Ultrasonic Relaxation in Aqueous Solutions of Butanediols BY SADAKATSU NISHIKAWA* AND MITSUO MASHIMA Department of Chemistry, Faculty of Science and Engineering, Saga University, Saga 840, Japan Received 12th June, 1981 Ultrasonic absorption and velocity have been measured to investigate the structural and dynamic properties of aqueous solutions of butane-1,Cdiol and butane-1,2-diol at 20 OC. In the former solution no excess absorption was found, and in the latter solution a single relaxational process was observed in the frequency range 15-220 MHz. The excess absorption mechanism has been analysed as a solute-solvent interaction, AB A+ B, and the rate constants for butane- 1 ,2-diol solution have been determined to be kf = 1.5 x 108 s-' and kb = 1.6 x 108 dm3 mo1-l s-' for the forward and backward steps, respectively.The influence of the position of hydroxy groups in the molecules on the water structure is discussed by a comparison with the results for solutions of the two dihydric alcohol. In preceeding papers'v we have reported the structure and kinetics of aqueous solutions of alcohols and ethers by means of ultrasonic methods. The characteristic properties of these solutions are the peak sound velocity concentration and the peak sound absorption concentration. Mechanistic models3 of these properties have been proposed for various non-electrolyte solutions, and more recently fluctuation models4~ have been suggested. Our interpretation of the absorption mechanism is based on an analysis of the concentration dependences of the relaxation frequencies; this is related to reaction rates and the maximum excess absorption per wavelength, which is associated with the volume and enthalpy changes of the reaction.We also base our interpretation on the nature of the solute molecules. The ultrasonic studies have been extended to aqueous solutions of dihydric alcohols in order to investigate whether the proposed model for aqueous solutions of alcohols and ethers is also applicable. For this purpose we have chosen butane- 1,2-diol and butane- 1,4-diol as the solutes. EXPERIMENTAL Butane- 1,2-diol and butane- 1 ,Cdiol were obtained from the Tokyo Kasei Kogyo Co., and were distilled under reduced pressure. The chemicals were subjected to gas-chromatographic analysis and showed purities of < 99.8%.Doubly distilled water was used as solvent. The desired concentrations were obtained by weighing. The ultrasonic pulse techniques was used to measure the absorption coefficient, a, in the frequency range 15-95 MHz using a 5 MHz fundamental crystal and in the range 60-220 MHz using a 20 MHz crystal. The uncertainty in the absorption coefficient was within f: 2.5 %. The ultrasonic velocity was measured by an interferometer operating at 2.5 MHz; uncertainties in the measurement were within f: 50 cm 0. The solution density was measured using a standard pyknometer having a volume of ca. 2.3 cm3. All the measurement cells were immersed in a water bath which was maintained at a constant temperature to better than fO.O1 OC. In order to calculate the ultrasonic, kinetic and thermodynamic parameters a Hitachi microcomputer was used.41 1249 FAR 11250 ULTRASONIC RELAXATION I N AQUEOUS BUTANEDIOLS RESULTS No frequency dependence of a / f 2 , wherefis the frequency, has been observed in aqueous solutions of butane-1,4-diol up to a concentration of 6.8 mol dm-3. On the other hand, excess absorption was found in solutions of butane- 1,2-diol. The observed spectra are all characteristic of a single relaxation, which is expressed as follows: or where A is the amplitude of the excess absorption, B is that of the background absorption, fr is the relaxation frequency, p is the excess absorption per wavelength, and c is the velocity of sound. Fig. 1 shows representative absorption spectra in aqueous solutions of butane- 1,2-diol and butane- 1,4-diol, which are expressed in terms of eqn (1).The ultrasonic parameters were determined so as to obtain the best fit to 1 I I 0 2o 10 50 100 500 fIMHz FIG. 1 .-Representative ultrasonic absorption spectra for aqueous solutions of butane- 1,2-diol and butane-lP-diol at 20 O C . Arrows show the relaxation frequency and solid curves are calculated using eqn (1). Butane-1,2-diol: (>, 2.25; 0, 3.04; 0, 5.07mol dm-3. Butane-1,Cdiol: 0, 2.48; 0, 4.13; 0, 6.82 mol dm-3. TABLE 1 .-ULTRASONIC PARAMETERS FOR AQUEOUS SOLUTION OF BUTANE- 1,2-DIOL 4 C e A B /mol dm-3 /10-17 s2 cm-l /10-17 s2 cm-l fr/MHz P / g c/m s-I 2.25 35.5 19.7 250 1.011 1627 3.04 46.6 48.4 173 1.015 1654 4.12 109 113 131 1.020 1667 5.07 169 131 114 1.020 1659 6.18 128 - 204 113 1.022 1638 6.90 105 220 140 1.021 1628 7.95 95.1 260 130 1.018 1594S.NISHIKAWA AND M. MASHIMA 1251 I I I 1 3 5 7 CJmol dm-3 FIG. 2.4oncentration dependences of excess absorption, A , and the background absorption, B. a, B for butane-1,2-diol; 0, A for butane-1,2-diol; 0, Bfor butane-1,Cdiol; 0, B for butane-1,Cdiol measured by Blandamer et al.' the experimental data, using a least-mean-squares method. Those for butane- 1,2-diol are given in table 1; the values of A and B are shown in fig. 2, along with those of B for butane- 1,4-diol as a function of concentration. In both solutions, the background absorption increases with concentration and has a higher value than would be expected from classical absorption, i.e. absorption due to viscous and thermal effects; this means that other excess absorptions are predicted in the higher frequency range.The amplitude of the excess absorption, A , for butane-1,2-diol shows a maximum at ca. 5.2 mol dm-3. The sound velocity passes through a maximum at 4.0 mol dm-3. Similar dependences of concentration on ultrasonic properties have been observed in aqueous solutions of monohydric alcohols and The proposed modell for the excess absorption mechanism in the megahertz frequency range is the interaction between solute and solvent, in which only non-hydrogen-bonded water molecules may participate. This is shown in reaction (2) where AB is the complex, A is the solute, B is the non-hydrogen-bonded water molecule and Ci are the equilibrium concentrations of each component. An important factor which may arise in the analysis of the relaxational process is a coupling to other reactions which occur in solution, e.g.internal rotation of the diols. When the relaxation frequencies are relatively close to each other, the slower process should be 41-21252 ULTRASONIC RELAXATION I N AQUEOUS BUTANEDIOLS influenced by the faster one. However, in aqueous solutions of butane- 1,2-diol, only a single relaxation process has been observed, and the influence caused by other reactions in our frequency range may be so small that, to a good approximation, only one equilibrium perturbation is the cause of the excess absorption. The relation between the relaxation frequency and the analytical concentrations of the solute and solvent is derived as follows for reaction (2): where Ce, Cw, B and K are the analytical concentrations of the solute and solvent, the mole fraction of non-hydrogen-bonded water and the equilibrium constant defined by K = k,/k,, respectively.The relaxation frequency passes through a minimum at 5.2 mol dm-3, and this condition may be used to obtain the relationship between j? and K. Then kb, B and K values are determined so as to obtain the best fit to eqn (3). The calculated values using these determined parameters are shown in fig. 3 by a solid line. In table 2 the rate and thermodynamic constants are listed along with those for monohydric alcohol solutions for comparison. 3001 ; I I I 1 I 3 5 7 9 CJmol dm-3 FIG. 3.-Relaxation frequency as a function of butane-1,2-diol concentration. The solid curve was calculated for the mechanism AB e A+ B, and the dashed one was determined for B = 0.175 and K = 0.620 dms m o P for the mechanism AB, e A + 2 B .TABLE 2.-RATE AND THERMODYNAMIC CONSTANTS FOR ALCOHOLS AND DIOL k b kf/s-' /dm3 mol-l s-l B ref. - 0.26 8 pure water - isopropyl alcohol 1.4 x lo8 8.8 x lo7 0.17 lc butane- 1,2-diol 1.5 x lo8 1 . 6 ~ lo8 0.19 this work propyl alcohol 1.6 x lo8 6.2 x 107 0.15 la t-butyl alcohol 1.2 x lo8 6.3 x 107 0.12 lbS. NISHIKAWA A N D M. MASHIMA 1253 Another parameter determined from ultrasonic absorption measurements is the maximum excess absorption per wavelength, pmax. For reaction (2) we have Af,c 7tpc2r - (AV- up AH/pCJ RT Pmax = - - 2 (4) r = ( i / v ) ( i / c l + 1/c2+ 1/c3- i/cT)-l ( 5 ) where p is the density, R is the gas constant, T is the absolute temperature, A V is the volume change occurring during the reaction, AH is the enthalpy change, up is the thermal expansion coefficient, C, is the specific heat at constant pressure, and V is the molar volume.To a good approximation pmax is almost proportional to p c T V , because the contribution of the concentration dependences of other terms to pmax is very small. Fig. 4 shows plots of pmax and p c T V . These confirm that the excess absorption mechanism may be due to the perturbation of the equilibrium shown in reaction (2). 2 I I I I 3 5 7 C,/mol dm-3 FIG. 4.4oncentration dependences of p,,, and p c T V for aqueous solutions of butane-1 ,Zdiol. DISCUSSION Andreare et aL3 have considered and reviewed various mechanisms in order to interpret the characteristic properties of non-electrolytes in aqueous solution.Recently approaches to the absorption mechanism have been taken into account using fluctuation However, depending upon the choice of solute, the magnitudes of the peak sound absorption are different and one or two relaxational absorptions are observed. Therefore we prefer to assume the normal perturbation of equilibrium as the cause of the excess absorption mechanism. Blandamer et a1.' have reported ultrasonic absorption results in butane- 1,4-diol aqueous solution in which no excess absorption was observed. They also found that the existance of the excess absorption in the megahertz frequency range depends on the structure of the alcohol, which seems to be consistent with our results.1254 ULTRASONIC RELAXATION I N AQUEOUS BUTANEDIOLS Although the interaction between butane-1,2-diol and water is attributed to the formation of a 1 : 1 complex, it might be expected that more than one water molecule is bonded to butane-1,2-diol because of the Occurrence of two hydroxy groups in the molecule.We also tested to see if the AB, e A + 2B mechanism was associated with the excess absorption. The relaxation frequency for this mechanism is expressed as 2nfr = kk(4[A] [B] + [BI2) + k;. Assuming appropriate values of /? and K (the detailed procedure for this calculation is described in a previous papere), each equilibrium concentration was calculated and the ratio k;/kk was determined so as to obtain the same value of Kas had been assumed and so as to reach a maximum of pcT’V when r’ = (1 / C , + 4/C, + 1 /C3 - 4/CT)/ V.When /? values in the range 0.16-0.19 are chosen, a K value which satisfies the above conditions is obtainable. However, the concentration dependence of the relaxation frequency is not so well interpreted (one set of results is shown in fig. 3 by a dashed line), and the probable errors in k; and k6 were larger than the probable values. Another reason for our conclusions is that the observed excess absorption is characteristic of a single relaxation process and therefore only one equilibrium perturbation between different molecular species is the cause of the observed excess absorption. One possible explanation of the ,single relaxation might be that intra- molecular hydrogen bonding could exist in the butane-l,2-diol molecule because of the very close positions of the two hydroxy groups.It is thus strange that no excess 100- 50 - I F - I- - I 2 3 4 5 6 carbon no./no. of OH groups FIG. 5.-Plots of the relaxation frequency range and carbon number per hydroxy group. 0 Butane-1,2-diol, 0 ethyl alcohol, 0 isopropyl alcohol, @ propyl alcohol, 0 t-butyl alcohol, 8 propyl cellulose, 0 butyl cellulose. absorption was found in butane- 1,4-diol solutions. By examining the ultrasonic absorption data for aqueous solution of various alcohols and ethers reported so far, it is found that the excess absorption depends strongly on the size of the alkyl group. In fig. 5 , the ranges of relaxation frequency observed in the solutions are plotted against the carbon number per hydroxy group.As the size of the hydrophobic group increases, the excess absorption appears in a lower frequency range and in a lower concentration range. Butane-l$diol has two hydroxy groups at each end and it may be considered that the number of alkyl groups per hydroxy group is two; however, the effect of the size of the alkyl group on the hydroxy group is less than that forS. NISHIKAWA AND M. MASHIMA 1255 butane-l,2-diol or ethyl alcohol. The excess absorption in ethyl alcohol solution is observed over a high frequency range,l0 and no excess absorption in methyl alcohol solution has been reported in the megahertz frequency range at room temperature.ll Therefore the hydrophobicity of butane- 1,4-diol seems to be small, and less than that of butane-l,2-diol and ethyl alcohol. At this stage we may conclude that the interaction between water and solutes containing hydroxy groups is strongly dependent on the strength of the hydrophobicity of the solute; the /3 parameter is very useful in estimating the effect of the solute on the water structure.We thank Miss F. Ikegami for performing some of the ultrasonic measurements. (a) S. Nishikawa, M. Mashima and T. Yasunaga, Bull. Chem. SOC. Jpn, 1975,424,661 ; (b) S. Nishikawa, M. Mashima, M. Maekawa and T. Yasunaga, Bull. Chem. SOC. Jpn, 1975,48,2353; (c) S. Nishikawa, M. Mashima and T. Yasunaga, Bull. Chem. SOC. Jpn, 1976, 49, 1413. * S. Nishikawa, M. Tanaka and M. Mashima, J. Phys. Chem., 1981, 85, 686. J. H. Andreae, P. D. Edmonds and J. F. McKellar, Acustica, 1965, 15, 74. (a) G. Atkinson, M. M. Emara, H. Endo and B. L. Atkinson, J. Phys. Chem., 1980, 84, 259; (b) G. Atkinson, S. Rajagopalan and B. L. Atkinson, J. Phys. Chem., 1981, 85, 733. (a) Y. Harada, Y. Suzuki and Y. Ishida, Phys. Rev. A, 1980, 21, 928; (b) Y . Harada, J. Phys. SOC. Jpn, 1980, 48, 705. N. Tatsumoto, J. Chem. Phys., 1967, 47, 4561. 1805. T. A. Litovitz and E. H. Carnevale, J. Appl. Phys., 1955, 26, 816. S. Nishikawa, Y. Yamashita and M. Mashima, Bull. Chem. SOC. Jpn, 1982, 55, in press. ' M. J. Blandamer, N. J. Hidden, M. C. R. Symons and N. C. Treloar, Trans. Faraday SOC., 1969,65, lo K. Takagi and K. Negishi, Jpn J. Phys., 1975, 14, 953. l1 J. Emery and S. Gasse, Acustica, 1979, 43, 205. (PAPER 1/949)