J. Phys. Chem. B 1997, 101, 7991-7997
7991
Solute-Solvent Interactions in Amide-Water Mixed Solvents Begon˜ a Garcı´a, Rafael Alcalde, and Jose´ M. Leal* UniVersidad de Burgos, Departamento de Quı´mica, Laboratorio de Quı´mica Fı´sica, 09001 Burgos, Spain
Jose´ S. Matos UniVersidad de Las Palmas de Gran Canaria, Departamento de Fı´sica, 35017 Las Palmas de Gran Canaria, Spain ReceiVed: August 30, 1996; In Final Form: June 24, 1997X
Excess volumes, mixing viscosities, and excess Gibbs energies of activation of viscous flow of the aqueous binary mixtures of the amides formamide, N-methylformamide, N,N-dimethylformamide, pyrrolidin-2-one, and N-methyl-2-pyrrolidinone were calculated from density and viscosity measurements. The values of these functions point to strong amide-water interactions with formation of a variety of aggregates, the nature of which depends on the extent of substitution of the amides; comparison of the functions of the same amides with alkan-1-ols reveal an important hydration effect. Various one-parameter and two-parameter empirical models for prediction of mixing viscosities were in good agreement with the experimental results only for the formamide-water system; none of the models predicted satisfactorily the behavior for the aqueous mixtures of both mono- and disubstituted amides.
Introduction Liquids can be classified according to the nature of the intermolecular forces between molecules, since the molecular interaction energy governs the distribution of molecules. Water, however, is a unique substance;1 it manifests remarkable and anomalous properties, such as a large heat capacity (which drops to less than one-half upon freezing or boiling) and a comparatively large liquid temperature range (which denotes long range forces in liquid water).2 Liquid water is strongly self-associated by hydrogen bonds; hydrogen bonding in water is believed to be highly cooperative, i.e., interaction of a water molecule with a cluster of H-bonded molecules is more favorable than interaction with a single molecule, so that water trimers and higher oligomers are even more stable than single dimers.3 On the other hand, amides are very interesting compounds; they possess the very common in nature donor-acceptor -CONH- peptide bond and display the property of self-association by the H-bond; in particular, cyclic amides (lactams) offer great interest because they are related to structural problems in molecular biology. Liquid mixtures containing the amide functional group constitute an important tool in the interpretation of complex molecules of biological interest; the abnormally high density of H-bonds in water allows forming or breaking such bonds in biomolecules at the lowest energetical cost, which confers biomolecules high reactivity at room temperatures.4 Due to the interest in connection with the peptide bahavior, much work has been published on amide-water systems to learn the manner in which water exercises thermodynamic and kinetic control over the chemical activities of polypeptides.5 However, only very few studies have been published on the composition dependence of physical properties of amide-water systems across the entire range of mole fractions. Despite the close similarity observed in many respects, the amide-alcohol and amide-water mixed solvents manifest quite X
a different behavior as solvent systems. Previously, we reported density and viscosity measurements for the amide-(C1-C10)alkan-1-ols mixed solvents as a function of mole fraction and discussed the behavior in terms of excess thermodynamic functions;6,7 several prediction equations for mixing viscosities based on empirical models were tested, in general with fairly good results. In order to extend the study of polar amidecontaining liquid mixtures, we report here the densities and viscosities measured at 298.15 K of the aqueous binary mixtures of the same amides: formamide, N-methylformamide, N,Ndimethylformamide, and the cyclic amides pyrrolidin-2-one and N-methyl-2-pyrrolidinone; the viscosity-mole fraction data of these mixtures were used to test the empirical one-parameter models for viscosity prediction put forward by NissanGrunberg,8 Hind-McLaughlin-Ubbelohde,9 and Teja-Rice10 and the two-parameter models by McAllister,11 Heric,12 Lobe,13 and Cao-Fredeslund-Rasmussen;14 these models yielded large deviations for amide-water mixtures compared to amidealcohol mixtures, this feature reflecting the complexity of the interactions between the amide and water molecules.
Abstract published in AdVance ACS Abstracts, September 1, 1997.
S1089-5647(96)02637-5 CCC: $14.00
© 1997 American Chemical Society
7992 J. Phys. Chem. B, Vol. 101, No. 40, 1997 Experimental Section The reactants formamide (FOR, Merck 99.8%), N-methylformamide (NMF, Fluka, >99%), N,N-dimethylformamide (DMF, Carlo Erba, >99.5%), pyrrolidin-2-one (PYR, Fluka, >99%), N-methyl-2-pyrrolidinone (NMP, Fluka, >99%), of the highest purity commercially available, were used without further purification; doubly distilled and deionized water was used. The liquids were degassed with ultrasound for several days before use and kept out of the light over Fluka Union Carbide 0.3 nm molecular sieves. The purity was assessed with a Perkin Elmer 990 gas chromatograph with a Hewlett Packard 3390A integrator for a column in liquid phase over a solid Supelcoport 100/120, 11/8 in., the working temperatures being 250, 275, and 150 °C for the detector, injector, and oven, respectively. In order to protect the mixtures from preferential evaporation, these were prepared by syringing amounts (weighed to ∆m ) 0.000 01 g with a Mettler AT 261 Delta Range balance) of the pure components into stoppered bottles. The mixtures were completely miscible over the whole composition range. Viscosities were measured with an automated AMV-200 Anton Paar microviscometer; it works under the measuring principle of the rolling ball: a gold-covered steel ball was introduced inside an inclined sample-filled glass capillary; the time taken ((0.01 s) for the ball to roll a fixed distance between two magnetic sensors was converted into viscosity measurements. By changing the inclination angle in 5° intervals over the range 15-90°, the shear stress was varied from 10 to 1000 s-1, which makes the instrument well suited even for nonNewtonian fluids. The capillary was placed inside a block thermostated with a Julabo F-30 thermostating bath ((0.01 K); a temperature sensor close to the capillary’s surface measures the temperature within the capillary block. To properly cover the viscosity range of the five amide-water systems, two different capillary diameters were used: a 0.9 mm capillary diameter (0.12 cm3 sample size) calibrated with 1-propanol as reference fluid and a 1.0 mm capillary diameter (0.15 cm3 sample size) calibrated with commercial V15 Anton Paar Rheologie (η ) 15.1 mPa‚s and F ) 0.8743 g cm-3 at 293.15 K). The calibration constants needed for converting the time readings into viscosity measurements were evaluated at every inclination angle as a function of the reference liquid and the density of the ball (7.85 g cm-3). The viscosities were calculated as an average of four readings at each of 8-10 inclination angles, with an stated accuracy better than 0.5%. The densities were measured with a microcomputer-controlled Anton Paar DMA 58 densimeter (0.7 cm3 sample size, accuracy 3 × 10-5 g cm-3, precision 5 × 10-6 g cm-3); the operation of the instrument is facilitated through a resident menu driven program and an internal Peltier element that ensures thermostatization (precision 0.01 K); it also takes care of electrical control of sample temperature and correct calibration. The apparatus was calibrated at the working temperature with doubly distilled and degassed water and n-nonane. The purity of the cosolvents was also assessed by comparing their densities and viscosities with literature values (Table 1). Results and Discussion Starting from the experimental densities (F, g cm-3) and the absolute dynamic viscosities (η, mPa‚s) measured at 298.15 K, the excess volumes, VE, mixing viscosities, ∆η, and excess Gibbs energies of activation for viscous flow, ∆aG*E, were
Garcı´a et al. TABLE 1: Properties of Pure Components G (g cm-3) and η (mPa‚s) at 298.15 K DMF
NMP
0.944 06a 0.944 4b 0.943 87c 0.943 8g 0.944 5h 0.943 93i 0.943 76j 0.945 39k 0.943 83l
1.028 32a 1.025 9b 1.025 9c 1.028 6e 1.028 3f 1.027 59l
0.805a 0.80b 0.802c 0.802 4g
1.66a 1.666c 1.663e 1.67f
NMF
PYR
FOR
Densities 0.999 29a 0.998 8b 1.000 0c 0.998 89l
1.107 47a 1.107b 1.110 0c 1.106 43l
1.129 75a 1.129 2b 1.129 15c 1.129 155d
Viscosities 1.76a 13.1a 1.65b 13.3b 13.3c
3.34a 3.22b 3.302c
a This work. b Reference 15. c Reference 16. d Reference 17. e Reference 18. f Reference 19. g Reference 20. h Reference 21. i Reference 22. j Reference 23. k Reference 24. l Reference 25.
determined using the equations:
VE ) V - (X1V1 + X2V2)
(1)
∆η ) η - (X1η1 + X2η2)
(2)
∆aG*E ) RT[ln ηV - (X1 ln η1V1 + X2 ln η2V2)]
(3)
where V ) (X1M1 + X2M2)/F is the molar volume of the mixture, Vi ) Mi/Fi that of the pure components (i ) 1 for the amide, absence of subscript refers to the mixture), M is the respective molar mass, R is the gas constant, T is the absolute temperature, and Xi is the mole fraction. The experimental densities as a function of composition for all five amide-water systems are given in Table 2; Table 3 collects the η, ∆η and ∆aG*E values as a function of the mixture composition. The Redlich-Kistertype equation (eq 4) was fitted to the excess YE (VE, ∆η, ∆aG*E) properties: k-1
YE ) X1X2
aj(X1 - X2)j ∑ j)0
(4)
The k coefficients aj were fitted by unweighted least squares and are listed in Table 4. The choice of the proper number of coefficients was based on the standard deviations and the F-test as criteria of goodness. The confidence level of the fittings was always better than 95%. The partial molar volumes of the amides V h 1 and the partial molar volumes at infinite dilution V h ∞1 were calculated by the intercept method using the equations
h E1 V h 1 ) V1 + V
(5)
V h E1 ) VE + X2 (∂VE/∂X1)P,T
(6)
with (∂VE/∂X1)P,T taken from eq 4. Using the values limX1f0(∂VE/∂X1)P,T and limX1f0VE ) 0, one obtains the V h ∞1 value. The amide partial excess molar volume at infinite dilution V h E,∞ is defined as 1
h ∞1 - V1 V h E,∞ 1 )V
(7)
and are listed in Table 5 along with the partial molar volumes at infinite dilution V h ∞1 . Analyses of Excess Volumes and Mixing Viscosities. The VE values were negative for all five amide-water systems
Interactions in Amide-Water Mixed Solvents
J. Phys. Chem. B, Vol. 101, No. 40, 1997 7993
TABLE 2: Densities G (g cm-3) of (X1)Amide + (1 - X1)Water Measured at 298.15 K over the Whole Composition Range X1
F
X1
F
X1
F
X1
F
1.084 53 1.088 93 1.092 22 1.092 51 1.100 91 1.106 34
0.642 33 0.673 82 0.701 08 0.826 82 0.857 88 1
1.106 36 1.108 91 1.111 03 1.119 64 1.121 62 1.129 75
0 0.057 12 0.070 05 0.099 34 0.129 52 0.181 32
0.997 05 1.015 92 1.019 66 1.027 77 1.035 28 1.046 89
0.190 32 0.211 30 0.259 36 0.272 48 0.300 14 0.347 26
FOR + Water 1.048 60 0.421 19 1.052 78 0.458 96 1.061 52 0.489 28 1.063 71 0.491 59 1.068 24 0.578 22 1.075 09 0.642 07
0 0.046 84 0.114 78 0.168 36 0.223 83
0.997 05 1.003 29 1.010 27 1.013 82 1.015 78
0.242 36 0.288 97 0.342 48 0.377 98 0.451 00
NMF + Water 1.016 20 0.558 48 1.016 57 0.573 64 1.016 25 0.679 59 1.015 72 0.704 15 1.014 13 0.840 12
1.011 01 1.010 54 1.007 31 1.006 63 1.002 95
0.867 02 0.931 48 1
1.002 24 1.000 74 0.999 29
0 0.055 76 0.102 31 0.149 12 0.177 27
0.997 05 0.996 35 0.996 92 0.996 96 0.996 55
0.240 95 0.297 52 0.330 42 0.360 99 0.412 44
DMF + Water 0.994 39 0.494 54 0.991 31 0.549 22 0.989 20 0.689 42 0.987 06 0.785 81 0.983 13 0.815 48
0.976 59 0.972 26 0.961 91 0.955 62 0.953 82
0.916 35 0.916 64 0.920 36 0.925 06 1
0.948 15 0.948 15 0.947 93 0.947 71 0.944 06
0 0.010 25 0.020 68 0.030 56 0.064 19 0.069 59
0.997 05 0.999 97 1.003 22 1.006 44 1.016 89 1.018 53
0.106 72 0.108 57 0.135 73 0.153 11 0.188 34 0.219 21
NMP + Water 1.028 05 0.262 11 1.028 33 0.302 63 1.033 88 0.360 65 1.036 84 0.423 96 1.041 40 0.515 53 1.044 15 0.563 79
1.046 52 1.047 46 1.047 10 1.045 98 1.043 20 1.042 42
0.663 04 0.708 83 0.777 03 0.859 10 1
1.038 04 1.037 53 1.034 16 1.032 97 1.028 32
0 0.047 46 0.078 77 0.108 99 0.148 85
0.997 05 1.020 09 1.032 92 1.044 16 1.056 07
0.205 23 0.268 04 0.291 26 0.344 65 0.423 39
PYR + Water 1.069 57 0.431 33 1.080 26 0.501 28 1.083 35 0.555 98 1.089 01 0.585 22 1.094 99 0.602 16
1.095 50 1.098 88 1.100 84 1.101 70 1.102 12
0.669 92 0.733 52 0.846 06 0.914 27 1
1.103 59 1.104 64 1.105 99 1.106 60 1.107 47
(Figure 1), the location of the minima changing with the amide. Substitution of H by CH3 at the N site caused a noticeable effect on the VE values: the tertiary amides (NMP and DMF) gave excess volumes larger than those of secondary amides (NMF and PYR), and the latter larger than those of the primary amide (FOR). At constant composition, X1 ) 0.4, the VE ratios tertiary: secondary:primary at the respective minima were (roughly) 8:4: 1. These VE values (except FOR-water) were analyzed by Davis using the segmented-composition model25 and discussed in terms of prevalent patterns of molecular aggregation. N,Ndialkylamides manifest no significant intermolecular H-bonding ability (DMF is not associated in the pure state), but they are sufficiently polar that the pure liquids are presumed to be highly structured. Primary and secondary amides are H-bonded, hence it may be assumed that their VE values are consistent with substantial variation of amide self-aggregation in switching from the pure liquids to water mixture. This volumetric bahaviour differs considerably from that of the same amides with (C1-C10)alkanols, for which VE increased with the alcohol chain length in the order VE(PYR) < VE(FOR) < VE(DMF) < VE(NMF), with some 1 cm3 mol-1 difference between two consecutive amides irrespective of the alcohol chain length; contrary to amide-water mixtures, stepwise introduction of CH3 groups left VE unchanged for alcoholamide mixtures.6,7 The VE vs X1 curves for aqueous DMF and NMP gave minima even more negative than those of the alcohol mixtures (PYR-MET, VE ) -0.697 cm3 mol-1 at X1 ) 0.4), suggesting that the structures of tertiary amides in water mixtures are even more compact than in the pure state. Due to their intermolecular H-bonding ability, the pure primary and secondary amides studied are self-associated to a greater extent than tertiary amides (PYR may form dimers and higher oligomers, FOR has three H-bond donors and three acceptors), which justifies the negative VE values of the latter; in view of the substitution effect caused on VE of alcohol-amide mixtures, it
may be inferred that the presence of water is by far the predominant factor responsible for such a behavior. In Table 5 we report V h E,∞ ≈ 1.2 cm3 mol-1 for FOR and 1 PYR; this value becomes twice and three times higher for monosubstituted (NMF and NMP) and bisubstituted (DMF) amides, respectively. The V1 values reported in this work agreed h ∞1 values to some 1%; to 0.1% with those by Davis,25 and the V however, higher differences were encountered in the V h E,∞ 1 values, possibly due to the following: (i) the greater number of data points reported by Davis in the vicinity of pure h E,∞ components allows a better precision in V h ∞1 and V 1 , and (ii) E our V values for PYR differred considerably from those by Davis (16.9%) but agreed reasonably well with those by ElAzzawi et al.26 and are in excellent good agreement with other literature values for FOR, NMF, DMF, and NMP, as shown in Figures 2 and 3. The comparatively small deviations in the V h E,∞ values (Table 5) are larger at higher mole fractions, this 1 effect showing that molar volumes at infinite dilution are not representative at other compositions; the V h E1 values at the minima (Figure 4) were strongly negative for tertiary amides and increase for secondary, and even more for primary, amides. The negative partial excess molar volumes may be taken either as a sign of strong solvation by H-bonding, accompanied by only minor (entropy-increasing) destruction of water structure, or as a sign of fitting of the alkyl groups into water cavities by interstitial solvation plus some iceberg formation, or as a consequence of both;18 Assarsson and Eirich reported a strong effect of the alkyl groups on V h E,∞ 1 ; the more negative the values the more symmetrical the alkyl groups. The possibility of solute fitting into solvent structures (clathrate formation) should be closely related to the relative size of the cosolvents. This effect was clearly established in amide-alcohol mixtures, but it is not sufficient to interpret the volumetric behavior of amide-water mixtures; the different behavior of mono-, bi-, and nonsubsti-
7994 J. Phys. Chem. B, Vol. 101, No. 40, 1997
Garcı´a et al.
TABLE 3: Viscosities η (mPa‚s), Mixing Viscosities ∆η (mPa‚s), and Excess Gibbs Energies of Activation ∆aG*E (J mol-1) of the (X1)Amide + (1 - X1)Water Mixtures Determined at 298.15 K X1
η
0 0.075 01 0.123 24 0.183 29 0.239 59 0.294 13 0.344 87 0.390 12 0.422 60
0.890 0.973 1.03 1.10 1.19 1.27 1.36 1.44 1.50
0 0.057 98 0.137 75 0.181 46 0.210 89 0.281 16 0.320 74 0.429 56
0.890 1.19 1.53 1.68 1.77 1.93 2.00 2.07
0 0.051 71 0.107 26 0.148 06 0.271 23 0.346 17 0.387 67 0.432 27
0.890 1.35 1.83 2.12 2.50 2.41 2.27 2.12
0 0.091 67 0.155 17 0.237 17 0.278 86 0.341 34 0.446 59 0.511 17 0.527 80
0.890 2.53 3.79 4.97 5.11 4.96 4.20 3.70 3.61
0 0.047 46 0.078 77 0.108 99 0.148 85 0.205 24 0.268 04 0.291 26 0.344 65
0.890 1.48 1.91 2.43 3.14 4.33 5.72 6.21 7.34
∆η
∆aG*E
X1
η
∆η
∆aG*E
1.62 1.70 1.83 2.00 2.30 2.39 2.81 3.34
-0.45 -0.46 -0.47 -0.47 -0.43 -0.40 -0.26
70 46 10 4 -22
-0.10 -0.16 -0.24 -0.28 -0.34 -0.37 -0.40 -0.42
FOR + Water 0.488 27 34 0.523 16 49 0.577 04 0.647 21 80 0.753 86 0.781 54 94 0.896 36 94 1 92
0.25 0.52 0.63 0.69 0.79 0.82 0.79
NMF + Water 0.503 34 0.606 98 1343 0.643 67 1547 0.695 02 1652 0.755 78 1792 0.810 61 1830 0.872 78 1
2.03 1.98 1.94 1.91 1.87 1.84 1.81 1.76
0.71 0.56 0.49 0.41 0.32 0.24 0.15
1562 1286 1153 995 794 614 409
0.46 0.95 1.24 1.63 1.55 1.41 1.27
DMF + Water 0.516 07 1222 0.550 01 2128 0.610 34 2579 0.688 49 3158 0.708 72 3119 0.835 13 2987 0.862 89 2826 1
1.82 1.70 1.48 1.25 1.21 0.982 0.954 0.805
0.97 0.86 0.64 0.42 0.38 0.16 0.14
1894 1426 1330 695 593
1.57 2.78 3.78 3.96 3.81 2.97 2.42 2.31
NMP + Water 0.544 07 2856 0.623 23 3925 0.691 75 4597 0.828 00 4639 0.856 07 4499 0.964 36 3916 0.979 85 3469 1 3370
3.46 2.92 2.62 2.01 1.98 1.72 1.71 1.66
2.15 1.55 1.17 0.48 0.43 0.09 0.07
3227 2607
0.01 0.06 0.21 0.43 0.94 1.56 1.76 2.24
PYR + Water 0.431 33 1123 0.501 28 1637 0.555 98 2105 0.602 16 2552 0.669 92 3053 0.733 52 3382 0.846 06 3445 0.914 27 3524 1
8.94 10.0 10.7 11.1 11.6 12.0 12.5 12.8 13.1
2.78 2.99 3.02 2.86 2.53 2.15 1.28 0.75
3437 3227 3000 2749 2346 1937 1144 648
Figure 1. Molar excess volumes VE vs X1 at 298.15 K of (X1)amide + (1 - X1)water: (9) FOR, (2) NMF, ([) DMF, (f) NMP, (b) PYR.
1065 935 214 144
tuted amides indicates that the H-bonding and hydration effects superimpose to the size effect. Ambrosone et al.27 reported densities in ternary poly(vinylidene fluoride)-water-DMF systems at 20 °C and found that in the absence of polymer the VDMF values decreased regularly with increasing WH2O (W ) weight fraction); the limiting VDMF value at infinite dilution is some 0.840 cm3 g-1, smaller than that of pure water (≈1.000 cm3 g-1). This apparent contradiction may actually be ascribed to the collapse of the icelike structure and the presence of monomeric water molecules, a result consistent with solute hydration effects. Figure 5 shows the η vs X1 curves for the five amide-water systems; the viscosities reported are in good agreement with literature values,28,29 although the maxima in this work occur at a slightly more aqueous composition. The large maxima suggest high association or complex formation between water and the peptido dipole; the appearance of such maxima was often found for systems of polar unlike molecules, as in ethanol-water, dioxane-water,30 diethylamine-water,31 and
Figure 2. Excess molar volumes at 298.15 K of (X1)amide + (1 X1)water mixtures: (f) and (b) this work, (*) ref 18, (crossed 0) ref 19, (O), and (g) ref 25, (x) ref 26.
DMSO-water,32 and N,N-disubstituted amides.18 The maxima in the NMP and DMF aqueous mixtures suggest strong heteroassociations by multiple H-bonding much in excess of the weak associations in the pure NMP and DMF. The discussion can be completed with the mixing viscosities and excess Gibbs energies of activation. The ∆η values (Figure 6) were positive and displayed maxima except for FOR-water; in contrast, the ∆η values for amide-alkan-1-ols mixtures were negative except FOR with propanol-pentanol and changed from negative to positive with increasing alcohol concentration.7 Likewise the ∆aG*E values (Figure 7) were large and positive for the amide-water systems, with maxima well defined except for FOR-water; in the amide-alcohol mixtures, however, the ∆aG*E values changed from negative to positive with increasing alcohol chain length, except for FOR. These features indicate that the water interactions are much stronger compared with alkan-1-ols. The ∆aG*E values may be considered a reliable measure to detect the presence of interactions between molecules; positive ∆aG*E values can be seen in binary mixtures with specific interactions between molecules; negative values indicate a behavior characteristic of mixtures with predominant dispersion forces.33-35 So far the results discussed reveal that secondary and tertiary amides interact strongly with water. The higher relative
Interactions in Amide-Water Mixed Solvents
J. Phys. Chem. B, Vol. 101, No. 40, 1997 7995
TABLE 4: Least-Squares Coefficients aj of the VE (cm3 mol-1), ∆η (mPa‚s), and ∆aG*E (J mol-1) Redlich-Kister fittings by Eq 4 system
YE
a0
a1
FOR + water
VE ∆η ∆aG*E VE ∆η ∆aG*E VE ∆η ∆aG*E VE ∆η ∆aG*E VE ∆η ∆aG*E
-0.5281 -1.81 341 -2.1381 2.87 6293 -4.3018 4.10 10018 -4.4324 10.18 14245 -2.1620 12.00 12952
0.3884 -0.62 -326 1.1939 -2.57 -4866 1.8130 -7.70 -10514 2.3417 -17.68 -15121 1.0644 -2.49 -7545
NMF + water
DMF + water
NMP + water
PYR + water
x
a2 -0.1958 -0.52 -349 0.04 2248 5.26 4679 -0.7687 15.09 9576 -0.3300 -13.30 2309
a3 0.1224 0.32 -189 -0.4818 0.99 -592 -1.3347 3.14 -938 3.38 -2576 -0.9391 3.80 -1463
a4
1.3123 -5.07 1613 2.4317 -21.27 1.3978 5.32 1864
a5
-2.6221 13.13
σy 0.0012 0.004 2 0.0040 0.002 8 0.0023 0.015 10 0.0042 0.029 24 0.0037 0.021 16
E 2 σy ) [∑(YEexp - Ycal ) /(nexp - n)]1/2, nexp ) number of measurements, n ) number of coefficients aj.
TABLE 5: Molar Volumes of the Amides at Infinite Dilution in water (V h ∞1 ), Excess Molar Volumes of the Amides at Infinite Dilution in Water (V h E,∞ 1 ) and Molar Volumes of Pure Liquid Amides V1 at 298.15 K amide FOR NMF DMF PYR NMP a
(100 × V h E,∞ V h ∞1 V h E,∞ V1a V h ∞1 a 1 )/ 1 ∞ -1 3 -1 3 -1 3 V h1 mol cm mol cm mol cm mol-1
cm3
38.63 56.26 73.96 75.63 93.91
-1.24 -2.85 -3.47 -1.22 -2.49
3.1 4.8 4.5 1.6 2.6
39.88 59.13 77.45 76.92 96.47
38.51 56.76 74.46 76.30 94.48
Reference 25.
Figure 4. Partial excess volumes of (X1)amide + (1 - X1)water: (9) FOR, (2) NMF, ([) DMF, (f) NMP, (b) PYR.
Figure 3. Excess molar volumes at 298.15 K of (X1)amide + (1 X1)water mixtures: (9), (2), and ([) this work, (0) ref 17, (4) ref 23, (g) and (]) ref 25.
permittivity of water ( ) 78.9) compared to those of alcohols (2.5-8 times lower)16 allows us to assume a greater hydration effect, hence a strong contraction of the solvent structure near the solute. The formation of “icelike” structures has been assumed as a predominant factor in order to interpret the behavior of hydrophobic solutes in amide-water mixtures.36,37 Symons et al.38-40 have shown how the solvent sensitivity of the CdO stretching band in the IR region can be used to probe solute-solvent interactions in aqueous systems. The spectroscopic probe is the carbonyl group for which the wavenumber of the band assigned to the CdO stretch depends on the extent and type of H-bonding of the solute to the components of the solvent; H-bonds may be formed by interaction with lone pairs
Figure 5. Viscosities η vs X1 at 298.15 K of (X1)amide + (1 - X1)water: (9) FOR, (2) NMF, ([) DMF, (f) NMP, (b) PYR.
and by electrostatic interaction to produce a linear CdO‚‚‚H-O configuration.41 This type of H-bond may be observed when the probe is bulky; the formation of H-bonds is responsible to a good extent for the icelike structures. h E, ∆η, and ∆aG*E values for FOR-water The small VE, V mixtures reflect a balance between dispersion forces and
7996 J. Phys. Chem. B, Vol. 101, No. 40, 1997
Garcı´a et al.
TABLE 6: Values of the Fitting Parameters, Standard Deviations, and Percentage Error for the Different Models Studied Nissan-Grunberg
Hind-McLaughlin-Ubbelohde
Teja-Rice
McAllister
system
d
σ
% error
η12
σ
% error
ψ12
σ
% error
ν12
ν21
σ
% error
r2/r1a
FOR + H2O NMF + H2O DMF + H2O NMP + H2O PYR + H2O
-0.304 1.849 3.489 4.882 3.719
0.01 0.25 0.50 1.2 1.1
0.5 12 27 30 18
1.190 2.761 3.129 7.229 12.039
0.05 0.18 0.49 1.05 0.49
2.7 9.2 28.9 27 10.9
0.959 1.108 1.300 1.448 1.301
0.07 0.16 0.23 0.51 0.58
3.3 8.5 17.9 18.7 7.3
1.789 1.517 0.618 0.601 8.971
1.319 4.583 13.553 68.565 24.656
0.01 0.05 0.01 0.32 0.25
0.4 2.4 6.1 9.5 4.5
0.768 0.674 0.616 0.572 0.617
Heric FOR + H2O NMF + H2O DMF + H2O NMP + H2O PYR + H2O a
Lobe
Cao-Fredenslund-Rasmussen
γ12
γ21
σ
% error
R12
R21
σ
% error
U21 - U11
U12 - U22
σ
% error
0.112 2.673 4.217 5.928 5.317
-0.166 -2.056 -4.696 -7.548 -2.924
0.01 0.05 0.12 0.32 0.25
0.4 2 6 9 4
2.819 0.118 27.962 -2.234 0.240
-1.255 -2.174 49.595 -5.442 5.493
0.03 0.04 0.19 0.43 0.46
1.4 2.1 10.8 11 7.3
2.38 591.6 603.9 147.1 553.5
153.5 631.5 625.6 14713 727.8
0.02 0.74 1.19 2.71 4.84
1.3 34 49 64 58
r2/r1 ) [M2F1/M1F2]1/3, σ, as defined in Table 4.
sterically hindered lone pair of electrons of the disubstituted nitrogen. Thus it is reasonable to assume that the polymeric species should be of the (N,N-disubstituted amide‚3H2O)n, (Nsubstituted amide‚2H2O)n type, whereas in FOR-water mixtures the heteroassociation is less important. Viscosity Mixture Models. 1. The Nissan-Grunberg correlation,8 based on the Arrhenius theory for the viscosity of a solution, was fitted to the absolute dynamic viscosities:
ln η ) X1 ln η1 + X2 ln η2 + X1X2d
Figure 6. Plot of mixing viscosities ∆η vs X1 at 298.15 K of (X1)amide + (1 - X1)water: (9) FOR, (2) NMF, ([) DMF, (f) NMP, (b) PYR.
(8)
The parameter d, characteristic of each system and independent of the mixture composition, can assume either positive or negative values and is a measure of the strength of the interactions between unlike molecules; positive d values reflect negative deviations from Raoult’s law. The d values were all positive except for that of FOR. 2. The Hind-McLaughlin-Ubbelohde equation9 gives a useful description of the behavior of the mixtures:
η ) X12η1 + X22η2 + 2X1X2η12
(9)
The parameter η12, also independent of the mixture composition, is included by analogy with second virial coefficients and may be tentatively attributed to unlike pair interactions. 3. The Teja-Rice method,10 based on the three-parameter corresponding states treatment for mixture compressibility factors, is a rather more complex model. The viscosities of the two pure cosolvents are determined not at the working temperature, but at a temperature T′ defined as
T′ ) T (Tci/Tcm)
Figure 7. Plot of excess Gibbs energies of activation ∆aG*E vs X1 at 298.15 K of (X1)amide + (1 - X1)water: (9) FOR, (2) NMF, ([) DMF, (f) NMP, (b) PYR.
heteroassociations. On the basis of VE measurements for NMPwater mixtures, McDonald et al.19 suggested the existence of transient (NMP‚2H2O)n polymeric species; Assarsson and Eirich18 suggested that two water molecules should interact strongly with the two lone pairs of electrons on the carbonyl oxygen, while a third molecule is held more weakly on the
(10)
where T stands for the working temperature (298.15 K in this work) and Tci for the critical temperature of pure components i; Tcm, the pseudocritical temperature of the mixture, depends on the mixture composition, on the critical temperature, Tc, and on the critical volume, Vc, of the pure components; Vc and Tc are related to the interaction parameter ψ12 of order unity, which must be found from the experimental data. To determine the viscosities of the pure components at the resulting T′ values, we calculated the η values of each of the two pure components at different temperatures and interpolated by fitting the η ) f(T) functions. 4. The McAllister equation,11 based on Eyring’s absolute reaction rates theory,42 leads to the semiempirical cubic equation (eq 11) for kinematic viscosities (ν ) η/F, centistoke (cSt)).
Interactions in Amide-Water Mixed Solvents
J. Phys. Chem. B, Vol. 101, No. 40, 1997 7997
ln ν ) X13ln ν1 + 3X12X2 ln ν12 + 3X1X22 ln ν21 + X23 ln ν2 + X23 ln M2/M1 + 3X1 X22 ln[1/3 + 2M2/3M1] + 3X12X2 ln[2/3 + M2/3M1] - ln[X1 + X2M2/M1] (11) where ν1, ν2, and ν stand for the kinematic viscosities of the pure components and of the liquid mixture, M1 and M2 for the respective molar masses, and ν12 and ν21 represent the interaction parameters between unlike molecules. Equation 11 can be used reliably only if the ratio of radii of the cosolvents, r2/r1, is 1.5 or less, a condition fulfilled in this work. 5. The predictive Heric equation12 for viscosity of binary mixtures was fitted to the (ν, X1) data pairs:
ln ν ) X1 ln ν1 + X2 ln ν2 + X1 ln M1 + X2 ln M2 ln (X1M1 + X2M2) + X1X2[γ12 + γ21(X1 - X2)] (12) where the γ12 and γ21 parameters were determined by least squares. 6. The Lobe equation13 was tested with the (ν, X1) data pairs:
ν ) φ1ν1 exp(φ2R*1) + φ2ν2 exp(φ1R*2)
(13)
where φ1 and φ2 are the volume fraction of the components; R*1 and R*2 may be expressed in a simplified form as:
R*1 ) R12 ln(ν2/ν1)
(14)
R*2 ) R21 ln(ν2/ν1)
(15)
The empirical parameters R12 and R21 were fitted with the experimental data and are given in Table 6 together with the standard deviations. 7. The Cao-Fredenslund-Rasmussen14 model, based on statistical thermodynamics, Eyring’s absolute reaction rates theory, and the corresponding states principle, develops the local composition concept and states a theoretical background for predicting mixture viscosities as a function of composition and temperature n
ln (ηV) )
n
n
Xi ln(ηiVi) - ∑qiniXi ∑θji ln τji ∑ i)1 i)1 j)1
(16)
where Vi and ηi are the molar volume and dynamic viscosity of the component i and V and η are the molar volume and viscosity of the mixture. The parameter qi may be calculated from the surface area of the UNIFAC group;43 θji, the local composition parameter, may be evaluated from the partition function of the mixture; ni represents a parameter of the pure component to be determined from correlation of the experimental viscosities as a function of temperature; τji, the interaction parameter, is expressed as
τji ) exp -[z(Uji - Uii)/2RT]
(17)
z being the coordination number of the lattice; Uji stands for the interaction potential energy between the i and j sites, and Uii may be obtained from the viscosity values of the pure components. For binary mixtures, U21 - U11 and U12 - U22 represent the two potential interaction energy parameters to be determined in the Cao et al. model. These models were tested with fairly good agreement (except the Teja-Rice model) for the amide-alkan-1-ols mixtures.7 Table 6 lists the parameters, standard deviations, and percentage errors for the seven models tested. In this work these equations yielded poor results for the same amides with water; the percentage errors were largest with tertiary amides, and only
the FOR-water system gave deviations within the experimental margin or error. Comparison of these results with those reported for amides-alcohols reflects the complexity of water as a liquid system; its behavior could not be described satisfactorily even by the most complex of the empirical models employed, a feature that might partly be ascribed to the size of the transient polymeric species. Acknowledgment. This work was supported by Junta de Castilla y Leon, Project BU 15/96. References and Notes (1) Franks, F. Water; The Royal Society of Chemistry: London, 1983. (2) Bassez, M.-P.; Lee, J.; Robinson, G. W. J. Phys. Chem. 1987, 91, 5818. Vendamuthu, M.; Singh, S.; Robinson, G. W. J. Phys. Chem. 1994, 98, 2222; 1995, 99, 9263. (3) Walsh, T. R.; Wales, D. J. J. Chem. Soc., Faraday Trans. 1996, 92, 2505. (4) Mare´chal, Y. J. Phys. Chem. 1993, 97, 2846. (5) Thompson, B.; La Plache, L. J. Phys. Chem. 1963, 67, 2230. (6) Hoyuelos, F. J.; Garcı´a, B.; Alcalde, R.; Ibeas, S.; Leal, J. M. J. Chem. Soc., Faraday Trans. 1996, 92, 219. Garcı´a, B.; Hoyuelos, F. J.; Alcalde, R.; Leal, J. M. Can. J. Chem. 1996, 74, 121. (7) Garcı´a, B.; Alcalde, R.; Leal, J. M.; Matos, J. S. J. Chem. Soc., Faraday Trans. 1996, 92, 3347; 1997, 93, 1115. (8) Nissan, A. H.; Grunberg, L. Nature (London) 1949, 164, 799. (9) Hind, R. H.; McLaughlin, E.; Ubbelohde, A. R. Trans. Faraday Soc. 1960, 56, 328. (10) Teja, A. S.; Rice, P. Ind. Eng. Chem. Fundam. 1981, 20, 77. (11) McAllister, R. A. AIChE. J. 1960, 6, 427. (12) Heric, E. L. J. Chem. Eng. Data 1966, 11, 66. (13) Lobe, U. M. M.S. Thesis, University of Rochester, Rochester, NY, 1973. (14) Cao, W.; Fredenslund, A.; Rasmussen, P. Ind. Eng. Chem. Res. 1992, 31, 2603. (15) SelectiVe SolVents; Physical Sciences Data 31; Elsevier: Amsterdam, 1989. (16) Riddick, J. A.; Bunger, W. B.; Sakano, T. K. In Techniques of Chemistry; Wiley: New York, 1986; Vol. II. (17) Boje, L.; Hvidt, A. J. Chem. Thermodyn. 1971, 3, 663. (18) Assarsson, P.; Eirich, F. R. J. Phys. Chem. 1968, 72, 2710. (19) McDonald, D. D.; Dunay, D.; Manlon, G.; Hyne, J. B. Can. J. Chem. Eng. 1971, 49, 420. (20) Kinart, C. M. Phys. Chem. Liq. 1994, 27, 25. (21) Bagha, O. P.; Rathnam, U. K.; Singh, S.; Sethi, B. P. S.; Raju, K. S. N. J. Chem. Eng. Data 1987, 32, 198. (22) Awwad, A. K.; Allos, E. I.; Salman, S. R. J. Chem. Eng. Data 1988, 33, 265. (23) de Visser, C.; Perron, G.; Salman, S. R. J. Chem. Eng. Data 1977, 22, 74. (24) Corradini, F.; Franchini, G. C.; Marchetti, A.; Tagliazucchi, M.; Tassi, L.; Tossi, G. J. Solution Chem. 1994, 23, 777. (25) Davis, M. Thermochim. Acta 1987, 120, 299. Davis, M. I.; Hernandez, M. E. J. Chem. Eng. Data 1995, 40, 674. (26) Al-Azzawi, S. F.; Awwad, A. M.; Al-Dujaili, A. M.; Al-Noori, M. K. J. Chem. Eng. Data 1990, 35, 463. (27) Ambrosone, L.; Sartorio, R.; Vitagliano, V. Fluid Phase Equilibr. 1993, 91, 177. (28) Jorgenson, W. L.; Swenson, C. J. J. Am. Chem. Soc. 1985, 107, 1489. (29) Eblinger, F.; Schneider, H. J. J. Phys. Chem. 1996, 100, 5533. (30) Geddes, J. A. J. Am. Chem. Soc. 1933, 55, 4832. (31) Barfield, W. J. Phys. Chem. 1959, 63, 1783. (32) Kenttamaa, J.; Lindberg, J. J. Suom. Kemistil. 1960, B33, 32. (33) Reed, T. M.; Taylor, T. E. J. Phys. Chem. 1959, 63, 58. (34) Meyer, R.; Meyer, M.; Metzer, J.; Peneloux, A. J. Chem. Phys. 1971, 62, 405. (35) Oswald, S.; Rathnam, M. U. Can. J. Chem. 1984, 62, 2851. (36) Frank, H.; Wen, W. Discuss. Faraday Soc. 1957, 24, 133. (37) Nemethy, G.; Scheraga, H. J. Chem. Phys. 1962, 36, 3382. (38) Symons, M. C. R.; Eaton, G. J. Chem. Soc., Faraday Trans. 1985, 81, 1963; 1988, 84, 3459. (39) Patel, K. B.; Eaton, G.; Symons, M. C. R. J. Chem. Soc., Faraday Trans. 1985, 81, 1775. (40) Eaton, G.; Symons, M. C. R.; Rastogi, P. P. J. Chem. Soc., Faraday Trans. 1989, 85, 3257. (41) Laurence, C.; Berthelot, M.; Helbert, M. Spectrochim. Acta, Part A 1985, 41, 883. (42) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. In The Properties of Gases and Liquids; McGraw-Hill: New York, 1988; pp 12, 14, 317. (43) Hansen, H. K.; Rasmussen, P.; Fredenslund, A. Vapor-Liquid Equilibria by UNIFAC Group Contribution. 5. Revision and extension. Ind. Eng. Chem. Res. 1991, 30, 2352.
