How the Concept of Solvent Polarity Investigated with Solvatochromic Probes Helps Studying Intermolecular Interactions

Abstract

Intermolecular interactions form the basis of the properties of solvents, such as their polarity, and are of central importance for chemistry; such interactions are widely discussed. Solvent effects were reported on the basis of various polarity probes with the E_T(30) polarity scale of Dimroth and Reichardt being of special interest because of its sensitivity, precise measurability and other advantages, and has been used for the investigation of solvent interactions. A two-parameter equation for the concentration dependence of medium effects has been developed, providing insights into structural changes in liquid phases. Moving from condensed gases to binary solvent mixtures, where the property of one solvent can be continuously transformed to the other, it was shown how the polarity of a solvent can be composed from the effect of polar functional groups and other structural elements that form the matrix. Thermochromism was discussed as well as the effect of very long-range interactions. Practical applications were demonstrated.

1. Introduction

Most chemical syntheses were carried out in the liquid phases [1] where the average distances between molecules are small [2]. Noncovalent intermolecular interactions [3] are important in such condensed phases; they dominate the properties of chemical materials, and will subsequently be analyzed below. Adjusting the pressure of gases is a useful method for setting intermolecular distances and allows the systematic study of such effects.

2. General Intermolecular Interactions

The impact of a molecular chemical material such as the pressure p of gases depends on the numbers of particles in a volume, more conveniently indicated by the molar concentration c. Starting from highly diluted gases with essentially independent particles, the impact p is expected to be proportional to the concentration c giving the differential Equation (1).

dp = const₁·dc

(1)

As the concentration increases, the impact is changed more and more due to interactions of the particles, and the changes are expected to increase with the concentration of particles. Inverse proportionality implies a basic approach leading to the differential Equation (2), where the constant E stands for the energetic effect of c on p.

dp = E/c·dc

(2)

Multiplying Equation (2) by c and dividing by the scaling factor c* for the discrimination between the two extrema of Equations (1) and (2) and adjusting the dimensions yields Equation (3), where c = 0 can be included (E/c* = const₂).

c/c*·dp = const₂·dc

(3)

The differential Equation (4) results from the addition of Equations (1) and (3) and the subsequent separation [4] of the variables p and c.

$$dp=\frac{{const}_2}{\left(\frac{c}{c*}+1\right)} dc$$

(4)

Finally, Equation (5) is obtained by the integration of Equation (4) with the integration constant p_o; the latter is zero for diluted gases because the pressure p vanishes for infinite dilution of gases.

$$p=E·\ln \left(\frac{c}{c*}+1\right)+p_o$$

(5)

Equation (5) ends up in the ideal gas equation for diluted gases by a Taylor series expansion and truncation after the linear term forming Equation (6), where c << c* and the concentration c is the number of moles n over the volume V.

$$p\approx \frac{E}{\left(c+c*\right)} · c \approx \frac{E}{c*} · c=\frac{E n}{c* V}$$

(6)

Thus, the ideal gas equation (7) is obtained with R·T = E/c*.

$$p·V\approx n · \frac{E}{c*}=n · R·T$$

(7)

Equation (5) is an exact description [5] of the concentration dependence of the pressure of gases such as is shown for the precisely measured isotherms by Michels and Michels [6]. A typical linear correlation (performance of target to actual comparison) according to Equation (5) is shown in Figure 1 (a high accuracy of the linear correlation is achieved where deviations from experimental data are within 10 to about 20 ppm).

When the CO₂ concentration c exceeds a threshold value c_k(I-II) of 3.1 mol·L⁻¹, the dependence on the pressure in the low concentration region I changes abruptly to reach the concentration region II (see Figure 2). Equation (5) is also valid for region II, but with different parameters E and c*, and p_o is different from 0.

$$p=p_o·e^{E ·c}+p^{*}$$

(8)

At even higher pressure, when c exceeds c_k(II-III) of 10 mol·L⁻¹ the region III is reached. There, an exponential increase in p with concentration c was found and can be described by Equation (8) where p* means a base pressure.

This more generally observed behavior of gases was interpreted in terms of structural changes in the medium; such effects are also considered to be fundamentally important for non-covalent interactions in solvent effects and will be more differentiated. The concentration c_k(I-II) for the transition from region I to region II of about 3.1 mol·L⁻¹ corresponds to an edge length of 8.1 Å of a cube for one molecule, with mean intermolecular distance of 4.5 Å because of the statistical molecular movement [2]. This means about twice the molecular length between the nuclei of oxygen of 2.3 Å [10]. The concentration c_k(II-III) for the transition from region II to region III of about 10 mol·L⁻¹ corresponds cube lengths of 5.5 Å and a mean intermolecular distance of 3.0 Å, not far away from the molecular dimensions and the intermolecular distance of 2.76 Å between the oxygen atoms in solid CO₂. There is a minimal restriction of the molecular motion in the region I, with a comparably abrupt change to permanent molecular contacts in region II. Finally, when c_k(II-III) is exceeded, the molecules are essentially densely packed, with further increases in concentration and density, respectively, is restricted by the prevailing effects of molecular compressibility, causing an exponential increase in pressure. The formation of the liquid phase is observed in region II. This may be due to limited miscibility of densely packed molecular aggregates with loosely packed assemblies. The surface tension between such structures is responsible for the formation of two phases, becomes smaller with an increasing temperature, and with lowering the range of two phases, and finally vanishes at the critical point [11] at 31.0 °C for carbon dioxide.

Further information can be obtained from the temperature dependence of the parameters of Equation (5). The values of E and c* in region I increase monotonically and smoothly with temperature T (see Figure 3), while in region II a slight increase is observed at lower temperatures, rising rapidly between 70 and 120 °C and increasing again slightly when this range is exceeded (this behavior is clearly observed, even being appreciable above the critical point of 31.0 °C). The influence of the temperature is interpreted in terms of region I essentially being dominated by isolated molecules, whereas region II has a complex dynamic arrangement of isolated molecules and aggregates. As a result, two phases formed at low temperatures due to their limited miscibility which at higher temperatures cause the rapid change in parameters shown in the inset of Figure 3, for which thermally induced dissociation of such aggregates is held responsible; the latter resembles the melting of clusters. Such assemblies are important for solvent effects and will be further discussed below.

3. General Solvent Effects

Condensed phases are widely used as media in chemistry and technology. Liquid phases are not only obviously used as solvents for an easier and more efficient handling of dissolved solids and to disperse them until the molecular level, but are also capable of interacting with substrates and imparting new properties through solvation. For example, the handling of the ethyl anion is very difficult in the gas phase because of the strongly exothermic tendency to lose one electron to form the ethyl radical [12,13]; on the other hand, a complexed and solvated ethyl anion such as the ethyl Grignard reagent [14] in ether is fully stable and applied in routine preparative chemistry. Moreover, an appreciable influence of solvents on the rate of chemical reactions was found, documented early on by Berthelot [15] in esterification reactions. More extended investigations [16] were made by Menschutkin, who studied the quarternization [17,18] of triethylamine [19]; he not only found a considerable influence of the solvent on the reaction rate, but also noted strong effects due to the ions involved. The polarity of a medium seemed to be of central importance. Menschutkin’s system was not ideal for the general study of solvent effects on chemical reaction rates because the effects involve both the electrophilic substrate for nucleophilic substitution reactions and the nucleophile itself; the separation of individual effects becomes difficult. Clausius Mossotti [20] and Kirkwood [21,22] took a physical approach to solvent effects using the relative dielectric permittivity (dielectric constant ε_r) as the fundamental physical property of a medium in which the solute occupies a spherical or more ellipsoidal volume in the homogenous solvent. The local electric field of the solute causes a polarization of the medium with pronounced effects of charged particles. Debye [23,24] described two extrema of polarization, the orientation polarization where the positions of atomic nuclei are altered, and the shift polarization when charge separation is induced by displacement of electrons only. Orientation polarization dominates in media consisting of sufficiently large dipoles and can be determined using the static permittivity or at low frequencies compared with the correlation time of molecular orientation; the Clausius–Mossotti function (Figure 4) was derived (solute occupies a spherical volume) to describe the effect proportional to (ε_r − 1)/(ε_r + 2). Higher frequencies as in the optical range are useful for determining shift polarization because the comparably heavy atomic nuclei can no more follow an external field; the index of refraction is a measure of this because it is quadratic with permittivity at such high frequencies [25]. However, the index of refraction is a complex number where the imaginary part concerns the optical absorption of the material. In general, solvents are colorless and thus transparent in the visible range, with absorption bands only in the UV and NIR causing anomalous dispersion there. As a consequence, the center of the visible range is far away from such interference and particular suitable for obtaining the real part of the index of refraction. The sodium D emission line at 589 nm was a versatile light source for the determination of the refractive index and proved to be a good choice because it is located approximately in the middle of the visible range, far from the absorption bands mentioned above. The polarization polarity is calculated from the index of refraction n at the wavelengths of the D line by the Lorentz–Lorenz function [25] (n² − 1)/(n² + 2).

According to the Debye function, solvent polarity by orientation (named dipolarity for short) and by displacement polarization (named polarizability for short) were discussed individually. The use of the relative dielectric permittivity (dielectric constant ε_r; see Figure 4, left) to describe the dipolarity of solvents [26] is not consistent with general chemical experience because of the rapid saturation at which 90% of the effect is achieved for ε_r = 28 (this is even worse in models for ellipsoidal occupancies). Moreover, the appreciable and chemically important difference in chemical solvent polarity between methanol and water is barely reflected in the model, and solvents such as N-methylformamide (ε_r = 182) and N-methylacetamide (ε_r = 191) would be incorrectly estimated to be even appreciably more polar than water (ε_r = 78). The Lorentz–Lorenz [27] function [28] in Figure 4, right, indicates a comparably narrow range of n_D values relevant for solvents most commonly used in preparative chemistry, between the lower limit given by polar water (n_D = 1.33) and the highly polarizable carbon disulfide (n_D = 1.62). The upper limit is given by the rarely used solvent diiodomethane (n_D = 1.74). Again, water is estimated to be less polar than N-methylacetamide (n_D = 1.43). Linear combinations between functions of ε_r and n_D did not yield substantial improvement [29,30,31,32,33]. Finally, a theory of dipole swarms was developed [34] but is limited to minor polar solvents. The mentioned discrepancies may be caused by the fact that a macroscopic volume property of a medium is characterization by permittivity, while chemical reactions and solvation are determined by microscopic, molecular effects.

1	2

lg (k/k_80E) = m·Y

(9)

Significant progress was made by using the solvolysis of tert-butyl chloride, compound 1, as a molecular polarity probe by Grunwald, Winstein, and Jones [35,36,37]. The logarithm of the rate constant k of the unimolecular ionization (S_N1 reaction) of an alkyl halide over the rate constant k_80E of the reference reaction of solvolysis of tert-butylchloride, compound 1, in 80% ethanol/water (80E) was set to the product of m as the reaction-characterizing parameter and Y as the solvent-characterizing parameter in Equation (9). This linear free energy relationship (LFE) [38] is equivalent to Hammett’s equation [39] for substituent effects. By definition, m becomes one for the solvolysis of tert-butylchloride (1) and Y becomes zero for the reference 80% ethanol/water (80E). The Y values for solvent polarity correspond well to chemical experience, but the polarity scale is not universal being limited to sufficiently strong ionizing solvents such as alcohols and mixtures of alcohols and water. Substrates more complex than 1 can lead to deviations [40].

Z = 28,591 [nm·kcal·mol⁻¹]/λ_max

(10)

Kosower introduced [41] the more universal solvatochromic polarity probe 2 in which ionization to generate charge was replaced by the reverse process, the loss of charge by an optically induced charge transfer (see Figure 5). Solvation affects the polar ground state of salt 2 and lowers its energy, while the electrically neutral electronically excited state is only slightly affected by solvent effects, due to the lost charge. The molar energy of electronic excitation of the maximum (λ_max) of the CT band of 2 is obtained by Equation (10) and was defined as the Z polarity scale; the dimension is not given in SI units because of the more convenient kcal/mol at the period of publications and is also retained here for polarity scales to avoid confusion (the energy has to be multiplied by 4.184 kJ·kcal⁻¹ to obtain SI units).

The Z scale exhibits a linear correlation with the Y scale for various solvents (see inset of Figure 6). This LFE indicates that the same effect is described. The Z-scale brought about an appreciable progress because it is not limited to strongly ionizing solvents (see open circles in Figure 6), but can be extended to solvents with lower polarity (see filled circles in Figure 6). However, polarity probe 2 is still not optimal because (i) the solubility in low-polarity solvents such as hydrocarbons is very low and impedes experimental work, (ii) the CT band is in the hypsochromic visible region and is shifted to the next absorption band for highly polar solvents so that spectral overlap interferes, (iii) the molar absorptivity of 1 is comparably low and requires appreciable concentrations for UV/Vis measurements with standard equipment, and this addition may alter the polarity of the solvent since it is a polar salt.

4. Pyridinium Phenolate Betaines

Covalent bonding of a negatively charged structural element to the positively charged pyridinium structure in 3 to form a zwitterionic betaine enabled an intramolecular light-induced charge transfer. As a result, substantial improvement was achieved not only by increasing the molar absorptivity, but also by further extending the polarity scales to low-polarity media due to the application of an electrically neutral polarity probe. The dipole moment of a structure with a single bond of an iminium anion to the pyridinium nitrogen atom was still small and resulted in moderate solvatochromism [42] (see further discussion in Refs. [43,44]), whereas with a 4-oxyphenyl anion [45] as the N-substituent, the charges were further separated, inducing strong solvatochromism [46]. Dimroth, Reichardt, and coworkers investigated [47] various N-4-oxyaryl derivatives for solvatochromism and found optimal properties of the betaine 30 (3, B30, CAS RN 10081-39-7), which provided a significant advance.

3	4

Dye 3 is remarkably strongly solvatochromic, so that solutions are yellow in water, red in methanol, violet in ethanol, blue in 1-butanol, green in acetone, and absorb in 1,4-dioxane in the NIR. The molar energy of light absorption at the maximum is called E_T(30) value of a solvent (transfer energy of betaine No. 30 in the first publication) is calculated analogously to Z in Equation (11) and are meanwhile determined for almost 400 solvents [48].

E_T(30) = 28,591 [nm·kcal·mol⁻¹]/λ_max

(11)

The E_T(30) values correlate linearly with the Y and Z values for various solvents (see Figure 6) and thus describe the same dipolarity effect of solvents. The linear correlation with Z values includes lipophilic solvents (filled circles) and polar protic solvents (open circles). The correlation with the Z values is of special importance for solvent effects because hydrogen bonds, as strong non-covalent interactions, are unimportant for the ion pair 2 (HI’s remarkably low boiling point of −35.4 °C, in spite of its high molecular weight, can be seen as an indicator of the absence of hydrogen bonds to I (see also the related discussion in ref. [49])). As a consequence, hydrogen bonds for 3 are estimated to be insignificant. Apparently, the five peripheral phenyl groups in 3 shield the betaine to such an extent that specific solvent effects play a minor role, but still allow the exceptionally strong solvatochromism. Dye 3 is a highly sensitive optical probe for other solvent effects as will be discussed later.

The tert-butyl derivative 4 (No. 26 in the first publication [47]) also exhibits very pronounced solvatochromism (E_T(26) values); however, the phenolate oxygen atom does not appear to be as efficiently shielded as in 3. A good linear correlation is obtained between E_T(30) and E_T(26) values (performance of target to actual comparison) for lipophilic solvents, shown as filled circles and the solid linear regression line in Figure 7. For hydrogen-bonding solvents (open circles and the dashed linear regression line), deviations from this line are observed forming a second linear regression. Obviously, the effect of hydrogen bonding causes a much stronger influence of solvents on the solvatochromic chromophore. The scattering of points within this second correlation is significantly larger than within the first, indicating a stronger contribution of specific solvent effects; such effects were already referred in the first reference to 4 [47].

The solvatochromism of a derivative of 4 without peripheral phenyl groups was studied by Sander and co-workers [50] and showed a linear correlation with E_T^N and E_T(30) values, respectively, for both hydrogen-bonding and non-hydrogen-bonding solvents. This indicates the dominance of dipolarity concerning solvatochromism such as for 3. The measurements of UV/Vis absorption spectra at low temperature in matrices of solid noble gases at 3 K and slightly higher temperatures such as 25 K gave spectra similar to those expected in the gas phase. The targeted addition of a small amount of water allowed the investigation of its influence and the formation of hydrogen bonds at low temperatures.

5	6

The limitations in the application of 3 could be overcome by slightly adapted derivatives. Dye 3 could not applied for acidic solutions such as acetic acid because of the protonation of the basic phenolate anion; Kessler and Wolfbeis [51] developed dye 5 in which the electron depletion by the chlorine atoms lowers the basicity sufficiently to study acidic media, while the solvatochromic behavior is similar to 3 so that extrapolations by linear correlation are possible. Wolfbeis named the polarity values obtained with 5 E_T(33) in continuation of the initial publication by Dimroth, Reichardt, and co-workers. The measurements of highly polar hydrogen bond-forming solvents and solution of salts becomes problematic with 3 because of its low solubility and tendency to aggregate [52]. Reichardt developed dye 6 with the more hydrophilic structure elements of pyridinyl [53] in the periphery of 3; the m-positions of the phenolic aryl substituents in 6 appear to cause minimal interference with solvatochromism, presumably because of the non-conjugation of the phenolate oxygen atom. As a result, the E_T(30) values of many polar and electrolyte-containing solvents can be estimated by extrapolation using 6.

7

The measurement of the E_T(30) values of media with very low dipolarity such as aliphatic hydrocarbons or tetramethylsilane is restricted due to the minimal solubility of the dye. The solubility-increasing effect of tert-butyl groups in lipophilic media [54] was applied to dye 7, whereby a substitution in the periphery allowed an increase in solubility in such media without significantly affecting solvatochromism so that the corresponding E_T(30) values could be obtained by extrapolation by means of a linear free energy relationship [55].

Finally, the experimental E_T(30) values were scaled for easier comparability, first according to Reichardt as a relative polarity measure (RPM) [56] where the value for n-hexane was set to 0.000 and RPM = [E_T(30)_n-hexane − E_T(30)_solvent]/E_T(30)_n-hexane. Next, the scaled E_T^N values were defined [57] where the value for tetramethylsilane was set to 0 and for water set to 1, such that E_T^N = [E_T(30)_solvent − E_T(30)_{tetrametylsilane}]/[E_T(30)_water − E_T(30)_{tetramethylsilane}]. The experimental E_T(30) values were retained here, although scaling is attractive, because all E_T^N values depend on only two references and their accuracy; if their values might be altered, such as by more precise measurements, the entire set of values would change. Moreover, the value for tetramethylsilane is less reliable because it was obtained by extrapolation, and the value for water is at the limit of direct measurements because of the low solubility of 3. On the other hand, each experimental E_T(30) value has obtained its individual accuracy, which is determined only by the particular experimental procedure, and is considered to be more reliable.

The molar energy of excitation of dye 3 in various solvents as E_T(30) values was taken from the maximum of the solvatochromic band since an efficient and precise measurement is possible. On the other hand, the band can be split [58] into more than a single Gaussian [59] band, and the point of gravity may be of greater physical significance than the maximum because it represents the thermal energy of chromophores. However, accurate determination is more difficult and requires a clear cut between the most bathochromic band and other partially overlapping bands of higher electronic energy, leading to uncertainties. As a consequence, the molar energy of excitation is retained for the following discussions, while trying to avoid over-interpretation.

5. Polarizability: Further Solvent Effects

The concept of estimating solvent polarity on the basis of solvatochromism was developed by Brooker [60] and co-workers based on the study of a large number of merocyanines in early work. He found essentially two branches of solvent effects [61] that appear to be orthogonal to each other, causing blue and red shifts in the absorption spectra as the polarity of the solvent is increased.

8	9

The most pronounced blue shift was observed for 8 (RN 3210-95-5) where the polarity scale based on the molar energy of electronic excitation was named χ_B, while a pronounced red shift was found for 9 (RN 2913-22-6), giving the polarity scale χ_R. A linear correlation between the χ_B scale and the Z scale was found for several pure solvents, and there is also a linear correlation between χ_B scale and the E_T(30) scale indicating that the same effect is described, essentially the dipolarity of solvents. Further study of 8 and 9 is hampered by their difficult synthesis; there is only one paper by Brooker (and a patent) referred to for 8 by the Chem. Abstr. and six papers for 9. As a consequence, χ_B is replaced here by a more accessible and similar E_T(30) scale and further discussion is focused to χ_R. The solvent effect in the χ_R scale correlates better [62] with a function of the refractive index of a medium than with dielectric permittivity. As a result, χ_R is mainly better attributed to the polarizability of a medium than its dipolarity. This was further confirmed by finding the missing link [63] between the two polarity scales: χ_B (or, respectively, the E_T(30) scale) and χ_R.

10

The 4-aminophthalimide 10 is solvatochromic in fluorescence and is similar to N-methyl-4-aminophthalimide, the fluorescent dye for Zelinski’s [64] universal polarity scale S.

The molar energy of fluorescence of 10 was defined as the ∑ scale for solvent polarity and correlates linearly with the E_T(30) scale for pure solvents (see Figure 8a). The light absorption of 10 is also solvatochromic and was defined as the σ scale for solvent polarity and correlates linearly with the χ_R scale (see Figure 8b). As a consequence, all solvent polarity scales can be interrelated.

The correlation in Figure 8b between σ and χ_R is interpreted in terms of the dynamics of light absorption of 10 with a low dipole moment electronic ground state and a much larger dipole moment in the electronically excited state (see Figure 9). The energy of the electronic ground state is only slightly affected by polar solvents. Light-induced electronic excitation increases the dipole moment of 10; however, solvation by re-orientation of the solvent molecules cannot follow this rapid, essentially vertical process. As a result, the polarizability of the solvent remains important and characterizes the solvent effect on this transition; the same effect is important for χ_R and explains the linear correlation between these two polarity scales shown in Figure 8b. The fluorescent lifetime of the electronically excited state of 10 in the order of nanoseconds is long enough for relaxation due to the re-orientation of the solvent molecules, and this process is energetically strongly influenced by the dipolarity of the solvent; consequently, a linear correlation of the molar energy of fluorescence (∑ scale) with the E_T(30) scale can be explained because both scales are affected by the same process of solvation. In summary, for the E_T(30) scale, solvation by dipolar re-orientation of the solvents is crucial, while the χ_R scale describes the polarizability of solvents.

Strong solvatochromic effects of other similar merocyanines were reported [65].

The high dipolarity of water (solvent 1) and aliphatic alcohols is manifested in Figure 8a and corresponds to chemical experience, while the polarizability of these solvents shown in Figure 8b is only in the middle range and is clearly exceeded by solvents such as formamide (20) and DMSO (15).

6. Various Solvent Effects: Multi-Parameter Equations

Two orthogonal solvent properties, the dipolarity and polarizability, have been described above and are the microscopic, molecular counterpart to Debye’s equation [23,24] of the linearly independent macroscopic orientation and shift polarization. This may stimulate the search [66] for further types of microscopic solvent effects that are linear independent from each other and thus should describe orthogonal molecular solvent properties. The hydrogen-bonding ability of solvents has already been discussed here with dye 4. Other solvent properties such as their Lewis acidity and basicity have been the subject of polarity scales such as Gutmann’s [67,68] donor and acceptor numbers, hydrogen donor and acceptor numbers, and more [69]. Different and specialized solvent scales are appropriate for different problems. Consequently, the characterization of solvents with a universal parameter set would be attractive. Various approaches were described in the literature, such as those by Kamlet, Taft and Abboud [70], Catalán et al. [71,72], Koppel and Palm [73], and Vitha et al. [74], two examples of which are detailed here.

XYZ = XYZ₀ + sπ* + aα + bβ

(12)

Kamlet, Taft, and Abboud developed the solvatochromic comparison method as multi-parameter fit in which solvent-dependent properties or processes denoted XYZ in Equation (12), such as the E_T(30) scale, depend on solvents for a linear set of parameter products; XYZ₀ is the intercept of such correlations, and s, a, and b are parameters to be individual to the solvent-dependent system. The parameters π*, α, and β describe characteristic properties of the respective solvent and are tabulated.

The multi-parameter Equation (12) was applied to the E_T(30) and Z polarity scales where the optimal parameters s, a, and b for a linear correlation were calculated by the application of the least squares method (see Figure 10). Acceptable linear correlations were found; the interpretation of the parameter a as a hydrogen-bond-donating property remains problematic, in particular for the Z scale. The value is comparably high, although no hydrogen bonds to I⁻ of 2 are expected.

A = A₀ + bSA + cSB + dSP + eSdP

(13)

Catalán followed a similar multi-parameter approach with Equation (13), where A describes a solvent-dependent process; b, c, d, and e are the process-dependent parameters and A₀ is the intercept of a linear correlation, while the tabulated parameters SdP (dipolarity), SP (polarizability), SA (acidity), and SB (basicity) characterize the medium.

The E_T(30) and Z scale were approached by the multi-parameter Equation (13), where the scale-dependent parameter b, c, d, and e were determined by the least squares method for 18 solvents (see Figure 11). The correlations were slightly better than in Figure 10; however, an additional parameter was required.

Several improvements to the multi-parameter concept have been developed [75], such as those by Spange [75] and co-workers. Hunter and co-workers [76,77] investigated competing hydrogen-bonding systems as polarity probes. Progress in correlations has been made for individual descriptions of groups of selected solvents; a universal and precise description of solvent effects is still lacking [78]. This may be caused by the interference of residual specific solvent effects with the polarity probes used. Furthermore, the terms of the applied multi-parameter fits might be not fully linearly independent so that cross terms become significant; this may become increasingly important for stronger anisotropic, more ellipsoidal-like solvent molecules where stronger solvent patterning is induced (this might result in liquid crystals) (see also below). As a result, empirical solvent polarity scales and their extension to multi-parameter equations are very useful for practical applications; however, an over-interpretation should be avoided because of their limitations. The size of solvent shells may be of further influence and will be the subject of the next chapter.

7. Solvent Shell

Solvated molecules are surrounded by directly molecular interacting solvent molecules; the extension of such interactions into the solvent is of special interest for solvent effects. This topic was investigated using the interaction of strong dipoles with various polar solvent molecules. Betaine B30 (3), the solvatochromic probe of the E_T(30) scale, exhibits a comparably large dipole moment of about 12 D [79,80,81,82] with a negative charge on the oxygen atom extending into the pyridinium ring with a positive charge. The interaction of the solvent molecules with this dipole moment causes the solvatochromism of 3. The large and extended electric dipole of 3 generates an electric field that extends into the solvent and can be used as a probe to estimate the extension of a significant solvent shell. For such an assay, two chromophores of 3 were combined [58] anti-colinearly to form the dyad 11.

11	12

The anti-colinearly dipoles in 11 compensate for large distances because no net dipole moment remains so that solvent effects become weak, while at small distances, the effects are still individual and strong so that the solvent effects of each chromophore remain unaffected by the attached second chromophore. The molar energy of excitation of 11 is calculated analogously to 3 and denoted E_T(30dyad).

The solvent effect on the UV/Vis spectra of 3 and 11 is very similar, as is indicated by the linear correlation between E_T(30) and E_T(30dyad) for various solvents (even benzyl alcohol, although an exception, in many cases, is acceptably included) (see Figure 12). The slope of such a correlation can be taken as a measure of the compensation of the dipoles in 11 where a slope of zero should be obtained for complete compensation and a slope of 1 for the absence of any compensation. The slope found experimentally is close to unity, indicating that there is no compensation of the anti-collinear dipoles; consequently, the significant solvent shell must be very thin, being not much more than one molecular layer of solvent thick. A possible artifact due to residual conjugation in 11 between the two chromophores could be excluded by using an aliphatic cage in 12 as an isolator; however, 12 gave the same result as 11 [58].

13

Finally, the very rigid diamantane was used as a spacer in 13. E_T(30diam) as the molar excitation energy of 13 was calculated analogously to 3.

The linear correlation between E_T(30) and E_T(30diam) for various pure solvents is shown in Figure 13; the slope of this correlation of close to unity indicates identical solvent effects in the E_T(30) and E_T(30diam), thus ruling out significant compensation of the dipoles in 13 with respect to the solvent shell.

As a consequence, the solvatochromism of the dyads (11, 12 and 13) based on phenolatebetaine 3 provides no evidence for compensation effects due to anti-colinear dipoles and indicates a very thin solvent shell, not much more than one molecular layer thick. The surprisingly thin solvent shell finds its counterpart in the thin surface of liquids such as the phase boundary of water and the gas phase, where investigations [83] indicate an essentially monomolecular active layer, with the hydrogen atoms directed toward the interior of the liquid phase, while the oxygen atoms were found to be in contact with the gas phase. The extraordinarily thin active solvent shell may explain some unaccounted solvent effects such as problems with the relative permittivity (dielectric constant) as a measure of solvent polarity due to some appreciable exceeding of water (see above) although water exhibits a higher polarity according to the chemical experience: The relative permittivity is a three-dimensional property of the volume of a liquid as it is for the refractive index, whereas solvent effects involve two-dimensional molecular surface effects. These can be similar; however, they need not to be identical.

8. Liquid Mixtures

Liquid mixtures are of particular interest for chemists and physicist because the properties of one component can be continuously transformed into the other by changing the composition. Polar molecules in a solvent are surrounded by solvent molecules in diluted solutions and move free of forces in the solvent because the outer sphere corresponds to the solvent. Energy and properties are independent from the positions of the polar molecules such as molecules in the gas phase at low pressure. As a consequence, the same formalism described in Section 2 for gases can be applied to polar additives to solvents: The effect p of the polar component at low concentration is expected to be proportional to its concentration c (dp = const₁·dc) (see also Equation (1)). However, at higher concentrations, this component is expected to interact with itself reducing the effect (dp = E/c·dc), where the constant E is a measure of the energetic interaction (see also Equation (2)). The next steps according to Section 2, combination and integration, result in Equation (5). Neither the nature of interaction of the polar component with the solvent nor the interaction with itself was specified. As a consequence, Equation (5) is to be experimentally verified for its application in binary liquid mixtures; p was set equal to E_T(30) so that Equation (14) is obtained where c* is the concentration of the polar component at which the interaction of the polar component becomes important and E_T(30)₀ is the E_T(30) value of the pure component of lower polarity.

$$E_{\mathrm{T}}(30)=E·\ln \left(\frac{c}{c*}+1\right)+{E_{\mathrm{T}}\left(30\right)}_{\mathrm{o}}$$

(14)

Further approaches [84,85] to the polarity of binary mixtures were reported in the literature.

The validity of Equation (14) for real systems was tested (performance of target to actual comparison) with the mixture N-tert-butylformamide/benzene for the E_T(30) polarity scale; a tert-butyl group was attached to the formamide to increase the solubility [86] in the aromatic hydrocarbon benzene and to be able to set a broad polarity range. A strongly curved relationship was obtained between the E_T(30) values and the concentration c of the more polar N-tert-butylformamide as is shown in the inset of Figure 14. The entire range of concentration c, spanning three decades, could be linearized by Equation (14) (see Figure 14). The strong curvature in the inset is a consequence of the comparably low c* value of 0.0167 mol·L⁻¹.

The description of real binary liquid systems using Equation (5) is not limited to the E_T(30) polarity scale, but is more universal [87], as shown by its application to common polarity scales in Figure 15. The validity of Equation (5) has been demonstrated for more than 80 binary mixtures. On the other hand, Equation (5) and Equation (14), respectively, can be used to investigate special properties of liquid mixtures. This will be shown in the next chapter on hydrogen-bonding solvents.

9. Hydrogen-Bonding Solvents

Particular attention should be paid to hydrogen bond-forming solvents since hydrogen bonds are strong and directed non-covalent molecular interactions. Therefore, patterning of solvents can be performed by such bonds. On the other hand, the lifetime of hydrogen bonds at room temperature is very short and is in the order of picoseconds [88]. However, the bonds are re-formed in a similarly short period of time, so that molecular sticking structures in the liquid are highly dynamic and enable fast exchange processes. Water, as the most prominent strong hydrogen bond donor is studied here because its low molecular weight allows it to reach the high molar concentration of 55.4 mol·L⁻¹. Water is combined with 1,4-dioxane as a moderate and low-polar hydrogen bond acceptor, where complete miscibility is crucial.

The E_T(30) values of water/1,4-dioxane mixtures as a function of the concentration c of water are shown in Figure 16. Their linear correlation between ln (c/c* + 1) is obtained for concentrations c below 26 mol·L⁻¹ as a critical concentration c_k (Figure 16, left line); this correlation corresponds to Figure 14. At higher concentrations, c > 26 mol·L⁻¹ (c > c_k), a second steeper correlation results (the c* values are low and similar so that the two lines can be combined in one diagram). This sudden change is already obvious in a simple logarithmic plot because of the low values of c* in both correlations (ln (c/c* + 1) ≈ ln c for c >> c*); see also the inset top left of Figure 16. The change in slope proceeds in a narrow concentration range and is attributed to a change in solvent structure and corresponds to such a condensation-like phase transition as described for carbon dioxide in Section 2. The formation of the hydrogen-bonded structure requires a sufficiently high concentration to overcome the dissociation at lower concentrations. On the other hand, one can extrapolate the correlation on the left side to higher concentrations until the concentration of pure water (dashed line) and obtain an E_T(30) value of 55.9. This value would be expected if water did not form a hydrogen bonding structure, and the difference from the actual value of 63.1 out of 7.2 units indicates the appreciable increase in solvent polarity due to the formation of the hydrogen-bonded structure.

The formation of double linear correlations according to Equation (5) is neither limited to the E_T(30) polarity scale nor to the mixture water/1,4-dioxane, as can be seen in Figure 17 [89]. Remarkably, the critical concentrations c_k for the transition from one linear correlation to the second are independent of the applied polarity scale within the limits of experimental error and are therefore attributed to a property of water (the kink appears at different position in Figure 17 due to the different scales in the coordinate system). It can surmise that water forms clathrate-like [90] structures at sufficiently high concentrations; however, these structures are very dynamic, unlike the crystalline clathrates such as the hydrate of methane.

10. Elevation of Polarity

As shown in the last chapter, hydrogen bonds can significantly increase the polarity of the solvent. Consequently, a combination of a moderately polar hydrogen bond donor and a less polar but strong acceptor should increase the solvent polarity.

Ways to increase solvent polarity were tested [91] using the E_T(30) polarity scale and the mixture 1-butanol as the more polar component and hydrogen bond donor and nitromethane as the less polar component and hydrogen bond acceptor. The E_T(30) values of such mixtures as a function of the molar concentration c of 1-butanol pass through a maximum at c_k = 3.3 mol·L⁻¹ and decrease again to reach the lower E_T(30) value of pure 1-butanol (see Figure 18). The polarity at c_k exceeds the polarity of pure 1-butanol by about 1.6 E_T(30) units. Such an excess of the solvent polarity is interpreted by the formation of a hydrogen-bridged association [91] between 1-butanol as the hydrogen bond donor and nitromethane as the hydrogen bond acceptor, such an associate being more polar than the individual components and means the polar component in Figure 18a bottom right (of course, the molar concentration of this associate is identical with the concentration of 1-butanol because of the 1:1 association). This means that all 1-butanol is captured to form this associate until not enough residual nitromethane is present with increasing concentrations of 1-butanol. Then, a mixture of this associate as the more polar component is formed with 1-butanol so that the polarity of the mixture decreases again because no further associate can be formed. The linear relation between E_T(30) and c_u, the molar concentration of nitromethane, in Figure 18b top right, further supports this interpretation because, according to Equation (5), the polarity increases by the formation of the hydrogen-bonded associate in the medium 1-butanol until all nitromethane is captured in the hydrogen-bonded associate and decreases again to finally reach the lower polarity of pure 1-butanol.

Such mixtures of hydrogen bond donors and acceptors are of particular interest [92] because they offer the possibility to preparing highly polar solvents from components of lower polarity. On the other hand, such mixture exhibits many properties of polar alcohols due to the possibility of rapid intermolecular proton exchange. A completely novel type of polar protic media can be constructed by using chloroform [93] since this solvent exhibits the tendency to form hydrogen bonds to strong hydrogen bond acceptors such as the dipolar aprotic solvents; however, unlike the alcohols, chloroform does not exhibit the tendency to exchange protons under neutral conditions. As a result, comparably polar protic solvents could be constructed without protons exchange. This might be of interest for various reasons.

11. Polarity around Miscibility Gaps

Homogeneous binary mixtures of very different polar solvents are possible such as 1,4-dioxane (E_T(30) of 36.0) and water (E_T(30) of 63.1), and one solvent in such mixtures can be used as a solubilizer for applications in complex mixtures. In most of such cases, the solubility of each solvent in the other is limited with the miscibility gap determined by the surface energy (surface tension) between both solvents.

The E_T(30) values of methanol/water mixtures as a function of the molar concentration c_p of water can be described by Equation (5) and form two linear correlations as shown in Figure 19 (squares above) [94]; a change in the solvent structure at high water content forms a kink as shown in Figure 16. The same type of double correlation is found for ethanol/water mixtures (triangles down) with a kink at about the same water concentration as for methanol/water (although at a different position on the abscissa because of the different scaling). The mixture of 1-propanol/water (triangles up) is a further example of this behavior starting with a lower E_T(30) value due to the lower polarity of 1-propanol. A miscibility gap is observed for 1-butanol/water (circles). However, similar linear correlations are found [95] in both the low water content range and high water content range where the expected kink is in the miscibility gap (biphasic region) and can be obtained by extrapolation. The similarity between the mixtures of 1-butanol/water and mixtures of lower alcohols indicate that the two types of solvent structure are miscible for the lower alcohols, but no longer completely for 1-butanol. This behavior, dominated by the solvent structure, seems to be more general.

12. Polar Functional Groups

The generality of Equation (5) for the polarity of the solvent naturally implies the domination of the polar component in the binary mixture, while the component with lower polarity essentially forms the matrix. The polarity of the more polar component is essentially generated by polar functional groups; as a consequence, the molar concentration of these polar groups should be of fundamental importance.

To verify this concept, the molar concentration of pure alcohols and water was calculated from their density and molecular weight and is identical to the molar concentration of their polar OH group. Plotting the E_T(30) values against their logarithmic concentration in Figure 20 (left) shows a linear relation for 1-propanol (3) and higher homologues [96]. A second steeper line is found for methanol (1) and water (0) indicating the hydrogen-bridging structure of these solvents. Interestingly, the E_T(30) value of ethanol (2) is close to the limit, indicating the special properties of ethanol as a solvent since the hydrogen-bridging structure is just being realized, while slight perturbance such as an increase in temperature or the addition of another component could change the structure to more isolated OH groups with different solvent properties. E_T(30) values for the molar concentrations (ln c_p) of OH groups in mixtures of ethanol with the less polar 1,4-dioxane or n-heptane fit well into the plot for pure 1-alkanoles, as shown in Figure 20 (right). It can be concluded that the polarity of solvents and solvent mixtures, respectively, is dominated by polar functional groups (polar structure elements) and structures or components with lower polarity essentially form the matrix. This concept was further extended and generalized by Spange and co-workers [97].

The piezochromism of 3, the pressure-dependent shift in the solvatochromic band, may be a further indicator of the importance of the molar concentration of OH groups for the polarity of the medium. An increase in the pressure [98] from atmospheric pressure to 2000 at shifts the solvatochromic band of 3 in ethanol until E_T(30) = 52.7 where the compressibility of ethanol increases the molar concentration from 17.1 to 24.6 mol/L. Such an increase in the concentration of OH groups could be made responsible for the observed increase in the E_T(30) values because the values are within the scope of the second linear correlation in Figure 20.

13. Thermochromism

Most investigations about solvent effects were realized at room temperature or slightly above because of experimental convenience; however, solvent effects are appreciably temperature-dependent. Pronounced effects can be expected for hydrogen-bonding solvents, since such bonds dominate at lower temperatures and become more and more loose at higher temperatures (compare, for example, the high specific heat of water).

The thermochromism of 3 in ethanol [99] is shown in Figure 21, where there is a precise linear relation between the temperature T and the polarity of the solvent as the E_T(30) values. As indicated before, the E_T(30) value of ethanol at room temperature is appreciably lower than of methanol; however, cooling to −75 °C increases the value so that it overtakes even methanol. The thermal expansion of ethanol [100] may be partially responsible for the effect (see, for example, Figure 20 for the effect of the content of OH groups in alcohols); this expansion is exactly proportional to temperature (compare the use in alcohol thermometers); however, one can estimate that the thermal expansion can only cover about 1/3 of the effect. The residual 2/3 is attributed to the loosening of hydrogen bonds by increasing the temperature. Remarkably, this must also be exactly linearly temperature-dependent because the high precision of the overall linear correlation.

14. Long-Reaching Noncovalent Interactions

Intermolecular interactions are important for solvent effects where direct molecular contacts appear to dominate; such interactions are strongly damped and become vanishing beyond the direct molecular contact. Longer distances are covered by dipole–dipole interactions such as those according to Förster’s mechanism [101,102], where a limit of interactions seems to be reached at more than 10 nm.

However, studies of the concentration dependence of the fluorescence lifetimes τ of strongly fluorescent dyes in Figure 22 indicate [4,103] that there are still interactions even at more than 100 nm because of the large intermolecular distance. Equation (5) was developed without restriction on the nature of interactions. Consequently, the equation can be also used to describe the concentration dependence of τ; see the inset of Figure 22.

The long-reaching interactions were attributed to the effect of evanescent waves of the electronically excited dye molecules. Electronical excitation requires comparably high energy input and is unimportant at room temperature. On the other hand, molecules are vibronically excited even at room temperature. As a consequence, such interactions might be part of solvent effects where an even further reaching can be expected due to the long wavelengths of vibronic energy. This could be the subject of further investigations.

15. Practical Applications

The visual effect in the solvatochromism of dye 3 facilitates its application in simple color tests. In anhydrous solvents or reagents, residual contents of water can be determined because these induce strong solvatochromic effects. For example, anhydrous tert-butylhydroperoxide is required for various applications in preparative chemistry and forms pure blue solutions [104] of 3. A low and unimportant water content shifts the color so that it is no longer pure blue, but acquires a very slight violet component, while a higher water content shifts the color to violet and further to red. A simple color test with 3 allows the rapid identification of solvents, as shown for disinfectants [105] and their components. It can also be used to determine the efficiency of methods for drying solvents, in particular, highly hygroscopic solvents such as ethanol. The measurement of the absorption maximum of dye 3 and application of Equation (5) allows the accurate determination of the composition [106] of binary mixture, in particular, the water content [107] of solvents. The use of solvatochromic fluorescent dyes [108] means an extension because higher diluted solutions can be applied and the optical quality of a sample is of minor importance.

Equation (5) was developed for general intermolecular interactions without specifying their nature or method of detection. As a consequence, a linear correlation according to Equation (5) was obtained for the densities [109] of mixture between various solvents and water such as is shown in Figure 23 (left for water/methanol). Similar linear correlations were obtained for the index of refraction corrected by the density (n_D²⁰/ρ), as shown in Figure 23 (right). Such correlations are useful for various applications such as precise interpolations.

16. Conclusions

The chemistry-dominating intermolecular interactions can be efficiently investigated by solvent polarity probes, whereby Dimroth and Reichardt’s E_T(30) scale certifies that because of the sensitivity of the optical method and other advantages, this essentially reflects the dipolarity of solvents; the polarizability of solvents is better characterized by Brooker’s χ_R scale. Zelinski’s universal polarity probe forms a link between both types of polarity scales because the fluorescence-dependent polarity scale S correlates linear with E_T(30) for various solvents, while the absorbance of the dye correlates with Brooker’s χ_R scale. Various solvent effects can be measured by means of multi-parameter approaches. Further insight into solvent effects and changes in the solvent structure were obtained by the developed two-parameter equation (5) for concentration-dependent effects. The equation includes condensed phases, binary mixtures where the property of one solvent can be continuously transformed into that of the other by changing the composition of the mixture, and even the effects in pure solvents with polar functional groups: The polar properties of media are dominated by polar groups or polar components, while other elements of structure or components essentially form the matrix. The appreciable thermochromism of 3 leading to a linear correlation between the E_T(30) scale and the temperature (either in °C or K) was reported in relation to the thermal expansion of the solvent, with about 1/3 of the effect attributed to thermal expansion and 2/3 to temperature-induced breaking of hydrogen bonds; both effects are strongly linear with the temperature. Finally, very far-reaching intermolecular interactions were studied using the two-parameter equation (5) indicating intermolecular interactions of electronically excited states even for distances of more than 100 nm. Practical applications were shown for analytics both for the polarity probes and the two-parameter equation (5), the latter of which can be a useful tool for further investigations.