raman intensity. In a previous paper,7 it is confirmed that the depolarization ratio of the C-X stretching mode for dihalogenoethanes little changes with increasing pressure up to 2500 x Pa. Therefore, the above assumption is reasonable for ethane derivatives in the pressure range investigated here, as a first approximation. Fig. 4 and 5 show the relationships between In (ZJI,) us.1 / T and P for the characteristic band of C-Cl and C-Br, respectively. The absolute values of ln(Ig/It) are quite different for C-Cl and C-Br bands but the volume and enthalpy differences, A V and AH, obtained from respective stretching vibrational modes are in excellent agreement with each other. The values thus obtained are summarized in table 2, together with the enthalpy difference in gaseous state found in the literature.12 Ultrasonic Spectroscopy Ultrasonic absorption and sound dispersion spectra of 1,2-BCE are shown in fig. 6 and 7 as a function of temperature. The ultrasonic relaxation is observed in the whole temperature range investigated. The relaxation spectra can be well expressed by the following single relaxation equation wherefrepresents the measuring frequency, f, the relaxation frequency, A the relaxation amplitude and B the absorption from processes other than relaxation.The solid curves in fig. 6 represent the single relaxation curves which are calculated from the linear least mean-squares method minimizing the total relative deviation from the experimental values. The fitting errors are within 3 % in this work. The relaxation parameters thus obtained are summarized in table 3.962 Rotational Isomers of 1 -Bromo-2-chloroethane 1 I I I I I 1 1 400 800 1200 1600 2000 24( p m 5 Pa Fig. 5. Relationships between the logarithmic ratio of integrated intensities and pressure, (0); C-Br stretching mode and (a) C-Cl stretching mode. Table 2. Enthalpy and volume differences obtained from the analysis of Raman intensities AH/kJ mol-' AV/cm3 mol-' AH,,"/kJ mol-1 1,2-DCE 0 - 2.7 6.2 1,2-DBE 3.6 - 5.2 8.4 1,2-BCE 0.4 - 2.0 7.7 "Ref.(12). The sound dispersion curves can also be expressed by the following single dispersion equation :13 where Urn and U, are the sound velocities at the high- and low-frequency limits, respectively, and f" is the dispersion frequency. If eqn (4) can well reproduce the experimental data, the plot between q/(v"- q) and l/f" should be linear. For example, the plot of the data at 25 "C is shown in fig. 8. The straight line was obtained and the dispersion parameters, U,, Uo, f" and the relaxation strength, E (= u",/(u" - E)), were estimated from the slope and intersection of the line. The data thus obtained are summarized in table 4.It is well known that the sound dispersion and sound absorption can be expressed as the real and imaginary parts of the propagating sound wave in a relaxing medium. If the relaxation and sound dispersion curves can be expressed by the single relaxation andS. Koda, H. Matsui and H . Nomura 963 300 200 400F ;OO--.--., loot \ 10 100 1000 fIMHz Fig. 6. Ultrasonic absorption as a function of frequency. Temperatures in "C. 12201 10601 , , I I I , , I I 1 1 , , , , , , , ,,Tf 5 100 1000 10000 f I M H Z Fig. 7. Dispersion of sound velocity. Temperatures in "C.964 Rotational Isomers of 1 -Brorno-2-chloroethane Table 3. Relaxation parameters estimated from the absorption data T/ "C f,/MHz 101'A/Np s2 cm-' 101'B/Np s2 cm-' r - 5 350f10 310& 10 30-60 0.042 5 420f20 260+ 10 30-60 0.041 15 680+30 230+ 10 3&50 0.056 25 780f30 220 + 10 30-50 0.060 10-17 s-2if2 Fig.8. Plot of u",/(UZ-- u",) us. l/f at 15 "C. Table 4. Relaxation parameters estimated from the sound velocity dispersion data T/ "C f"/MHz U,,/ms-l U,/ms-l E -5 350 1160 1202 0.068 5 530 1130 1166 0.061 15 850 1099 1133 0.059 25 950 1067 1098 0.056 dispersion equations, respectively, i.e. eqn (3) and (4), then the following Cole-Cole type equation should hold between the a and V at each measuring frequency.13 where a'3, is the absorption per wavelength. As a typical example, the above ColeCole plot is shown in fig. 9 for 1,2-BCE at 15 "C. In fig. 9, the data are on the half circle within experimental errors in the whole temperature ranges.This indicates that our data analysis is self-consistent. Taking account of the discussion for the ultrasonic data of 1,2-DCE5 and 1,2- DBE,' the ultrasonic relaxation and sound dispersion are ascribed to the rotational isomerism of the 1,2-BCE molecule in liquid state. As pointed out previou~ly,~~~ the free-energy difference AG between the twoS. Koda, H. Matsui and H. Nomura 965 Fig. 9. Plot of -- us. -. : conformers can be evaluated according to the following equation for the rotational isomerism : r = Y'(. RT C, where r is the relaxation strength and values A V and AH are obtained from the Raman spectroscopy. The relaxation strength, r, can be calculated as r = AfrU/2. In eqn (6), g, and g, are, respectively, the degeneracies of the lower and upper energy levels of the two conformers, 8 is the expansion coefficient, C, is the heat capacity at constant pressure and the other symbols have their usual meanings.If the rate constant of the backward reaction is large in comparison with that for the forward reaction, the relaxation frequency, f,, can be described in terms of the following Eyring-type equation :14 f, = V e x p 2nh (- AG:/RT) (7) where AG: is the activation energy and AG: = AH- TAS. Fig. 10 shows the plot of lnf, against 1/T which provides the activation enthalpy, AH and also activation entropy, 9, from the slope and intersection, respectively. The thermodynamic parameters thus estimated are summarized in table 4 together with those of 1 ,2-DCE5 and 1 ,2-DBE6 obtained previously. Discussion AHliquid between two conformers consists of the two parts, that is, intra- and inter- molecular interactions in liquid state.As the AH,,, can be ascribed mainly to be intramolecular interaction, A ( = AH,,, - AHliquid) is a good measure of the inter- molecular interaction in the liquid state. As shown in table 2, the A of 1,2-BCE has966 Rotational Isomers of 1 - Bromo-2-chloroethane 3.8 4.0 4.2 4.4 104/RT Fig. 10. Plot of In (2nf,/T) us. l / R T . Table 5. Summary of the thermodynamic parameters (25 "C) AG/kJ mol-' AS/J K-' mol-1 AH'/kJ mol-1 A$/J K-l mol-1 AG:/kJ mol-1 1,2-DCE 4 - 12 8 - 27 16 1,2-DBE 7 - 10 12 - 17 17 1,2-BCE 2 - 4 16 -4 17 large values similarly as for the cases of 1,2-DCE, and 1,2-DBE, indicating that 1,2-BCE molecules are in fairly strong molecular interaction.However, as shown in tables 2 and 5, the volume difference, AV, and also entropy difference, AS, of 1,2-BCE are small compared with those of 1,2-DCE, and 1,2-DBE. This means that in the case of 1,2-BCE, the local configuration is similar for trans and gauche forms and the differences in packing states are rather small in comparing with those of the 1,2-DCE, and 1,2-DBE. On the other hand, the activation free energy, AGI? of 1,2-BCE is almost equal to those of 1,2-DCE, and 1,2-DBE. In other words, the rate constants of backward reaction of conformational isomerism are in the same order of magnitude for 1,2-DCE, 1,2-DBE and 1,2-BCE. In our previous paper,4 the ultrasonic relaxation frequencies of dihalogenoethanes deviated from those expected from other halogenoalkanes.The relaxation frequencies of 1,2-BCE observed locate in the lower frequency side than that of 1 ,2-DCE and are nearly equal to that of 1,2-DBE at the same temperature, but they still deviate from those of halogenoalkane homologues. The large values of the relaxation frequency, f,, mean that the process of the rotational isomerism for dihalogenoethanes is much faster than those of other halogenoalkanes. If the molecular collision process dominates the rotational isomerism, the short relaxation times of dihalogenoethanes for rotational isomerism suggest that the energy transfer from translation to rotation induced by molecular collision occurs more easily for these dihalogenoalkanes than for other homologues. Combination of the Raman and ultrasonic relaxation spectroscopic data permitsS. Koda, H .Matsui and H. Nomura 967 experimental determination of the free-energy difference between two conformers. The free energy difference, AG, is also related to the equilibrium constant, K , of the conformational equilibrium which can be expressed as : K = exp (- AG/RT) = (n,/n,) = (IgsZt/ZtsZ,). Therefore, we can estimate the ratio of the absolute Raman scattering cross-section between tram and gauche conformers. From the data of AG and Ig/It of 1,2-DCE, we estimated the values of Cl,/n, for C-Cl stretching vibrational mode as 0.21,, while n,/n, for C-Br can be estimated as 0.33, from the data of 1,2-DBE. Using the data for 1,2-BCE, the values of Qt/Q, for C-Cl and C-Br stretching vibrational mode can be obtained simultaneously as 2.87, and 0.48,, respectively. Although the nJQ, values for C-Br obtained from 1,2-DBE and 1,2-BCE are nearly equal, those for C-Cl are quite different.These situations can easily be understood from the Raman spectra of 1,l-DCE, 1,2-DBE and 1,2-BCE, as shown in fig. 3. Unfortunately, no data are available on the absolute Raman scattering cross-section of 1,2-DCE, 1,2-DBE and 1,2-BCE investigated here. Therefore, discussion on this matter is impossible at this stage. However, it is worthwhile pointing out that this method is very useful for estimating the absolute Raman scattering cross-section. We express our deep gratitude to Prof. K. Takagi of Tokyo University for his helpful advice in constructing our HRB apparatus. This work was supported in part by a Grant- in-Aid for Scientific Research from the Ministry of Education, Science and Culture (No. 6 1 134043). References 1 H. Nomura, Y. Udagawa and K. Murasawa, J. Mol. Struct., 1985, 126, 229. 2 H. Nomura and S . Koda, Bull. Chem. SOC. Jpn, 1985, 58, 2917. 3 H. Nomura, S. Koda and K. Hamada, J. Chem. SOC., Faraday Trans. 1, 1987, 83, 527. 4 H. Nomura, S. Koda and K. Hamada, J. Chem Soc., Faraday Trans. I, 1988, 84, in press. 5 W. Seki, P.-K. Choi and K. Takagi, Chem. Phys. Lett., 1983, 98, 518. 6 K. Takagi, P.-K. Choi and W. Seki, J . Chem. Phys., 1983, 79, 964. 7 H. Nomura, K. Murasawa, N. Ito, F. Iida and Y. Udagawa, Bull. Chem. Soc. Jpn, 1984, 57, 3321. 8 K. Takagi and K. Negishi, J. Appl. Phys., 1975, 14, 29. 9 M. Greespan and C. E. Tschiegg, J . Acoustic Soc. Am., 1959, 31, 75. 10 S. K. Mukhopadhyay, Acoustica, 1956, 6, 25. 11 S. Koda, H. Nomura, M. Nakamura and Y. Miyahara, Bull. Chem. SOC. Jpn, 1985, 58, 1484. 12 J. Powling and H. J. Bernstein, J. Am. Chem. SOC., 195 1, 73, 18 15. 13 K. F. Hertzfeld and T. A. Litovitz, Absorption and Dispersion of Ultrasonic Waves (Academic Press, 14 A. J. Matheson, Molecular Acoustics (John Wiley, Chichester, 1971). New York, 1959). Paper 8/02225T; Receiued 3rd June, 1988