J. Chem. SOC.,Faraday Trans. 2, 1983,79, 731-743 Ultrasonic Studies of Rotational Isomerism in Various Methylhexanes BY AKLM. AWWAD, ALASTAIRM. NORTHAND RICHARDA. PETHRICK" Department of Pure and Applied Chemistry, University of Strathclyde, Thomas Graham Building, Glasgow G1 1XL Received 11th October, 1982 Ultrasonic attenuations and velocities are reported for 2-methylhexane, 3-methylhexane, 2,2-dimethylhexane, 2,5-dimethylhexane and 2,2,4-trimethylhexane over a temperature range from 296 to 253 K.The dispersion in the attentuation conforms to a single relaxation process, and a study of its temperature dependence was used to obtain activation energies and energy differences for rotational isomerism. Comparison of the activation parameter obtained experimentally with those from predictions based on non-bonded van der Waals interactions between neighbouring groups allows identification of the equilibrium conforma- tions involved in the rotational isomeric process.Branched-chain hydrocarbons have been much used in recent years to test the validity of various theories of the liquid In particular, detailed thermo- dynamic studies have been made of mixtures of branched-chain and linear hydrocarbons, 1-3*6,7 often with a view to justifying approaches based on gas-like or solid-state anal~gies.~-l~ In such work deviations from ideal behaviour are explained in terms of conformational and packing geometries, and yet detailed quantitative observations of the rotational isomerism in branched-chain hydro- carbons are very limited.To correct this deficiency we have embarked upon a systematic evaluation of internal rotational energies in common branched alkanes using ultrasonic relaxation, a technique ideally suited to the energy values involved. In a recent paper" we reported the correlation between predicted and observed conformational energetics in six methyl-substituted pentanes, and in this paper we evaluate five methyl-substituted hexanes. EXPERIMENTAL 2-methylhexane, 3 -methylhexane, 2,2-dimet hylhexane, 2,5 -dimethylhexane and 2,2,4- trimethylhexane were obtained from Fluorochem (U.K.) Ltd and dried over molecular sieves (B.D.H. type 4A) before use. Their purity was better than 99%. The densities, refractive indices and ultrasonic velocities are presented in table 1 and are in good agreement with literature values. 16-*' Viscosity, density and ultrasonic measurements were made exactly as reported pre- viously.l5 RESULTS VISCOSITIES AND DENSITIES Again measured viscosities and densities were fitted to the empirical equations In q =A +Bv{[T("C)+273.151-TO} (1) 73 1 ROTATIONAL ISOMERISM IN METHYLHEXANES Table 1.Densities, p, refractive indices, nD, and ultrasonic velocities, c, of liquids studied at 293 K p/c cm-3 nD elms-' component obs. lit." obs. lit.' obs. lit.' ~~ 2-methylhexane 0.678 88 0.678 5 1.384 87 1.384 85 1126.9 1120 0.678 9 1121 3 -me thylhexane 0.687 39 0.687 10 1.388 67 1.388 64 1148.2 1136 0.687 0 1141 1145 2,2 -dime th ylhexane 0.695 38 0.695 3 1.393 52 1.393 49 1138.2 1135 0.695 2 2,5 -dime thylhexane 0.693 84 0.693 0 1.392 49 1.392 46 1141.8 1137 0.693 5 1133 2,2,4-trimethylhexane 0.715 67 0.715 6 1.40335 1.4033 1164.9 -~~ a Ref.(16)-(20); ref. (17) and (18);'ref. (19)-(21). Table 2. Viscosity and density temperature-dependence parameters 2 -methylhexane -2.04 274 111 0.696 -8.52 3-methylhexane -1.98 243 123 0.704 -8.53 2,3 -dimethylhexane -1.42 127 182 0.712 -8.37 2,5 -dimethylhexane -1.53 167 150 0.710 -8.18 2,2,4- trimeth ylhexane -1.24 112 195 0.730 -7.56 and the parameters are listed in table 2. ULTRASONIC RELAXATION An example (illustrating the frequencies used and the experimental errors) of the ultrasonic attenuation as a function of temperature and frequency is presented for 3-methylhexane in fig.1. The variation of attenuation with frequency can be expressed as (df2)=A/D + (f/fC>'l +B (3) where A, B and fc are adjustable constants. Computer fits to the data for each compound yielded the parameters summarized in table 3. Continuing the analysis as before,15 ;he required linear dependence of log (relaxation frequency) and of log (Tpma,/C ) on T-' (where pma, is the maximum value of the absorption per wavelength due to the relaxation at f =fc) are illustrated in fig. 2 and 3, respectively. Finally, the derived energy parameters are summarized in table 4. The above analysis assumes that the volume changes associated with the rota- tional isomeric process are negligible, which need not necessarily be the case, and hence the values of AH*and ASeare subject to some uncertainty.A. M. AWWAD, A. M. NORTH AND R. A. PETHRICK 10i 100 300 1000 fIMHz Fig. 1. Variation of the ultrasonic absorption coefficient with frequency for 3-methylhexane at @, 27.2; A, 19.75; A,8; 0,-1.2; U, -16.2"C. Table 3. Ultrasonic relaxation parameters molecule T/"C A/lO1' s2 m-' B/lO'' s2 m-' fJMHz 2 -me thy1 hexane 22.9 t2.5 28 4s 46.5 40 300 240 1.7 56.5 37.5 200 -12.2 70 35 170 -23.9 89 33 120 3-methylhexane 27.2 19.75 33 48 43 37 330 295 8.0 77 27 255 -1.2 107 25 180 -16.2 124 26 140 2,2,4-trimethylhexane 22.0 10.4 90 118 42 36 200 160 -1.2 138 36 120 2,5 -dimethylhexane 22.4 10.3 71 90 43 39.5 300 250 2.8 111 38 200 -2.5 129 33 180 2,2-dimethylhexane 26.10 16.00 43 63 34 27 370 270 5.4 79 25 220 -5.9 94 22 190 ROTATIONAL ISOMERISM IN METHYLHEXANES c i *.,-A 3.2 3.4 3.6 3.8 4 4.1 103~/T Fig.2. Arrhenius plot of relaxation frequencies for ., 2-methylhexane; 0,3-methylhexane; II,2,2 -dime thy1 hexane ; 0,2 5 -dime thylhexane ; L,2,2,4- trime t hylhexane . -5.2 3.4 3.6 3.8 4.0 1O'K/ T Fig. 3. Plot of log(Tp,/c2) against 1/T for A, 2-methylhexane; ., 3-methylhexane; 0, 2,2 -dime thylhexane ; 0,2,5 -dime thylhexane ; a,2,2,4-trimethylhexane. SHEAR AND VOLUME VISCOSITY The B parameters presented in table 3 are associated with the classical contribu- tion to the acoustic absorption: 2 T2 (4)classical viscous thermal A.M. AWWAD, A. M. NORTH AND R. A. PETHRICK 0 4 v, 4 v, 4 rl rl 4 I I I 2 o? 04 c'! l-l m c .d Q 9) .- F .d aCcd n m Wu I e,u n n cuI su n 0 0 m t 0 00 rl 0-\D 9) ccd X Q h f: 93 ROTATIONAL ISOMERISM IN METHYLHEXANES Table 5. Shear and volume contributions to the acoustic attenuation and the K parameter shear volume T/”C (a/f2)/io-15s2 m-’ (a/f2)/i0-15s2m-’ K = d 7 7 S 22.9 10.9 2 -me thy1 hexane 35.6 3.3 12.5 10.6 29.4 2.8 1.7 10.6 26.9 2.5 -12.2 10.8 24.2 2.2 -23.9 11.3 21.7 1.9 27.2 10.2 3-methylhexane 32.8 3.2 19.75 10.0 26.0 2.6 8.0 9.9 17.1 1.7 -1.2 10.0 15.0 1.5 -16.2 10.4 15.6 1.5 2.2 2,2,4- trime thyl hexane 15.1 26.9 1.8 10.4 15.6 20.4 1.3 -1.2 16.9 19.1 1.1 22.4 2,5 -dime thylhexane 12.3 30.7 2.5 10.3 12.2 27.3 2.3 2.8 12.2 25.8 2.1 -2.5 13.3 20.7 1.6 26.1 2,2 -dime th ylhexane 13.6 20.4 1.5 16 13.6 13.4 1.0 5.4 14.0 11 0.8 -5.9 14.9 7.1 0.5 where c is the velocity of sound, 77, and are, respectively, the shear and volume viscosities, y is the ratio of the specific heat at constant pressure, C,,, to that at constant volume, C,,, K is the thermal conductivity and p is the density.In an organic liquid the thermal contribution to the attenuation is negligible, and the major contribution is made by the viscous term.The magnitude of the shear viscosity was determined by ancillary flow measurements (table 2). Using the density and the sound velocity it is possible to calculate the shear contribution to the total attenuation: so the residue can be associated with the volume viscosity Analysis of the data presented in table 3 leads to the contributions presented in table 5. We have also tabulated the ratio, K, of the volume to shear components. The volume viscosity in an organic liquid can arise from processes such as rotational isomerism, or fluctuations in the structure of the liquid. In this work we have subtracted the contribution due to rotational isomerism, and therefore can A. M. AWWAD, A. M. NORTH AND R.A. PETHRICK 0 120 240 3 60 O/O Fig. 4. Energy-angle relationship for 2-methylhexane. associate the remaining absorptions with fluctuations of the liquid structure occur- ring at frequencies higher than those used in this study. The magnitude of this contribution is clearly dependent upon the stereochemistry of the molecules being studied, and reflects their ability to cluster into more densely packed structures. THEORETICAL ROTATIONAL ENERGIES Unlike the previous system investigated,” rotations about more than two bonds have to be considered to include all possible isomeric states. However, the linear portion of the hydrocarbon chain will exhibit a rotational isomeric potential closely resembling that of the unbranched hydrocarbons with AE’, AHe known to be considerably lower than those associated with rotation about the more hindered methyl-substituted bonds.In the methylhexanes, in all but one case the problem thus reduced to consideration of rotational motion about the two bonds C(2)-C(3) and C(3)-C(4). The intergroup potentials used in the calculations, their applicability and their deficiencies are discussed in the previous paper. ’*These calculations are believed to provide a useful basis for the representation of the changes in the potential energy as a function of azimuthal angle, although since they are derived from inert gas force fields they may not be considered to be absolute. Preliminary quantum- mechanical calculations have indicated that these semi-empirical calculations are qualitatively correct.The resulting energy profiles are presented in fig. 4-8, and the values of AEt and AHe compared with experimental quantities in table 4. DISCUSSION In the calculations presented in fig. 4-8 it has been assumed that the linear ‘tails’ of the molecules adopt an all-trans structure. Clearly, since the activation energy for the rotational isomerism of this part of the molecule is relatively low, ca. 8 kJ mol-l, the minimum-energy structure can be rapidly achieved when rota- tions occur about the more hindered C(2)-C(3) or C(3)-C(4) bonds. In support ROTATIONAL ISOMERISM IN METHYLHEXANES 0 120 24 0 360 @/" Fig. 5. Energy-angle relationship for 3-methylhexane. A. M. AWWAD, A. M. NORTH AND R.A. PETHRICK ---46.6 ---32 -2 25 0 120 24 0 360elo 30 0 120 24 0 360el" Fig. 6. Energy-angle relationship for 2,2-dimethylhexane. ROTATIONAL ISOMERISM IN METHYLHEXANES ,d62 l+. I I I I I 0 120 2 40 360elo Fig. 7. Energy-angle relationship for 2,5-dimethylhexane. of this assumption, ultrasonic studies of linear hydrocarbons have indicated that conformational changes at room temperature occur at rates >lo8s-' and contribute only a small increment to the observed attenuation. 2-METHYLHEXANE Reasonable agreement between theory and experiment is obtained for AE* by assuming that the process corresponds to rotation about the C(2)-C(3) bond and involves the doubly degenerate 60 and 180" states and the 300" state. The discrepancy between experiment and theory for the rather small value of AH0 probably reflects inadequacies in the form of the potential function used, and we feel that the acoustic value is a more dependable quantity for use in conformational equilibrium considerations.3-METHYLHEXANE We can consider rotation about either the C(2)-C(3) or C(3)-C(4) bonds. The energy differences and activation energies are very similar and it is not possible from these experiments to differentiate between these processes. It therefore seems likely that the observed relaxation is the result of both. However, since agreement between theory and experiment appears based on a single profile, we suggest that isomerism involves two asynchronous motions rather than one coordinated process.--42.5 .--34.5 --29.8 --27.9 120 240 360 0 120 240 360 ---46.6 ---32.2 251 1 I 0 120 240 3 1el0 Fig. 8. Energy-angle relationship for 2,2,4-trimethylhexane. 742 ROTATIONAL ISOMERISM IN METHYLHEXANES 2,2-DIMETHYLHEXANE Rotation about the C(2)-C(3) bond is an isoenergetic process, and so is acoustically inactive. However, rotation about C(3)-C(4) leads to the generation of states with a profile which might be expected to reflect the observed relaxation. Comparison with theory indicates a poor agreement, and this probably reflects inadequacies of the potential for interactions of the t-butyl group. Again we suggest that the acoustic data form a more reliable base for conformational equilibrium calculations.2,5 -DIMETHYLHEXANE Rotations about C(2)-C(3) and C(4)-C(5) are identical. In this case the theoretical energy difference for exchange between the degenerate 60 and 180* positions and the 300 O position is larger than that observed experimentally, although the activation parameters are in reasonable agreement. 2,2,4-TRIMETHY LHEXANE Rotations about C(2)-C(3) lead to isoenergetic states which will not be observed acoustically. There are two other possible isomeric processes which must be considered. First, rotation about C(3)-C(4) leads to a doubly degenerate lower energy state and a single upper state. Rotation about C(4)-C(5) leads to a similar situation. Again from the acoustic data we are unable to decide between these two possibilities, and presumably both occur with possibly some degree of coordi-nation.The values of the entropy difference associated with the internal rotational process in these systems are high. This reflects the complexity of the processes being observed and is probably a consequence of the ‘cogwheeling’ effect of neighbouring methyl groups in formation of the eclipsed transition state. We acknowledge with pleasure the award of a maintenance grant by the Petroleum Research Institute of Iraq to A.M.A. M. Barbe and D. Patterson, J. Solution Chem., 1980,9, 753. M. Barbe and D. Patterson, J. Phys. Chem., 1978, 82, 40. V. T. Lam, P. Picker, D. Patterson and P. Tancrede, J. Chem. SOC., Faraday Trans.2, 1974, 70, 1465. P. Tancrede, P. Bothorel, P. de St. Romain and D. Patterson, J. Chem. SOC., Faraday Trans. 2, 1977, 73, 15. A. Heintz and R. N. Lichtenthaler, Angew. Chem., Int. Ed. Engl., 1982, 21, 184. A. Heintz, R. N. 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