1. Introduction

2. Methods

Figure 1. a (left panel). Dependence of DI as function of x(water) for methanol/water (blue), 2-propanol/water (red) and 2-methyl-2-propanol/water (grey); Figure 1b (right panel). N_av,z (in mol/cm³) of 2-methyl-2-propanol/water mixture as a function of x(water). N_av,x (blue) and N_av,w (red).

Figure 1. a (left panel). Dependence of DI as function of x(water) for methanol/water (blue), 2-propanol/water (red) and 2-methyl-2-propanol/water (grey); Figure 1b (right panel). N_av,z (in mol/cm³) of 2-methyl-2-propanol/water mixture as a function of x(water). N_av,x (blue) and N_av,w (red).

3. Results

3.2. Refractive Index of Aqueous Solvent Mixtures

The suitability of equation (10) is exemplified for several amide derivative/water, DMSO/water and 1,4-dioxane/water mixtures for which E_T(30) values are reported and discussed below. These solvent mixtures belong to the class where no enhancement of the water structure is evident [107]. The literature references for ${\mathrm{n}}_{\mathrm{D}}^{20}$  data are listed in the Tables of the supporting information section. For NMF/water, no usable refractive index data could be found in the literature.

The representation of the refractive index measured at 589 nm wavelength (${\mathrm{n}}_{\mathrm{D}}^{20}$ ) as a function of N_av,x,CH results in a straight line as seen in Figure 2a and from Equation (11) to Equation (15). 1,2-ethanediol/water and glycerol/water mixtures, which both show excellent linearity of ${\mathrm{n}}_{\mathrm{D}}^{20}$  as a function of N_av,x,CH , are outlined in chapter 3.4.6.

$$\begin{gathered} {\mathrm{n}}_{\mathrm{D}}^{20}=1.5N\mathrm{av},x,\mathrm{CH}+1.34 \\ \mathrm{n}=12(\mathrm{FA}/\mathrm{water}); \mathrm{r}=0.9997. \end{gathered}$$

(11)

$$\begin{gathered} {\mathrm{n}}_{\mathrm{D}}^{20}=1.736N\mathrm{av},x,\mathrm{CH}+1.334 \\ \mathrm{n}=8(\mathrm{NFM}/\mathrm{water}); \mathrm{r}=0.9977. \end{gathered}$$

(12)

$$\begin{gathered} {\mathrm{n}}_{\mathrm{D}}^{20}=1.065N\mathrm{av},x,\mathrm{CH}+1.34 \\ \mathrm{n}=14(\mathrm{DMF}/\mathrm{water}); \mathrm{r}=0.988. \end{gathered}$$

(13)

$$\begin{gathered} {\mathrm{n}}_{\mathrm{D}}^{20}=1.5N\mathrm{av},x,\mathrm{CH}+1.34 \\ \mathrm{n}=18(\mathrm{DMSO}/\mathrm{water}); \mathrm{r}=0.9952. \end{gathered}$$

(14)

$$\begin{gathered} {\mathrm{n}}_{\mathrm{D}}^{20}=1.5N\mathrm{av},x,\mathrm{CH}+1.34 \\ \mathrm{n}=12(\mathrm{1,4-dioxane}/\mathrm{water}); \mathrm{r}=0.9977. \end{gathered}$$

(15)

Figure 2. a (left panel) Correlations of refractive index ${\mathrm{n}}_{\mathrm{D}}^{20}$ as function of N_av,x,CH (mol/cm³) for co-solvents that do not enhance the water structure of co-solvent/water mixtures; Figure 2b (right). Plots of refractive index ${\mathrm{n}}_{\mathrm{D}}^{20}$ as function of N_av,x,CH (mol/cm³) for co-solvents that enhance the water structure of co-solvent/water mixtures; to a) FA/water (red), water/N-formylmorpholine (NFM) (yellow), DMF/water (grey), 1,4-dioxane/water (light blue) and DMSO/water (deep blue); to b) methanol/water (blue), ethanol/water (red), 2-propanol/water (grey), and 2-methyl-2-propanol/water (yellow).

Figure 2. a (left panel) Correlations of refractive index ${\mathrm{n}}_{\mathrm{D}}^{20}$ as function of N_av,x,CH (mol/cm³) for co-solvents that do not enhance the water structure of co-solvent/water mixtures; Figure 2b (right). Plots of refractive index ${\mathrm{n}}_{\mathrm{D}}^{20}$ as function of N_av,x,CH (mol/cm³) for co-solvents that enhance the water structure of co-solvent/water mixtures; to a) FA/water (red), water/N-formylmorpholine (NFM) (yellow), DMF/water (grey), 1,4-dioxane/water (light blue) and DMSO/water (deep blue); to b) methanol/water (blue), ethanol/water (red), 2-propanol/water (grey), and 2-methyl-2-propanol/water (yellow).

The positive slopes Δ${\mathrm{n}}_{\mathrm{D}}^{20}$ /ΔN_av,x,CH and the excellent quality of the correlations${\mathrm{n}}_{\mathrm{D}}^{20}$  as a function of N_av,x,CH for several co-solvent/water mixtures are a clear proof of the physical sense of this approach for solvent mixtures because it fulfills the theoretical requirement of Beer`s approximation and the LLR [47,67,69]. The E_T(30) parameter of aqueous solvent mixtures decreases with increasing ${\mathrm{n}}_{\mathrm{D}}^{20}$  for these co-solvent/water mixtures that do no show an enhancement of the water structure. For each specific solvent mixture, a separate correlation is found. These results are seen in Figure S2 and explained at the appropriate place in the following text where the special mixture is discussed.

The convincing linear relationships in Figure 2a are clear evidence for both the correctness of the quantity N_av,x,CH and the approach of Equation (4b) and Equation (10) in the analysis of the refractive index of aqueous solvent mixtures as long as alcohol/water mixtures are not taken into account. Remarkably, the linearity ${\mathrm{n}}_{\mathrm{D}}^{20}$  as a function of N_av,x,CH does not apply to alcohol/water mixtures in which there is an anhancement of the water structure [106,107,109-112]. In particular, the methanol/water and ethanol/water systems give a maximum curve of ${\mathrm{n}}_{\mathrm{D}}^{20}$  as a function of composition amount; see Figure 2b. For the other alcohol/water mixtures an asymptotic curve is obtained, but still with positive slope along the curve; Figure 2b. In the past, there are empirical concepts to circumvent the non-linearity ${\mathrm{n}}_{\mathrm{D}}^{20}$   as function of composition for methanol/water; i.e. by using the quotient ${\mathrm{n}}_{\mathrm{D}}^{20}$  /density instead ${\mathrm{n}}_{\mathrm{D}}^{20}$  alone [109]. But the physical background is more complicated and still under study. Recent studies have shown that microdomains of water and ethanol/water are present at the mesoscale, consisting of different refractive indices [108]. Depending on the balance of segregation and aggregation of these areas [109], the non-linearity of${ \mathrm{n}}_{\mathrm{D}}^{20}$   as a function of composition is due to the coexistence of two different microdomains with different compositions and thus different refractive index. The ratio of the two ranges is a function of the original solvent proportions before mixing. The polarization effects and dipolar dispersion forces, which are relevant for methanol/water mixtures, can have an additional influence [60,92,93]. Figure 2b clearly supports the hypothesis of the coexistence of different microdomains of water/alcohol mixtures [89,90,108]. Basically, the alcohol/water mixtures that show an enhancement of the water structure according to Marcus do not show a linear dependency ${\mathrm{n}}_{\mathrm{D}}^{20}$   on N_av,x,CH.

Alcohol/water mixtures are further discussed in this paper under the aspect of co-existence of different microdomains.

3.4. Solvatochromism of B30 in Aqueous Solvent Mixtures

This part of the manuscript is the central concern. It is about correcting many misinterpretations in the literature. The most E_T(30) data of the solvent mixtures for evaluation were taken from the numerous publications in ref [1-4,11-20] and others. Some special comments are required on the data sets used, as several aspects have to be taken into account. You have to check which E_T(30) value corresponds exactly to the indicated concentration because molar fraction, weight fraction and volume content are used alternately [1,2,8,11-20].

For the evaluation, the densities of the mixture are needed for each specific composition and temperature of the mixture. This was the most difficult task to accomplish. Fortunately, the densities of alcohol/water mixtures often correlate significantly with the mole fraction (x) within certain sections of composition. Thus, unknown densities for special compositions can be calculated by correlation equations using precise data from literature. References are given in the captions of Figures and Tables in the supplementary materials, SI, section.

Advantageously, many of the measured E_T(30) values from literature agree very well between different authors for series of measurements. We have compared the data of Reichardt [2] and Rosés [18,19,20] and found that an almost perfect agreement of the measured E_T(30) values as a function of N_av,x is found. As example see Figure S4a for ethanol/water mixture. For this task it was necessary to convert the volume percentages from [1,2] to mole fraction. Despite the very good agreement, a data set from the same source was mostly used for the investigation if sufficient measured values were available. For the FA/water mixture, data from two different references were mixed because the authors' measurements covered different composition ranges [21,117]. There are only very small deviations. If one remains within one data series, regression coefficient r approach one for FA/water. For the NMF/water mixtures, there is no great variation obove x(water) >0.02, see suppoting information of [21].

The high quality of the whole data set from Rosés should be emphasized. Rosés also used the carboxylate substituted betaine dye of B30; the B30-COONa to investigate alcohol water mixtures due to the weak solubility of B30 in pure water and highly water concentrated mixtures [19]. There is an almost perfect agreement betweeen E_T(30) and E_T(30-COONa) over the whole composition range. This aspect is taken up again in the discussion section.

The perfect complementarity of the different E_T(30) values for DMSO/water from several references [7,12,14,118,119] should be noted (see Figures S4b). All data sets fit exactly in one relationship (see later). However, there are very small differences [ΔE_T(30) ~1 kcal) between the authors result.

Since the E_T(30) data sets for 1,2-ethanediol/water show some not tolerable differences in the low water concentration range between the data from [12] and [15], we used only the data set from [12] which fit well (see Figure S5).

The perfect complementary alignment of the E_T(30) data from [13] and [19] for the 2-methyl-2-propanol/water mixture at high water concentration is also particularly noteworthy.

An unfortunately frequent problem was that many measured UV/Vis data of several solvatochromic dyes were neither given accurately in tables nor in supporting information [6,10]. Either only the evaluated results of the coefficients of the applied solvation models were given, or artificially modified parameters instead of the original spectroscopic data. Also, often only the diagrams were shown without the data being additionally given in tabular form. Unfortunately, this data could hardly be used. All secure data used for the correlation analyses are compiled in tables in the supplement materials section together with the physical data on properties of the solvent mixtures from the literature.

To support the correlations of E_T(30) as a function of N_av,x, , Kosower's Z-scale was deemed appropriate [120-122], because of the linear correlation of Z with the E_T(30) parameter [1,34,35]. However, this turned out not to be the case. It is essential to clarify the situation of the different Z-values for DMSO/water and ethanol/water mixtures from the literature, because only the Z-values given by Kosower were determined directly with K [120, 121]. The Z-values used by Marcus for correlations were calculated by himself indirectly using Brownstein's S-values [123] (see note in citation 23 of marcus paper) [12]. The same applies to Gowland's Z-values, which were also determined indirectly by 4-pyridine-N-oxide via a correlation equation [123,124]. We are convinced the main problem is the reproducible measurement of Z values with Kosower`s dye, because in [124] it was mentioned that Z value is dependent on concentration of K in ethanol/water.

To test whether case ii. of preferential solvation is significant, literature data of other negatively solvatochromic probes such as B1 [(2,4,6-triphenyl-1-pyridinium)-phenolate] [1], Brooker`s Merocyanine (BM) [125] or Fe [126] were taken into account, although fewer data points per correlation are available. For this purpose the qualitative results EP or the UV/Vis absorption energy at peak maximum ν_max(Fe) as a function of N_av,x are examined.

3.4.1. 1,2-Ethanediol/Water, Methanol/Water and Ethanol/Water Mixtures

The reason for consideration 1,2-ethanediol/water mixtures compared to methanol/water and ethanol/water mixtures is the following. In all three systems, the enthalpy of mixing is exothermic over the entire composition range [81,82,127]. While 1,2-ethanediol as co-solvent does not enhance the water structure, methanol and ethanol do [106,107].

As mentioned, the relation E_T(30) as function of x(water) result in a curved line regardless whether methanol/water, ethanol/water or 1,2-ethanediol/water mixtures are considered as seen in Figure 3b. This has been discussed in the introduction and is sufficiently described in the literature [2,8,10-20]. The greater the molar mass difference, the more non-uniform the mixture, the greater the DI_max ethanediol/water mixtures (green) > ethanol/water mixtures (blue) > methanol/water mixtures (grey). This in turn depends on x(water) in the mixture. It can be clearly stated that the strongest curvature along a line of E_T(30) as a function of x(water) for each specific co-solvent/water mixtures occurs when DI is highest. This is a purely physical effect that has nothing to do with specific solvation.

The situation is different if E_T(30) is theoretically correctly correlated with N_av,x (see Figure 3a, left hand panel). Then one obtains an excellent linear correlation for the 1,2-ethanediol/water mixtures [Equation (17) and (18)]. This overall result is of great significance. The 1,2-ethanediol/water mixtures shows no abrupt structural changes over the entire composition range [74,107,127]. Despite the curved form of E_T(30) as a function of x(water), an excellent linear correlation of E_T(30) with N_av,x is obtained for 1,2-ethanediol/water mixtures. The interpretation of the E_T(30) course as function of N_av,x for the 1,2-ethenediol/water mixtures requires an essential comment, because each 1,2-ethanediol molecule contains two OH groups. Therefore, the number of OH dipoles per 1,2-ethanediol is doubled [62]. For the ethanediol/water mixtures, the hydroxyl group density regarding the number of total OH dipoles is taken into account by use of the D_HBD (density of OH groups) quantity and calculated by means of Equation (9) using the partial OH concentration of the 1,2-ethanediol component in the mixture (see Table S2). The determined function E_T(30) versus D_HBD for 1,2-ethanediol/water mixtures according to Equation (9) is the red-dot line in Figure 3b. This curve is completely congruent with the relationship E_T(30) as function of N_av,x for methanol/water mixtures in the water rich section (N_av,x > 0.04 mol/cm³). However, it is remarkable that the correlation E_T(30) versus N_av,x methanol/water mixtures from Nav,x <0.04 mol/cm³ runs parallel to the correlation E_T(30) versus N_av,x (deep blue) for 1,2-ethanediol/water mixtures indicating the variation of OH-dipoles influence on E_T(30). This result shows convincingly the strong impact of the total number of OH groups of binary aqueous mixtures in terms of D_HBD,av,x or Nav,x on E_T(30) [62]. These unambiguous results completely rule out a preferential solvation of B30 in methanol/water, ethanol/water as well as 1,2-ethanediol/water mixtures relating to scenario ii. The results for the methanol/water and ethanol/water mixtures do also not really correspond to the scenario i. It is always the total number of dipoles per volume that determines the E_T(30) value within certain composition ranges, independent of structural variations.

A kink can be seen in the correlation line E_T(30) as a function of N_av,x for methanol/water and ethanol/water mixtures in Figure 3a.The kink of this line is attributed to structure variation at N_av,x = 0.038 mol/cm³ of the methanol/water mixtures. At N_av,x = 0.0384 mol/cm³ , the methanol/water mixtures shows the largest refractive index and largest volume contraction. However, the linear plots of E_T(30) as function of N_av,x for each solvent mixture section are of excellent quality as seen by Equations (17) – (20).

E_T(30) = 181.3 N_av,x + 53.02,
n = 12 (1,2-ethanediol/water) ; r = 0.999.

(17)

E_T(30) = 341.1 D_HBD + 44,
n = 12 (1,2-ethanediol/water); r = 0.999.

(18)

E_T(30) = 342 N_av,x + 44.02,
n = 7 (methanol/water; N_av,x >0.04 ) ; r = 0.9957.

(19a)

E_T(30) = 162 N_av,x + 51,5
n = 6 (methanol/water; N_av,x < 0.04 ; r = 0.9985.

(19b)

E_T(30) = 500.7 N_av,x + 35.6,
n = 8 (ethanol/water; N_av,x > 0.04; r = 0.995.

(20a)

E_T(30) = 158.6 N_av,x + 49.27,
n = 10 (ethanol/water; N_av,x < 0.04 ); r = 0.998.

(20b)

In the literature there are various physical data on the properties of methanol/water mixtures indicating structure variation in the range between x(water) = 0.5 to 0.6; corresponding to N_av,x = 0.035 and 0.04 mol/cm³ [85-94]. This wide distribution is also confirmed by the heat of interaction as a function of composition, with the largest measured heat of about -850 kJ/mol in a range from x(water)~06 to 0.75 [80,81]. The refractive index of methanol/water mixtures reaches its maximum at x(water) = 0.6 [109-111]. The highest heat of the exothermic interaction is at x(water) = 0.6 [81, 82] (N_av,x = 0.038 mol/cm³) which is completely reflected by the DI_max of the methanol/water mixtures that is the highest at x(water) = 0.6 (see Figure 1b).

However, the overall situation with these two monohydric alcohol-water mixtures is not entirely clear. For ethanol/water mixtures, the function E_T(30) versus N_av,x shows a clear kink at exactly N_av,x = 0.04 mol/cm³ of the total number of dipoles corresponding to x(water) = 0.8. The excess molar volume for ethanol/water mixtures is at x(water) = 0.6, but the heat of interaction is highest at x(water) = 0.82 to 0.845 [81, 82]. Hence, the refractive index maximum of ethanol/water mixtures does not correpond to the thermodynamics as apparently found for methanol/water mixtures. The different courses of the methanol/water and ethanol/water mixtures composition with regard to the refractive index were also noted by Langhals [109]. For the ethanol/water mixtures, the plots E_T(30) as function of N_av,x or x(water) are clearly determined by the thermodynamics. Exactly at this composition where the greatest heat of inteaction is measured, the graphs show a kink in the line indicating the strucure alteration [5,80,81,83,88]. These correspondences between the curves in Figure 3a and the thermodynamics or refractive index show the influence of the physical properties of the mixture on E_T(30).

But there are several additional aspects to consider. Bentley [28] has shown that the volume fraction correlates better with the static dielectric constant or E_T(30) of alcohol-water mixtures compared to the mole fraction as a composition parameter of alcohol-water mixtures. The volume fraction was also recommended in a recent publication to explain the E_T(30) as a function of solvent composition more accurately than using the mole fraction [128]. Accordingly, for ethanol/water and methanol/water mixtures, the N_av,w and N_av,v quantities were calculated and empirically tested as variables for correlation with E_T(30) [62]. It seems surprising that the N_av,w and N_av,v quantities give a much better linear relationship with E_T(30) than using N_av,x when the entire composition range is considered. The methanol/water and ethanol/water mixtures fit smoothly into the series of primary alcohols if the overall data set E_T(30) of primary alcohols are considered; see Equation (21) and Equation (22) and Figure .S6 in the supplement materials part. The overall correlations including 42 data points are convincing.

E_T(30) = 313 N_av,v + 46.7,
n = 42 (methanol/water, ethanol/water and primary alcohol); r = 0.994.

(21)

E_T(30) = 304.8 N_av,w + 46.7,
n = 42 (methanol/water, ethanol/water and primary n-alcohol); r = 0.994.

(22)

There is no qualitative difference whether the function E_T(30) versus N_av,v or E_T(30) versus N_av,w is considered.

Therefore, the motivation for use the volume fraction given in [128] should be reconsidered. The mass fraction would give related results. Regardless of which alcohol/water mixture is used, the actual curve E_T(30) versus N_av,w or N_av,v is not really strictly linear, although a very good regression coefficient can be calculated for linearity. The data dots along the relationship showed a significant pattern like a string of pearls as seen in Figure S6 in the supporting materials part. This is an important detail. Thus, the subtleties observed in the correlation of E_T(30) with N_av,x do not vanish, but are merely diminished in the plots E_T(30) as function of either N_av,w or N_av,v. The approximate linearity of E_T(30) as a function of N_av,w and N_av,v is due to the stronger algorithmic consideration of the inhomogeneity of the solvent components in N_av,w or N_av,v (see Figure 1b).

These results clearly show that the discussed preferential solvation of B30 by water is meaningless for methanol/water and ethanol/water mixtures. This is also an indication that polarizablity forces and dipolar effects of the molecules of the solvent mixture act collectively upon B30. In 1963, in the first paper on phenolate betaine dyes, Dimroth and Reichardt also studied the better water soluble B1 probe in ethanol/water mixtures [1]. Data see Table S4. There is also a very good correlation of E_T(1) as function of N_av,v, as seen by Equation (23). The correlation of E_T(1) as function of N_av,x is equivalent to that of E_T(30) as function of N_av,x .

E_T(1) = 216.7 N_av,v + 57.95,
n = 10 (B1 in ethanol/water and water), r = 0.988.

(23)

If pure water is omitted from Equation (23), the correlation quality is significantly improved to r = 0.999. This is also a strong indication that B1 is preferentially enriched in ethanol/water rich domains when the mixture is investigated.

The x_b values of BM (x_b is the shift of the UV/Vis peak of BM in methanol/water) [125]) do correlate with N_av,x very well; see Equation (24).

x_b = 201.2 N_av,x + 57.8,
n = 11 (BM in methanol/water), r = 0.997.

(24)

Consequently, the preferential solvation of BM in methanol/water as assumed by Machado [26] or Tanaka [129] is not applicable when N_av,x is used instead of x(water) to evaluate solvatochromism. The methanol/water mixtures were also investigated by Taha using the Fe probe [126]. There is also a linear correlation and no bended curve for ν_max(Fe) as function of N_av,x , Equation (25).

ν_max(Fe) [10³ cm^-1] = 36.66 N_av,x + 17. 32,
n = 11 (Fe in methanol/water), r = 0.992.

(25)

It should be mentioned that for methanol/water mixtures the correlation of EP as a function of N_av,x or N _av,v are quite similar from an arithmetic point of view (unpublished).

For ethanol/water mixtures, the ν_max(Fe) shows a similar correlation with excellent quality as reported previously [43]. The correlations of ν_max(Fe) with x(water) in place with N_av,x is worse. These results clearly show that several types of negatively solvatochromic dyes such as B30, B1, BM and Fe do not indicate preferential solvation in the methanol/water and ethanol/water mixtures. Thus the linear correlations of EP parameters as function of N_av,x according to Equation (2) are clearly confirmed by other solvatochromic dyes despite the fewer data set compared to E_T(30). Since different solvatochromic probes show the same dependencies of EP as a function of N _av,x, it is quite clear that the solvent structure determines the solvatochromism and not preferential solvation of scenario ii. This is in complete agreement with older results from Langhals [5].

3.4.2. FA/Water and Related Amide/Water Mixtures

FA/water is the only binary aqueous mixing system considered in this study that fulfils the thermodynamics of ideal mixing [66,106,107]. The heat of mixing is endothermic and the entropy is positive over the entire composition range. The mixing entropy is highest at x = 0.5 [130-133]. The best linear correlations ( r approach one) of E_T(30) as function of N_avx over the entire composition range of the solvent mixture are found for FA/water, NMF/water and 1,2-ethanediol/water mixtures (see Figure 3b and Figure 4a).

Figure 4. a (left panel). Correlations of E_T(30) (kcal/mol) as function of N_av,x (mol/cm³) FA/water (yellow), NMF/water (grey), N-formylmorpholine/water (blue) and DMF/water(red) mixtures. Data see Table S2 to S5; Figure 4b (right panel). Correlations of E_T(30) (kcal/mol) as function of N_av,x (mol/cm³) for DMSO/water mixtures (red, all data); Blue dots are data from [15] (O Connor).

Figure 4. a (left panel). Correlations of E_T(30) (kcal/mol) as function of N_av,x (mol/cm³) FA/water (yellow), NMF/water (grey), N-formylmorpholine/water (blue) and DMF/water(red) mixtures. Data see Table S2 to S5; Figure 4b (right panel). Correlations of E_T(30) (kcal/mol) as function of N_av,x (mol/cm³) for DMSO/water mixtures (red, all data); Blue dots are data from [15] (O Connor).

For FA/water mixtures the linear correlations E_T(30) as function of N_av,x is of excellent quality; see Figure 4a as well as Equation (26).

E_T(30) = 229 N_av,x + 50.2,
n = 16 (FA/water); r = 0.999.

(26)

The perfect linearity can be explained by the outstanding physical properties of the FA/water mixing system [106,107,133-134]. The water like structure of FA is due to the fact that water and FA molecules can exchange positions without changing the solvent structure [134], only the V_E [Equation (8)] is hardly changed [133]. Thus, no segregation occurs and the average number of dipoles per volume determines the E_T(30) at ambient temperature perfectly. Furthermore, for NMF/water, NFM/water and DMF/water mixtures there are also excellent linear correlations of E_T(30) as function of N_av,x in the section of higher water content; x_co-solvent < 0.35 due to similar physical properties of these mixtures [107,135-137]. The physical data of the solvent mixtures NMF/water, DMF/water and NFM/water mixtures are given in Tables S2 to S5 in the supporting materials section [130-137].

E_T(30) = 212 N_av,x + 50.5,
n = 17 (NMF/water); r = 0.993.

(27)

The slight bend in the curve of lower water content is due to the nonlinear change in density as function of composition [135-137]. Thus, water is more seen as a solute rather than solvent in accordance to [75] when N_av,x < 0.035 mol/cm³. However, an excellent linear correlation of the refractive index as a function of N_av,x,CH is seen for all mixtures (see Figure 2a) over the entire composition range, including the range of low water concentrations.

3.4.3. DMSO/Water Mixture

The DMSO-water mixtures are a challenge in terms of physics among binary aqueous solvent systems due to the unclear themodynamics at higher DMSO content [138-146]. It was therefore chosen for this fundamental work as educational illustration. There is a great deal of physical studies on this mixtures, so only those that are relevant to explaining solvatochromism in relation to N_av,x will be referred to. The following analysis will show where the problems lie. There results a very good linear correlation of E_T(30) with N_av,x including E_T(30) data from several references, Equation (28) and Figure 4b.

E_T(30) = 432 N_av,x + 39.7,
n = 22 (DMSO/water) r = 0.993.

(28)

Despite the overall correlation E_T(30) with N_av,x seems convincing due to the clear linearity, there is a small kink in the linear plot at N_av,x ≈ 0.025 to 0.03 mol/cm³. If only the data from [14] were considered, see equations (29a) and (29b).

E_T(30) = 414 N_av,x + 40.7,
n = 9 (DMSO/water rich; N_av,x > 0.02); r = 0.998.

(29a)

E_T(30) = 624 N_av,x + 36.2,
n = 5 (DMSO/water low; N_av,x < 0.02) ; r = 0.999.

(29b)

This small effect has a significant physical background because the density of the system changes significantly at this composition [138,140]. However, the density measurements in the DMSO-rich region reported in literature are not consistent. In the water-rich section from N_av,x < 0.05541 mol/cm³ (pure water) to N_av,x = 0.03 mol/cm³ the density of water/DMSO mixtures decreases linearly with increasing water content. The density behaves nearly constant in the section of high DMSO content from N_avx = 0.03 (60% weight DMSO) to 0.014 mol/cm³ (pure DMSO) (see Table S9). In [140] was reported that density even slightly decreases; but this has no real influence on the data evaluation regarding the interpretation of the E_T(30) values in terms of N_{av,x .} Note, exactly at this mixture composition N_av,x = 0.028 mol/cm³ the plot E_T(30) as function of N_av,x has a slight, imperceptible kink.

However, the correlation of the UV/Vis absorption energy of cis-dicyano-bis(1,10-phenanthroline)-iron II (Fe) [ ν_max10^-3 cm^-1 (Fe)] [126] as function of N_av,x for DMSO/water mixtures clearly shows a linear dependence, see Equation (30).

ν_max10^-3 cm^-1 (Fe) = 67.7 N_av,x + 15.8,
n = 12 (DMSO/water), r = 0.996.

(30)

In the literature, there are several investigations on the DMSO/water mixtures using different solvatochromic probes [12,15,147-149]. Regardless of the type of probe used, it can be clearly stated that at N_av,x ≈ 0.03 mol/cm³ a slight change in the course of the parameters as function of composition is observed. Thus, the physical structural change of the DMSO/water system determines the empirical parameter and not artificially constructed acid-base properties of the solvent system [147,149]. This result is in complete agreement with the prediction in the introduction that no differences should occur in case ii. when different probes are used. For reasons of space, the analyses of the Kamlet-Taft (KAT) parameters of DMSO/water [147] are presented in the Figure S6 in the supporting information part. As consequence of this result, the determination of individual empirical polarity parameters in terms of the KAT or Catalán scale is meaningless for DMSO/water mixtures. Furthermore, a curved function of the E_T(30) value of the solvatochromic probe on x(water) of DMSO/water mixtures is found [see (Figure 5) of [12]] that would become linear if the x(water) would be replaced by N_av,x.

The change in the course of solvatochromic parameter after KAT at N_av,x about 0.03 mol/cm³ is clearly attributed to physical changes in the solvent structure. Furthermore, if one plot the static dielectric constant (ε_r ) as function of N_av,x the kink at N_av,x at 0.03 mol/cm³ becomes also obvious (see Figure S7). The ε_r data are from [143]. This feature is also shown in the plot of E_T(30) as a function of ε_r (Figure S8) or ${\mathrm{n}}_{\mathrm{D}}^{20}$   (Figure 2b). While the correlation of ${\mathrm{n}}_{\mathrm{D}}^{20}$   as a function of N_av,CH is nearly linear (Figure 2a), the correlation of E_T(30) as function of ${\mathrm{n}}_{\mathrm{D}}^{20}$   shows a slight kink corresponding to N_av,x = 0.03 (see Figure S2).

As resume to the DMSO/water mixtures, the overall comcentration of dipoles (water + DMSO) of the system determines the solvatochromic property and not preferential solvation. This is a clear result. Surprising is actually only the quite good linearity of the function E_T(30) against N_av,x when many data from the literature are used together. This shows that B30 is not very sensitive to physical changes in the DMSO/water system at RT. Therefore, the solvatochromic method is not well suited to detect the physical change in the liquid structure of DMSO/water at distinct composition.

What is the reason for the good linearity of E_T(30) as a function of N_av,x although larger structural changes of the mixture occur at N_av,x = 0.03 mol/cm³? The complexity of water dynamics of DMSO/water mixtures was profoundly studied by ultrafast IR-experiments and dielectric spectroscopy [141-143]. These results are very important to partly explain the results of the correlations in this study. The average lifetime of the water bonded DMSO is changed (decreases) nearly linearly with the mole fraction of water which is consistent that E_T(30) nearly linearly increases with water content (see also Figure 5 in [141]). This explains why the barely perceptible kink in the correlation may negligible, because the water dynamics overcome the local structuring around the dye solute. Thus, the water−water component lifetime is independent of water concentration in the section of high DMSO content N_av,x < 0.03 mol/cm³. Obviously, there are neither water/DMSO nor B30/water complexes relevant for the determination of E_T(30) as the solvent mixture has a high dynamic at 298 K [142,143]. Thus, despite DMSO/water or B30/water complexes are present, they cannot be recognized by B30 because of the fast dynamics of the binary solvent system. The situation is similar to other solvatochromic dyes as seen in Figure S9.

Therefore, other physical measurements such as dielectric spectroscopy are more suitable than solvatochromic probe molecules for analysing the structure of DMSO/water mixtures. The outstanding behavior of the DMSO/water mixtures at higher DMSO content N_av,x < 0.028 mol/cm³ was the subject of numerous simulation experiments [144-146]. Obviously, the behavior at N_av,x < 0.03 mol/cm³ is attributed to the entropy increase of the system, which can still hardly be understood theoretically [146], because the experimentally determined heat of interaction is exothermic over the entire composition range. In a further work we want to take up the DMSO/water system again, because it provides some very concise method-dependent result series, which are to be evaluated in depth with regard to composition quantities (see also discussion).

3.4.4. 1,4-Dioxane/Water Mixtures

The 1,4-dioxane-water mixtures were also subjected to numerous physical investigations [150-161]. Dependencies of UV/Vis-absorption energy maxima of solvatochromic dyes such as B30, Fe, different 7-N,N-diethylaminocoumarins, M540 or harmaline as function of dioxane-water composition were extensively studied in literature [2,5,69,126,157-161].

The thermodynamics of the binary system 1,4-dioxane/water is characterised by the transition from exothermic heat of mixing to endothermic heat of mixing with increasing 1,4-dioxane content [150]. This is the decisive contrast to the DMSO/water system. Heat of interaction Δ_rH is exothermic and has its mostly exothermic heat at about x(water) = 0.8 (yellow dot in Figure 5b) corresponding to N_av,x = 0.032 mol/cm³; N_av,v = 0.018 mol/cm^3.. The largest partial molar volume of water in 1,4-dioxane/water mixtures is at x = 0.8 [151]. Δ_rH is zero at x(water) = 0.52 (N_av,x = 0.02 mol/cm³). With this composition, the mixture has the highest density and the lowest -TΔS value. At x(water) < 0.52, the heat of interaction becomes endothermic.

For the evaluation in this work, the volume fractions of the 1,4-dioxane/water solvent mixtures given in [2] were re-converted to the average molar concentration of the solvent dipoles. Unfortunately, the extensive data set from [6] could not be used because the specific E_T(30) data were not documented in tabular form. Fortunately, there is an excellent agreement between the E_T(30) data of four different literature sources as shown in Table S7. The E_T(30) data from these four different sources fit perfectly in one relationship. To evaluate the influence of the inhomogeneity of the mixture in terms of composition, we have plotted E_T(30) as function of N_av,x and N_av,v as well as x(water) (Figure 5a and 5b).

The correlation of E_T(30)as function of N_av,x results in two consecutive linear lines with a kink at Nav,x = 0.015 [x(water) = 0.3] mol/cm³; see Equation (31a) and (31b) and Figure 5a. At this composition, there is also the strongest curvature (at E_T(30) ~ 46 kcal/mol) in the curve E_T(30) as function of x(water) in the 1,4-dioxane-rich section (see Figure 5b).

E_T(30) = 2997.5 N_av,x + 2.123
r = 0.944, n= 7 (N_av,x < 0.02 mol/cm³, 1,4-dioxane rich section)

(31a)

E_T(30) = 398,8 N_av,x + 40.42
r = 0.997, n= 12 (N_av,x > 0.02 mol/cm^3, water rich section)

(31b)

The kink in the grey/red-dot curve (Figure 5a) approach approximately that composition N_av,x = 0.02 mol/cm³ at which the mixture behaves athermic Δ_rH_mixing = 0. A similar result is found for the correlation of ν_max10^-3 cm^-1 (Fe) as function of N_av,x . There is a bend in the curve. However, there are too few data in the dioxane-rich section to make a clear statement. The correlation of E_T(30) as a function of N_av,v (blue dots in Figure 5a) gives an asymptotic curve without linearity of special sections.

Water and 1,4-dioxane are subject to fine structuring over the entire composition range, in which both types of molecule are always involved [153-156]. The volumetric structure of 1,4-dioxane/water mixtures changes significantly in the section from N_av,x < 0.02 mol/cm³. Acccordingly, the strongest bend in the graph correponds to that composition where the significant change in the volumetric structure of the 1,4-dioxane/water mixtures takes place. Exactly at E_T(30) = 47 kcal/mol (N_av,x = 0.018 mol/cm³) the dielectric relaxation time τ1 passes through a mximum ( τ1 ≈ 25 ps) for 1,4-dioxane/water mixtures [154]. The use of N_av,X(water) after Equation (9) as a mixture composition parameter gives a similar diagram pattern as when N_av,x is used, indicating that 1,4-dioxane and water are always involved together in the volumetric structure and thus in the solvation of dissolved B30. Thus, 1,4-dioxane does not enhance the water structure in any way, which is in complete agreement with the Marcus classification [107].

It is worth analysing the correlations of E_T(30) as a function of x(water) from the point of view of thermodynamics and the structural change of the dioxane-water mixture, as shown in Figure 5b.At x(water) = 0.52 (N_av,x = 0.02 mol/cm³ ) the curve E_T(30) as a function of x(water) shows an inflection point (not marked in Figure 5b). Exactly at this composition this binary solvent system behaves a-thermal, i.e. Δ_rH_mixing = 0 and has the largest excess molar volume [150,151]. The strong curvature E_T(30) as function of x(water) = 0.8, (yellow marked) (N_av,v = 0.015 mol/cm³ ) is clearly due to the inherent mass inhomogeneity of the mixture, as shown in the simultaneous graph for the DI (Figure 5b). At this composition the mixture has the highest exothermic heat. This result is consistent to the results from the thermodynamics of methanol/water and ethanol/water mixture. These results are good indications that x(water) reflects the thermodynamics of the mixture in relation to other measurands more comprehensive than the N_av,x quantity, which is physically reasonable. Thus, the S-shaped function E_T(30) versus x(water) (Figure 5b, red dots) is attributed to the change in interaction heat as function of composition. This feature is only partly recognized when N_av,x is used as composition size as seen in Figure 5a. There is no bend or kink in the plot E_T(30) as function of N_av,x at N_av,x ~ 0.032 mol/cm³ (largest exothermic heat) but at N_av,x = 0.02 mol/cm³ (zero heat).

The linear function of E_T(30) as function of N_av,x in the water-rich section N_av,x > 0.02 mol/cm³ is due to the fact that the average concentration of both the water dipoles and 1,4-dioxane molecules determines the E_T(30) value. Both fractions are permanently intermixed and show no segregation [154,155]. Somewhat below this threshold at N_av,x = 0.018 mol/cm³ , a clear kink in the curve E_T(30) as a function of N_av,x can be seen. The larger E_T(30) in the dioxane rich fraction, compared to an hypothetical linear plot E_T(30) versus N_av,x, , can be readily explained by results of Buchner: “This indicates a largely microheterogeneous structure for such mixtures, with the presence of water-rich domains of significant size in the dioxane-rich fraction”[155]. Thus, B30 preferentially measures the water-enriched sections of 1,4-dioxane/water domains within the composition spectrum. Obviously, the water clusters are solvated by 1,4-dioxane excess and the B30 is enriched in the 1,4-dioxane clusters below N_av,x <0.015 mol/cm³.

The refractive index as function of composition of the 1,4-dioxane/mixture with respect to N_av,xCH (see Figure 2a, red dots) and Equation (15) results in a linear plot. This is in line with the fact that the static dielectric constant εr is also a linear function of N_av,x including the pure 1,4-dioxane (see Figure S8b). For this examination the composition data x(water) from [154] were converted to N_av,x. However, in contrast, the correlation of E_T(30) as function of ε_r or ${\mathrm{n}}_{\mathrm{D}}^{20}$   is not linear over the entire composition range due to the pure 1,4-dioxane or the 1,4-dioxane-rich fraction does not linearly fit; see Figure S8a. As consequence the B30 probe reflects the volumetric structure of 1,4-dioxane/water differently compared to volumetric physical polarity-related measurements as dielectric spectroscopy or refraction index.

In summary, the 1,4-dioxane/water system presents a challenge with regard to the formation of solvent structures as a function of the quantitative composition, since different physical methods (UV/vis spectroscopy of B30, dielectric spectroscopy, refractive index, calorimetry) register different dependencies of the measurand on the different composition sizes. Note that only x and N_av,x are physically reasoned quantities that relate to thermodynamic and UV/Vis-spectroscopic quantities, respectively. Despite this concern, in summary, the complex dependence of E_T(30) on the 1,4-dioxane/water composition in terms of N_av,x, N_av,xv or x(water) can be interpreted readily using the results of binary solvent system physics and mixture inhomogeneity, in which thermodynamics, concentration of dipoles and solvent dynamics play a role. Despite this reluctance, it can be clearly stated that the specific solvation of B30 by HBD solvent molecules is not responsible for that UV/Vis shift. The E_T(30) value is mainly determined by the concentration of the water dipoles, which are permanently intermixt by 1,4-dioxane molecules.

3.4.5. 2-Propanol/Water and 2-methyl-2-propanol/Water Mixtures

In this chapter, the mixtures 2-propanol/water and 2-methyl-2-propanol/water mixtures are considered, which show a change in the heat with increasing alcohol content in the sense of a reversal from exothermic to endothermic heat [81,82] similar to the 1,4-dioxane/water system [150]. Especially, the 2-methyl-2-propanol/water mixtures have been the subject of research and speculative interpretations during the last decades [162-171]. A mystical character was attributed to this special mixture because of the method-dependent results of the mixture [171].

At first the correlations of E_T(30) as function of N_av,x and x(water) will be discussed; Figure (6a) and (6b).

The representation of E_T(30) as a function of mole fraction x(water) shows qualitatively similar courses for all mixtures. These graphics are presented in the Figure S10 in the supporting information section. Comparing the curves E_T(30) with that of the inhomogeneity (DI) of the solvent mixture both as a function of x(water), see Figure 3b and Figure 6b, the same result is recognized for 2-propanol/water and 2-methyl-2-propanol mixtures compared to methanol/water, ethanol/water, and 1,4-dioxane/water mixtures. The strongest bending of the plot E_T(30) versus x(water) always occurs immediately after the greatest inhomogeneity. This "immediately after" corresponds to about 1.5 kcal/mol with respect to E_T(30) which is illustrated by the horizontal lines (grey and green dots) between the two curves as seen in Figure 6b. This scenario holds for all M_av,w/M_av,x, plots regardless of the type of alcohol/water mixture. Only with methanol/water mixtures is the composition range not so sharply defined.

The curves E_T(30) as a function of N_av,x for methanol/water, ethanol/water, 2-propanol/water and 2-methyl-2-propanol/water mixtures differ qualitatively for both methanol/water and ethanol/water mixtures compared to 2-propanol/water and 2-methyl-2-propanol /water mixtures in the section of low water content. Hence, the graphs E_T(30) as function of N_av,x show an inflection points; at about 0.031 mol/cm³ and 0.0273 mol/cm³, for 2-propanol/water and 2-methyl-2-propanol/water mixtures, respectively. At lower water concentration, the binary solvent systems 2-propanol/water (x(water) < 0.5; N_av,x = 0.02 mol/cm³) and 2-methyl-2-propanol mixtures (x (water) < 0.55; N_avx = 0.018 mol/cm³) are endothermic in terms of mixing interaction heat. At about x = 0.65 to x = 0.5 (water) (N_av,x ≈ 0.03, see Figure 6a) both systems behave a-thermic; i.e ΔH_mixing = 0. Exactly at this composition, the curve E_T(30) as a function of N_av,x (see Figure 6a) shows an inflection point. Same result is found for the 1,4-dioxane/water mixtures (see Figure 5b). This indicates the change in water structure and its influence in the solvation mechanism of the B30 probe. In the endothermic range, both curves E_T(30) versus N_av,x show higher E_T(30) than expected from linearity. In this section, the mixing entropy is positive and the water portion in the mixture obviously determines the E_T(30) more than in the water-rich section. The dielectric relaxation time clearly decreases from lower to higher water content, i.e. in the water-poor section a more temporally stable structure is present than in the water-rich section. This is an important detail that is also observed for other related solvent systems which show endothermic mixing heat in the composition section of the non-aqueous component at x(co-solvent) > 0.5 such as acetone/water or acetonitrile/water mixtures to be published later.

The Fe complex was also studied in 2-propanol/water mixtures. In accordance with the correlations of E_T(30) versus N_av,x, the plot ν_max (Fe) as function of N_av,x (see Figure S11) also shows a related pattern as that of Figure 6a indicating the influence of the physical structure of the solvent as function of composition similar as for B30.

Furthermore, there are numerous studies using positive solvatochromic probes such as Nile red [7], 4-nitroaniline, [18], 4-nitroanisole, [18] 4-(1-azetidinyl) benzonitrile [170] or coumarin 343 and 480 [171] in various alcohol/water mixtures. The profound analyses of the results of positive solvatochroomic dyes in methanol/water, ethanol/water, 2-propanol/water, and 2-methyl-2-propanol/water mixtures will be reported in a later publication.. As preview, these analyses support the conclusions of this study but underline that the solvation thermodynamics is dependent on the probe used especially in the water rich section [172-174].

While 2-propanol/water and 2-methyl-2-propanol/water mixtures show similar pattern E_T(30) as function of N_av,x, the 2-butoxyethanol/water mixtures behaves differently due to hydrophobic solvation which will be discussed in the final chapter..

3.4.6. 2-Butoxyethanol/Water Mixtures

As a final example, the solvatochromism of B30 in 2-butoxyethanol (BE)/water mixtures will be re-analysed; the E_T(30) data are from reference [7]. BE itself is partially hydrophobic, but mixes completely with water at room temperature [175]. At higher temperatures, however, segregation occurs. The BE-water mixtures have been the subject of numerous physical investigations due to its self-structuring properties [176-185]. The self-propelled agglomeration of the BE molecules in water has been proven by various scattering methods [176,177]. At x(BE) > 0.02 agglomeration begins to occur resulting in an inhomogeneous solvent mixture at the level at about 1 nm [176]. However, other studies showed that 130 nm aggregates are present [177]. The inhomogeneity of the BE/water mixing system is complicated by the fact that this feature can be observed on different length and time scales [180-183,185].

The BE/water and 2-methyl-2-propanol/water mixtures are often compared with regard to their similarity [185]. We will demonstrate that the two solvent mixtures are completely different in spite of the discussion in literature. The microstructures of both solvent mixtures are very subtle and are strongly influenced by the composition in the water rich section. However, the heat of mixing is exothermic nearly over the entire composition range for BE/water mixtures, but weakly endothermic at high BE (ca 95 wt %) concentration [179,180]. Furthermore, photo-switchable spiro compounds were measured in BE/water mixtures [184]. It was suspected that the solvent structure of BE/water is affected by this type of photo-switching. Thus, one cannot exclude the possibility that the dissolved probe molecule co-determines the fine structure of BE/water mixtures which make the whole situation complicated. Therefore, only the analysis of the E_T(30) values is discussed here. Unfortunately, the interesting solvatochromic results of El Seoud on this solvent system were not given as original data [22]. If one plots E_T(30) as function of N_{av,x ,} for BE/water mixtures an asymmetric course results as seen in Figure 7a (grey dots).

The crucial section of low BE content serves special attention, (N_av,x = 0,0497 mol/cm³) (grey dot line); x(BE) ≈ 0.02) or N_av,xCH = 0,015 mol/cm³, as aggregate formation of the BE molecules takes place at this composition [176] and B30 dye is obviously absorbed by these BE-rich agglomerates leading to an abrupt decrease in E_T(30) at N_av,x ≈ 0.05 mol/cm³. This is consistent with the fact that E_T(30) decreases abruptly with increasing C-H concentration due to the BE component at N_av,CH = 0.017 mol/cm³ (not shown). There is only a narrow transition.

This result exactly fulfils scenario i. mentioned in the introduction. The agglomeration of BE is driven by hydrophobic interaction, as additionally suggested by the analysis of the fluorescence of coumarin and related probe molecules in BE/water mixtures [185,186]. Obviously, the trapping of probes is also determined by the solvent cage proerty of the BE/water mixtures. This is in contrast to 2-methyl-2-propanol/water mixtures, where strong thermal fluctuations in partial concentration occur [187]. Thus, a true hydrophobic solvation of B30 does not take place in 2-methyl-2-propanol/water mixtures, instead the partial water structures are changed depending on the composition as discussed in the previous chapter [187,188].

The two binary solvent mixtures glycerol/water and ethanediol/water show a perfect mixing behaviour in the sense of the Marcus classification, so that there is no enhancement of the water structure in any way [88,106]. These two mixtures are documented in Figure 7b as references. For glycerol/water and 1,2-ethanediol/water mixtures perfect linear correlations of ${\mathrm{n}}_{\mathrm{D}}^{20}$   as function of N_avx,CH result; see Equation (32) and (33) [88,189]. The same holds for the correlation of the static dielectric constant as function of N_av,x for glycerol/water (unpublished).

$$\begin{gathered} {\mathrm{n}}_{\mathrm{D}}^{20}=2.062N_{\mathrm{avx},\mathrm{CH}}+1.335 \\ \mathrm{n}=12(\mathrm{glycerol}/\mathrm{water}); \mathrm{r}=0.9999 \end{gathered}$$

(32)

$$\begin{gathered} {\mathrm{n}}_{\mathrm{D}}^{20}=1.381N_{\mathrm{avx},\mathrm{CH}}+1.333 \\ \mathrm{n}=14(\mathrm{1,2-ethanediol}/\mathrm{water}); \mathrm{r}=0.997 \end{gathered}$$

(33)

The larger slopes of Δ${\mathrm{n}}_{\mathrm{D}}^{20}$/ ΔN_avx,CH for glycerol/water and 1,2-ethanediol/water mixtures compared to BE/water mixtures are attributed to the influence of the polarizability of the hydrogen bond network and the higher refraction of the C-O bond compared to C-H [60,62,105]. This aspect is important for sugars and polyhydric alcohols, as will be documented in a later article.

The change in the overall bulck solvent structure of 2-methyl-2-propanol/water mixtures as function of composition is also clearly visible in the plot of the refractive index as function of N_av,CH (yellow dot line in Figure 2b and Figure 7b) that shows a kink at about 0.035 to 0.04 mol/cm³. Remarkably, the kink in the graph E_T(30) as function of N_av,x is also obsevved at this composition; see Figure 6a. In this concentration range the thermodynamic changes from exothermic to endothermic with increasing N_av,CH for 2-methy-2-propanol/water mixtures. This thermodynamic scenario does not apply to BE/water mixtures [179,180].

Remarkably, the correlation of ${\mathrm{n}}_{\mathrm{D}}^{20}$   as function of Na_v,CH for BE/water mixtures is linear over the whole composition range; see Equation (34) and Figure 7b (grey dot line).

$$\begin{gathered} {\mathrm{n}}_{\mathrm{D}}^{20}=0.876N_{\mathrm{avx},\mathrm{CH}}+1.353 \\ \mathrm{n}=11(\mathrm{BE}/\mathrm{water}); \mathrm{r}=0.998 \end{gathered}$$

(34)

Obviously, BE as a co-solvent does not enhance the water structure, but water enhances the BE structure. That is the special thing. According to the Marcus classification, this is the inverse scenario regarding enhancement of solvent structures. These considerations convincingly show the qualitative differences between BE/water and 2-methyl-2-propanol/water mixtures. The different solvation behavior of B30 in BE/water mixtures compared to 2-methyl-2-propanol/water mixtures can also be supported by considering the DI from Equation (6b). The BE/water mixtures show the greatest inhomogeneity with respect to DI at x(water) = 0.85 (N_av,x = 0.029 mol/cm³), while the kink in the curve E_T(30) as a function of N_av,x occurs well away from this at ≈ 0.045 mol/cm³. This is the crucial difference of BE/water mixtures compared to all other (monohydric) alcohol/water mixtures investigated in this work. Therefore, this result could be used as criterion to define preferential solvation scenario of case i. However, the results do not exclude that the B30 dye itself has an influence on the solvent cage of the BE/water mixture at low BE content, as mentioned in the references [184 ,185] for other solutes.

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