Solvation in Binary Mixtures of Water and Polar Aprotic Solvents

Thermo-solvatochromism of two polarity probes, 2,6-diphenyl-4-(2,4,6-triphenyl- ... roacetone,2 the spontaneous decarboxylation of benzisoxazole-...
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J. Phys. Chem. B 2007, 111, 6173-6180

6173

Solvation in Binary Mixtures of Water and Polar Aprotic Solvents: Theoretical Calculations of the Concentrations of Solvent-Water Hydrogen-Bonded Species and Application to Thermosolvatochromism of Polarity Probes Priscilla L. Silva,† Erick L. Bastos,‡ and Omar A. El Seoud*,† Instituto de Quı´mica, UniVersidade de Sa˜ o Paulo, C.P. 26077, 05513-970 Sa˜ o Paulo, S.P., Brazil, and Centro de Cieˆ ncias Naturais e Humanas, Fundac¸ a˜ o UniVersidade Federal do ABC, Santo Andre´ , SP, Brazil ReceiVed: December 14, 2006; In Final Form: March 5, 2007

Thermo-solvatochromism of two polarity probes, 2,6-diphenyl-4-(2,4,6-triphenyl- pyridinium-1-yl)phenolate, RB, and 2,6-dichloro-4-(2,4,6-triphenylpyridinium-1-yl) phenolate, WB, in aqueous acetone, Me2CO, and aqueous dimethylsulfoxide, DMSO, has been studied. The data obtained have been analyzed according to a recently introduced solvation model that explicitly considers the presence of 1:1 organic solvent-water hydrogen-bonded species, S-W, in the bulk binary mixture and its exchange equilibria with (S) and (W) in the solvation shell of the probe. Calculations require reliable values of Kdissoc, the dissociation constant of S-W. Previously, this has been calculated from the dependence of the densities of binary solvent mixtures on their composition. Using iteration, the volume of the hydrogen-bonded species, VS-W, and Kdissoc were obtained simultaneously from the same set of experimental data. This approach may be potentially suspect because Kdissoc, and VS-W are highly correlated. Therefore, we extended a recently introduced approach for the calculation of Valcohol-W to binary mixtures of water with acetone, acetonitrile, N,N-dimethylformamide, DMSO, and pyridine. This approach includes: Determination of VS-W from ab initio calculations by the COSMO solvation model; correction of these volumes for the nonideal behavior of the binary solvent mixtures at different temperatures; use of corrected VS-W as a constant (not an adjustable parameter) in the equation that is employed to calculate Kdissoc (from density versus binary solvent composition). Solvation of RB and WB by Me2CO-W showed different behavior from that of aqueous DMSO. Thus, water is able to displace Me2CO more efficiently than DMSO from the probe solvation shell. Me2CO-W and DMSO-W displace their corresponding precursor solvents; this is more efficient for the former case because the strong DMSO-W interactions attenuate the solvation capacity of this species. Temperature increase resulted in desolvation of both probes, due to concomitant decrease of the structures of the component solvents.

Introduction Interest in studying the properties of binary mixtures of organic solvents and water stems from their high solubilization and ionizations powers, and because their properties can be continuously varied by simply changing the ratio between the two components.1 Additionally, rates and equilibrium constants and activation parameters of many simple reactions depend in a complex, nonlinear way on the composition of these mixed solvents. Examples are the reversible hydration of 1,3-dichloroacetone,2 the spontaneous decarboxylation of benzisoxazole3-carboxylate,3 and the pH-independent hydrolysis of activated esters.4 The binary mixtures addressed in the present work are those of water, W, with acetone, Me2CO; acetonitrile, MeCN; N,N-dimethylformamide, DMF; dimethylsulfoxide, DMSO, and pyridine, Py. These are employed in organic synthesis;5 acetone has been studied as a model system for hydration of the carbonyl group;6 DMF and DMSO are extensively employed in electrochemistry;7 the relatively high nucleophilicity of Py has been exploited, e.g., in catalyzing acyl-transfer reactions.8 The above-mentioned applications underline the need to understand the mechanism of solvation in binary solvent * Corresponding author fax: 55-11-3091-3874; e-mail: 〈elseoud@ iq.usp.br〉 † Universidade de Sa ˜ o Paulo. ‡ Fundac ¸ a˜o Universidade Federal do ABC.

systems; this can be readily achieved by studying solvatochromic indicators. These are substances (hereafter designated as “probes”) whose UV-vis spectra, absorption or emission are highly sensitive to the properties of the medium; the data thus obtained have been employed to analyze both solvent-probe and solvent-solvent interactions. Extensive use has been made of an empirical solvent polarity scale, ET(probe) calculated from ET(probe) ) 28591.5/λmax (nm). This scale converts the electronic transition within the probe into the corresponding intramolecular charge-transfer energy in kcal/mol. Thermosolvatochromism refers to the study of the effects of temperature on solvatochromism, hence on solvation.9,10 We have shown that thermosolvatochromic data of zwitterionic probes in aqueous alcohols and aqueous 2-alkoxyethanols are best analyzed by considering that the medium is composed of three species: the organic solvent, S; water, W; and a 1:1 hydrogen-bonded “complex” solvent, S-W. Dependence of density of the binary mixture on its composition has been employed to calculate the equilibrium constant of dissociation of the S-W complex, Kdissoc, from which the “effective” concentrations of the (three) solvent species in “bulk” mixture were obtained. The input data to calculate Kdissoc include MS, MW, MS-W, VS, and VW, along with initial estimates of Kdissoc and VS-W. Here, M and V refer to the molar mass and molar volume of the appropriate solvent species, respectively. Kdissoc

10.1021/jp068596l CCC: $37.00 © 2007 American Chemical Society Published on Web 05/16/2007

6174 J. Phys. Chem. B, Vol. 111, No. 22, 2007

Figure 1. Molecular structures, pKa of the conjugate acids in water, and log P of RB and WB, respectively.

and VS-W are obtained, simultaneously, by regression analysis.11,12 Recently, we have shown that this approach to calculate Kdissoc may be subjected to uncertainty because the latter constant and VS-W are highly correlated; this is a typical example of multicollinearity; discussed in detail elsewhere.13 The consequences of multicollinearity include larger standard errors in the quantities calculated and lower statistical significance of the results independent of the value of the regression coefficient. In limiting cases, more than one result may be obtained by iteration; these correspond to noticeably different combinations of the quantities calculated.14 The above-mentioned problem has prompted us to reexamine this very important aspect of binary solvent mixtures, namely the formation and some properties of the S-W complexes formed. Using ab initio calculations, we have calculated the volumes of several alcohol-water complexes and then corrected their values for the nonideality of these binary mixtures, at different temperatures. The volumes thus obtained were employed as constants, not as adjustable parameters, in the equation employed to calculate Kdissoc. The equilibrium constants obtained furnished the effective concentrations of the solvent species present; these were used to treat the thermosolvatochromic data of RB in aqueous ethanol.15 In the present work, we have extended this approach to mixtures of water with five polar aprotic solvents: Me2CO, MeCN, DMF, DMSO, and Py, respectively. The consistency of the present approach is shown by the fact that the molar volumes calculated for eleven solvents (W, five alcohols, and five dipolar aprotic solvents) correlate linearly with their experimentally determined counterparts. Calculated values of Kdissoc were employed to obtain the effective concentrations of all solvent species present. These were employed in the treatment of the thermosolvatochromic data in Me2CO-W and DMSO-W of two probes, namely, 2,6-diphenyl-4-(2,4,6triphenylpyridinium-1-yl) phenolate (RB) and 2,6-dichloro-4(2,4,6-triphenylpyridinium-1-yl) phenolate (WB); the corresponding solvent polarity scales are termed ET(30) and ET(33), respectively. Their molecular structures, pKa of the conjugate acids in water, and log P, a measure of probe lipophilicity, vide infra, are shown in Figure 1. Binary mixtures of the two solvents showed distinct behaviors: W displaces Me2CO but not DMSO efficiently from the probe solvation shell; the mixed solvent is more efficient in displacing the precursor solvents in case of Me2CO than in the case of DMSO due to the strong interactions of the latter solvent with W. Finally, temperature increase resulted in a gradual desolvation of the probes due to temperature-induced solvent structure perturbation. Experimental Section Materials. RB and WB were available from a previous study.16 Acetone and DMSO (emPACada Quı´mica, DF) were

Silva et al. purified by standard procedures;17 their densities (DMA-40 resonating tube digital densimeter, Anton Paar, Graz) and ET(30) values were in excellent agreement with their literature values.9 Thermo-Solvatochromic Studies. Glass-distilled, deionized water was used throughout. All binary mixtures were prepared by weight at 25 °C. Aliquots of the probe solution in acetone were pipetted into 1 mL volumetric tubes, followed by evaporation of acetone at room temperature, under reduced pressure, in the presence of P4O10. The solvent (or binary mixtures, 16 per set) whose polarity is to be determined was added, the probe dissolved and the UV-vis spectrum of its solution recorded (Shimadzu UV-2550, UV-vis spectometer) The following are relevant experimental data: Temperature control inside the thermostatted cell-holder ( 0.05 °C; final probe concentrations 2 × 10-4 mol/L; number of spectra recorder, 2 at a rate of 120 nm/min; λmax calculated from the first derivative of the absorption spectrum; uncertainties in ET(probe), 0.20 and 0.15 kcal/mol for RB and WB, respectively. Because of the low bp of acetone (56.2 °C)18 and high mp of DMSO (18.4 °C),18 thermosolvatochromism was studied at 10, 25, and 40 οC and at 25, 40, and 60 °C, in Me2CO and DMSO, respectively. Quantum Chemical Calculations. The structures of solvents, water, and S-W complexes were optimized without constraints by using the density functional theory (DFT) at Becke’s three parameter hybrid functional, using the correlation functional of Lee, Yang, and Parr (B3LYP) level with the 6-31+G(3d,p) basis set.19 Stationary points were confirmed as minima via vibrational frequency calculations. Optimized geometries were used to calculate the solvent-accessible volumes using the conductorlike screening model for real solvents (COSMO or C-PCM) with the 6-31+G(3d,p) basis set.20,21 All calculations were performed by using the Gaussian 03 program package.22 Threedimensional structures and surfaces were calculated by using ArgusLab 4.0.1 software.23 All calculations were performed at the advanced computing facilities (LCCA) of the University of Sa˜o Paulo. Results and Discussion The ensuing discussion is organized as follows: A comment on the indicators employed is made; the solvent-exchange model is presented; steps for treating the thermosolvatochromic data are listed; the strategy for the theoretical calculation of VS-W and calculation of Kdissoc from density data is presented; the thermosolvatochromic data obtained are discussed. The equations essential to follow the discussion are given below; additional details of the calculations are found in Supporting Information.11,12,15 The Probes Studied. RB has been employed because there are extensive data on its solvatochromism, both in pure solvents and in binary mixtures.9,24 Although WB is structurally related to RB, it has a much lower pKa, due to the presence of the two chlorine atoms ortho to its phenolate oxygen, see Figure 1. Interestingly, however, both indicators have similar sensitivities to solvent “acidity” or hydrogen-bond donation capacity, as calculated from the Taft-Kamlet-Abboud equation.25 Briefly, this similar response results from the following structural features: Steric: The two ortho-chlorine atoms of WB lie in the plane of the phenolate ring, whereas the two ortho-phenyl rings of RB are twisted in opposite directions with respect to the plane of the phenolate ring. This attenuates hydrogenbonding of the solvent to RB; Electronic: The C-Cl bonds are appreciably polarized; the chlorine atom may form (additional) hydrogen-bonds with suitable donors, e.g., the solvent.16

Solvation in Binary Mixtures of Water and Polar Aprotic Solvents The two indicators also differ in their hydropobicity; this property may be quantified by log P ) log([probe]n-octanol/ [probe]water), where both solvents are mutually saturated.26 There is no reliable value of log P for RB, due to its negligible solubility in water, ca. 2 × 10-6 mol/L,9 the corresponding value for WB is 1.79.16 In summary, although the indicators employed are structurally related, they are expected to show some difference in their response toward solute-solvent interactions. The Solvent Exchange Model. The model that we have recently introduced explicitly considers the exchange equilibria (in the probe solvation shell) of all solvent species present, namely, S, W, and S-W, as shown by the following equations: 11

S + W h S-W

(1)

probe(S)m + mW h probe(W)m + mS

(2)

probe(W)m + m(S-W) h probe(S-W)m + mW

(3)

probe(S)m + m(S-W) h probe(S-W)m + mS

(4)

where (m) represents the number of solvent molecules whose exchange, in the probe solvation shell, affects ET; value of (m) should not be confused with the total number of molecules that solVate the probe. An important consequence of eqs 1-4 is that the observed ET (Εobs T ) is given as the sum of the polarities of S S-W , multiplied by the solvent species present, EW T , ET, and ΕT the corresponding mole fraction in the probe solvation shell, probe probe χprobe , and χS-W , respectively. The latter are based on W , χS effectiVe, not analytical concentrations of (S) and (W) in the bulk mixture: probe W probe SET + χprobe EST + χS-W ET Eobs T ) χW S

W

(5)

The relationship between bulk solvent composition and that of the probe solvation shell is given by the equilibrium constants of eqs 2-4. These have been termed solvent “fractionation factors”; their values (after algebraic manipulation) are given by

φW/S )

probe χprobe W /χS effective Bk; effective m (χBk; /χS ) W

φS-W/S )

φS-W/W )

probe probe χS-W /χS ffective Bk; e effective m (χS-W /χBk; ) S probe probe χS-W /χW

Bk; effective Bk; effective m (χS-W /χW )

)

φS-W/S φW/S

(6)

J. Phys. Chem. B, Vol. 111, No. 22, 2007 6175 and bulk binary mixture have the same composition, then all φ values should be unity. At this point, it is convenient to address two working assumptions in the solvation model employed, namely, a single value is attributed to (m); the stoichiometry of S-W is taken as 1:1. Success of the first may be attributed to the fact that values of (m) are close to unity for a large number of mixtures of water with organic solvents.11,12,15 There is ample experimental and theoretical evidence for the formation of hydrogenbonded species in binary solvent mixtures, as shown for Me2CO,27 MeCN,28 DMF,29 DMSO,30-32 and Py.33 These studies suggest 1:1 as well as other stoichiometries for the complex solvents. The use of 1:1 stoichiometry for S-W is a practical and convenient assumption because it renders subsequent calculations tractable; it has been previously employed to describe solvatochromism.34 Mixed solvent species with stoichiometry other than 1:1 may be treated, to a good approximation, as mixtures of the 1:1 structure plus excess of a pure solvent. Additionally, the 1:1 model has been successfully employed to fit the data obtained by employing spectroscopic techniques that are particularly suitable to determine the stoichiometry of S-W aggregates, including the dependence on [W] of 1H NMR chemical shifts, peak area, and wavenumber of ν˜ ΟΗ (IR).35,36 Using 1H NMR spectroscopy, the stoichiometry of mixtures of dipolar aprotic solvents and water has been calculated; both 1:1 and 2:1 S-W complexes were considered. The ratios K1-1/K2-1 were found to be 10, 26, and 132 for Me2CO, MeCN, and DMSO, respectively.36,37 In summary, our data can be conveniently analyzed by considering 1:1 S-W complexes only. Treatment of Solvatochromic Data. This treatment involves the following steps:11,12,15 (1) Calculation of VS-W and Kdissoc simultaneously from the dependence of densities of the binary solvent mixtures on their composition; (2) Calculation (based on Kdissoc) of effective χS, χW, and χS-W for the different solvent mixtures employed; (3) Calculation of the corresponding φW/S, φS-W/S, and φ S-W/W from the dependence of ETobs on solvent composition, by employing en (9):11,12

Eobs T ) effective m S effective m W ) ET + φW/S (χBk; ) ET + (χBk; S W Bk; effective m S-W ) ET φS-W/S (χS-W ffective m

effective m effective m Bk; e (χBk; ) + φW/S(χBk; ) + φS-W/S (χS-W S W

(7)

(8)

where Bk refers to bulk mixture and χ is already defined. Probe solvation can be readily understood from the value of φ. Equation 6, W substituting for S, describes the composition, in terms of pure solvents, of the probe solvation shell, relative to that of bulk mixture. For φW/S >1, the solvation shell is richer in (W) than the bulk mixture; the converse holds for φW/S < 1, i.e., the probe is preferentially solvated by (S). The same line of reasoning applies to the values of φS-W/S (complex solvent substituting S) and φS-W/W, (complex solvent substituting W), eqs 7 and 8, respectively. In other words, the significance of larger than unity values of φS-W/S and φS-W/W is that the complex solvent displaces efficiently its precursor solvents. Finally, if solvation were ideal, i.e., the probe solvation shell

) (9)

The input data to solve en 9 include experimentally deterBk;effective mined Eobs , T , ET(probe)S, ET(probe)W, and calculated χW Bk;effective Bk;effective , and χS-W . Values of φW/S, φS-W/S, and ES-W χS T are then calculated from en 9 by iteration. Finally, φS-W/W is calculated by dividing φS-W/S by φW/S. The preceding discussion underlines the importance of calculation of Kdissoc, based on a reliable value of VS-W. Theoretical Calculations of Vs-, and Calculations of Kdissoc from Density Data. As discussed above,15 values of Kdissoc and VS-W calculated, simultaneously, from density data,38 are highly dependent. Thus we have introduced a novel approach for calculating VS-W for alcohol-water complexes, which eliminates the potential multicollinearity problem and provides reliable dissociation constants.15 Theoretical calculation of the molar volumes of 1:1 S-W complexes is based on geometry optimization of the precursor components (S and W) and of the 1:1 S-W complex, followed by correction for the nonideality of the binary mixtures, at different temperatures. Value of

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TABLE 1: Selected Geometric Parameters and Dipole Moments of the Solvent-Water Hydrogen-Bonded Complexes, Calculated by the B3LYP/6-31+G(3d,p) Basis Seta d(HO..Hw..X(S)), (Å) ∠(O..Hw..X(S)), °

complex MeCN-W Me2CO-W DMF-W DMSO-W Py-W

2.07 1.91 1.89 1.84 1.94

µvacuum (D)

177.85 165.84 167.26 159.19 176.30

6.06 4.10 4.26 2.72 4.70

a d(HO..Hw..X(S)) refers to the equilibrium distance between proton (Hw) (transferred from the water molecule) and the heteroatom (X) of solvent (N or O); the corresponding angle is given by ∠(O..Hw..X(S)). For all complexes examined, the point group is C1.

TABLE 2: Molar Volumes (VMSC, in Cm3 Mol-1) of W, S, and S-W, Obtained with COSMO/B3LYP/6-31+G(3d,p) solvent/ROH-W water Me2CO MeCN DMF DMSO Py Me2CO-W MeCN-W DMF-W DMSO-W Py-W

VMSC, COSMO 15.30 50.46 38.36 52.39 50.00 55.95 64.00 52.26 74.28 69.48 78.44

VS-W (employed as a fixed parameter), along with molar volumes of the precursor solvents and densities of the binary mixtures are then employed to calculate Kdissoc. The procedure employed in the present work was as follows: (i) The level of theory chosen to optimize the geometry of S-W complexes was based on obtaining satisfactory data for W, including its dipole moment (µ) and energy of dimerization (∆EW), both quantities have been measured experimentally. Use of DFT with B3LYP functional and 6-31+G(3d,p) basis set resulted in a µ(W) ) 1.885 D and ∆EW ) -4.81 kcal/mol; which are in good agreement with experimental values, µ(W) ) 1.854 D and ∆EW ) -4.9 to -5.2 kcal/mol.39 The same basis set also gave satisfactory µ for the solvents studied, as shown in Table SI-1 (Table 1 of the Supporting Information); (ii) In the binary mixtures studied, water is the hydrogenbond donor. The distances, angles, and µ that characterize the S-W complexes are listed in Table 1. Full three-dimensional representations of these complexes are depicted in Figure SI-1 (Figure 1 of the Supporting Information). (iii) Next, we employed the COSMO model at the B3LYP/ 6-31+G(3d,p) level of theory in order to calculate the cavity volume occupied by pure solvent and by S-W in a water continuum. The solvent cavity volumes thus obtained (VSC in Å3) were converted into molar volumes (VMSC, in cm3 mol-1). Table 2 shows the values calculated for W, S and S-W, respectively. (iv) The calculations that originated the data of Table 2 have no provision for the effect of temperature on the volume of S-W. We assumed that the dependence of the volume of S-W on temperature follows the same equation of the precursor pure solvents.21 This assumption was also considered for alcoholwater complexes and resulted in a satisfactory corrected molar volumes.15 The procedure employed in the present work was as follows: (theoretical) VMSC of pure liquids (Table 2) were plotted against their experimental, i.e., density-based molar volumes, VW and VS, respectively, in the temperatures 25, 35,

Figure 2. Relationship between experimentally determined molar volumes of solvents, VM, and theoretically calculated molar volumes. VMSC (COSMO/B3LYP/6-31+G(3d,p)) for binary mixtures of water and pure solvents. For each solvent, the spread of VM (at each VMSC) covers the temperature range 25-50 °C. Data for alcohols were taken from ref 15.

40, 45, and 50 °C, as shown in Figure 2. The last Figure also includes the corresponding values for the alcohols whose values of VMSC were previously calculated. At each temperature, the points of all 11 solVents lie on the same straight line; this is satisfactory and corroborates the reliability of the calculation strategy employed. Temperature-dependent volumes of S-W were then calculated by using the same regression coefficients of the resulting linear correlations at the five temperatures chosen. The linear equations that describe the relationship between VMSC and density-based molar volumes are listed in Table SI-2. (v) The volumes calculated in the preceding step refer to isolated S-W species; they do not account for volume changes due to the presence of these species in bulk nonideal mixtures.15 Since the nonideal behavior of (bulk) binary mixtures may be expressed in terms of excess functions, we corrected the abovementioned volumes of S-W by adding the appropriate excess volumes (VME,R, cm3/mol). The volume corrections employed and the final values of corrected volumes (VS-W), at different temperatures, are listed in Table SI-3. (vi) VS-W of Table SI-3 were then employed (as constants) in order to fit the experimental density versus mixture composition data; typical results are shown in Figure SI-2. Values of Kdissoc were calculated, and the corresponding results are listed in Table 3. An attempt to calculate Kdissoc for S-W complexes by employing VS-W ) VS + VW showed that this approach is inadequate since the model simply does not fit the density data (plots not shown). As expected, Kdissoc increases (i.e., S-W association decreases) as a function of increasing temperature. As Figure SI-3 shows, the van’t Hoff equation applies satisfactorily to all solvents, i.e., the corresponding ∆Cp is essentially temperatureindependent in the T-range studied.40 Values of Kdissoc were employed to calculate the effective mole fractions of the solvent species present, as depicted in Figure 3. These concentrations were employed in eq 9 to calculate the values of the appropriate φs. Thermo-Solvatochromism in Binary Solvent Mixtures. Figure 4 shows the dependence of ET (probe)obs on xanalytical , w at 40 οC, for RB and WB, respectively, whereas the solvent polarity/temperature/solvent composition contours are shown in Figure 5. The dependence of φ on the probe, the binary mixture

Solvation in Binary Mixtures of Water and Polar Aprotic Solvents TABLE 3: Dependence of the Dissociation Constants of Solvent-Water Complexes, Kdissoc, on Temperaturea T (°C)

S-W

VS-W (cm3 mol-1)

Kdissoc

r2

106 × Chi2

15

Me2CO

75.80

0.03153

0.9990

0.882

25

Me2CO MeCN DMF DMSO Py

77.01 59.97 90.12 84.68 94.68

0.03520 0.09923 0.00949 0.00940 0.01401

0.9905 0.9893 0.9992 0.9916 0.9808

0.981 2.282 0.937 1.029 1.421

35

Me2CO MeCN DMF DMSO Py

78.04 60.50 91.14 85.66 95.75

0.03806 0.10658 0.00963 0.00956 0.01421

0.9869 0.9978 0.9965 0.9876 0.9935

1.915 2.005 2.954 1.654 0.898

40

Me2CO MeCN DMF DMSO Py

78.59 60.77 91.66 85.99 96.31

0.03895 0.10952 0.00973 0.00963 0.01432

0.9975 0.9835 0.9891 0.9866 0.9932

3.585 1.164 0.809 1.123 0.850

45

Me2COb MeCN DMF DMSO Py

79.17 61.03 92.17 86.44 96.88

0.04034 0.11313 0.00980 0.00970 0.01440

0.9979 0.9911 0.9924 0.9864 0.9881

0.866 2.034 1.498 1.136 0.672

50

MeCN DMF DMSO Py

61.30 92.71 86.73 97.43

0.11662 0.00984 0.00978 0.01451

0.9960 0.9985 0.9920 0.9911

2.311 0.747 1.496 4.544

a The regression coefficient r2, and Chi2 are those obtained from the correlation between the density of the binary mixture and its composition, see Figure SI-2. b Value obtained by extrapolation.

Figure 3. Species distribution at 25 °C for mixtures of water with Me2CO, MeCN, DMF, DMSO, and Py, respectively.

and the temperature is shown in Table 4. The following comments may be extracted from these data: (vii) Instead of reporting extensive lists of ET(probe) and solvent compositions, we have calculated the (polynomial) dependence of polarity on the analytical mole fraction of water, and present the regression coefficients in Table SI-4. The degree of polynomial employed is that which gave the best data fit, as indicated by the multiple correlation coefficients, r2, and the standard deviation, (SD); (viii) All plots shown in Figures 4 and 5 are nonlinear; this may be attributed to several factors and/or solute-solvent interaction mechanisms. Nonideal behavior may originate from dielectric enrichment, i.e., enrichment of the solvation shell in

J. Phys. Chem. B, Vol. 111, No. 22, 2007 6177 the solvent of higher relative permittivity, r.39 This mechanism can be rejected, however, because if dielectric enrichment were operative, all curves of Figure 4 should lie above, not below the straight line that connects the polarities of the two pure liquids. A part of the data of Me2CO lies above the line, but there is no reason to expect that dielectric enrichment is operative only for this solvent and not for DMSO whose r is higher. Another reason for nonideal behavior is preferential solvation of the probe by a component of the mixture because of solute-solvent specific interactions, e.g., hydrogen-bonding and dipole-dipole interactions. A large body of experimental data and theoretical calculations, e.g., of the Kirkwood-Buff integral functions (that describe W-W, S-S, and S-W interactions), has shown that the binary mixtures employed are microheterogeneous; there exist micro-domains composed of organic solvent surrounded by water, and of water solvated by organic solvent. The onset and composition of these microdomains depend on the pair of solvents. There exists the possibility of preferential solvation of the probe in the less polar microdomains, leading to below-the-line deviation, as shown in Figures 4 and 5.41-44 In summary, nonideal solvation behavior is not unexpected; (ix) To compare the deviation from linearity for both indicators, ET(probe) of Figure 4 can be converted into a reduced, dimensionless polarity scale, ErT (probe) ) ET(probe)S-W ET(probe)S/ET (probe)W - ET (probe)S. The resulting plots (not shown) show that for the same solvent, at each temperature, the deviation from linearity is larger for RB, the more hydrophobic probe. This shows that solute-solvent solvophobic interactions are important to solvation, as argued elsewhere.11,12c (x) Results of application of eq 9 are listed in Table 4. The fit of the model to our thermosolvatochromic data is shown by values of (r2) and Chi2, and by the excellent agreement between experimental and calculated ET(probe)S and ET(probe)W, respectively. The results of Table 4 are discussed in terms of their dependence on the structure of the probe and the protic solvent (at the same temperature, T) and on T, for the same probe and binary mixture. Values of (m) are close to unity, and decrease as a function of increasing T. Likewise, for each probe in each solvent, all values of φ, ET(probe)S, ET(probe)W, and ET(probe)S-W decrease as a function of increasing T. This probe desolvation agrees with the known effect of temperature on solvent structure because of less efficient hydrogen-bonding and dipolar interactions.44 (xi) Mixtures of water with the two dipolar aprotic solvents show distinct behaviors. Consider first the exchange of the pure solvents, φW/Me2CO > 1, whereas φW/DMSO < 1, i.e., water is more efficient in displacing Me2CO than DMSO from the probe solvation shell. Acetone is not strongly dipolar, see Table SI-1, and solvates positive centers better than negative ones,45 i.e., it interacts less with the probe phenolate oxygen, being displaced by water, because the latter is capable of solvating both types of centers effectively. Similar to solvation by alcohols, φW/DMSO is unity, i.e., the mixed solvent is efficient in displacing the precursor solvents. The above-mentioned conclusion about the weak interactions of Me2CO with the probe is corroborated by the fact that φMe2CO-W/Me2CO are > φMe2CO-W/W, i.e., the complex solvent displaces Me2CO from the probe solvation shell more efficiently than it displaces

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Figure 4. Dependence of the empirical solvent polarity parameter ET(probe) on the analytical mole fraction of water, at 40 °C for mixtures of water with acetone and DMSO, respectively. The straight lines were plotted to guide the eye; they represent ideal solvation of the dye by the mixture.

Figure 5. Solvent polarity/temperature/solvent composition contours for RB in acetone and DMSO, respectively.

TABLE 4: Analysis of Thermosolvatochromic Data in Aprotic Solvents Mixtures probe solvent temperature (°C)

WB

RB

acetone 25 40 DMSO 40 60 acetone 25 40 DMSO 40 60

10 0.975 0.953 25 1.047 1.029 10 1.143 1.128 25 1.289 1.236

m

φW/S

φS-W/S

φS-W/W

ET(S)

ET(W)

ET(S-W)

Chi2

r2

0.997 2.969 3.067 1.070 0.452 0.476 1.209 2.516 2.547 1.321 0.519 0.545

2.907 18.488 16.729 0.412 2.358 2.284 2.475 39.455 35.168 0.490 3.160 2.968

20.098 6.277 5.455 2.417 5.219 4.798 41.697 15.681 13.808 3.285 6.089 5.442

6.913 51.34 [( 0.09] 50.56 [( 0.10] 5.869 53.97 [( 0.18] 53.66 [( 0.18] 16.847 42.13 [( 0.22] 41.71 [( 0.15] 6.704 44.94 [( 0.14] 44.62 [( 0.07]

51.80 [( 0.12] 70.26 [( 0.09] 69.77 [( 0.10] 54.28 [( 0.08] 69.91 [( 0.19] 69.35 [( 0.19] 42.62 [( 0.19] 63.17 [( 0.21] 62.65 [( 0.15] 45,35 [( 0.08] 62.65 [( 0.18] 62.24 [( 0.09]

70.72 [( 0.12] 57.08 [( 0.52] 55.59 [( 0.78] 70.27 [( 0.09] 61.25 [( 1.39] 60.60 [( 1.59] 63.69 [( 0.18] 50.38 [( 0.54] 49.53 [( 0.50] 63,08 [( 0.11] 48.41 [( 1.68] 48.41 [( 0.93]

58.37 [( 0.53] 0.0094 0.0129 61.83 [( 0.58] 0.0424 0.0417 51.02 [( 0.41] 0.0539 0.0270 49,13 [( 0.15] 0.0394 0.0097

0.0170 0.9997 0.9997 0.0101 0.9990 0.9990 0.0405 0.99884 0.99944 0,0295 0.99932 0.99983

0.9996

water. This is the inverse of what has been observed for solvation by aqueous alcohols and 2-alkoxyethanols, where the mixed solvents were always more efficient in displacing water than the organic solvent. On the other hand, all φDMSO-W/W are

0.9998 0.9992 0,99936

> φDMSO-W/DMSO, i.e., the mixed solvent displaces water more efficiently than DMSO. Values of φDMSO-W/W and φDMSO-W/DMSO are much smaller than the corresponding values for Me2CO, i.e., the efficiency of DMSO-W in displacing the precursor

Solvation in Binary Mixtures of Water and Polar Aprotic Solvents solvents is less than the corresponding one of Me2CO-W. This may be attributed to the fact that the interaction of DMSO with W attenuates the solvation efficiency of the complex solvent. Evidence showing that DMSO-W interactions are stronger than W-W interactions include theoretical calculations;32 IR; 1H and 13C NMR;46 neutron scattering;47 and electron-spray mass spectroscopy.31 The structure of the mixed solvent is given by (CH3)2Sδ+dOδ-...Haδ+...Oδ--Hb, where, for simplicity, (Ha) is drawn symmetrically between the two oxygen atoms, and (Hb) is the site for hydrogen-bonding with the probe phenolate oxygen. As argued elsewhere, the formation of mixed solvent partially deactivates (Hb) toward further hydrogen-bonding, this deactivation is greater the stronger the basicity of S.48 Because of the high basicity of DMSO, its mixed solvent (with W) may be considered as a deactivated species both in hydrogen-bonding to the probe phenolate oxygen, and electrostatic interaction with the probe positively charged nitrogen, this leads to the small φ observed;12c (xii) Table 4 shows that as a function of increasing temperature, (m), ET(probe)S, ET(probe)W, φS-W/S, and φS-W/W decrease, whereas φW/S increases. The decrease in polarities of pure solvents can be attributed to a decrease of solvent stabilization of the probe ground state, as a result of the concomitant decrease of solvent structure, and hydrogen-bonding ability.49 Preferential “clustering” of water and solvents as a function of increasing temperature means that the strength of S-W interactions decrease in the same direction,43,44,50 with a concomitant decrease in its ability to displace both S and W. This explains the decrease of φS-W/S and φS-W/W as a function of increasing T. As discussed previously,11,12,16 hydrogenbonding of water with probe ground-state is less susceptible to temperature increase than that of the organic component. This leads to a measurable “depletion” of pure solvent in the probe solvation shell, so that φW/S increases as a function of increasing temperature. Conclusion

J. Phys. Chem. B, Vol. 111, No. 22, 2007 6179 Supporting Information Available: Figure SI-1, optimized geometries of solvent-water hydrogen-bonded complexes; Figure SI-2, dependence of solution density on the volume fraction of solvent in the binary mixture; Figure SI-3, application of the van’t Hoff equation to Kdissoc of solvent-water complexes; Figure SI-4, dependence of the excess volume of aqueous solvents on the volume fraction of (S), at different temperatures; Table SI-1, calculated and experimental dipole moments of water and solvents; Table SI-2. Correlation of experimental molar volumes of solvents and molar volumes calculated from optimized geometries; Table SI-3, corrected molar volumes of solvent-water 1:1 complexes; Table SI-4, dependence of thermosolvatochromic responses on the analytical mole fraction of water in binary mixtures; Methods and equations for calculations of dissociation constants of solvent-water complexes from density data; The solvent molar volume; The dependence of molar volumes of solvent-water complexes on temperature; Correction for calculated molar volumes. This material is available free of charge via the Internet at http:// pubs.acs.org. Abbreviations COSMO (C-PMC) ET(probe) ET(30) ET(33) Kdissoc MS MS-W MW RB S-W VSC VMSC VMTh VME,R VM

conductor-like screening model. empirical solvent polarity scale of a solvatochromic probe, in kcal mol-1. empirical solvent polarity scale of RB, in kcal mol-1. empirical solvent polarity scale of WB, in kcal mol-1. dissociation constant of the S-W species. relative molecular mass of the solvent, S. relative molecular mass of the species S-W relative molecular mass of water. 2,6-diphenyl-4-(2,4,6-triphenylpyridinium-1-yl)phenolate. 1:1 solvent-water hydrogen-bonded species. solvent cavity volumes. theoretical molar volume. theoretical molar volume, corrected for temperature. excess molar volume as a function of volume fraction. general experimental molar volume of solvent (water or dipolar aprotic). experimental molar volume of dipolar aprotic solvent. experimental molar volume of water. molar volume of the hydrogen-bonded alcohol-water species, corrected for temperature and nonideality of the binary mixture. 2,6-dichloro-4-(2,4,6-triphenylpyridinium-1-yl)phenolate volume fraction scale. mole fraction scale. solvent fractionation factor. solution density.

Thermo-solvatochromism of two zwitterionic probes in binary solvent mixtures is treated according to a solvent exchange model that explicitly considers the equilibria between the species present in solution (S, W, and S-W) and the corresponding ones in the probe solvation shell. Application of this model requires knowledge of the effective concentrations of the abovementioned solvent species (from Kdissoc) as well as the equilibrium constants for their exchange in the solvation shell (defined by φ). Reliable values of Kdissoc may be obtained from theoretically calculated VS-W, corrected for the nonideality of the binary solvent mixtures at different temperatures. Information about the thermosolvatochromism of RB and WB in mixtures of water with acetone and with DMSO was obtained from φ. Values of the latter have been rationalized in terms of probe-solvent interaction mechanisms, in particular hydrogenbonding and hydrophobic interactions with S and S-W. Temperature increase results in gradual desolvation of the probe because of the concomitant decrease of solvent structure.

References and Notes

Acknowledgment. We thank FAPESP (State of Sa˜o Paulo Research Foundation) for financial support, predoctoral fellowship to P. L. Silva, postdoctoral fellowship to E. L. Bastos; CNPq (National Council for Scientific and Technological Research) for a research productivity fellowship to O. A. El Seoud. We thank Clarissa T. Martin and Michelle S. Lima for their help and the LCCA laboratory for making the programs and computation facilities available to us.

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