J. CHEM. SOC. FARADAY TRANS., 1994, 90(6). 859-864 2-Methoxyethanol-Water Solvent System :Static Relative Permittivity from -10 to +80 OC Fulvio Corradini, Luigi Marcheselli, Andrea Marchetti, Mara Tagliazucchi, Lorenzo Tassi and Giuseppe Tosi Department of Chemistry, University of Modena, via G. Campi, 183,41100 Modena, Italy A detailed dielectric study of 2-methoxyethanol (ME)-water (W) mixtures has been carried out as a function of temperature in the range -10 to +80"C and over the entire binary composition range (0 dx d 1). The experi- mental data, obtained by the heterodyne beat method at 2 MHz, were used to test some empirical relations of the type E = s(T), E = E(X) and E = E(T,x), in order to assess the empirical performances in dielectric behaviour of these mixtures, including the experimental conditions which are able to modify such patterns.The data reported here for ME-W binary mixtures were useful trying to understand the relative discriminating ability of both com- ponents towards cooperative intermolecular interactions in the liquid state, the quantitative similarities and differences between the chosen pure species, the intermolecular phenomena and interactions influencing the dielectric properties of the mixtures and the usefulness of a qualitative description of the possible formation of solventsosolvent complex species involving hydrogen-bonding, dipole-dipole and other interactions. 2-Methoxyethanol (ME) has been widely investigated as a non-aqueous solvent in the past' and it is an important potentially acidic solvent for analytical and industrial pur-poses. The study of physico-chemical properties of binary mixtures of ME with other solvents helps to clarify its struc- tural arrangements at the molecular level.In order to investi- gate the molecular orientations and interactions occurring between the unlike species of the binary mixtures, static rela- tive permittivities at different mole fractions of ME in water (W) at 19 temperatures ranging from -10 to +80 "C hake been determined. Note that ME differs from W in its steric, hindrance, quad- rupolar charge distributions and number of proton-donating and -accepting sites; furthermore, its hydrogen-bond donat- ing tendency seems to be partially overshadowed by its quasi-aprotic nature (Kautoprot at 20'C),' and by the fact = that ME can exist in two conformations, gauche or anti with respect to the two substituent groups in the alkyl chain, -OH and -OCH,.In the gauche conformation, a strong intramolecular hydrogen bond is formed between the two groups, reducing the possibility of interaction with neigh- bouring molecules ;under these conditions only intermolecu- lar dipolar interactions or hydrogen-bond behaviour can OCCU~.~ Taking into account the bifunctional nature of the ME component, dielectric studies of its binary mixtures with water are of interest in elucidating the structural arrange- ments and molecular interactions between unlike species. Furthermore, it is possible to estimate the magnitude of the deviation of the dielectric behaviour for ideal mixtures bv applying a general relationship between the pure-componen t properties and the binary composition, thus tentatively derik -ing the stoichiometry of solvent-cosolvent complex moieties.Experimental Materials ME (containing <0.05% of water by weight, found by Karl-Fischer titrations) was Carlo Erba (Milan) high-purity grade reagent. The solvent was preserved over 3 %i molecular sieves for several days before use, and the final purity was checked by gas chromatography (99.7%), confirming the absence of other significant organic components. Water. utilized for the preparation of the binary mixtures and as the pure solvent, was doubly distilled over KMnO, in a quartz apparatus and had a specific conductance <55 nS cm-'.Apparatus and Procedure The solvent mixtures were prepared by weight through a Mettler PM 4800 A-range, operating in a dry box to avoid contact with atmospheric moisture. The probable error in the ME mole fraction (xl) is estimated to <1.5 x lo-,. The equipment and the experimental procedures for stan- dardization of cells and relative permittivity measurements have been described elsewhere., The relative permittivities for the standards were taken from ref. 5. The experiments were generally repeated at least 10 times for each composition and at each temperature, with a con- fidence interval of 95%, and the results were averaged. The reproducibility of measurements expressed as the standard deviation a(&)was ca.& 0.2%. The thermostatted measuring cell was encased in a poly- urethane protective jacket, and the temperature control was provided by a Lauda K2R thermostat bath maintained to & 0.02"C.The temperature was measured by a Pt 100 ther-moresistor (Tersid, Milan) immersed in the measuring cell, and resistances were measured with a Wayne Kerr 6425 Pre-cision Component Analyzer. Karl-Fischer titrations were performed with an automatic titration system (Crison model KF 431) equipped with a digital burette (Crison model 738). Results and Discussion The experimental relative permittivities measured for these binary solvent mixtures (A, B, . . . M) are presented in Table 1, where x1 indicates the mole fraction of ME and where some values are absent owing to phase separation.Furthermore, for the two mixtures H (xl = 0.0892) and I (xl = 0.0545) it was impossible to determine the static relative permittivity at temperatures higher than 40 and 30 "C, respectively, even though a high degree of accuracy was achieved for the prep- aration of different sample mixtures and the cells were refilled J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 Experimental relative permittivities (E) for 2-methoxyethanol(l) water (2) binary mixtures at various temperatures t/T 1.oooO 0.6756 0.4792 0.3494 0.2564 A B C D E -10 20.03 30.10 40.14 47.20 55.59 -5 19.55 29.09 39.05 46.08 53.96 0 19.08 28.13 38.03 44.90 52.62 5 18.63 27.28 37.10 43.68 51.32 10 18.19 26.46 36.1 1 42.5 1 49.79 15 17.75 25.7 1 35.01 41.30 48.64 20 17.35 24.97 34.17 40.18 47.40 25 16.94 24.28 33.19 39.12 46.16 30 16.54 23.52 32.18 38.08 44.76 35 16.17 22.89 31.39 37.26 43.69 40 15.76 22.2 1 30.60 36.21 42.42 45 15.38 21.52 29.68 35.16 41.35 50 15.02 20.77 28.81 34.23 40.22 55 14.68 20.18 28.12 33.49 39.34 60 14.32 19.56 27.40 32.43 38.19 65 14.04 19.02 26.58 31.59 37.13 70 13.71 18.52 25.76 30.92 36.12 75 13.34 17.80 25.14 30.10 35.34 80 13.01 17.24 24.43 29.15 34.45 many times.This probably arises from the high specific con- ductance of these solutions which is dependent on the tem- perature and the composition of the mixture.The relative permittivity in its expanded form e =E' -id' contains a real (E') and an imaginary (d') contribution; probably for the two abovementioned mixtures E" is always greater than E', making it impossible to determine the relative permittivity by the het- erodyne beat method.6 A comparison between the data of the present work and those of literature for pure ME at various temperatures and for its binary mixtures with water at 25"C, has been made. Our values agree very well with those of ref. 7 for binary mixtures, while the contrary is true for pure ME as reported in ref. 8, although the difference is small in the range 30- 40 "C. The dependence of our relative permittivities on the tem- perature has been checked by using the equation' In E = a.+alT where T is in K and the ai coefficients are empirical fitting parameters, listed in Table 2 along with the standard devi- ation a(ln E) for each mixture. Eqn. (1) appears to be ade- quate to represent the experimental measurements as the average difference dE is evaluated as follows : CNI%,lc -Eexp IA&= N where Nis the number of experimental points (186) of Table 1. Using this equation dE = k0.06. Table 2 Coefficients aiand standard deviations a(ln E) of eqn. (1) for the 2-methoxyethanol(l)-water(2) solvent system 1.m 4.250 92 -4.766 90 1.3 0.6756 5.004 89 -6.094 83 3.2 0.4792 5.149 77 -5.529 44 2.0 0.3494 5.262 50 -5.345 76 2.3 0.2564 5.421 31 -5.337 77 2.0 0.1865 5.592 14 -5.494 30 1.6 0.1327 5.548 44 -4.974 87 1.3 0.0892 5.978 32 -6.242 82 1.2 0.0545 5.857 88 -5.564 04 1.4 0.0249 5.896 23 -5.403 30 1.3 O.oo00 5.697 8 1 -4.487 67 0.8 0.1865 0.1327 0.0892 0.0545 0.0249 O.oo00 F G H I L M 63.09 69.28 76.28 61.40 67.55 73.95 78.67 59.74 65.9 1 71.67 76.5 1 83.00 87.45 58.20 64.34 69.63 74.39 80.80 85.48 56.72 62.80 67.5 1 72.54 78.64 83.67 55.11 6 1.28 65.41 70.52 76.7 1 81.82 53.67 59.82 63.43 68.58 74.63 80.1 1 52.19 58.3 1 61.36 66.62 72.64 78.3 1 50.81 56.96 59.42 64.66 70.76 76.56 49.40 55.42 57.65 -68.86 74.80 48.12 54.20 55.84 -67.01 73.23 -46.68 52.77 -65.26 7 1.46 -45.36 51.56 -63.55 70.00 -44.30 50.20 -61.82 68.45 42.96 49.00 --60.16 66.85 41.79 47.75 --58.55 65.42 40.83 46.50 --56.87 63.87 39.56 45.34 --55.33 62.47 38.49 44.30 --53.84 61.10 In order to investigate the E =E(xl) correlation, we plotted in Fig.1 the trend of E us. water mole fraction (xJ. The trend is non-linear and a polynomial expansion of the typeg (3) has been employed to fit the isothermal experimental relative permittivity data. The flj coefficients (for j =4) are sum-marized in Table 3, along with the standard deviations at each temperature. The usefulness of this equation is shown by the average uncertainty = f0.46 over all the experimental data. Obviously, it should not be employed when reliable experimental data are not available, i.e. in the range 0.0249 <x1 <0.1327 at temperatures 240"C,in order to avoid obtaining extrapolated values with no physical signifi- cance.In order to investigate the possibility of representing the dielectric properties of this solvent system through a single function of the type E =E(T,xl), the experimental values were fitted by the equation ij In E = yij ~'x', (4)00 obtained by combining the eqn. (1) and (3). This three- dimensional correlation model appears to be very useful in 80i -10°C A 60 E 40 20 1 I I I I 0.0 0.2 0.4 0.6 0.8 1.o x2 Fig. 1 Experimental trend E us. x2 for the 2-methoxyethanol (1)-water (2) solvent system from -10to +80 "C J. CHEM.SOC. FARADAY TRANS., 1994, VOL. 90 861 Table 3 Coefficients Bj of eqn. (3)for the 2-methoxyethanol(l)-water(2)solvent system at different temperatures tl”c Bo B1 82 83 84 -10 4.561 45 -2.829 12 3.66403 -4.153 14 1.75400 -5 4.496 58 -2.420 23 2.33255 -2.525 88 1.089 67 0 4.473 52 -2.495 37 2.753 10 -3.322 77 1.54015 5 4.448 7 1 -2.537 03 3.005 58 -3.810 81 1.81811 10 4.425 35 -2.601 02 3.297 10 -4.304 99 2.084 09 15 4.400 8 1 -2.637 52 3.441 86 -4.547 52 2.218 48 20 4.37691 -2.706 04 3.816 34 -5.214 74 2.581 14 25 4.35155 -2.758 48 4.075 78 -5.650 25 2.81 1 08 30 4.326 56 -2.80464 4.282 97 -6.022 85 3.023 61 35 4.306 02 -2.872 23 4.598 47 -6.553 01 3.303 69 40 4.282 41 -2.931 76 4.870 18 -7.006 45 3.543 16 45 4.260 85 -2.775 88 3.841 80 -5.250 77 2.656 99 50 4.238 52 -2.834 03 4.109 78 -5.768 14 2.962 66 55 4.213 96 -2.869 78 4.401 70 -6.377 20 3.317 25 60 4.189 80 -2.921 87 4.593 82 -6.669 14 3.468 60 65 4.16611 -2.95300 4.68355 -6.80521 3.55049 70 4.13945 -2.933 07 4.601 97 -6.71465 3.523 98 75 4.11 6 21 -3.038 54 5.265 30 -8.02030 4.267 99 80 4.09205 -3.041 89 5.21049 -7.938 73 4.24344 ofIn E) x lo2 1.2 1.1 0.9 1.1 1.2 1.2 1.5 1.6 1.8 1.9 2.2 1.7 1.8 1.9 2.2 2.2 2.2 2.4 2.7 interpolating the static relative permittivity for any pair of independent variable quantities T and xl.The use of this model equation must be avoided in the abovementioned con- ditions because the limitations of eqn. (3) are reflected in eqn. (4). This fitting equation, whose coefficients yii, as evaluated by the TSP” statistical package, are reported in Table 4, provides a set of calculated values that are in very good agreement with the experimental values with an average uncertainty L\E = kO.47.Excess Functions When dealing with completely miscible binary liquids, it seems very useful to examine how their excess properties depend on the composition of the mixture. This fact requires the choice of a suitable criterion to establish the significance of ideal mixing behaviour and the ideal composition depen- dence. For thermodynamic properties, the ideal composition dependence may be defined within the widely accepted gener- alization of Raoult’s law.ll Since ideal behaviour has not been theoretically established for non-thermodynamic proper- ties such as E, many models and theories have been sug- gested.I2-l6 Even if the various definitions of ideality appear to be sufficiently consistent, many ambiguities regarding the detailed interpretations of the different excess relative permit- Table 4 Coefficients yij of eqn.(4)for the 2-methoxyethanol-water solvent system and standard deviation ofln E) variable ij ~~~ quantity Yij 00 5.76600 01 -0.527 57 02 -6.008 31 03 12.937 36 04 -7.91675 10 -4.73687 x lo-’ 11 -7.26200 x lo-’ 12 3.24082 x 13 -5.99401 x 14 3.47638 x 1.3 x tivity curves are present. As a consequence, in order to avoid the misleading use of insuficiently tested and proved theories, it is more prudent to apply an intuitive, but reliable, approach that translates non-thermodynamic quantities into quasi-thermodynamic quantities.Therefore, following sugges- tions in the literature,” the deviation of the dielectric behav- iour of the real systems from ideality can be evaluated by the equation : & = EE + EIXl + E2X2 (5) where cE is the excess function, and and c2 are the values for the two pure species at each temperature. Note (Fig. 2) that cE appears always to be very large and negative at each temperature investigated. In order to consider also the variation of cE with composi- tion, the excess data were isothermally fitted by a smoothing equation of the type’* 5 EE = x1x2 1 U&l -(6)k=O whose uk coefficients are listed in Table 5, along with the standard deviations g(cE).Note that the curves of Fig. 2 exhibit a pronounced, broad, minimum centred around x2 x 0.65, i.e. ME :W = 1 :2; the cE value corresponding to this 0 EE -1 0 -20 0.0 0.2 0.4 0.6 0.8 1 .o x2 Fig. 2 Isothermal excess relative permittivity curves for the 2-methoxyethanol (1)-water (2)solvent system calculate by eqn. (6) J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 5 Coefficientsakof eqn. (6) for the 2-methoxyethanol-water solvent system at various temperatures tpC 00 a1 a2 0 -63.04 -89.69 21.89 5 -62.56 -82.23 3.95 10 -62.07 -75.00 -13.32 15 -61.56 -68.04 -0.39 20 -61.04 -61.41 -45.53 25 -60.52 -54.87 -60.78 30 -59.98 -48.70 -74.99 35 -59.43 -42.77 -88.75 40 -58.93 -35.73 -105.84 45 -60.06 11.44 -202.58 50 -59.63 20.34 -222.92 55 -59.19 28.90 -242.36 60 -58.73 36.80 -260.25 65 -58.26 44.47 -277.43 70 -57.78 51.62 -293.35 75 -57.28 58.43 -308.47 80 -56.78 64.87 -322.53 minimum becomes more negative as the temperature is decreased, so that it is -18.8 at 0“C.In many theories explaining the behaviour of non-electrolyte solutions, the major contribution to the deviation from ideal mixtures is attributed to the hydrogen-bonding tendency between components, the dipole-dipole interactions and specific interactions such as dispersion forces.lg In general, when negative deviations from ideal behaviour of thermomechanical properties (p, q, E ...) occur in mixtures of components whose molecules are very different in shape and size, these deviations can be accounted for by geometric effects.” In this light, note that both components of these mixtures show considerable proton-donating and proton- accepting ability, although the number of active sites is differ- ent for the two pure species.Furthermore, the W molecules are smaller than those of ME, the molar volumes being Vl = 79.237 cm3 mol-’ and V2 = 18.068 cm3 mol-’ at 25°C.21 Hence, the large difference in the shape and molecular size of these two components can reasonably be invoked as an important factor in arranging unlike species in the final liquid structure of the mixtures. Taking into account all these con- siderations, the negative deviations from ideality for the system under study can therefore be related to intermolecular hydrogen bonding and other interactions” between the com- ponents of the mixture.According to suggestions in the literat~re,~~ the formation of a complex species could be supposed, having an approx- imating composition corresponding to the minima of Fig. 2. Therefore, the minimum in the excess relative permittivity could indicate a maximum in the structuredness between dif- ferent components in mixtures. After the above considerations, note that the trend of E~ us. temperature (Fig. 3) suggests that the mixtures studied may be separated into three distinct composition groups. In the absence of substantiated explanations in the literature we expect that phenomena that depend on the molecular and supramolecular composition could occur to induce this dis- tinction. By studying the thermodynamic properties of binary mix- tures with water, other authorsz4 have argued that the addi- tion of a cosolvent progressively inhibits cooperative fluctuations in the hydrogen-bonding connectivity of the water molecules, these network interactions being progres- sively replaced by a water-cosolvent mixed connectivity.In a3 a4 a5 o@E) x 10 387.18 -782.17 383.27 4.0 349.25 -623.93 254.34 3.8 312.33 -471.03 130.27 4.0 276.78 -324.35 11.58 4.4 243.02 -185.31 -100.90 4.9 209.45 -49.03 -210.31 5.5 177.74 78.76 -3 12.77 6.2 147.44 201.97 -41 1.67 7.7 110.68 355.14 -534.40 8.4 -205.38 1254.22 -1048.94 4.5 -256.06 1438.72 -1183.69 5.0 -304.99 16 16.01 -1312.90 5.4 -349.76 1779.15 -1432.22 5.8 -393.37 1936.29 -1546.49 6.2 -433.93 2082.78 -1653.29 6.5 -472.35 2221.59 -1754.43 6.8 -508.79 2351.86 -1849.04 7.1 pentamers (as the minimal units) and more complex cluster units which fluctuate rapidly between low-density-low-entropy forms and high-density-high-entropyforrn~.~~*’~Fur-thermore, it was hypothesized that the average size of the fluctuating units should increase with decreasing tem-perature, or upon hydration of partially hydrophobic species.This is the case, for example, of water-hydrazine mixtures, whose excess thermodynamic properties could be separated into three regions. A brief examination of the excess relative permittivities of the ME-W mixtures could lead to similar observations.Obviously, the pattern that will be described requires that the dielectric properties are very sensitive both to hydrogen- bonding interactions and to cooperative fluctuations. (i) Region MI, 0 < x1 z0.1 (Mixtures H, I and L) In this composition range, cE exhibits a clear dependence on composition, reflecting a breaking off of the cooperative fluc- tuation units. Furthermore, as deE/dT < 0, the trend of the curves is influenced strongly by the hydrophobic character of ME. An explanation for this is that in dilute aqueous solution ME may exist in the predominant gauche cyclic conformationz7 and in this arrangement strong intramolecu- lar hydrogen bonding would reduce the ME-W hydrogen-bonding tendency and increase the hydrophobicity of ME.Note that an increase in temperature should favour ME anti conformers (without the intramolecular hydrogen bond) rather than the gauche conformers. As a consequence, in this I -20 t particular, an explanation of the magnitude and the trends of 0 20 40 60 the thermodynamic properties in the aqueous mixtures con- t/”csidered, could lie in cooperative fluctuation phenomena Fig. 3 Excess relative permittivity 11s. temperature for the 2-which are characteristic of water, involving tetramers and methoxyethanol (1)-water (2) solvent system J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 configuration the ME molecules may interact better with water, providing a more reliable and ordered mixing struc- ture of the medium, whose constituent units could be hetero- aggregated entities of the type ME 2W and fluctuating water units; the large deviation from ideality for these mixtures with increasing the temperature is indicative of molecular aggregation of the cosolvent.28 A further description in terms of structural models could be made taking into account the fact that the upper limit for MI corresponds to the cosolvent concentration beyond which the solvated heterocluster structures cannot exist, as dcE/dT is negative in this region and positive for greater ME con- tents.On this basis, we could suggest that the binary mixture having dcE/dT = 0 could be taken as the limiting composi- tion of the existence of solvated heteroaggregated clusters.On the other hand, the solvent properties of these mixtures could also be described in terms of fluctuating behaviour, since the MI composition range seems to suggest fluctuations in the homocooperative water units. (ii) Region MI,,0.1 < x1 x 0.3 (Mixtures E, F and G) The increasing trend of cE with temperature (Fig. 3) reflects the progressive loss of W-W hydrogen bonding, clearly showing a tendency to quasi-ideal behaviour in the mixture sequence E -= F < G. At the molecular level and on the basis of the preceding remarks, we can describe the curves of this region as follows. Starting from the MI limit region, the mixing properties are characterized by the W-W inter- and intra-connectivities ; with increasing the organic cosolvent ratio the homecoopera- tive interactions decrease, and are progressively replaced by hetero ME-W connectivities. Therefore, the upper composi- tion limit of the M, region may be considered as that com- position where the solvent-cosolvent hydrogen-bonding interactions become predominant.This limit could corre-spond to the formation of the complex solventxosolvent moieties of stoichiometric ratio ME : W = 1 :2, x1 2 0.33. Furthermore, at this composition limit all the ME and W molecules should be involved in the heteroaggregated ME 2W clusters, which corresponds to the maximum devi- ation from ideality and the maximum structuredness of the pure species, as shown in Fig.2 by the relatively smooth variation of cE within a broad minimum. From Fig. 2 it is possible to see the strong dependence of cE on the composi- tion of the ME-W mixture both in the upper MII limit region and over the entire MIregion. (iii) Region MIII,0.3 x x1 < 1 (Mixtures B, C and D) In this region, the variation of the excess property reflects a molecular situation in which mixed hydrogen-bonding con- nectivities replace those of the pure organic solvent. Increas- ing temperature causes little deviations from ideality, while the contrary is true for increasing water content, in the sequence B c C c D. Since at the molecular level the hydrogen-bonding interactions in pure ME display no signifi- cant cooperativity compared with W, starting from the upper limit of the MII region (xl x 0.3), the increasing ME-ME homoconnectivity should lead to the disappearance of het- eroclusters; consequently, one-dimensional and successively two- and three-dimensionally ordered structures due to the ME-ME interactions should take place up to the pure ME species.Conclusions The theories and empirical treatments used here to analyse the experimental relative permittivity data of ME-W mix-tures appear to be the most simple and are adequate for the present system, even if for a few mixtures it was impossible to obtain the experimental E values and, as a consequence, the calculating procedures must be used ‘with a grain of salt’. However, in connection with our previous work, we have tried to justify some experimental evidence through conjec- tures regarding the formation of adduct species whose pres- ence, however, may be revealed only by indirectly measurable properties. It seems very likely that by mixing the two components, ME acts as a structure breaker with respect to pure water.Furthermore, such a breaking off and the large change in intermolecular forces on passing from pure to mixed species, would have an appreciable effect on the properties of the molecules and, as a consequence, on the macroscopic experi- mental behaviour of the systems. Following the approach of Payne and Theodorou,’ attempts have been made to explain the behaviour of these liquid mixtures on the basis of the sign and the magnitude of excess quantity cEthat, as it is always negative and very large, could be mainly associated with the formation of solvent- cosolvent complex moieties with a lower dipole moment.The stoichiometric ratio of these complex species corresponds to the maximum deviation of the excess quantity cE from ideali- ty, i.e. ME : W x 1 : 2 mole ratio at all the temperatures investigated. The excess relative permittivity investigated here, cE, and the excess molar volumes VE studied previously2’ provide similar evidence : both functions are negative, and the magni- tude of the deviation increases with the temperature. The authors are thankful to Prof. C. Preti for providing helpful suggestions and encouragement to carry out this work.L. M. is grateful to Hospal-Dasco s.p.a. (Modena, Italy) for the award of a Junior Research Fellowship. 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