J. Phys. Chem. 1995, 99, 4787-4793
4787
Solvation of DMF in the NJV-Dimethylformamide+Alcohol+Water Mixtures Investigated by Means of the Kirkwood-Buff Integrals Jan Zielkiewicz Department of Chemistry, Technical University of Gdarisk, Narutowicza 11/12 Gdarisk, Poland Received: October 6, I994@
Using Kirkwood and Buffs theory of solutions, the local compositions in the N,N-dimethylformamide solvation microsphere have been estimated. The investigated mixtures are DMF+A+water, where A = methanol, ethanol, and n-propanol, at the temperature 313.15 K. It has been found that in the DMF-rich region, at XDMF > 0.8, the solvation process is governed by the entropy term mainly, and deviations of the local mole fractions from the bulk ones are very small. At low DMF mole fractions, below approximately, 0.15 the preferential hydration of DMF molecules is observed. At very low DMF concentrations, lower than 0.001 in mole fraction scale, the effect of preferential hydration is observed in the range 0.2- 1.0 alcohol mole fraction; in the waterrich region (above a water mole fraction of 0.8) solvation of the DMF molecules is nearly random. The limit between both these regions is clearly visible for propanol and ethanol and slightly visible for methanol. Since the local mole fractions reflect the influence of two main factors, differences in molecular sizes and differences in the intermolecular interactions, then analyzing these values, we may estimate the second mentioned factor. This allows ordering the water and alcohol molecules according to their increasing acidity toward the oxygen atom of the amide group as water % methanol > ethanol > n-propanol, with the close proximity of water and methanol in this ranking.
Introduction Dimethylformamide as an aprotic solvent is an example of a “pure” dipolar fluid. Since the hydrogen bond is absent,’ the liquid structure of the neat DMF is determined by the dipoledipole interactions between molecules. Addition of water modifies this picture; hydrogen bonds between oxygen atoms of the amide group and water molecules are created. In the literature are many papers showing (by using various experimental techniques) that association complexes of the D W n H 2 0 type exist in the DMF+water We may expect that in the DMFSalcohol mixtures similar complexes will be created. In fact, there are some papers reporting the heteroassociation between DMF and alcohol But similarity between DMF-water and DMF-alcohol association cannot be exactly complete. Water molecules create four hydrogen bonds forming three-dimensional structures, while alcohol molecules may create two hydrogen bonds only, forming linear polymeric structure^.^ Therefore, the structure of DMF-water and DMF-alcohol mixtures may considerably differ on the molecular level. It is interesting, therefore, to establish the association of DMF molecules in a mixed solvent containing both water and alcohol. This will be considered in the present paper. A detailed description of such complicated temary mixtures in terms of association constants is nearly impossible, requiring exact knowledge of all existing equilibria. On the other hand, a description using some accessible models of solutions does not seem encouraging: over 100 different models have been proposed during the last 30 years to describe nonelectrolyte solutions.1° This shows that there is no single model satisfactorily describing thermodynamic properties of solutions. In fact, values of thermodynamic functions depend on so many different contributions, the majority of which having to be omitted by each model, that the resulting description can be only poor. In this situation Kirkwood and Buff‘s theory of solutions”) appears as a valuable tool for solution investigations. The theory @
Abstract published in Advance ACS Absrracts, March 1, 1995.
0022-365419512099-4787$09.00/0
describes thermodynamic properties of solutions in an exact manner in the whole concentration range using values
G , = hm(g, - 1)4nr2 d r called the Kirkwood-Buff integrals or fluctuation integrals, which may be determined from experimental values of thermodynamic quantities such as chemical potential, partial molar volumes, and isothermal compressibility.12 It is important to notice that the radial distribution function, gy, present in eq 1, reflects the solution structure on the microscopic level, and so we may expect that the G, values contain some information about this structure. In fact, as it was pointed out by Ben Naim,l2 the ciG, values (where ci = NilV is the concentration of i species in the mixture) describe the total average excess (or deficiency) of i molecules in the entire surrounding of a j molecule. On the other hand, it is well-known that the radial distribution function g, differs considerably from unity within distances of only about a few molecular diameters. Therefore, we may assume that the total average excess (or deficiency) of i molecules in the surrounding of a j molecule is contained in the sphere of radius R, equal to a few (four to six) molecular diameters only. Then the integral (1) may be divided into two terms:
G, =
h ‘(g, - 1)4nr2 d r + hy(g, - 1)4nr2d r hRc(gy - 1)4nr2 d r (2) R
%
There is a clearly visible relation between Kirkwood-Buff solution theory and the well-known local composition concept. Resulting from this theory, the possibility of evaluating the local composition was pointed out by many author^'^-'^ and seems a convenient tool for description of solvation processes and solutions’ deviation from ideality. The aim of this work is the description of the solvation of DMF by alcohol and water molecules in the temary mixture DMF+alcohol+water, using 0 1995 American Chemical Society
4788 J. Phys. Chem., Vol. 99, No. 13, 1995
Zielkiewicz
Kirkwood and Buff's theory of solutions. Obtained results will be helpful in understanding the solvation of the amide group in alcohol-water mixtures; here we should remember that the DMF molecule may interact with the hydroxyl group by the oxygen atom only,8 because the free electron pair on the nitrogen atom is protected by methyl groups and does not interact with the hydrogen atom of the OH group.
Data Sources The p,@, and isothermal compressibility, K, data required for calculations have been selected from the literature, mainly from the previous works from this laboratory. The @ data at the temperature 313.15 K were taken from Zielkiewicz and Oraczl' for methanol, Zielkiewicz and Konitz18for ethanol, and Zielkiewicz and Konitz19 for propanol. The p data for these mixtures at 313.15 K were taken from Zielkiewicz20 for methanol, from Zielkiewicz21 for ethanol, and from Zielkiewicz22for propanol. The isothermal compressibility factors were taken from B"mer23 for dimethylformamide,from Diaz Pena and T a r d a j ~ sfor ~ ~alcohols, and from ref 25 for water. The value of this factor for binary and for temary mixtures, K , was calculated from pure component values using the following equation:26 K
=CKi(bi
(3)
i
where ~i is the isothermal compressibility factor of the ith compound, and 4i is its volume fraction in the investigated mixture.
Formulas and Calculations The Gv values for the investigated mixtures are connected with thermodynamic quantities by the following equations: 1 Au 6, G.. = --- cicj det(A) cj (4)
i3ln v .
(7) For the temary mixtures these expressions are more complicated. The obtained Gu values allow the estimation of the local compositions in the following way. The ciGu values designate, as pointed out previously, the total average excess (or deficiency) of the i molecules in the surrounding of a central j molecule. Equation 2 may therefore be rewritten as
Nu = ciGu
+ ciV,
(8)
where Nu is the total number of i molecules around the central molecule J in the volume V, (=4nRC3/3). The local mole fractions of i molecules around the central j molecule, xu, may be defined as Xii
Nij =-
(9)
i
and this may be, after considerable algebra, expressed in terms of Gu values as follows: xi(Gu x;; =
'
+ V,) -- xi(eGij+ 1)
C x i G u + V,
c&Gu+
i
(10)
1
I
c',
where E = according to Ben Naim's works.15J6 Defining the 6~ values as
6 11. .= x 1.1. - x '.
(1 1)
(Le. the dv is the deviation of the local mole fraction from the bulk one) and expanding this equation as a Maclaurin power series about the value E = 0, we yield the linear coefficients of preferential solvation, di, as the first term of these expressions:
dyl = x ~ x ~ ( G, , GI21 + X I X ~ ( G-I IG13)
In this expressions the det(A) is the determinant of the matrix A with the elements Aij; A0 is the cofactor of the element Ad; dij is the Kronecker 6 function, ci = NJV, where V = m i V i is the volume of the system, Ni is the number of moles, and Vi is the partial molar volumes of the components; and K is the isothermal compressibility factor. The pu values are defined as
where pi is the chemical potential of the i component:
For the binary mixtures these equations reduce to the form wellknown in the literature:
VI v2 GI, = RTK - DV For binary mixtures, or for the temary mixture in a very diluted region, eqs 12 reduce to the expressions given by Ben
J. Phys. Chem., Vol. 99, No. 13, 1995 4789
Solvation of DMF
ro
I
1
0.5
0.4
0.6
0.b
1 .o
XDMF l.0
in” into existing polymeric structures of water or alcohol. This conclusion agrees with the literature data revealing the existence the DMF-water and DMF-alcohol association Moreover, we may interpret the observed 6:1 values as the result, in the greater part, of the differences in the molecular sizes of DMF and water (or alcohol) molecules. This may be shown in the following way. Figure l b presents for comparison the concentration dependence of 6il values which have been calculated as follows: the VE was assumed equal to 0 in the whole concentration range; the @ was calculated assuming is equal to 0 and SE calculated according to the Flory and Huggins theory; the K values were taken from literature. Similarity of both these pictures (la, experimental; lb, including the entropy term only) suggests that the mixing process, in the case of the investigated binary mixtures, is dominated by the excess entropy rather than the excess enthalpy. Solvation of DMF in the ternary DMF( l)+alcohol(2)+water(3) mixture is described by the 6yl values. Figure 2 presents plots of 6il and &, calculated from experimental data, as a function of the DMF mole fraction in the mixture; the 6: curves are calculated at a constant value of the ratio
+
r = x2/(xz x g )
+
xij = xi 6,
= xi+ diy = xi+ s p c
(14)
Results and Discussion For a description of ternary mixtures DMF(l)+alcohol(2)+water(3) the 6; values (defined according to eq 12 will be used. Preferential solvation is always present, and, although in many cases it is relatively weak, it affects the thermodynamic properties of the solution. The 6; values reflect changes of local mole fractions of i species around the central j molecule, and they depend on two main factors: the energy of intermolecular interactions (as it was first pointed out by Wilson in his well-known local composition ideaz7) and differences in molecular sizes. The influence of both these factors in the case of simple associated solutions containing alcohols and hydrocarbon has been investigated previously.28 Here we have undertaken the attempt to split both these effects in the investigated systems. We start from the description of binary mixtures. Figure l a presents the plot of the 6:1 value as a function of the DMF mole fraction, calculated from experimental data for the DMF( l)+A(2) binary mixtures; A represents here the second component of the binary mixture, namely, A = water, methanol, ethanol, or propanol. Figure l a shows relatively small values of 6;, not exceeding 20 cm3; for comparison, this value for the alcohol+hydrocarbon mixtures was foundz8 to be about 1000 cm3. This small value shows that the DMF molecule “builds
(15)
where x2 and xg are mole fractions of alcohol and water, respectively, according to the description of the ternary mixture. Observing the run of the 6: curves, we may divide the whole concentration range of DMF into three regions: the DMF-rich region (XDW above about 0.Q the dilution region (at the DMF mole fraction below approximately 0.15), and an intermediate region. Solvation of the DMF molecule differs in each of these regions. In the DMF-rich region solvation of the DMF by the alcohol and water molecules is determined by the “geometric” factor (the differences in molecular sizes between molecules of various species), as can be seen by comparing Figures 2 and 3. In Figure 3 the concentration dependence of 6: values is presented, using the 6s: calculated, as above, under the assumption that = 0 and @ equals the value calculated by the Flory and Huggins theory. So, Figure 3 serves as a “reference level” in the interpretation of 6:’s determined experimentally. The similarity of Figures 2 and 3 at XDW > 0.8 suggests that in this region the mixing process is controlled by the entropy term mainly and that there is no preferential solvation of DMF by water or alcohol molecules, other than that generated by the geometric reasons. In the dilution region (at XDMF < 0.15) the situation is different. In this region we can observe clearly visible growth of the 6:1 value; this behavior of 6:1 is accompanied by a lowering of the 6:1 values. This is clearly visible for propanol and for ethanol. For the DMFfmethanol+water mixture differences between Figures 2 and 3 in this region are small, and they are visible in the high-dilution region only. We suppose that the differences between Figures 2 and 3 in this region result from differences in proton-donating ability between water and alcohol molecules. Since the hydrogen bond forms between the hydrogen atom of the hydroxyl group and the free electron pair on the oxygen atom of the amide group8, then the phenomenon of preferential solvation reflects (after consideration of differences in molecular sizes) relative acidities of alcohol and water toward this oxygen atom. If so, we may arrange the water and alcohol molecules according to their relative acidity vs the oxygen atom of the
Zielkiewicz
4790 . I Phys. . Chem., Vol. 99, No. 13, 1995
-*a.o -
0.2 1
0.4
0.65
o.E
l.o 1
XDMF
40 35 30 25 20 15 10 5 0 -48.0
0.2
0.4
0.6
0.8
I
1.0
XOUF
XDMF
0.2
0.4
0.6
o.8
XDMF
Figure 2. Concentration dependence of 8; values calculated from experimental data. The several rows present the 8: values for DMF+A+water for various alcohols: from top to bottom, A = methanol, A = ethanol, A = propanol, A = propanol, expanded 8; scale. The individual curves are calculated at various values of the r ratio (defined by eq 15): (1) r = 1.0; (2) r = 0.75; (3) r = 0.50; (4) r = 0.25; (5) r = 0.0. amide group as follows: water % methanol > ethanol > n-propanol (16) as is suggested by a comparison of both Figures 2 and 3. The position of water in this ordering, nearly the same as methanol, seems surprising. We may intuitively expect that the water molecules should have greater ability for proton donation than does methanol. Moreover, this ordering of the alcohols
differs from that determined by Frange et al.29 They found that the relative acidities of alcohols vs the pyridine N-oxide are methanol > n-propanol > ethanol measured by means of UV spectroscopy in cyclohexane and carbon tetrachloride solutions. The observed discrepancy may be due to the different donor and, first of all, to the different
Solvation of DMF
-
J. Phys. Chem., Vol. 99, No. 13, 1995 4791
0.2 1
0.4
0.6 5
o.8
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.
1
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0.2
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,
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,
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XWF
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J
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XDLlF
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60 50 40
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,$l
-10
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-51
I 0.2 0.4 0.6 0.8 1.0
-'8.0 XDMF
XDMF
Figure 3. Concentration dependence of 6; values calculated under the assumptions of pictures are the same as in Figure 2.
character of the medium used in both series of experiments: the UV measurements were carried out in a nondonor solvent of low dielectric constant, so they represent only alcohol-donor interactions, while those reported in this work refer to polar, comparatively strongly H-bonding mixtures resulting in a variety of molecular interactions. The effect of alcohol-water interactions is difficult to discuss for the following reasons. Three factors mainly determined the
= 0 and @ = GF-H (see text). Ordering and description
structure of alcoholfwater mixtures:30(1) the hydrogen bonding between hydroxyl groups (from water and alcohol), (2) the hydrophobic intractions, and (3) the entropy contributions. The final state is the result of the subtle balance between these factors. In the case of the investigated alcoholfwater systems, the hydrophobic part of the n-propanol molecule is greater than that of ethanol (and the hydrophobic part of ethanol is greater than that of methanol), and the contribution from hydrophobic
4792 J. Phys. Chem., Vol. 99, No. 13, 1995
interactions varies systematically from n-propanol to methanol. The n-propanol+water and ethanol+water mixtures have been investigated recently using the small angle X-ray scattering method30q31 and interpreted by the authors as consistent with the conclusion on formation of micelle-like clusters for propanol+water mixtures30previously reported in the literature. They, however, pointed out that these clusters do not exist as main components in the aqueous solutions of ethanol.31 We may think, therefore, that the microscopic structure of alcohol+water mixtures varies with changing the alcohol from n-propanol to methanol. Such considerations are true in the case of alcoholfwater binary mixtures, but after addition of the DMF into this mixture (with creation of the ternary mixture) the balance between mentioned factors (1-3) is perturbed by creation of a hydrogen bond with the oxygen atom of the amide group; it is difficult, however, to predict the extent of this perturbation. Therefore, the ordering (16) is only a very speculative one. At very low concentrations of DMF (at, say, X D
