686
J. Phys. Chem. 1981, 85, 686-689
exclusively to the first term in eq 1. As the temperature is increased the second term increases in importance until, a t 295 K, it accounts for -85% of the nonradiative deactivation for the perprotio compounds and -97% for the perdeuterio compounds. In comparing the ambient temperature results for the solid samples to those for fluid solutions of the same complexes12the nonradiative deactivation rates increase by two orders of magnitude in going from solid state to fluid solution. Therefore eq 1, as written, accounts for only 170of the overall nonradiative deactivation occurring for these complexes in ambient temperature fluid solution.
-
This suggests that the nonradiative pathways which couple the LF excited states of the solvated complexes to the solvent medium control the excited state lifetimes in fluid solutions. Acknowledgment. P.C.F. acknowledges support from the National Science Foundation. R.J.W. acknowledges the Department of Energy, Office of Basic Energy Sciences for support of this work. M.A.B. is grateful to the University of California for a Regent's Fellowship. The rhodium used in this study was provided on loan from Matthey Bishop, Inc.
Structure and Kinetics in Aqueous Solutions of Ethers by Ultrasonic Methods Sadakatsu Nishikawa,' Michiko Tanaka, and Mitsuo Mashima Depat7ment of Chemistty, Faculty of Science and Engineering, Saga University, Saga 840, Japan (Received: February 26, 1980; I n Final Form: June 18, 1080)
Ultrasonic absorption and velocity have been measured in aqueous solutions of ethyl cellosolve (ethylene glycol monoethyl ether), propyl cellosolve (ethylene glycol monopropyl ether), and butyl cellosolve (ethylene glycol monobutyl ether) in the frequency range of 2.5-220 MHz at 25 "C. In the case of ethyl cellosolve, no excess absorption has been observed. One relaxational process in aqueous solution of propyl cellosolve and two processes in that of butyl cellosolve have been found. These relaxation mechanisms were interpreted by a model which was associated with the solute-solvent interactions and molecular aggregation of the solute. The structure of the solvent, liquid water, has been considered from the ultrasonic results, and the effects of ethers on the solvent have been compared with those of other nonelectrolytes.
Introduction The structural properties of aqueous solutions of nonelectrolytes have been studied by various physicochemical techniques so far, and ultrasonic methods have been applied to the kinetic investigations. The results of the absorption and velocity for a number of nonelectrolyte solutions have been reported by many investigators.lt2 However, the interpretations of the absorption mechanisms do not yet seem to be satisfactory, because, even now, some new mode1s3p4have been proposed based on the information about water structure obtained in recent years. We have also shown the excess absorption mechanism in aqueous solutions of alcohols, which relates to the solute-solvent interactions and the hydrophobicity of the solute molecules, considering the structure of liquid water. The typical feature of the ultrasonic absorption for these solutions is the peak sound absorption concentration (PSAC). However, the mechanisms may not be elucidated if the absorption measurements are done in a narrow frequency range or the solutes are restricted. For example, only a single relaxational process exists in aqueous solutions of isopropyl and allyl alcohols though the PSAC is observed. On the other hand, tert-butyl and n-propyl alcohol solutions have two relaxational processes in the frequency range of 2.5-220 M H Z . ~In~ addition, ~ other (1)J. H.Andreae, P. D. Edmonds, and J. F. McKellar, Acustica, 16, 74 (1965). (2)M. J. Blandermer and D. Waddington, Adu. Mol. Relaxation I n teract. Processes, 2, 1 (1970). ( 3 ) K. Tamura, M. Maekawa, and T. Yasunaga, J . Phys. Chem., 81, 2122 (1977). (4)S. G.Brwun, P. G. Sorensen, and A. Hvidt, Acta Chem. Scand., Ser. A , 28, 1047 (1974). 0022-385418112085-0686$01.25/0
excess absorption processes have been found in the GHz frequency range in the aqueous solutions of alcohols.' The purpose of the present investigation is t o extend further the studies of the aqueous solutions of nonelectrolytes by ultrasonic methods. Three ethers were chosen, and the ultrasonic absorption and the velocity were measured as a function of the concentrations. The results will be compared with those of the aqueous solutions of the alcohols. Experimental Section Chemicals. Ethyl cellosolve (ethylene glycol monoethyl ether), propyl cellosolve (ethylene glycol monopropyl ether) and butyl cellosolve (ethylene glycol monobutyl ether) from Wako Pure Chemical Industries were distilled once, and the purities were determined by gas-chromatographic method to be more than 99.8%. Doubly distilled water was used as a solvent. The solutions were made up at the required concentrations by weight. Methods. The ultrasonic pulse method was used for the absorption measurements in the frequency range of 2.5-220 MHz with 0.5-, 5-, and 20-MHz x-cut quartz transducers? The uncertainty in the absorption coefficient was within f2.5%. The sound velocity was measured by a singaround technique a t 1.92 MHz and an interferometer a t 5 MHz in which the uncertainties were *50 s-l. The same (5) (a) S. Nishikawa, M. Mashima, and T. Yasunaga, Bull. Chem. SOC. Jpn., 48,661 (1975); (b)S.Nishikawa, M. Mashima, M. Maekawa, and T. Yasunaga, ibid., 48,2353 (1975). (6)S. Nishikawa, M. Mashima, and T. Yasunaga, Bull. Chem. SOC. Jpn., 49,1413 (1976). (7) K. Oda, R.Hayakawa, and Y. Wada, Jpn. J . Appl. Phys., 14,1113 (1975);16, 1009 (1976). (8)N. Tataumoto, J . Chem. Phys., 47,4561 (1967).
0 1981 American Chemlcal Soclety
Structure and Kinetics of Ethers
The Journal of Physical Chemktty, Vol. 85, No. 6, 7981 087
TABLE I: Ultrasonic Parameters for Aqueous Solution of Butyl Cellosolve at 25 "C
-
a
Ce, M
c , m s-I 1556 1556 1553 1547 1542 1535 1526 1516 1508 1492 1477 1464 1451 Appendix.
P , g cmk3
0.750 0.800 0.897 1.00 1.10 1.25 1.50 1.73 2.00 2.50 3.00 3.50 4.00
0.9941 0.9941 0.9934 0.9925 0.9917 0.9902 0.9879 0.9852 0.9823 0.9768 0.9702 0.9654 0.9592 The rms is defined in the
f,,, MHz
31.1 41.2 35.1 39.7 26.7 30.6 32.3 44.3 44.7 45.5 62.7 61.3 67.3
frz,
1017~,, s2 cm-'
MHz
5.13 5.50 6.35 6.80 4.62 5.27 5.94 6.58 7.07 5.45 6.70 5.37 3.98
117 119 279 446 990 1056 1238 912 878 801 590 481 427
1017~,, sz cm-I
1017~, sz cm"
rmsa
25.3 24.3 32.3 27.2 46.5 50.9 66.2 93.3 72.1 76.3 93.4 113 109
2.86 2.76 22.2 34.7 28.0 73.7 44.6 82.0 74.5 37.5 31.1 34.9 43.5
127 337 1836 2848 3629 3000 2293 2172 2027 1764 1161 1202 1065
will concentrate on the investigation of the butyl cellosolve solution in more detail in this paper. In order to examine the mechanisms of the observed relaxational absorptions, we consider the model proposed for the aqueous solutions of alcohols in the previous paper.5 The model is as follows:
0 3 M propyl cellosolve
8 5 M ethyl cellosolve
ABm
&
fa,
A mB
f
where A is the monomer of ether, A,, is the aggregate of ether, B is the monomer of water, and ABmis the complex of the ether with water. Only monomers of water are assumed to participate in the reaction. The first step is considered t o be much faster than the second. Then, the following relations between the relaxation frequencies and the concentrations are derived:
. MHz
Flgure 1. Observed ultrasonic absorption spectra for butyl cellosolve, propyl cellosolve, and ethyl cellosolve at 25 'C. The arrows show the relaxation frequency.
results were obtained by both methods. The density of the solution was determined by standard pycnometers of - 2 cm3. All of the equipment was immersed in a water bath which was maintained at 25 "C within fO.O1 "C. Results Figure 1 shows the absorption spectra obtained in the aqueous solutions. In general, the absorption caused by the several relaxation processes can be described by eq 1, a/f2 = CAi/[l i
+ (f/fri121 + B
(1)
where a is the absorption coefficient, f is the frequency, is the relaxation frequency for the ith process, Ai is the amplitude of the excess absorption, and B is the background absorption. In the case of the butyl cellosolve solution, two relaxational absorptions were observed and the spectra were analyzed with a nonlinear least-squares computer program (details are given in the Appendix). For a single relaxational process, such as that observed in the aqueous solution of propyl cellosolve, the ultrasonic parameters could be determined so as to obtain the straight line of the plots of [ l + ( f / f , ) 2 ] - 1 vs. alp, changing f , with the help of the linear relation. On the other hand, no excess absorption was observed for the ethyl cellosolve solution. The background absorptions, B, for these three solutions are all higher than those expected from the classical absorption due to viscous and thermal conductive effects. Therefore, other excess absorptions may be found in the higher frequency range. The concentration dependence of the ultrasonic parameters for the aqueous solution of propyl cellosolve seems to be identical with that of the solutions of isopropyl and allyl alcohol^.^^^ Therefore, we
fri
n2k21k23C2mC3n-1
k32
+ k23n2C3n-1- kl2 + k21(m2C2m-lC3+ Czm) (4)
where C2 and C3are the equilibrium molar concentrations of the components, B and A, respectively. In this paper, we have used concentrations instead of activities in order to analyze the reaction mechanisms, which we will discuss in a later section. The maximum excess absorption per wavelength for the ith process is given by eq 5?J0 where P m a x i = Aifric/2 = [ ? r p c 2 r i / ( R T ) ] [Avi - a p m r n i / ( p C p m ) l 2 (5) p is the density, c is the sound velocity, R is the gas constant, T is the absolute temperature, ( z P m is the high-frequency limit of the thermal expansion coefficient, C," is that of the constant pressure specific heat, and AVi and AHi are the parameters related to the volume and enthalpy changes of the reaction. The Fi terms in eq 5 for the reaction considered here are given by eq 6 and 7,where
I'z =
'v[
n-1 % - r1k21C2m)+ (n-l+ c3
CT
'1
C4 is the concentration of the component A, and
1-1
CT = C1
(9)M. Eigen and L. de Maeyer, Tech. Org. Chem., 8, (1963). (10)G. G.Hammes and W. Knoche, J. Chem. Phys., 31,488 (1966).
688
Nlshikawa et al.
The Journal of Physical Chemistty, Vol. 85, No. 6, 1981
TABLE 11: Thermodynamic and Rate Parameters for Aqueous Solutions of Alcohols and Ether at 25 "C k12, s-' k , , , M-I 8' k 3 2 , s-' P AG,, kcal pure
water allyl alcohol isopropyl alcohol n-propyl alcohol tert-butyl alcohol butyl cellosolve
1.5 X 1.4 X 1.6 X 1.2 x 4.2 X
i s. I
7.2 x 8.8 x 6.2 x 6.3 x 1.7 X
10' 10' 10'
lo8 10'
107
107 10'
6.9 x 107 4.9 x 10' 3.0 x 107
0.15
0.12 0.029
401
d0.1
9 60
0.63 0.86 0.94 1.0 1.2 2.1
0.26 0.19 0.17
107 107
n
ref
13, 16 5b
6 5a 5b this work
40.4
I I
0
1
; 4
4
Ce, M Figure 2. Concentration dependence of the relaxation frequency, frl, for the aqueous solution of the butyl cellosolve at 25 OC.
+ C2 + C3+ Cq. If one water molecule interacts with an
Figure 3. Comparison between the experimental pmx and the calculated pc2r1vfor the aqueous solution of the butyl cellosolve.
ether and if the concentration of the aggregate is small, eq 3 can be expressed by analytical concentrations as in eq 8, where ,8 is the mole fraction of the water monomer,
aqueous media. The ultrasonic absorption mechanisms so far proposed seem to be insufficient to explain the relation between the cause of the ultrasonic absorption and 2rfr1 = 1/71 = k21[(Ce - PC, + K d 2 + 4Pc&121''~ (8) the molecular structures of solute and solvent. The nature of water seems to play an important role in the ultrasonic K12is the equilibrium constant defined by Kl2 = k12/kZ1, properties of nonelectrolyte aqueous solutions. In order and C, and C, are the analytical concentrations of ether to examine the observed absorption mechanisms, it may and water, respectively. As is seen in Table I, the relaxbe a reasonable assumption that solvent water consists of ation frequencies frl go through a minimum around 1.25 only two states, that is, the monomer and the cluster. This M of the butyl cellosolve. Therefore, the minimum constructure model for water is the simplest one which has dition which provides the relation between p and KI2was used to determine the rate and equilibrium c ~ n s t a n t s . ~ been used to explain successfully the ultrasonic absorption in pure water by Hall13and Litovitz and Carne~ale.'~The The values of kzl and K12 were calculated so as to obtain relaxation time associated with the reaction between the the best fit of the experimental data to eq 8, changing the monomer and the cluster is expected t o be less than 10-l' value of P. These results are listed in Table I1 along with sI3, which is beyond our time scale measured here. those of some alcohol solutions. The solid line in Figure Therefore, the excess absorptions observed in our fre2 is the calculated one using the values in Table 11. Then quency range are characteristic of the aqueous solutions the estimation of the maximum excess absorption per of ethers. wavelength is possible according t o eq 5. It is a good We discuss the excess absorption mechanism in the approximation that pmaxis proportional to pc21', because higher frequency range (26-67 MHz) in the first place. It the square term of the right-hand side in eq 5 may be was not observed in the concentration less than 0.7 M, and constant. The circles in Figure 3 are the experiment@ the sound velocity showed the maximum value around this values of pm1, and the solid line is the calculated pc21'lV concentration. This type of ultrasonic behavior is found values. in many aqueous solutions of alcohols though the relaxaNext, the excess absorption observed in the lower fretion times for the solution with a small hydrophobic group quency range is analyzed. Equation 4 can be transformed are ~ h o r t e r . ~The J ~ probable cause of the excess absorpt o eq 9. The concentration terms, C3 and (1- 71k21C2), tion observed may be the solutesolvent interactions which 2rfr2 = 1 / 7 2 = n2k23C3n-1(I- 71k21C2) k32 (9) are shown by eq 2. The reason that the excess absorption is not found in the Concentration less than 0.7 M may be increase monotonically with the analytical concentration that the solute may not touch the water monomer if it of the butyl cellosolve. However, the observed relaxation dissolves in the cluster of water, that is, in the cage of water frequencies, fr2, seem to be concentration independent. molecules. With increasing solute concentration, it may This means that the backward rate constant, k32, is much interact with the monomers. This interaction seems to be larger than the first term of eq 9. In the case of the alcohol associated with the hydrogen bonding between solute and solutions, the relaxation frequencies increase with con~entration.~
Discussion Though the PSAC has been observed in nonaqueous systerns,l1J2 the discussion here will be restricted to
(11) J. Lang and R. Zana, Trans. Faraday SOC.,66, 597 (1970). (12)J. Rasing and F. Garland, Acta Chern. Scand., 24, 2419 (1970). (13)L.Hall, Phys. Rev., 73, 775 (1948). (14)T. A.Libvitz and E. H.Carnevale,J. Appl. Phys., 26,816 (1955). (15)K.Takagi and K. Negishi, Jpn. J . Appl. Phys., 14,953 (1976).
Structure and Kinetics of Ethers
The Journal of Physical Chemistry, Vol. 85,No. 6, 1981 089
solvent molecules, and the complex formed by one water al.7 have observed excess absorption in the GHz range, and one butyl cellosolve may be a reasonable pair. In the which is well explained by the association reaction through analysis of the absorption, concentrations were used inhydrogen bonding. We consider that the same relaxation stead of their activities, even though the solutions may not process as that of tert-butyl and n-propyl alcohols has been found in the butyl cellosolve solution. Finally, this kind be ideal. If the activities are taken into account, eq 3 for 1:l complex formation can be expressed by 1 / = ~ ~ of absorption has also been seen in aqueous solutions of ( ~ A ~ B / Y A B+) (C3)k21+ C~ ymk12where yij is the activity some amines with large hydrophobic groups, and the cause coefficient for each reactant, and the rate constants obof it is due to the aggregation reaction through hydrotained are approximately the products of the real rate phobic interaction.ls On the basis of these results, we have constant and the activity coefficient. It is very difficult concluded that the butyl cellosolve molecules may aggregate in the aqueous medium by means of the hydrophobic to estimate the activity coefficient for the monomer in interaction. As the relaxation frequencies reflect the water though the mean coefficient has been reported. backward rate constant, the aggregation number could not According to Glew et al. and Knight’s16results, the activity be determined. However, it is estimated to be more than coefficient of water is close to unity for some solutes though 4 because the p value is quite small compared with that it behaves unexpectedly. Further, it is a good approximation that the activity coefficient for the ether monomer of tert-butyl alcohol. is identical with that of the complex AB. Therefore, the In conclusion, the excess absorption mechanisms in rate constants determined in this study seem to be reaaqueous solutions of butyl cellosolve are attributed to the interaction of the solute with water monomer and the sonable and appropriate for measures of the properties of aggregation reaction through the hydrophobic interaction, aqueous solutions. However, the pretty large deviations and both of them are causes of PSAC. With decreasing of the experimental values from the calculated curves in hydrophobicity of the solute molecule, the aggregation Figures 2 and 3 at high concentrations might be due to the change of the coefficients. The parameter, p, which is the reaction may not occur. The ultrasonic properties of the aqueous solutions of ether are quite similar to those of mole fraction of the monomer of liquid water, is helpful in considering the effect of the solute on the water strucalcohols though the strength of the hydrophobic interaction is different. ture. Nomotol’ has interpreted the structural properties of various nonelectrolyte solutions in a very wide concenAppendix tration range by using the two-states model and has deProcedure for Determining the Ultrasonic Absorption termined the p values with the solute concentrations. The Parameters with the Help of a Least Mean Squares concentration range studied here is not so wide compared Method. In the case of the two relaxation processes, eq with his; therefore, we assume for simplicity that the is 1 is transformed to independent of the concentration. In Table 11,the p value for the butyl cellosolve is shown along with those for some q1 alcohols. In pure water, it was taken from the literaq2 +B (AI) yc = p 2 + xi ture.13J7 The free-energy change, AGw of the two states in water was calculated from the relation P/(1 - p) = xi = f‘,pi = fr?, ~2 = frz2, q i Adr?and where yi = b/f‘>, exp[--AG,/(RT)]. From this table, it is seen that the q 2 = A?f,Z2. Equation A1 can be expanded, giving monomers of water shift to the clusters when the butyl cellosolve dissolves in it. When the p values of aqueous yc = yp + ddq1 y’)nql + m ) . q 2 solutions of alcohols are compared with that of the butyl %)Ap1 aP1 cellosolve, it is also found that the fraction of water monomer decreases with increasing size of the hydrophobic $!)AP~ + 642) group in the solute molecules but is almost constant when the excess absorption in the lower frequency range is not where ycocan be calculated from the initial values of pl, observed (in the cases of isopropyl and allyl alcohols). p2,ql, q2, and B which are determined graphically so as From these facts, it may be concluded that the butyl to get a best fit of the experimental values. We define: cellosolve acts strongly as a structure promoter for water because of the large portion of the hydrophobic part in the molecule. Next, the relaxation process observed in the lower frequency range (around 5 MHz) will be considered. First, the excess absorption appears only when the solute has a relatively large hydrophobic group; that is, the absorption has not been observed in the aqueous solutions of ethyl From the relations d(CAy?)/aAp, = 0, d ( ~ A y ~ ) / d A=p Z cellosolve and propyl cellosolve. Second, the absorption 0, d(CAyi2)/dAql = 0, d(CAy?)/dAq2 = 0, and dis found above some critical concentration. The excess (CAy?)/dAB = 0, we get five linear equations which absorption amplitude, Az, increases steeply in a narrow provide the values of Apl, Ap2, Aql, Aq2, and AB. Then, concentration range. Third, Tamura et aL3have reported PI + API, PZ+ APZ, 41 + & , q 2 + A ~ z and , B + AB are that the absorption mechanism is associated with the agused as new initial parameters for eq A2. The above gregate formed by the hydrogen bonding for the aqueous procedures are repeated until the value of rms = {[Chi dd solution of tert-butyl alcohol. On the other hand, Oda et - yi expt?]/n31/2 has a minimum where N is the number of experimental frequencies.
+-
(
(16)D. N. Glw, H. D. Makand, and N. S. Rath in “Hydrogen Bonded Solvent Systems”, A. K. Covington and P. Jones, Eds., Taylor and Francis, London, 1968. (17)0. Nomoto, J . Phys. SOC.Jpn., 11, 1146 (1956).
(
(
+
(
+
(g)O
(18)S. Niahikawa, T. Yasunaga, and K. Takahashi, Bull. Chem. SOC, Jpn., 46, 2992 (1973).
