Supporting information for: Preferential Solvation of a Highly Medium Responsive Pentacyanoferrate(II)
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1 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, Uppsala, Sweden Tel: rafpapadakis@gmail.com
2 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) 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± ± ± ± FA/H 2 O 147.0± ± ± ± NMF/H 2 O ± ± ± ± 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± ± FA/H 2 O ± ± NMF/H 2 O ± ± Sensitivity to parameter E T (30) Correlation coefficient S1
3 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 (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 π π = 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 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
4 preferential solvation index Z ps (see main text, Eq.3) could be considered as non-contaminated with dielectric non-ideality 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
5 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 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 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
8 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, S2. Marcus, Y. The Use of Chemical Probes for the Characterization of Solvent Mixtures. Part 2. Aqueous Mixtures J. Chem. Soc. Perkin Trans , S3. Suppan, P. Local Polarity of Solvent Mixtures in the Field of Electronically Excited Molecules and Exciplexes. J. Chem. Soc. Faraday Trans , 83, 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, 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, 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, S7
9 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, S8
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