7359
J. Phys. Chem. 1993,97,7359-7363
Comparative Study of Hydrophobic Effects in Water/Alcohol and Water/Ethylene Glycol, Water/Ethanolamine, Water/Ethylenediamine, and Water/2-Methoxyethanol Systems Yudu Cheng’ Department of Biology, Johns Hopkins University, 144 Mudd Ha11/3400 N. Charles St., Baltimore, Maryland 21 21 8-2685
Monique Pag4 L’lnstitut Fraqais du P4trole. 1 et 4 Ave de Bois Prtau, B.P. 311,92506 Rueil-Malmaison, France
Carmel Jolicoeur D4partement de chimie, Universit4 de Sherbrooke, Sherbrooke, Qutbec, Canada, Jl K 2Rl Received: February 9, 1993;In Final Form: March 24, I993
The magnitude of hydrophobic effects present in water/alcohol mixtures and in mixtures of water with various bifunctional cosolvents (ethylene glycol, 2-methoxyethanol, ethanolamine, and ethylenediamine) has been investigated through the Kirkwood-Buff (K-B) theory. The K-B integrals (Gv) reflect the overall affinity between species i and j (i.e., balance of repulsive and attractive contributions). In water/alcohol mixtures, Gv values exhibit complex composition dependence, with sharp extrema in G11, G12, and G22 over a narrow range of water-rich compositions; these features are further seen to be strongly dependent on the size of the hydrocarbon group of the cosolvent molecule. For mixtures of water with the bifunctional cosolvents, all systems exhibit analogous G,, variations, mostly a weak monotonous increase with cosolvent mole fraction. With due acknowledgment for the excluded volume (V,) contributions to Gii,which vary in the different solvent mixtures examined here, it is readily apparent that in water/alcohol mixtures with 0 < x2 5 0.3,the hydrophobic effects promote correlation among water molecules (GI 1) and among cosolvent molecules (G22). In water/bifunctional cosolvent mixtures, the various interactive components exhibit little correlation, and the hydrophobic effects appear greatly reduced. These observations point to important differences in the intermolecular processes occurring in aqueous mixtures of the mono- and bifunctional cosolvents studied here, in line with previous discussion on the thermodynamic properties of these mixtures.
Introduction The molecular phenomena generally referred to as the “hydrophobiceffect”comprise two related processes. First, apolar solutes promote a stabilization of the extensive, but thermally sensitive, hydrogen-bonded network of liquid water, an effect known as “hydrophobic hydration”. Second, the apolar solutes in water exhibit a tendency to aggregate, Le., “hydrophobic interaction”. Both of these processes are characteristic features of the hydrophobic effect. Studies of the hydrophobic effect are designed to unravel the nature of these processes through investigations of the behavior of hydrocarbons and/or organic cosolvents in aqueous solution. Organic cosolvents exhibit much higher solubilities in water than hydrocarbons due to their polar functional groups (OH for alcohols, NH2 for amines, etc.). However, in dilute solutions, organic cosolvents frequently exhibit features similar to those of hydr0carbons.I Studies of such features (hydrophobic hydration and interaction) have attracted considerable attention since they have been shown to influence protein conformation and thermodynamic stability.2~~ It has been recently proposed that the Kirkwood-Buff theory may be used to elucidate some aspects of hydrophobic phenomena.4’5 The main interest of the approach lies in that it yields the integrals (G,,)over space of the pair radial correlation functions (g,,(r)). The Gi, integrals reflect the overall affinity between the different pairs of species (water-water, water-cosolvent, cosolTo whom corr~pondenceshould be a d d r d .
vent-cosolvent) without detailed knowledge of the pair correlation functions, which remain inaccessible for most binary systems. The hydrophobic effect, and concomitant interactions between thevarious species in the aqueous system, should thus be evidenced through the G, functions. The approach may be summarized as follows. The Kirkwood-Buff integral, Go,is defined by6
where g&) is the pair correlation function for species i and j . It has been shown7 that the thermodynamic properties which are composition-dependent at given temperature and pressure may be expressed in terms of G&) values derived from the various pair correlation functions. However, what is involved in the present work is the inversion of those relationships, a procedure which allows the definition of G, in terms of readily measurable thermodynamic quantities. According to the inverse approach, the molar Kirkwood-Buff integrals can be expressed in the forms
G , , = RTK,-
G,, = G,,
v1v, DV
+L (:x2
0 1993 American Chemical Society
V)
Cheng et al.
7360 The Journal of Physical Chemistry, Vol. 97, No. 28, 1993 where D is given by
D=l+x,(-)
a In y i axi
(7a) T,P (i
= 1,2)
(3)
and Vis the molar volume of the mixture. The Kirkwood-Buff (K-B) inversion approach has been applied to thermodynamic data for numerous water/cosolvent systems&15 and yielded valuable information on hydrophobic effects in these systems, in relation to the integrals GI1, G12, and GZZ.An overview of recent studies in this area shows the following general trends for the K-B integrals with increasing cosolvent concentration: (1) G1l and G22 values are commonly found to increase with XZ, whereas Gl2 values mostly exhibit a decrease with XZ,and (2) in many cases, extrema are observed in Gij vs x2, particularly in mixtures involving monofunctional cosolvents, Le., one having only one polar functional group. It is apparent, nevertheless, that more detailed studies of the K-B integrals in aqueous systems are required to relate their composition dependence to specific molecular parameters of the hydrophobic cosolvents or to molecular processes in which they participate. The present work was thus initiated to compare the variations in the K-B integrals, particularly in water-rich compositions, for two types of aqueous mixtures: waterln-alcohol (monofunctional cosolvent) and waterlethylene glycol (EG), /ethanolamine (EA), /ethylenediamine (ED), and /Zmethoxyethanol (2-ME) (bifunctional cosolvents). It may be expected that more specific information on the nature of hydrophobic effects can be obtained from studies of these systems, which have a common apolar group (-CH2CH2-) and one or two functional groups of different types. The following discussion emphasizes recent results on mixtures containing bifunctional cosolvents, with systematic reference to water/alcohol systems which have been extensively investigated.lCl9
where
The data for G: were found in the l i t e r a t ~ r e . ~ ~ - ~ ~ The G: values as a function of mole fraction in W/EG and W/EA systems have been given byZ2 (9)
where the parameters Aij and C..( i , j = 1, 2) may be fitted by using data of both H", and G f a s described by Van Ness.22 However, the Willson equation was used to represent G: for the W/2-ME and W/ED systems:
-: G - x1ln(x, + AlzxZ)- xz ln(xz + Azlxl)
(10) RT where A12 and A21 are the Willson parameters. Literature data2&z9were also used to compute Gij for water/ 1-PrOH mixtures. It is found that the molar excess free energies of this system can also be expressed in terms of eq 10 with two Willson parameters A12 = 0.6244 and A21 = 0.044 72, respectively. It can be shown that the activity coefficients y1and yzderived from either eq 9 or eq 10 are thermodynamically consistent; Le., they satisfy the Gibbs-Duhem equation.
Results and Discussion
Experimental Data and Calculations The experimental data required to calculate the KirkwoodBuff integrals for the systems of interest here are available from recent literature.20J The measurements of adiabatic compressibilities ( K ~ ) ,isobaric specific heat (cp),and densities (d)of the systems W/EG, W/EA, W/ED,and W/2-MEhavebeenreported recently in the entire composition range at three temperatures: 10, 25, and 40 "C (5, 25, and 45 OC for the W/EG system). The isothermal compressibility, KT, can be obtained through the relation (4)
where a is the thermal expansion coefficient of the mixture. The apparent molar volume of the cosolvent, V,, is calculated from
The Kirkwood-Buff integrals for W/l-PrOH and W/EG, W/EA, W/ED, and W/Z-ME over the entire composition range are presented in Figure 1. 1-PrOH was chosen for this comparison since it can be considered as one of the members of the homologous series of the bifunctional cosolvents studied here, as shown in Table I. From Figure 1, it is readily seen that the composition dependence of Gtjin the system W / 1-PrOH exhibits maxima or minima but only monotonous increasing trends in Gij for the systems W/EG, /EA, /ED, and /2-ME. The Kirkwood-Buff integrals for a symmetrical ideal system yield
+ G22 - 2G12 = 0
A = GI,
+
where dl is the density of water; MI and M2 the molar mass; and and x2 the mole fraction of water and cosolvent, respectively. The partial molar volumes were computed according to XI
v2=v,+xx
(3) T,P
VI =
(xlMl + x M
2)
- xzvz
Xld
The activity coefficients are related to the molar excess free energy G: by
(1 1)
Equation 11 shows that the net resulting affinity between various molecules must cancel out if the distribution of molecular species in a mixture approachescomplete randomness. For real mixtures, the above equation may be generalized in the form
A = GI, G2, - 2G12 =f(x) (12) where A x ) is a composition-dependent function describing nonideality. The variation in Ax) with x2 for the different cosolvents is illustrated in Figure 2. The latter shows, again, a sharp distinction between 1-PrOH and the bifunctional cosolvents examined here. With the latter,f(x) exhibit substantial variations only in the range 0 < x2 5 0.1; at higher cosolvent mole fractions, Ax) is low and nearly invariant, suggesting molecular randomness in the mixture or some form of compensation (or "parity") in the various Gij functions. In all the systems considered here, the major features offlx) are found in the water-rich compositions; it is thus reasonable to conclude that the underlying molecular phenomena are related to the particular features of liquid water, including the hydrophobic effect. The differences in the variation off(x) for 1-PrOH
The Journal of Physical Chemistry, Vol. 97,No. 28, 1993 7361
Comparative Study of Hydrophobic Effect
TABLE I: Homologous Series of Cosolvents functional ethylene chain cosolvent group ( 1) 1-propanol HO -CH2CHr ethylene glycol HO -CHzCHr ethanolamine HO -CHzCHr ethylenediamine HzN -CH2CHr 2-methoxyethanol HO -CHzCHr
TABLE II: Main Features of Association Processes in Liquid Water and o-Alcohols
functional group (2) CH3 OH NHz NH2 OC&
water
H bonding no. of H bonds possible associative structure
Yes 4
n-alcohols
Yes 2
infinite, 3-D linear polymers or irregular network aggregatea dielectric relaxation time single, 10-11 s range, 10-9-10-11 s
TABLE III: Peak q 2 Values for Water/mAlcohol Systems alcohol G22“ x2 (max) MeOH 4-35 0.33 EtOH 0.12 0.10 1-PrOH 8.16 0.06 t-BuOH 6.5 0.12 Unit of G22: lo2cm3mol-’. xz: mole fractionof alcoholat maximum Gzz.
Figure 2. The functionflx) defined by eq 12 for several systems at 25 OC: (1) W/1-PrOH, (2) W/ED, (3) W/Z-ME, (4) W/EA, ( 5 ) W/EG.
the apolar group, limits the extent and range of intermolecular association in liquid alcohols and precludes the type of threedimensional association which is dominant in liquid water. Although detailed knowledge of the polymeric entities present in neat alcohols is still lacking, the X-ray radial distribution functions indicate the formation of linear p o l y m e r ~ . ~ Table ~ J ~ I1 summarizes some of the relevant differences between liquid water and alcohols. In the light of the differences in the molecular features and associative processes of water and n-alcohols, the latter are more appropriately viewed as “soluble hydrocarbons” than as “alkylated water”. The mismatch in the association processes may lead to mutual exclusion of the two hydrogen-bonded networks; this phenomenon in itself would influence thedistribution of molecular species and thus the G,,andf(x) functions, Le., increase 1,l and 2,2 molecular correlations. Another possible consequence is that the alcohol molecules can disrupt the molecular association and fluctuation processes in liquid water (and vice versa), an effect discussed by Huot et and Pagke2’Clearly, all of these effects must be envisaged in the interpretation of the K-B integrals. The Kirkwood-Buff integrals for water/alcohol systems have been calculated (not shown) for MeOH,9J1 EtOH,4+’Jl and ~ - B U O H . ~ J ~InJ ~all J ~systems, maxima were found in the composition dependence of G22 and G11, while minima were observed in the G12 curves. A review of the data for water/ alcohol systems shows a high G22 value in the water/l-PrOH system.34 Table I11lists the G22 peak amplitudesand mole fraction at Gz2(max) for several alcohols. The peak amplitudes increase in the order
and the bifunctional cosolvents, however, indicate different types of molecular processes. This aspect is of central importance to the present work and will be discussed further below. Interactionsin Water/Alcobol Systems. It is generally accepted that there exists extensive hydrogen bonding in either water or alcohol, but the types of molecular associations are quite different and, to a large extent, mutually incompatible. Liquid water retains sensitive hydrogen-bonding fluctuations which are highly significant to all its properties. The short-lived clusters are threedimensional and have a single dielectric relaxation time, lo-” s . M Liquid alcohols are also associated through hydrogen bonding to form short-lived aggregates; the latter, in contrast to water, show a range of dielectric relaxation times, typically between le9and lo-” s.31 The extensive hydrogen bonding has also a marked effect on the properties of neat alcohols, although it does not lead to the high degree of structure openness found in liquid water. Experimental evidence generally shows that, within neat n-alcohols, the molecules participate in two hydrogen bonds (on the average), the hydroxy group acting once as a proton donor and once as a proton acceptor. This, together with the steric hindrance due to
MeOH < EtOH < t-BuOH < 1-PrOH indicating a significant relation between the size of the apolar group and the affinity between the cosolvent molecules. Compared to MeOH, EtOH shows a stronger alcohol-alcohol affinity due to its longer aliphatic chain, and 1-PrOH shows a still higher peak value; 1-BuOH also shows a high peak value, but lower than that for 1-PrOH, the branching apparently reducing the effect. It is now generally agreed35that, in the water-rich region, there exists a hydrophobic cosphere around the aliphatic chain which bears some resemblance to clathrate hydrates, and that this hydrophobic (hydration) effect increases with chain length. Accordingly, the observed dependence of G22 on aliphatic chain further indicates a relationship between hydrophobic hydration and alcohol-alcohol (hydrophobic interaction) affinity in these water/alcohol systems. Interactions in Water/Bifunctional Cosolvent Mixtures. As noted earlier, the composition dependence of the G,, values in water/ bifunctional cosolvent mixtures differs sharply from that observed in water/alcohol mixtures. This is particularly evident in the concentration range 0 < x~ C 0.1 as illustrated from the features of the different K-B integrals shown in Figure 3.
-800
!
0
I
I 0.8
0.8
1/0
l/O
I
I
I 0.8
0.8
l/O
l/O
I
0.8
xz Figure 1. Kirkwood-Buff integrals for the systems W/1-PrOH, W/EG, W/EA, W/ED, and W/2-ME at 25 OC. 1600.00
I
I
n
1400.00 1200.00
- 1000.00
n
E“
\ 000.00 n-
t u
600.00
W
400.00
X
W
+
200.00
0.00 -200.00
’
0.60
I
o.lo
o.io
1
0.60
1
o.do
I. o
x2
Cheng et al.
7362 The Journal of Physical Chemistry, Vol. 97, No. 28, 1993
-
G22 values for 1-PrOH and for the other cosolvents exhibit 1 significant differences in their limiting values (x2 0) as well
I 70.00 60.00 50.00
\ 30.00
n
E
20.00
W c c
10.00
4
/
I
I
/
x2 900.00
700.00 500.00
c?
g
500.00
\ n
E
100.00
u
v
W/W
w-100.00
3
-300.00
’
/
-500.00 0.60
I
I
0.d2
0.04
0.06
I
0.08
x2
T-
-50.00
W/Z-ME
-100.00
=0
150.00
E
\-200.00
n
E
0 -250.00
W
N
-300.00
-350.00 -400.00
I
I
I
0.10
as in their concentration dependence. Positive G22 values are only found with 1-PrOH, suggesting that the excluded volume effect is dominant in the interactions involving all the bifunctional cosolvents. G12values also exhibit marked differences for water/ 1-PrOH and water/bifunctional cosolvent systems; in W / 1-PrOH, G12 decreases sharply with increasing xz, showing repulsive interactions above the excluded volume effect. The replacement of one apolar portion (CH3) of 1-PrOH by a polar group (either OH or NH2) yields a significant difference in the various intermolecular affinities. This clearly shows that the polar functional groupscan alter theintermolecular processoccurring in thewater/ alcohol system. Of particular interest is the replacement of CH3 by OCH3,comparing 1-PrOH to 1-methoxyethanol. In the latter, the aliphatic content of the 1-PrOH is maintained, but the added ether oxygen strongly perturbs the GI, values. In relation to the “compatibility” between the liquid structures of water and of n-alcohols discussed above, the bifunctional cosolvents can beviewed in two ways: (1) Because thesecosolvents bear a larger number of H-bonding (donor and acceptor) sites, they are better able to participate in a three-dimensional H-bonding network. (2) Alternately, the extensive H bonding between the cosolvent and the water molecules will be highly disruptive to the unique water structure. Indeed, EG has been examined as an analogue of waterIz0 while EA, ED, and 2-ME have been viewed as homologues of EG with varying hydrogenated bonding sites, conformation, et^.^&^* Studies of the second derivative thermodynamic properties of water, alcohol, and EG indicated that EG and water appear related in terms of low-energy contributions (which usually arise from intermolecular interactions, conformational effects, hydrogen bonding, as well as order4isorder effects), whereas ethanol is more closely related to hydrocarbons.20 This implies that EG and water are more mutually compatible in terms of their H-bonding structure, as manifested by the ‘quasi-ideal” Kirkwood-Buff integrals shown in Figure 2. Comparing aqueous mixtures of 1-PrOH and of the various bifunctional cosolvents, it appears that the apolar ethylene group of these cosolvents is not significantly involved in hydrophobic effects (hydration or interactions). This is likely the result of strong water/polar group interactions which preclude the organization of the clathrate-like H-bonded network around the ethylene group. The intermolecular process appearing in the water/EG, /EA, /ED, and /2-ME mixtures is apparently related to both the polarity and the size of the functional groups. The polarity of the functional groups follows the order NH2 > OH > OCH3; the G, values shown in Figure 3 are generally consistent with this order. Nevertheless, there is an exception for the W/2-ME mixture, the G22 of which appeared between that of W/ED and those of W/EG and W/EA. This suggests that the size of the functional groups should also be taken into account to specify the particulars of each cosolvent, an effect which may be further discussed in terms of the excluded volume. As noted earlier, G22 values of the water/ 1-PrOH mixtures are positive in the water-rich region, whereas those of the water/EG, /EA, /ED, and /2-ME mixtures are negative over the entire composition range (Figure 3). The Kirkwood-Buff integrals in fact contain two contributions: G,
Jm[gi,(r)- 1]4& d r
where V,is theexcludedvolumecontributionandztjtheinteractive term.39 Providing that V, remains constant at all mixture
The Journal of Physical Chemistry, Vol. 97, No. 28, 1993 7363
Comparative Study of Hydrophobic Effect
On the other hand, the rather small differences noted in the mixtures involving the different bifunctional cosolvents are not surprising. Indeed, the dominant interactions in these systems are of rather high energies (hydrogen bonding, dipolar), and subtle differences due to low-energy phenomena are not readily evidenced in free energy functions, or in the first T o r P derivative of free energies. It was shown earlier2021 that second, or higher, derivative properties are much more discriminant toward low-energy processes in aqueous mixtures.
compositions, the positive contribution can only arise from I,,. Positive G,, values thus require strongly interactive (highly correlated) species. If large changes in the i j pair correlation occur over a narrow composition range, extrema may be observed on Gij,as is the case with water/l-PrOH mixtures. As such, the negative Gijwithout extrema may be attributed to weakinteractive components. In comparisons of Gi, values involving different species, the excluded volume contribution must be duely accounted for. For example, comparing G22 values in W/EG and W/Z-ME (Figure 3b), the latter are more negative than the former, in spite of the fact that the additional methyl group in 2-ME should lead to enhanced hydrophobic interactions and higher G22 values (larger attractive component). It is thus safely concluded that the lower G22 values of W/Z-ME are due to a higher excluded volume. Similarly, the lower G22 values in the system W/ED relative to W/EG would seem related to a greater repulsive term (V,) in ED-ED interactions.
Acknowledgment. We acknowledgewith pleasure the support of this work by the grants of NSERC of Canada and FCAR of Qubbec. References and Notes
Conclusion The Go integrals of direct pair correlation functions, which can be obtained through the inverted Kirkwood-Buff (K-B) theory, provide a useful quantitative means of describing dominant molecular interactions in aqueous mixtures. Applied to water/ cosolvent systems where the cosolvents are either monofunctional (e.g., n-alcohols) or bifunctional (ethylene glycol, ethanolamine, ethylenediamine, and 2-methoxyethanol), the K-B approach yields valuable quantitative information on hydrophobic effects. In the W/n-ROH mixtures, G, values vary markedly with ~ 2 especially in the range 0 < x2 < 0.3. G11 increases consistent with enhanced water-water correlation; G22 also increases with x2 showing high ROH/ROH affinity. Both of these effects become more important with increasing length of the aliphatic chain in the n-alcohols. The observationsare thus entirely consistent with theconcept of hydrophobichydration (enhanced water structure) and hydrophobic interaction (attraction between the apolar solutes). In aqueous mixtures of bifunctional cosolvents, the variation of Gij with x2 is sharply different from that observed in W/nROH systems. Gij values show little evidence of correlation between the various species, pointing to more random distributions of species. The apolar - C H 2 C H r portion of the cosolvents investigated shows no evidence of hydrophobic effect (hydration or interaction). The intermolecular processes in these systems appear largely dominated by water/polar group interactions and by repulsive (excluded volume) effects dependent on the size of the polar groups. The K-B Gij integrals reflect some balance of attractive and repulsive forces and thus may be viewed as related to free energy coefficients(both the radial distributiong&) and potential V&) are required to compute energies); the formal relation of Gt, to free energies is illustrated in Eq. 2 and following. Given that hydrophobic effects, except in extreme cases such as surfactant micellization, contribute only weakly to free energy coefficients?O it is remarkable that the Gij values reveal such a sharp contrast between the two groups of water/cosolvent systems examined here. In particular, the distinction between CHsCH2CH20H and CH30CH2CH20H is striking.
,
(1) Franks, F. TheHydrophobicInteractions. In Water,acomprehensive treatise; 1975; Vol. 4, Chapter 1, p 1. (2) Kauzmann, W. Adv. Protein Chem. 1959, 14, 1. (3) Privalov, P. L.; Gill, S. J. Adv. Protein Chem. 1988, 39, 191. (4) Ben-Naim, A. In Advancesin Thermodynamics,Vol.2 Fluctuation Theory ofMixtures; Taylor C Francis: New York, 1990; p 211. (5) Ben-Naim, A. Cell Biophys. 1988, 12, 255. (6) Kirkwood, J. G.; Buff, F. P. J. Chem. Phys. 1951, 19, 774. (7) Ben-Naim, A. Water and Aqueous Solutions; Plenum Press: New York, 1974; Chapter 4. (8) Bale, H. D.; Shepler, R. E.; Sorgen, D. K. Phys. Chem. Liq. 1968, I, 181. (9) Donkenloot, M. C. A. J . Solution Chem. 1979,8,293. (10) Patil. K.J. J. Solution Chem. 1981. 10. 315. ( l l j Maticoli, E.; Lepori, L. J. Cheh. Pj?ys.’1984,80, 2856. (12) Kato, T. J. Phys. Chem. 1984,88, 1248. (13) Nishikawa, K.; Kodera, Y.; Iijima, T.J. Phys. Chem. 1987,91,3694. (14) Lepori, L.; Mettcoli, E. J. Phys. Chem. 1988,92, 6997. (15) Zaitsev, A. L.;Petrenko, V. E.: Kessler. Yu. M. J. Solution Chem. 1989, 18, 115. (16) Franks, F.; Ives, D. J. G. Quart. Rev. Chem. Soc. 1966, 20, 1. (17) Franks, F. In Physico-ChemicalProcessesin Mixed AqueousSolwnrs; Elsevier: New York, 1967; p 50. (18) Yaccobi, M.; Ben-Naim, A. J. Solution Chem. 1973, 2, 425. (19) Franks, F.; Desnoyers, J. E. In Water Sciences Reviews; Franks, F., Ed.; University Press: Cambridge, 1985; Vol. 1, p 171. (20) Huot, J.-Y.; Battistel, E.; Lumry, R.; Villeneuve, G.; Lavallt, J.-F.; Anusiem, A.; Jolicoeur, C. J. Solution Chem. 1988, 17, 601. (21) Pagt, M., PkD. Thesis, Universitt de Sherbrooke, 1990. (22) Villamanan, M. M.; Gonzale, C.; van Ness, H. C. J. Chem. Eng. Data 1984, 29, 427. (23) Touhara,H.;Okazalti,S.;Okino, F.;Tanaka, H.;Ikari,K.;Nakanishi, K. J. Chem. Thermodyn. 1982,14, 145. (24) Efrcmova, S.A,; Komaroav, L. F.; Garber, Yu. I.; Tikhanovich, V. Zh. Prikl. Khim. Ueninwad 1988. 61. 2579. (25) Ragaini, V.; Zaiderighi, L.;Santi, R. Atti. Soc. Peloritana Sci. Fis. Mat. Nut. 1968, 14, 537. (26) Butler, J. A. V.; Thomson, D. W.; Maclennan, W. H. J. Chem. SOC. 1933,674. (27) Benson, G. C.; Kiyohara, 0. J. Solution Chem. 1980, 9, 791. (28) Benson, G. C.; Darcy, P. J.; Kiyohara, 0. J. Solution Chem. 1980, 9, 931. (29) Kiyohara, 0.;Benson, 0. C. J. Solution Chem. 1981, 10, 281. (30) Frank, H. S.;Wen,W. Y.Discuss. Faraday Soc. 1957,24, 133. (31) Magat, M. In Hydrogen Bonding, Hadzi, D., Thompson, H. W., Eds.; Pergamon Press: London, 1959. (32) Zachariasen, W. H. J. Chem. Phys. 1935,3, 158. (33) Harvey, G. G. J. Chem. Phys. 1938, 6, 111; 1939,7,879. (34) Cheng, Y. Ph.D. Thesis, Universitt de Sherbrooke, 1992. (35) Row, A. H.; Desnoyen, J. E. Proc. Indian. Acad. Sci. (Chem.Sci.) 1987, 98, 435. (36) Dack, M. R. Chem. SOC.Rev. 1975, 4, 211. (37) Kartsev, V.N.; Buslaeva, M. N.; Tsepulin, V. V.; Dudnikova, K. T. Russ. J . Phys. Chem. 1984, 58, 1634. (38) Kartsev, V. N.; Rodnikove, M. N.; Tsepulin, V. V.; Dudnikova, K. T.; Markova, V. G. Zh. Srrukr. Khim. 1986,27,671. (39) Angell, C. A. J. Phys. Chem. 1971, 75, 3698.
