Supporting information for: Preferential Solvation of a Highly Medium Responsive Pentacyanoferrate(II) Complex in Binary Solvent Mixtures: Understanding the Role of Dielectric Enrichment and the Specificity of Solute-Solvent Interactions Raffaello Papadakis* a a Department of Chemistry Ångström, Uppsala University, Box 523, 751 20 Uppsala, Sweden Tel: +46728368595 Email: rafpapadakis@gmail.com
1. Determination of the contribution of the solvatochromic parameters The following general multiparametric model is assumed. This model correlates the physicochemical quantity Q with the parameters X1,, Xi,, Xn, according to Eq. S1 n Q = Q 0 + x i X i i=1 (S1) where, Qo is the intercept of this linear model (Q = Q o when X1=X 2 = =Xi= =Xn =0) and x1,, xi,, xn are the coefficients of the parameters X1,, Xi,, Xn, respectively, expressing the sensitivity of the physicochemical quantity Q to the parameters X1,, Xi,, Xn. Q o and the coefficients x 1,, x i,, x n are obtained through linear multiparametric regression analysis. In this work, n=2 since, the solvatochromic equation employed in this work consists of only two parameters (π* and α) according to Eq. S2. E CT = E CT,0 + sπ + aα (S2) The relative contribution of each one of the parameters X i [symbolized as P(X i )] to the quantity Q, can be calculated through Eq. S3. In this equation (x i ) is calculated through Eq. S4 where, X i and Q are the mean values of the parameter X i and of the quantity Q, respectively, and finally x i corresponds to the absolute regression value of x i obtained from the regression analysis. P(X i ) = 100(x i) n (x i ) i=1 (S3) m (X ij X i ) 2 (x i ) j=1 = x i m (S4) (Q j Q ) 2 j=1 ( ) m is the number of series of data, e.g. number of different solvent mixtures (in this work m=11 for the three types of BSMs studied). 1 2 2. Sensitivities of E CT to parameters π and α and correlations with parameter E T (30) The sensitivities of E CT to solvatochromic parameters π and α expressing dipolarity/polarizability and HBDacidity respectively were determined through linear regressions as shown in Table S1. Table S1 E CT = E CT,0 + sπ E CT = E CT,0 + aα Solvent E CT,0 (kcal/mol) s (kcal/mol) R E CT,0 (kcal/mol) a (kcal/mol) R mixture MeOH/H 2 O 31.07±1.75 19.38±2.18 0.947-7.014±5.846 50.60±5.54 0.950 FA/H 2 O 147.0±35.0-87.27± 30.48 0.690 41.77± 0.19 16.30± 1.58 0.960 NMF/H 2 O -10.37±1.88 56.74± 1.95 0.995 27.53± 0.91 20.95± 1.13 0.987 Sensitivity to parameter π Sensitivity to parameter α Correlation coefficient Correlations of E CT with Reichardt s polarity scale in Table S2. Table S2 E CT = E CT,0 + r E T (30) Solvent E CT,0 (kcal/mol) r (-) R mixture MeOH/H 2 O 26.80±10.90 1.260±0.189 0.913 FA/H 2 O -21.95±4.21 1.173±0.072 0.984 NMF/H 2 O -27.79±3.15 1.263±0.055 0.991 Sensitivity to parameter E T (30) Correlation coefficient S1
3. Determination of the parameters α and π* for NMF/water mixtures The solvatochromic parameters α and π* of NMF/water mixtures of Table 4 were determined using published methodologies because no published experimentally obtained data could be found. For parameter π* the product of the functions P(ε) and R(n 2 ) * was used according to published methodologies 1 (see Equations S5 and S6). P(ε) = ε 1 2ε + 1 R(n 2 ) = n2 1 2n 2 + 1 (S5) (S6) The Linear Solvation Relationship (LSER) (Eq. S7) relating the product P(ε). R(n 2 ) and the solvatochromic parameter π* was then used. The equation is corrected so that the neat-solvent π* values of water and NMF (0.90 and 1.09 respectively) are the two extremes i.e. 0.90 π 1.09. π = 1.965 10.57 P(ε) R(n 2 ) (S7) Then for the solvatochromic parameter α suitable LSER involving E T (30) (Reichardt s polarity scale) and the solvatochromic parameter π* (determined as described above) was used as previously reported. 2 4. Separating dielectric non-ideality from preferential solvation effects Suppan s model on dielectric enrichment provides an efficient way for the separation of dielectric non-ideality from preferential solvation in BSMs. In order to achieve that the so-called experimental non-linearity ratio has to be calculated according to Eq. S8. 3 In this equation E CT is the experimentally determined charge transfer energy, E CT, linear is given by Eq. S9, x P is the bulk mole fraction of the most polar solvent of the two solvents of the BSM and finally ΔE p n is given by Eq. S10 where E CT,p and E CT,n are the charge transfer energies measured in neat polar and less polar solvent of the BSM respectively. ρ exp = 1 (E CT E 0 CT,linear )dx p ΔE p n (S8) E CT,linear = x p E CT,p + x n E CT,n (S9) ΔE p n = E CT,p E CT,n (S10) According to Suppan the preferential solvation ration ρ ps can then be determined through Eq. S11 knowing ρ exp from Eq.S8 and by obtaining the dielectric non-ideality ratio ρ ni via Eq. S12 (in this equation φ(x p ) represents the Onsager polarity function (for details see main text)). Finally, the preferential solvation index Z ps which is not contaminated by the dielectric non-ideality of the BSM is given by the expression S14 which has been obtained by Suppan as well as other authors in the past. 3,4,5 ρ exp = ρ ps + ρ ni (S11) ρ ni = 1 (φ exp φ 0 linear )dx p Δφ p n (S12) φ linear = x p φ p + x n φ n (S13) ρ ps = 0.31Z ps (S14) What was found in all three cases of BSMs was that the ρ ni is higher than ρ exp. This has been observed also in cases of BSMs of polar solvents in the past and it was concluded that in cases where ρ exp < ρ ni the obtained * n values were determined through: n 1.1ε S2
preferential solvation index Z ps (see main text, Eq.3) could be considered as non-contaminated with dielectric non-ideality. 6 5. Local mole fractions obtained using Suppan s model as a function of bulk mole fractions Figure S1. Local mole fractions of MeOH calculated using Suppan s model as a function of bulk mole fraction of MeOH determined for MeOH/water mixtures with dye 1 as a solute. Figure S2. Local mole fractions of FA calculated using Suppan s model as a function of bulk mole fraction of FA determined for FA/water mixtures with dye 1 as a solute. S3
Figure S3. Local mole fractions of NMF calculated using Suppan s model as a function of bulk mole fraction of NMF determined for NMF/water mixtures with dye 1 as a solute. S4
6. Solvent local mole fractions determined through the Bosch-Rosés model Table S2. Local mole fractions of MeOH (S2) and water (S1) and their one-to-one complex (S12) Table S3. Local mole fractions of FA (S2) and water (S1) and their one-to-one complex (S12) Table S3. Local mole fractions of NMF (S2) and water (S1) and their one-to-one complex (S12) S5
7. Calculated local fractions through different models Figure S4. Local mole fractions calculated through various models as a function of bulk mole fraction of MeOH, all determined for MeOH/water mixtures with dye 1 as a solute. Blue rhombs: y 12 of Bosch and Rosés (for 0 x MeOH < 0.9) and y MeOH of Bosch and Rosés for 0.9 x MeOH 1; blue line: polynomial fit y 12 (x MeOH ); Red squares: y MeOH obtained through Suppan s model (see also Figure S1) red line: polynomial fit y MeOH,Suppan (x MeOH ); Green triangles: y MeOH obtained as described in ref. 7 and 8 green line: polynomial fit y MeOH,JSN (x MeOH ); dashed line: ideal line y MeOH = x MeOH. Figure S5. Local mole fractions calculated through various models as a function of bulk mole fraction of FA, all determined for FA/water mixtures with dye 1 as a solute. Blue rhombs: y 12 of Bosch and Rosés y 12 of Bosch and Rosés (for 0 x MeOH < 0.85) and y FA of Bosch and Rosés for 0.85 x MeOH 1; blue line: polynomial fit y 12 (x FA ); Red squares: y FA obtained through Suppan s model (see also Figure S2) red line: polynomial fit y FA,Suppan (x FA ); Green triangles: y FA obtained as described in ref. 7 and 8, green line: polynomial fit y FA,JSN (x FA ); dashed line: ideal line y FA = x FA. S6
Figure S6. Local mole fractions calculated through various models as a function of bulk mole fraction of NMF, all determined for NMF/water mixtures with dye 1 as a solute. Blue rhombs: y 12 of Bosch and Rosés (for:0 x NMF < 0.9, and y NMF Bosch and Rosés for 0.9 x NMF 1; blue line: polynomial fit y 12 (x NMF ); Green triangles: y NMF obtained through Suppan s model (see also Figure S3), green line: polynomial fit y NMF,Suppan (x NMF ); Red squares: y NMF obtained as described in ref. 7 and 8, red line: polynomial fit y NMF,JSN (x NMF ); dashed line: ideal line y NMF = x NMF. Supplementary References: S1. Marcus, Y. The Properties of Organic Liquids That Are Relevant to Their Use as Solvating Solvents. Chem. Soc. Rev. 1993, 409-416. S2. Marcus, Y. The Use of Chemical Probes for the Characterization of Solvent Mixtures. Part 2. Aqueous Mixtures J. Chem. Soc. Perkin Trans. 2 1994, 1751-1758. S3. Suppan, P. Local Polarity of Solvent Mixtures in the Field of Electronically Excited Molecules and Exciplexes. J. Chem. Soc. Faraday Trans. 1 1987, 83, 495-509. S4. Khajehpour, M.; Kauffman, J. F. Dielectric Enrichment of 1-(9-Anthryl)-3-(4-N,N-dimethylaniline) Propane in Hexane-Ethanol Mixtures. J. Phys. Chem. A 2000, 104, 7151-7159. S5. Khajehpour, M.; Welch, C. M.; Kleiner, K. A.; Kauffman, J. F. Separation of Dielectric Nonideality from Preferential Solvation in Binary Solvent Systems: An Experimental Examination of the Relationship between Solvatochromism and Local Solvent Composition around a Dipolar Solute. J. Phys. Chem. A 2001, 105, 5372-5379. S6. Kaur, H.; Koley, S.; Ghosh, S. Probe Dependent Solvation Dynamics Study in a Microscopically Immiscible Dimethyl Sulfoxide Glycerol Binary Solvent. J. Phys. Chem. B 2014, 118, 7577 7585. S7
S7. The yjsn values mentioned in Figures S4-6 have been reported in ref 8 by the author and coworkers and they were obtained through the expression: y A,JSN = (E CT,m E CT,B )/( E CT,A E CT,B ) where y A,JSN is the local mole fraction of solvent A for a certain BSM of solvents A and B, E CT,m is the charge transfer energy of 1 determined for that BSM, and E CT,A and E CT,B are the charge transfer energies of 1 determined in neat solvents A and B respectively. S8. Papadakis, R.; Tsolomitis, A. Solvatochromism and Preferential Solvation of 4-Pentacyanoferrate 4 -Aryl Substituted Bipyridinium Complexes in Binary Mixtures of Hydroxylic and non-hydroxylic Solvents. J. Solution Chem. 2011, 40, 1108-1125. S8