J . Chem. SOC., Faraday Trans. I, 1988, 84(2), 665-674 Dynamic Studies of the Interaction between Diols and Water by Ultrasonic Methods Part 4. - 3-Methylbutane- 1,3-diol and 2,2-Dimethylpropane- 1,3-diol Solutions Sadakatsu Nishikawa," Naohiko Nakayama and Nobuyoshi Nakao Department of Chemistry, Faculty of Science and Engineering, Saga University, Saga 840, Japan In order to justify the relationship between the structures of diols in aqueous media and their ultrasonic properties, measurements of ultrasonic ab- sorption, sound velocity, density and viscosity have been made in aqueous solutions of 3-methylbutane- 1,3-diol and 2,2-dimethylpropane- 1,3-diol, which are isomers of each other. In both solutions, a single relaxational ultrasonic absorption has been observed in the frequency range 15-220 MHz.The absorption mechanism has been interpreted in terms of reaction kinetics associated with the interaction between the solute and solvent. As a result, the effect of the solute on the solvent (water) structure has been estimated, and it has been found that these diols act as water-structure promoters. Furthermore, the greater the hydrophobicity of the solute molecule, the more effectively it promotes the water structure. The trend in hydrophobicity determined from sound absorption has been confirmed from the concentration dependences of the compressibility. The correlation between the solvent structural parameters and the compressibility has been examined. The apparent molar volume has also been determined and is discussed with regard to the ultrasonic parameters.In previous studies1 of aqueous solutions of various diols by ultrasonic methods, the conformations or the structures of the diol molecules in an aqueous medium have been predicted to affect the ultrasonic characteristics ; i.e. relaxational absorption associated with an interaction between solute and solvent has sometimes been observed, depending upon the structure of the solute. In addition, relaxational absorption due to the conformational changes in some diols would be expected both in aqueous and organic solutions. In order to justify such predictions, ultrasonic absorption and velocity results are required in other solutions. For this purpose, we have chosen two diols, 3- methylbutane- 1,3-diol and 2,2-dimethylpropane- 1,3-diol, which are isomers.In this paper we report ultrasonic absorption, ultrasonic velocity, density and viscosity results in these solutions, and these are compared with results reported previously. Experimental The chemicals used in this study were purchased from the Tokyo Kasei Co. Ltd and were the purest grades obtainable. 3-Methylbutane- 1,3-diol was distilled under reduced pressure. 2,2-Dimethylpropane- 1,3-diol was a solid at room temperature and was used without further purification. The sample solutions were prepared with doubly distilled water by weighing at their desired concentrations. The concentration of the 2,2- dimethylpropane-1,3-diol solution was limited to 5 mol dm-3 because of its solubility in water. The ultrasonic absorption coefficient was measured by an improved pulse method in the frequency range 15-220 MHz : details have been given elsewhere.2 An interferometer 665666 Interaction between Diols and Water 2 3 4 5 CJmol dm-3 Fig.1. Concentration dependence of the ultrasonic absorption in an aqueous solution of 2,2- dimethylpropane-1,3-diol at various frequencies at 25 "C: 0, 14.54; 0, 45.52; a; 92.63 and 8, 222.1 MHz. at 2.5 MHz and a 'sing-around' meter at 1.92 MHz were used to determine the sound velocity. By both methods the value of the sound velocity was obtained to within an accuracy of better than +1 m s-l. The solution density was measured using a pyknometer of volume ca. 4cm3. The viscosity coefficient was measured using an Ubbelode viscometer. All items of apparatus were immersed in a water bath whose temperature was controlled to within k0.002 "C.Results and Discussion Fig. 1 shows the ultrasonic absorption coefficient divided by the square of the measurement frequency, ( a / f 2 ) , at various frequencies for an aqueous solution of 2,2- dimethylpropane- 1,3-diol at 25 "C. For concentrations < 2.0 mol dm-3 the (a/f2) values are independent of the frequency, and it was not possible to measure the absorption at concentrations > 5 mol dm-3 because of the diol's solubility in water. However, the values of (a/f2) in the range 2.7-5.0mol dm-3 have been found to depend considerably on both the frequency and the concentration, as is seen in fig. 1. In a solution of 3-methylbutane- 1,3-diol the absorption measurements were carried out in the concentration range up to 6.99 mol dm-3 at 20 "C and the absorption is dependent on frequency in the range above 2.02 mol dm-3.When the absorption mechanism is5000 I000 " ' 500 E v) P I 2 1 h N i a S. Nishikawa, N. Nakayama and N. Nakao I I I - - I I I 667 . - 10 5c 100 500 f/M& Fig. 2. Ultrasonic absorption plots in aqueous solution of 2,2-dimethylpropane- 1,3-diol: @,2.75; a, 3.00; 0, 3.60 and a, 5.00 mol d ~ n - ~ . f/MHz Fig. 3. Ultrasonic absorption plots in aqueous solution of 3-methylbutane-l,3-diol at 20 "C: 8, 3.02; 0, 4.03; a, 5.02; 0, 5.97 and (>, 6.99 mol dm-3.668 Interaction between Diols and Water Table 1. Ultrasonic and thermodynamic parameters in aqueous solutions of 3-methylbutane- 1,3- diol and 2,2-dimethylpropane- 1,3-diol C,/mol dm-3 f,/MHz A/lO-" s2cm-' B/10-" s2 cm-' v/m s-' p / g q/cP 2.02 3.02 3.50 4.03 4.50 5.02 5.58 5.76 5.97 6.58 6.99 2.75 2.90 3 .OO 3.10 3.20 3.40 3.50 3.60 3.75 3.80 4.00 4.25 4.50 5.00 3-methylbutane- 1,3-diol solution at 25 "C 210 22.6 25.9 1635 127 43.5 73.7 1678 116 105 91.1 1689 114 163 118 1693 114 210 157 1690 114 253 198 1682 127 288 234 1672 135 357 217 1664 131 329 285 1660 165 355 347 1640 139 436 434 1624 2,2-dimethylpropane- 1,3-diol solution at 25 "C 97.6 82.6 55.2 1642 96.4 85.4 73.1 1645 94.8 97.6 83.6 1646 98.8 128 72.5 1648 92.9 111 92.4 1649 88.3 165 91.5 1651 87.9 160 106 1651 85.0 195 94.8 1650 89.4 201 111 1650 91.2 210 112 1650 95.9 213 126 1648 99.6 242 130 1645 101 226 132 1642 103 267 267 1630 1.0042 1.0078 1.0095 1.0101 1.0104 1.0096 1.0089 1.0076 1.0072 1.0939 1.0018 1.0065 1.0068 1.0075 1.0072 1.0075 1.0077 1.0078 1.0080 1.0080 1.0083 1.0084 1.0082 1.008 1 1.0071 - - - - - - - - - - - 2.7 18 2.909 3.074 3.21 1 3.364 3.635 3.848 3.872 4.222 4.400 4.882 5.398 6.103 8.27 1 interpreted, it may be appropriate to analyse the frequency dependence of the absorption coefficient.If the absorption is associated with a relaxation process, it may be expressed by the following equation : wheref, is the relaxation frequency and A and B are constants. Fig. 2 and 3 show the frequency dependence of the absorption for both solutions. All the spectra are well represented by eqn (1). The ultrasonic parameters have been determined by a least- squares computer program, and the solid curves in the figures indicate the calculated values.Ultrasonic results determined thus are listed in table 1, along with other ultrasonic and thermodynamic parameters. In order to illustrate the concentration dependence of the excess absorption amplitude, A, and the background absorption, B, the results are shown in fig. 4 for an aqueous solution of 2,2-dimethylpropane- 1,3-diol. They increase monotonically with the analytical concentration. These trends are contrasted by those observed in many non-electrolyte aqueous solutions ;3 i.e. the peak sound absorption vs. concentration phenomena are usually observed in solutions of non- electrolytes that have a hydroxy group. In order to see if the observed relaxational absorption is due to a viscosity effect, the viscosity coefficient, 7, has been measured in the solutions and the classical absorption (denoted by the subscript cl) has been calculated using the equation (a/. 2)c1 = 8Z27/3PV3 (2)" I E N S.Nishikawa, N . Nakayama and N . Nakao 300b 200 too 669 2 3 4 5 CJmol dm-3 Fig. 4. Concentration dependences of the excess absorption amplitude, A , (0) the background absorption, B, (0) and the classical absorption, ( C C / ~ ~ ) ~ , , (0) for an aqueous solution of 2,2-dimethylpropane- 1,3-diol at 25 "C. where p is the solution density and v is the sound velocity. The results are also shown in fig. 4, and it is seen that the observed absorption is not associated with the viscous one. The background absorption, B, is still higher than that of the classical absorption, which may indicate that another relaxation process may exist in the higher frequency range. On the other hand, characteristic trends in the relaxation frequencies were found in both solutions, as is seen in fig.5 : they show a minimum. In the solution of 3-methylbutane- 1,3-diol, the relaxation frequency exists at a high frequency range, so that the absorption measurements were carried out at 20 "C in order to obtain the ultrasonic parameters as accurately as possible. From the dependence of the ultrasonic parameter, fr, on the concentration, we consider that a plausible absorption mechanism may be one due to a reaction associated with interactions between the solute and solvent. Following previous interpretations, the model may be simply expressed by k f AB$A+B (3) kb where k, and k, are the forward and backward rate constants, respectively, and AB is the complex formed by the solute A and solvent B.To a good approximation we can say that the solvent water molecules consist of non-hydrogen- bonded and hydrogen-bonded molecules, and the former may participate in the reaction under consideration. Further, it is assumed that the reaction associated with the formation and breakage of water hydrogen bonds is so fast4 that it is expected not to affect the solute-solvent interactions. Under these assumptions the relationship between the relaxation frequency and the analytical concentrations for the process expressed by eqn (2) is derived as5670 Interaction between Diols and Water 2 4 6 C,/mol dm-3 Fig. 5. Concentration dependences of the relaxation frequency for aqueous solutions of 2,2-dimethylpropane- 1,3-diol (0) and 3-methylbutane- 1,3-diol (0).Table 2. Rate and thermodynamic constants for aqueous solutions of diols ~~ solute k,/ 1 O8 s-' k,/ 1 O8 dm3 mo1-1 s-l P ref. a a a (1 6) pentane- 1,5-diol - - - 3-methylbutane- 1,3-diol 1.1 kO.1 2.1 fO.l 0.155 f 0.004 this work 2,2-dimethylpropane- 1,3-diol 0.99 If: 0.07 2.2 & 0.2 0.104 f 0.002 this work a No chemical excess absorption. where Ce and Cw are the analytical concentrations of solute and solvent, respectively, p is the fraction of non-hydrogen-bonded water molecules and K,, is defined as K,, = k,/k,. The rate and thermodynamic parameters in eqn (4) were determined so as to obtain the best fit of the experimental data, f,, to the equation by means of a non-linear least-squares program.The determined values are listed in fable 2. The value of p is considered to be the fraction of less structured water molecules, and is smaller than that in pure water.6 This means that the solute acts as a promoter of water structure. In this case p is expected not to be so dependent on temperature. For example, the enthalpy change and entropy change between the two states of water have been estimated to be 8 kJ mol-1 and 15 J mol-1 K-l for an aqueous solution of ally1 Cello~olve.~ Although the measurement temperatures for the two solutions in this study are different, it may be appropriate to compare the results : the value of B for the 3-methylbutane- 1,3-diol solution is smaller than that for the 2,2-dimethylpropane- 1,3- diol solution.From the structure of these two molecules, it is expected that the two C(2) methyl groups in the latter solute may be bulky and hydrogen-bonded water may form around the hydrophobic part of the solute molecule. This is also expected from the differences in solubility of the two diols in water. Note that no excess absorption is observed in the solution of pentane- 1,5-diol, another isomer.1bS. Nishikawa, N . Nakayama and N. Nakao 67 1 I I I I I I 2 4 6 C,/mol dm-3 Fig. 6. Plots of the maximum excess absorption per unit wavelength and the calculated pv2T as a function of concentration: (0) and (1) for a solution of 3-methylbutane-1,3-diol; (0) and (2) for a solution of 2,2-dimethylpropane- 1,3 diol. Another parameter obtained from measurements of the sound absorption and velocity is the maximum excess absorption per wavelength, ,urnax, which is related to the standard volume change of the reaction, AV, and the standard enthalpy change, AH.It is derived as follows: ( 5 ) where R is the gas constant, Tis the temperature, a, is the thermal expansion coefficient, C , is the specific heat at the low-frequency limit, C," is that at the high-frequency limit and I' is a concentration term expressed by ,urn,, = zpv2T ( A V - a, AH/PC,")~ (C,"/CP)/2RT r = [ 1 / c A + ~ / c B + 1 / c A B - ~ / ( c A + c ~ + c A B ) ] - ' (6) where Ci indicates the equilibrium concentration of reactant i. In order to obtain the changes in volume and enthalpy of the reaction, values of the two specific heats and the thermal expansion coefficient are necessary.However, these are not readily available. In a previous study1' we determined these volume and enthalpy changes on the assumption that the heat capacity was close to that of a 2-butoxyethanol solution. However, in the case of the present solutions, the contribution of specific-heat terms may be very important. Despite this uncertainty, we considered that the most effective term in determining the concentration dependence of ,urnax is pv2T. Fig. 6 shows the experimental values of the maximum excess absorption per wavelength and the calculated value of p v 2 r In the low concentration range the dependences resemble each other, while at higher concentrations they do not. This type of trend has also been observed in other diol solutions, and has been attributed to a relaxation process associated with rotational isomerization in the concentrated solution.' There may also be relaxation due to conformational changes of the solutes in concentrated solutions.Desnoyers' group8 has studied thermodynamic properties of various non-electrolytes672 Interaction between Diols and Water I I I 4 2 4 6 CJmol dm-3 Fig. 7. Concentration dependences of the apparent molar volume for solutions of 3-methylbutane- 1,3-diol (0) and 2,2-dimethylpropane- 1,3-diol (0). in aqueous media. They have reported that when the hydrophobicity of the solute increases, characteristic concentration dependences of the apparent molar volume and compressibility are observed in the solution. In order to see how the present solutes behave, the concentration dependences of these parameters were determined using the following relations : where q5v is the apparent molar volume, po is the solvent density, Me is the molecular weight of the solute and m is the molality, which is obtained from the molarity of the solutions.The adiabatic compressibility, K,, and the apparent molar compressibility, r ~ 5 ~ , of the solution are obtained from the results for the sound velocity and the solution (8) density using the equations lc, = 1/@v2) and A = K , A + 10OO(lcs - Kw)/mPo (9) #v = M e / P - - Po)/(mPPrJ) (7) where IC, is the compressibility of the solvent water. Fig. 7 shows the concentration dependence of the apparent molar volume for the two solutions. The curve for the 2,2- dimethylpropane- 1.3diol solution is not so sharp as that of the 3-methylbutane- 1.3diol solution, although the hydrophobicity of the former is considered to be larger from the absorption results ; i.e.the value of /3 for the 2,2-dimethylpropane- 1,3-diol solution isOO S. Nishikawa, N. Nakayama and N . Nakao 673 1 I I - 0. I 0.2 0.3 mole fraction, x Fig. 8. Concentration dependences of the apparent molar compressibility for solutions of 3-methylbutane- 1,3-diol (0) and 2,2-dimethylpropane- 1,3-diol (@). 0.2 P 0.1 C I / I 1 0.05 0.1 0 0.15 X min Fig. 9. Plots of j3 and the mole fraction where the compressibility shows a minimum, x,,,: 0 3-methylbutane- 1,3-diol; a, 2,2-dimethylpropane- 1,3-diol; 0, 2-butoxyethanol ; 0, 2-isobu- toxyethanol; (>, 2-t-butoxyethanol ; a, 3-methoxy-3-methylbutan- 1-01.674 Interaction between Diols and Water smaller than that for the 3-methylbutane- 1,3-diol solution. The trends in the apparent molar volume and the hydrophobicity of the solute might not hold for solutions of the present isomers.Fig. 8 shows the dependence of the apparent molar compressibility for the two solutions. The curve for the 2,2-dimethylpropane- 1,3-diol solution is seen to increase more sharply than that of the 3-methylbutane- 1,3-diol solution. This result is consistent with the prediction from the work of Desnoyers and coworkers.' The calculated compressibility passes through a minimum. In order to illustrate the correlation between compressibility and absorption, plots of B and the mole fraction at which the compressibility shows a minimum are shown in fig. 9, and are seen to pass through the origin. In solutions of some ethers which are isomers each other the same dependence has been found,3b although the slope is different, depending on the type of isomeric group. If the minimum-compressibility concentration were very low, the solute would be expected to act as a very effective promoter of water structure. This work was partly supported by The Naito Foundation. References 1 (a) S. Nishikawa and M. Mashima, J. Chem. SOC., Faraday Trans I , 1982,78, 1294; (b) S. Nishikawa, J. Chem. SOC., Faraday Trans. I , 1983,79,2651; (c) S. Nishikawa and N. Nakao, J. Chem. SOC., Faraday Trans. I , 1985, 81, 1931. 2 S. Nishikwa and K. Kotegawa, J. Phys. Chem., 1985, 89, 2896. 3 (a) M. Blandamer, Introduction to Chemical Ultrasonics (Academic Press, London, 1983); (b) S. 4 L. Hall, Phys. Rev., 1948, 73, 775. 5 S. Nishikawa, M. Mashima and T. Yasunaga, Bull. Chem. SOC. Jpn, 1975, 48, 661. 6 C. M. Davis Jr and J. Jarzynski, A&. Mol. Relax. Process, 1968, 1, 155. 7 S. Nishikawa and T. Yamaguchi, Bull. Chem. SOC. Jpn, 1983,56, 1585. 8 (a) G. ROUX, G. Perron and J. E. Desnoyers, J. Solution Chem., 1978, 7, 639. (b) J. Lara and J. E. Nishikawa, R. Shinohara and G. Tanaka, Bull. Chem. SOC. Jpn, 1986, 59, 827. Desnoyers, J. Solution Chem., 1981, 10, 465. Paper 7/1042; Received 15th June, 1987