2620
A.
(16) J. Diederichsen and H. G. Wolfhard, Proc. R . SOC. London, Ser. A , 236, 89 (1956). (17) Farhataziz and A. 8. Ross, Natl. Stand. Ref. Data Ser., Nafl. Bur. Stand., 59 (1977).
Djavanbakht, J. Lang, and R. Zana
(18) S.W. Benson, "Thermochemical Kinetics", 2nd ed, Wiley, New York, N.Y., 1976. (19) J. A. Kerr in "Comprehensive Chemical Kinetics", Vol. 18, C. H. Bamford and C. F. H. Tipper, Ed., Elsevier, Amsterdam, 1976, p 39.
Ultrasonic Absorption in Relation to Hydrogen Bonding in Solutions of Alcohols. 2. Ultrasonic Relaxation Spectra of Solutions of Alcohols in Cyclohexane A. Djavanbakht,+ J. Lang, and R. Zana" CNRS, Centre de Recherches sur ies Macromol6cuies 6, rue Boussingault, 67083 Strasbourg, Cedex, France (Received March 23, 1977) Publication costs assisted by CNRS
The ultrasonic absorption of solutions of ethanol, 1-butanol, 1-octanol, 1-dodecanol, 1-hexadecanol, 3-octanol, 2-methyl-3-heptano1,and 2,4-dimethyl-3-hexanolin cyclohexane at 25 "C has been measured in the frequency range 4-250 MHz. The relaxation spectra of all of the investigated solutions could be fitted to a relaxation equation with a single relaxation frequency. The results have been interpreted on the basis of a reaction mechanism where n alcohol molecules associate to give cyclic and noncyclic n-mers. The absorption is attributed to the perturbation by the sound waves of the association equilibrium leading to noncyclic n-mers. For all primary alcohols no fit to the data could be obtained for n = 3 but equally good fits were obtained for n = 4 and n = 5, except with 1-hexadecanol for which n = 5 provides the best fit. The results indicate that (1) the rate of association of alcohol molecules through H bonds is close to its diffusion-controlled limit, even for the most hindered alcohol investigated; (2) the dissociation rate constant of one alcohol molecule from a noncyclic n-mer is only very slightly dependent on the alcohol chain length for primary alcohols. This rate constant increases with the degree of steric hindrance, reflecting the decreased stability of noncyclic aggregates. For 2methyl-3-heptanol the best fit to the data is obtained for n = 3. Likewise, the results for 2,4-dimethyl-3-hexanol appear to indicate that the association of this alcohol is essentially restricted to dimerization. Larger associated species appear to be present only in very small amount. The relation between ultrasonic absorption data and dipole moment data for octanol solutions is examined.
I. Introduction involves cyclic and noncyclic polymers1~2~5~s~10~15~16~zg according to Infrared NMR,7-9 vapor pressure osmometry,8J0J1 vapor density,ll partition coefficient,13J4 monomer (A) --L small noncyclic polymer (A, ) cryo~copy,~ dielectric constant,15-17 relaxation,16-20caloJ/' (1) rimetry,6J3*21-23 ultrasonic a b s o r p t i ~ n , and ~ ~ -chemical ~~ cyclic polymer (A,' n4c) kinetics31 have been extensively used for the study of the association of alcohols in solution through H bonding. In Bordewijk15recently pointed out that the discrimination between different association models cannot be achieved spite of this very large number of studies an examination by investigating properties which vary monotonically with of the literature till about 1970 reveals considerable the total alcohol concentration. Indeed the calculated confusion in the understanding of the association behavior variations of such properties are not very sensitive to the of alcohols. In the past few years, however, some concensus model (for instance to different sets of values of n and n' appears to have been reached among workers about several in reaction 1)as those of properties which show a maxiimportant features of the self-association of alcohols in mum and/or a minimum as the alcohol concentration is nonpolar solvents such as saturated hydrocarbons or CC14. increased. This explains the renewed interest in mea(i) Fairly dilute alcohol solutions (at concentrations below surements of apparent dipole moment pa of alcohols in 0.5 M) appear to contain, in addition to the monomeric solution. y, goes through a maximum at a concentration alcohol, a t least two associated species.1-6,8-16,29,32 This which depends on the solvent15-17(0.02, 0.04, and 0.4 M conclusion results from the fact that the best fit to the for 1-octanol in cyclohexane, CC14, and benzene, data, whichever the investigated property, is obtained by respectively16). This maximum has been attributed to the using at least two equilibrium association constants. (ii) relative variations of concentration of high dipole moment At concentration below 0.5 M the association does not linear (but small) polymers and of low dipole moment proceed to large aggregate^.^^^^^^ Trimers8 and tetramers1 It must be noted that studies of static cyclic p01ymers.l~~~~ are most often invoked for the interpretation of the results. constant of alcohol solutions have yielded much Dimers appear to be present only in small a m o u n t s ' ~ ~ ~ ~ Jdielectric ~ more information than dielectric relaxation studies. Inbut the authors disagree on whether this amount can be deed, two out of the three relaxation processes found for neglected in the mass conservation equation.'Jl (iii) The alcohol solutions are of intramolecular origin and make presently accepted model, which agrees with the results extremely complicated the study of the third process which of the most recent studies by means of various methods, results from the intermolecular association of alcohol molecules, in the case of dielectric relaxation.20 Present address: 163 Manoutcheri Ave., Meched, Iran, f
The Journal of Physlcal Chemistry, Voi. 81, No. 26, 1977
Ultrasonic Relaxation Spectra of Alcohols in Cyclohexane
Ultrasonic absorption is another property of alcohol solutions which shows a nonmonotonous change with the u alcohol c o n ~ e n t r a t i o n . ~ *At- ~low ~ concentration the absorption of alcohol solutions is close to that of the solvent 'E then increases very rapidly and linearly with concentration, N goes through a maximum, and d e c r e a ~ e s . ~As ~ -for ~ ~pa ,~~ \ -d the position of the maximum of ultrasonic absorption is h 0 very sensitive to the nature of the solvent and practically independent of the alcohol alkyl chain length. In fact there appears to be a correlation between the changes of paand of the excess absorption with concentration. This point is examined further in the Discussion. However the changes of absorption are much more pronounced than those of pa. They should therefore provide a much more severe test to any postulated model than pa data. The purpose of the systematic ultrasonic absorption studies that we started a few years ag026*29 was to obtain information on the values of n and n'in reaction 1 and to check the range of validity of this association mechanism Figure 1. Ultrasonic relaxation spectra of 0.012 M solutions of ethanol for various alcohols in different solvents. (O),I-octanol (CI), and I-hexadecanol (+) in cyclohexane at 25 OC. In previous s t ~ d i e s we ~ ~have , ~ ~shown that the assoThe solid curves have been obtained by a weighted least-squares f i i n g ciation of primary alcohols in non H-bonding solvents must of the experimental results to the eq 4. The broken lines give the values of B for the three solutions. proceed to species larger than dimers (see footnote 33) and that the ultrasonic absorption of alcohol solutions cannot of small amounts of alcohols in cyclohexane results in a be due t o the reversible cyclization of small linear polysmall change of ao/$. This change can be evaluated to mers, Attempts were made29to account for the position a good approximation by measuring the absorption of a of the absorption maximum essentially in terms of two cyclohexane solution of the saturated hydrocarbon with models. The first one, which has been reported by Fletcher an alkyl chain identical with that of the alcohol.29 (iv) and Heller,l assumes the formation of linear and cyclic Finally, the excess ultrasonic absorption of alcohol solutetramers (A4 and A4C, respectively) according to tions in cyclohexane is quite large, even at concentration 4 A - A , + A4c (2) down to 0.05 M.24126-29 This allows measurements to be performed in a range of concentrations where nonideality In this model, dimers and trimers are assumed to be effects other than those due to association are small and present in negligible amount and are not taken into accan be neglected. count in the mass conservation equation. The second model proposed by Tucker and Becker6 11. Experimental Section assumes the formation of a linear trimer (A3) and of a cyclic multimer. To fit our data we assumed the The ultrasonic absorptions ( c y / $ values) of alcohol solutions were measured using the same equipment as in 4A- A, + A + A4c (3) previous studies, in the frequency range 3.94-250 MHz.%$% When using the equilibrium constants reported by Fletcher The various alcohols (ethanol, 1-butanol, 1-octanol, and Heller,l and Tucker and Beckera the values calculated 1-dodecanol, 1-hexadecanol, 3-octanol, 2-methyl-3-hepfor the concentration where the maximum of ultrasonic tanol, and 2,4-dimethyl-3-hexanol) were purchased from absorption occurs were found to be too large with respect Fluka (Switzerland). The first five alcohols were of to the experimental results.29 A choice between reactions purissimum grade and the other three were of purum 2 and 3 was therefore not possible on the basis of these grade. All these compounds were used without further calculations. purification. The cyclohexane was freshly double distilled The purpose of this second part of our work is to report before use. the results of measurements of ultrasonic absorption The solutions were prepared by weighing in both the performed on solutions of primary alcohols and of three alcohol and the solvent required to prepare 100 or 150 cm3 isomeric octanols in cyclohexane, as a function of the of solution. alcohol concentration c, and the ultrasonic frequency. 111. Results These data have permitted us to obtain new information on the association behavior of alcohols in solution. For the sake of illustrating the results we have shown Cyclohexane was used as solvent throughout the present in Figure 1the ultrasonic absorption spectra of solutions investigation for the following reasons. (i) It has been of ethanol, 1-octanol, and 1-hexadecanol in cyclohexane. extensively used in investigations of alcohols by means of The absorption a / f ; is plotted against the frequency in a a variety of methods.7J4J6i24,27-29 (ii) Its interaction with semilogarithmic plot. The values of cy/? for all of the alcohols is quite weak, and probably comparable with that investigated solutions are available as supplementary between normal alkanes and alcohols. The latter is material (see paragraph a t end of text regarding supplecharacterized by an enthalpy of about -0.2 k c a l / m 0 1 , ~ ~ ~ ~ ~ mentary material). In all instances the experimental as compared with -0.5 and -2 kcal/mol for the interaction results could be fitted very satisfactorily to the eq 4 which between alcohols and C C 4 and toluene, r e s p e c t i ~ e l y . ~ , ~ J ~ These values are to be compared with the intrinsic en(4) thalpy of formation of an H bond, about -5 kcal/ m01.1J1596921-23(iii) The ultrasonic absorption of pure cyclohexane ( c y o / f 2 = 195 X cm-l s2, where a. is the holds for a single relaxation frequency process. cyclohexane absorption coefficient and f the ultrasonic For each alcohol solution the constant B was set equal frequency) is in the medium range.26,29The introduction to the a / f ; value of an equimolecular solution of the alkane N -
?'
L
Y
L
The Journal of Physical Chemistry, Vol. 81, No. 26, 1977
A. Djavanbakht, J. Lang, and R. Zana
2622
with an alkyl chain identical with that of the alcohol. (In all instances these a/f values were found to be independent o f f in the frequency range investigated.) The validity of this procedure has been demonstrated in a previous In fitting the a/f" vs. f data to eq 4 a two-parameter weighted least-squares fitting procedure was adopted, where the parameters R and fR are determined by minimization of the quantity
TABLE I: Values of the Relaxation Frequencies and Amplitudes ~ _ _ _ _ _ _ Alcohol Methanol
(4') 1-Butanol,
c,M
--__1 0 1 7 ~ ,fR, 1017~1, cm-'sZ MHz cm-' s2
0.098 0.12
94 90
72 79
194 194
0.06 0.09 0.12 0.16 0.20 0.25
70 107 106 100 90 79
45 51 67 88 109 136
194 193 193 191 191 190
0.06
86
41
194
where (a/fz)cdcdis the value of the absorption calculated 129 CM,o = cM,f = 0.125 M 0.089 50 193 by means of eq 4 for a given set of R and fR values. 0.12 131 66 192 0.16 In Figure 1 the solid lines have been obtained as just 132 75 191 0.22 116 106 189 described. In all instances the root mean square deviation 0.31 98 126 186 [ 2 / p ]lj2 where p is the number of experimental points was about 1% or less, and therefore smaller than the exper1-Octanol, 0.047 91 30 192 C M , ~= 0.120 M, 0.085 170 l, to be about 41 190 imental uncertainty on ( a / f ) , x p testimated CM,f = 0.126 M 0.12 187 50 188 2%. This result provides convincing evidence that the 0.19 173 71 184 ultrasonic relaxation spectra of alcohol solutions in cy0.276 147 89 179 clohexane are characteristic of a single relaxation time. 1-Dodecanol, The values of R , f R , and B for the various systems in0.05 115 25 190 CM,= ~ 0.117 M, 0.087 215 33 187 vestigated are listed in Table I. It can be seen that fR cM,f = 0.13 M 0.12 226 40 184 increases and that R goes through a maximum as the 0.16 222 52 180 alcohol concentration is increased except for the hindered 0.22 201 68 174 isomer 2,4-dimethyl-3-hexanol, in agreement with ob0.305 173 76 168 servations made in other s t ~ d i e s . ~ ~ ~ ~ ~ ~ ~ ~ - ~ ~ 1-Hexadecanol, 0.04 74 20 190 The errors on fR and R have been evaluated by changing C M , ~ =0.115 M, 0.085 138 27 185 at random and by a relative amount between 2 and -2% cM9f = 0.13 M 0.118 252 36 182 values found for a given alcohol solution, and the (a/f"),,d 0.16 255 43 177 fitting each of the sets of a/f values so obtained to eq 4, 0.21 233 54 172 using the above weighted least-squares procedure. The 0.27 205 68 165 relative error on R is about 7%. The error on fR is of about 10% for R > 100 X cm-' s2 but increases rapidly as 0.07 25 58 191 R decreases. 0.14 85 69 186 As part of this study we have also determined the curves 0.22 113 92 182 0.30 123 116 a/f" vs. c a t 9.09 MHz and 25 " C for all of the primary 177 0.45 117 163 169 alcohols except 1-octanol. For this alcohol and for its three 0.60 112 195 161 isomers (3-octanol, 2-methyl-3-heptano1, and 2,4-dimethyl-3-hexanol) the a/f vs. c curves were determined 2-Methyl-3-heptanol, 0.15 64 82 186 C M ,= ~ C M ,= ~ 0.55 M 0.25 98 115 180 a t 6.49 MHz in a previous Finally, for 1-butanol 0.40 111 161 171 the a/f vs. c curve was also determined at 85.3 MHz. As 0.80 102 277 153 was emphasized above and as is shown below such results 1 9 3 329 147 provide a very severe test to any association model which 2,4-Dimethyl-3-hexanol 0.25 36 144 183 may be postulated for alcohols. Here again the excess 0.40 56 187 176 absorption due to the association of the alcohol was ob0.65 68 215 1 64 tained by taking the difference between the absorptions 0.90 72 242 154 of equimolar solutions of the alcohol under study and of which the two ends of the polymer are fairly close to each the corresponding saturated hydrocarbon, for instance, other. The probability for these two ends to H bond n-hexadecane in the case of 1-hexadecanol. The excess together may then be larger than for H bonding with a free absorptions, referred to as h / f , are given as supplealcohol molecule, thereby resulting in a cyclization of the mentary material (see paragraph at end of text). noncyclic species. The general mechanism 5 has been IV. Discussion favored with respect to the one which could be derived 1. The Association Model. The following general refrom the model of Tucker and Beckers because it is difaction mechanism, derived from that postulated by ficult to explain why stable noncyclic species would still Fletcher and Heller,l was adopted for the purpose of fitting have to incorporate one or several additional monomeric the results of Table I and the Aalf" data alcohol molecules to give stable cyclic species. 2. The Equations. It has been previously2gpointed out n A + A,, =+A,, (5) that the excess absorption of alcohol solutions is very likely due to the perturbation by the sound waves of the assoHowever, in contradistinction with these workers, we do ciation-dissociation equilibrium in reaction mechanism 5. not assume that the noncyclic species A,, is linear. Rather, In this mechanism all species intermediate between the A, is believed to adopt a conformation intermediate bemonomer and A, are assumed to be present in the solution tween the linear and cyclic conformations, owing to steric only in very small amount. It is understood, however, that hindrance of the alkyl chain which may favor a bending A, is formed by the following series of bimolecular reof the successive .-OH-OH-OH bonds. Because of this actions: bending there may be a certain aggregation number for The Journal of Physical Chemistry, Vol. 6 1, No. 26, 1977
2623
Ultrasonic Relaxation Spectra of Alcohols in Cyclohexane k,
A+ A e A ,
However the above derivation shows that k- represents the rate constant for the dissociation of one monomer from the aggregate A, in the case of the series of bimolecular reactions 6, rather than the rate constant for the dissociation of A, in nA, as one would think when considering reaction 16. The relaxation amplitude, obtained following the usual calculation^,^^ is given by
K, = k,/k-,
k-,
As far as kinetics goes the Bodenstein approximation can be used for A2, As, ..., A,-,. Writing d[A2]/dt = d[AJ/dt = ... = d[A,-,]/dt = 0 leads to the equation
[An - 1 1 =
KiK2***Kn-3Kn-2[Al"-'+ k[A,]a k - ( n - 2 ) + k-[A]a
Moreover, since reaction mechanism 5 assumes, in agreement with the experimental observations, that all intermediate species are present only in very small amount, we have
K1 mKz e * . * < < K = k / k The combination of this equation with eq l l a results in *
*
a
S k,
(1lb)
On the other hand, since there is only a very small amount of dimer one has
[&]/[AI
=
ki[Al/h-,
1
KT[A](n - 1)2 103RTh-(n2&[AIn-' + 1)?
(7)
where
k,!" k - z w
R=--2n2pv
where p, u, 0, and C, are the density, ultrasonic velocity, expansion coefficient, and specific heat capacity of the alcohol solution in cyclohexane. For the dilute solutions used in this study, these quantities can be taken as equal to those for cyclohexane. At 25 "Cwe found 2r2pv/103RT = 7.78 X cgs and O/(pC,) = 3.55 cm3/kcal when the concentrations are expressed in mol/L and the average volume change AVO and enthalpy change AHo for the formation of one H bond in cm3/mol and kcal/mol, respectively. In this study we have assumed that AVO can be neglected with respect to the enthalpy term in eq 17. Indeed JAVOIis probably less than 3 cm3/moLs4 On the other hand, lAHol is larger than 5 kcal/mo1.1~2~5~6~21-23 Thus AVO represents less than 15% of the enthalpy term and may be neglected when considering the errors resulting from the approximations involved in the derivation of eq 14, 17, 19, and 20 (see below), particularly the assumed absence of species other than A, A,, and A,c. R is related to the excess absorption A a / f by the equation R A &_
-
f 2
1t
It can be shown that at a given frequency f , A a / f goes through a maximum at a concentration cM,f given by ' M , f = lAIIM,f
lA1M.f =
n2 KT(n- 2)
Kc is the cyclization constant for the n-mer. At low frequency, where ( w / k J 2
