#### 4.1. Ionization of Fluoresceins with Blocked Carboxylic Group and Similar Compounds

Following conclusions were made basing on the spectra of the molecular and ionic forms of the dyes.

First, let us consider the absorption bands of dyes unable to lactone formation (

Scheme 3). To this group belong compounds with a carboxylic group blocked by esterification, namely, ethylfluorescein,

n-decyl fluorescein,

n-hexadecyl fluorescein, ethyl eosin, and

n-decyleosin; a dye without the carboxylic group, i.e., 6-hydroxy-9-phenylfluorone; and sulfonefluorescein, a compound bearing the SO

_{3}H group instead of COOH. In the last case, the formation of an intramolecular ester called “sultone cycle”, is not typical at least in the presence of water. In

Figure 1a, the spectra of 6-hydroxy-9-phenylfluorone cation H

_{2}R

^{+}, neutral form HR, and anion R

^{−} are shown. They correspond to the H

_{2}Z

^{+}, HQ, and X

^{−} types of bands. In this paper, we use the symbols Z, Q, and X in order to distinguish between three states of the xanthene portion, namely, cationic, neutral, or quinonoidal, and anionic, respectively. Of course, this does not reflect the real distribution of the electronic density. In particular, the 3- and 6-oxygen atoms in the X

^{−} structure are equal.

In the case of alkyl fluorescein, alkyl eosin, and some other model compounds the ionization occurs in two steps. However, the formation of cations of eosin dyes occurs in very acidic media and was not studied here. In the case of sulfonefuorescein, G = SO_{3}^{−} and all the three species have one positive charge less.

The spectra of the quinonoid molecule HQ exhibit two main maxima around 465 and 495 nm (

Figure 1a). The ratios of the maximal absorbances of the molecule and anion, A

_{max}(HQ)/A

_{max}(X

^{−}) or, in fact, A

_{max}(HR)/A

_{max}(R

^{−}) for 6-hydroxy-9-phenylfluorone are 0.305 and 0.253. For ethyl fluorescein, the A

_{max}(HQ)/A

_{max}(X

^{−}) values are 0.335 and 0.290, whereas for

n-decyl fluorescein, 0.294 and 0.260. The relative absorption of the molecular form is somewhat lower for ethyl eosin: A

_{max}(HQ)/A

_{max}(X

^{−}) = 0.222.

For these dyes, the $\mathrm{p}{K}_{\mathrm{a}0}^{\mathrm{a}}$ and $\mathrm{p}{K}_{\mathrm{a}1}^{\mathrm{a}}$ values correspond to the transitions H_{2}Z^{+}→HQ and HQ→X^{−}, respectively. For ethyl eosin and n-decyl eosin, the H_{2}Z^{+} cations appear in acidic region and their spectra were not observable. In the case of sulfonefluorescein, the molecular and ionic structures are H_{2}Z^{±}, HQ^{−}, and X^{2−}, owing to the presence of additional SO_{3}^{−} group. In this case, the transitions refer to $\mathrm{p}{K}_{\mathrm{a}1}^{\mathrm{a}}$ and $\mathrm{p}{K}_{\mathrm{a}2}^{\mathrm{a}}$, respectively.

#### 4.2. Detailed Scheme of Protolytic Equilibria in the Micellar Pseudophase

Much more complicated is the equilibrium in the case of the main group of fluorescein dyes with the free COOH group. Basing on a series of our previous studies [

7,

15,

31,

37,

38,

39,

40,

41,

42,

47,

48,

57], we propose the following generalized scheme of a detailed protolytic equilibrium (

Scheme 4). The symbols H

_{3}R

^{+}, H

_{2}R, HR

^{−}, and R

^{2−} designate the stoichiometric composition irrespective of the molecular (ionic) structure. Molecules and anions may be equilibrium mixtures of different tautomers depending on the specificity of each of the dyes. The possible tautomers of the neutral form H

_{2}R are well known. It deals about the zwitter-ion H

_{2}Z

^{±}, quinonoid H

_{2}Q, and colorless lactone H

_{2}L. Their structures in solid state [

37,

58,

59] and solution [

13,

16,

17,

28,

29,

30,

32,

36,

60,

61] are well documented by different authors. The H

_{2}Z

^{±} tautomer was observed mainly for fluorescein in water [

7,

57,

61]. The fraction of the H

_{2}Q tautomer decreases while that of H

_{2}L increases on going from water to organic solvents [

13,

30,

37,

39,

40,

41,

57,

60] or different kinds of organized solutions, such as micellar solutions of colloidal surfactants [

7,

13,

16,

17,

39], direct or reversed microemulsions [

15,

39,

62], solutions of dendrimers [

63], calixarenes [

64], and cyclodextrins [

65]. Monoanions HR

^{−} of HQ

^{−} type are usually observed for fluorescein and its derivatives bearing halogen atoms in the phthalic acid residue [

15,

62]. Contrary to it, the same substituents in the xanthene moiety favor formation of the HX

^{−} tautomer [

13,

15,

16,

17,

29,

30,

37,

39,

40,

41,

50,

57,

62,

63]. This was already mentioned in earlier publications [

60,

66,

67,

68,

69]. In some rare cases, for instance, in entire dimethyl sulfoxide, the last tautomer was observed even for fluorescein, as admixture to HQ

^{−} [

41]. However, both experiments [

43,

44,

45] and quantum-chemical calculations [

42] show that in vacuum the HX

^{−} tautomer predominates. Involving of nitro derivatives in research led to interesting results. In this case, both R

^{2−} and HR

^{−} anions may form lactonic anions L

^{2−} and HL

^{−} [

15,

29,

37,

38,

47,

48]. The lactonic structure of 2,4,5,7-tetranitrofluorescein dianion R

^{2−} in solution was proved using IR- and NMR-spectroscopy [

37,

38]. Previously, such kind of tautomerism was described only for phenolphthalein and its derivatives [

70,

71,

72,

73]. The introduction of NO

_{2} groups in 2, 4, 5, or 7 positions of fluorescein evidently decreases the electronic density on the nodal carbon atom, which results in the last-named effect and in a substantial stabilization of the H

_{2}L tautomer [

37,

38,

47,

48]. We do not consider here more complicated equilibria of aminofluoresceins because of the presence of additional acid-base centers [

34,

35,

40]. Fluoro derivatives of fluorescein obey the same regularities as the chloro- and bromofluoreseins [

39]. Interesting data were published recently for silicone analogues of fluorescein, dyes with Si(CH

_{3})

_{2} group instead of the pyrane oxygen [

25].

In this study, we have selected a set of dyes for which all the listed types of tautomerism are characteristic to one degree or another (

Scheme 4). The constants of the tautomeric equilibria are as follows:

Hereafter, we use the equilibrium concentrations instead of activities. Accordingly, the fractions

$\alpha $ of the tautomers should be expressed using the above tautomerization constants:

The tautomerization constants and correspondingly the

$\alpha $ values are in fact extrathermodynamic quantities. However, their estimates may be made using some reliable assumptions concerning the absorption spectra in the visible [

7,

31,

37,

40,

57,

61]. The molar absorptivities at the band maxima of H

_{2}Q should be equated to that of the HQ

^{−} species of the same dyes, for which the tautomers of HX

^{−} and HL

^{−} types are not typical. Otherwise, they may be equated to the molecular forms of corresponding compounds with the carboxylic group being blocked. For example, for the H

_{2}Q tautomer of fluorescein, the anion HR

^{−} of the same dye, the molecule HQ of fluorescein esters, 6-hydroxy-9-phenylfluorone, and the HR

^{−} ion of sulfonefluorescein are such model species. The maximal molar absorptivity of the H

_{2}Z

^{±} tautomer should be equated to that of the H

_{3}Z

^{+} cation. The HR

^{−} spectrum of eosin coincides with the spectrum of the anion R

^{−} of ethyleosin in the micellar media under study that allows supposing a structure of HX

^{−} type [

7]. At the same time, the band of R

^{2−} of eosin (X

^{2−} structure) is hypsochromically shifted by ca. 13 nm, thus exhibiting the role of the carboxylate group COO

^{−} [

7]. For R

^{2−} of fluorescein (also X

^{2−} structure), the corresponding absorption band shift with respect to the maxima of the anions of fluorescein esters and 6-hydroxy-9-phenylfluorone reaches 17 nm (

Table 2). Such shifts are of universal character and have been confirmed theoretically [

74]. They are also observed for tautomers of the “Z” type; compare the absorption bands of cation of fluorescein esters and 6-hydroxy-9-phenylfluorone, on the one hand, and of the zwitter-ion of sulfonefluorescein. Unfortunately, corresponding model compounds are not available for all the dyes under study. Hence, sufficiently accurate numerical estimates are not always possible, but semi-quantitative evaluations may be made. However, it should be also kept in mind that it is impossible to directly estimate too large or too small values of the tautomerization constants. In addition, the presence of colorless lactones in an equilibrium mixture of tautomers may be surely stated only on substantial decrease in the molar absorptivity.

The so-called microscopic ionization constants are following:

Finally, the experimentally determined

$\mathrm{p}{K}_{\mathrm{a}}$ values can be expressed through the

$\mathrm{p}k$ and

$\alpha $ in the following manner:

Returning to the compounds considered in

Section 4.1, it should be noted that in this case

$\mathrm{p}{K}_{\mathrm{a}0}=\mathrm{p}{k}_{0,\mathrm{OH}}$ and

$\mathrm{p}{K}_{\mathrm{a}1}$ =

$\mathrm{p}{k}_{1,\mathrm{OH}}$. For sulfonefluorescein,

$\mathrm{p}{K}_{\mathrm{a}1}$ =

$\mathrm{p}{k}_{1,Z}$ and

$\mathrm{p}{K}_{\mathrm{a}2}$ =

$\mathrm{p}{k}_{2,\mathrm{OH}}$.

#### 4.3. Classification of Fluorescein Dyes According to the Type of Tautomerism of Anions

Below we will consider the tautomeric equilibria of anions in the medium under study. As for molecular forms, the lactone predominates. The fraction of quinonoidal tautomer is very small, especially for nitrofluoresceins. The zwitter-ionic tautomer is not detected in the spectra at all; generally speaking, this tautomer was previously observed only for fluorescein in water and aqueous solutions with small additives of organic solvents.

**Fluorescein type of the ionic equilibrium:** HQ

^{−}→X

^{2−} (

Figure 3a). The monoanion HR

^{−} of fluorescein exists in solution as HQ

^{−} tautomer, with two main band maxima, 455 and 480 nm; for the dianion R

^{2−}, X

^{2−} structure,

${\lambda}_{\mathrm{max}}$ = 500 nm [

7]. The A

_{max}(HR

^{−})/A

_{max}(R

^{2−}) ratios are 0.290 and 0.279, respectively, which is similar to the A

_{max}(HR)/A

_{max}(R

^{−}) values of the corresponding esters and 6-hydroxy-9-phenylfluorone (see above). For sulfonefluorescein, the monoanionic spectra also exhibits two maxima; A

_{max}(HR

^{−})/A

_{max}(R

^{2−}) = 0.357 and 0.305. For 3′,4′,5′,6′-tetrabromofluorescein, the corresponding ratios are 0.317 and 0.245. For this group of dyes,

$\mathrm{p}{K}_{\mathrm{a}2}^{\mathrm{a}}$ =

$\mathrm{p}{k}_{2,\mathrm{OH}}$. For the above dyes,

$\mathrm{p}{K}_{\mathrm{a}2}^{\mathrm{a}}$ = 7.00 to 7.27. For thiofluorescein this value was somewhat higher, 7.77, while

$\mathrm{p}{K}_{\mathrm{a}2}^{\mathrm{a}}$ = 6.56 of 4-nitrothiofluorescein reflects the influence of the substituent NO

_{2}.

**Eosin type of ionic equilibria:** HX

^{−}→X

^{2−} (

Figure 3b). Another type of monoanions HR

^{−} is the HX

^{−} tautomer, with the principal absorption band shifted bathochormically compared to the X

^{2−} band. For these dyes of the eosin type, the A

_{max}(HR

^{−})/A

_{max}(R

^{2−}) values are 0.944 (eosin); 1.15 (2,4,5,7-tetrabromothiofluorescein); and 1.10 (4,5-dinitro-

N-ethylazafluorescein). For 4,5-dinitrofluorescein and 4,5-dinitrothiofluorescein, the A

_{max}(HR

^{−})/A

_{max}(R

^{2−}) ratio equals to 1.069 and 0.842, respectively. Note, that in the last two cases, the

${K}_{\mathrm{a}1}^{\mathrm{a}}$ and

${K}_{\mathrm{a}2}^{\mathrm{a}}$ values are close and the (possible) errors in estimation A

_{max}(HR

^{−}) value [Equation (7)] may increase. The dye 4,5-dinitro-2,7-dibromofluorescein with A

_{max}(HR

^{−})/A

_{max}(R

^{2−}) = 1.293 can also be conditionally ranked to the same group. However, the last value substantially exceeds unity and may reflect the presence of some fraction of the R

^{2−} ions in the lactonic form L

^{2−}.

For the compounds of the eosin type, $\mathrm{p}{K}_{\mathrm{a}2}^{\mathrm{a}}$ = $\mathrm{p}{k}_{2,\mathrm{COOH}}$. These values are 5.76 and 6.07 for eosin and thioeosin, respectively; for four 4,5-dinitro derivatives, $\mathrm{p}{k}_{2,\mathrm{COOH}}$ = 4.63 to 5.21, which reflects the inductive effects of two NO_{2} groups.

Strictly speaking, the intensities of the HX

^{−} and X

^{2−} bands do not have to match exactly. For example, the maximal molar absorptivities of single-charged anions of ethylfluorescein and ethyleosin in various solvents and micellar media are close to that of dianions of fluorescein and eosin, respectively, but some small deviations are still observed [

7,

16,

17,

31]. The same was repeatedly observed for the HR

^{−} and R

^{2−} ions (in fact, HX

^{−} and X

^{2−} tautomers) of eosin and erythrosin in different organic solvents [

30,

37,

39,

57] and micellar pseudophases [

7,

13,

15,

16,

17].

**Intervening type:** (HQ

^{−} ⇄ HX

^{−})→X

^{2−} (

Figure 3c). More serious deviation of the ratio A

_{max}(HR

^{−})/A

_{max}(R

^{2−}) from unity was fixed for 4,5-dibromofluorescein (0.466) and earlier [

7] for 2,7-dichlorofluorescein (0.717). At the same time, some less intensive absorption corresponding to the HQ

^{−} tautomer is observable (

Figure 3c). The transformations of these two compounds are a good illustration of the mobility of tautomeric equilibria. In water, the HQ

^{−} tautomer is predominating for the HR

^{−} ions, and the

$\mathrm{p}{K}_{\mathrm{a}2}$ values at ionic strength of 0.05 M are 4.96 and 4.94, while the thermodynamic are 5.21 and 5.19, respectively [

7,

62], whereas that of eosin equals to 3.75 [

69]. By contrast, in the CTAC micellar system (

Table 1) the

$\mathrm{p}{K}_{\mathrm{a}2}^{\mathrm{a}}$ values for the dihalogen derivatives, 5.79 and 6.00, are much closer to the

$\mathrm{p}{K}_{\mathrm{a}2}^{\mathrm{a}}$ = 5.76 of eosin. This should be explained by the partial conversion of the “carboxylate” tautomer HQ

^{−} to HX

^{−}. As result, the

$\mathrm{p}{K}_{\mathrm{a}2}^{\mathrm{a}}$s of the dihalogen derivatives approach

$\mathrm{p}{k}_{2,\mathrm{COOH}}$. Equation (20) demonstrates the factors that determine the position of the tautomeric equilibrium of the monoanion.

**Lactonic anions type:** (HX

^{−} $\rightleftarrows $ HL

^{−})

$\to $(X

^{2−} $\rightleftarrows $ L

^{2−}) (

Figure 3d). Finally, a group of hydroxyxanthene dyes able to formation of lactonic anions should be regarded. Here, besides anions of HX

^{−} and X

^{2−} types, the ions HL

^{−} and L

^{2−} appear. As it was mentioned above, 4,5-dinitro-2,7-dibromofluorescein may be also considered as a (potential) member of this group. But much more expressed are the A

_{max}(HR

^{−})/A

_{max}(R

^{2−}) values for 4,5-dibromo-2,7-dinitrofluorescein (4.62) and 4,5-dibromo-2-nitrofluorescein (0.566). In 50 mas % ethanol, the corresponding ratios are 1.52 and 0.35, respectively [

47]. For 2,4,5,7-tetranitrofluorescein (

Figure 1d), the X

^{2−} fraction is negligible and the L

^{2−} tautomer predominates;

${\lambda}_{\mathrm{max}}$ = 405 nm, molar absorptivity

${E}_{\mathrm{max}}$ = 30 × 10

^{3} M

^{−1} cm

^{−1}. The presence of the HX

^{−} tautomer of the monoanion is evident because the value

${E}_{\mathrm{max}}$ = 61.9 × 10

^{3} M

^{−1} cm

^{−1} registered at 525 nm [

37]. At the same time, the fraction of HL

^{−} is less understandable.

In order to clarify the mobility of the X^{2−} ⇄ L^{2−} tautomeric equilibria, we determined the absorption spectra of the 4,5-dibromo-2,7-dinitrofluorescein dianion R^{2−} in different solvents.

#### 4.4. Chain-Ring Tautomerism of the Dianion of 4,5-dibromo-2,7-dinitrofluorescein

The chain-ring tautomerism of the dianion of 4,5-dibromo-2,7-dinitrofluorescein, X

^{2−} ⇄ L

^{2−}, was additionally studied in H

_{2}O–ethanol and H

_{2}O–acetone mixtures. Some representative spectra are shown in

Figure 4. The data clearly demonstrate the dependence of tautomeric equilibrium state on the solvent composition (

Scheme 5).

In the CTAC micellar solutions at 4.0 M KCl, the molar maximal absorptivities,

${E}_{\mathrm{max}}$, of the R

^{2−} and HR

^{−} ions are 17.2 × 10

^{3} and 43.3 × 10

^{3} M

^{−1} cm

^{−1}, respectively. For the structures of X

^{2−}, HX

^{−}, and X

^{−} in this organized solvent, the

${E}_{\mathrm{max}}$ values are much higher [

7]. For the R

^{2−} ions of fluorescein, sulfonefluorescein, and eosin

${E}_{\mathrm{max}}$ = (85.9, 83.7, and 103.4) × 10

^{3} M

^{−1} cm

^{−1}. For HR

^{−} of eosin and R

^{−} of ethyl eosin, these values are 97.6 × 10

^{3} and 97.1 × 10

^{3} M

^{−1} cm

^{−1}. For these dye anions, the variations of solvent nature [

7] result in

${\lambda}_{\mathrm{max}}$ changes whereas the alterations of molar absorptivities are much less expressed than that in

Figure 4 and should be classified as common solvatochromic effects.

It should be noted that it is precisely the pronounced dependence of the molar absorptivity on the solvent nature that convincingly indicates the mobility of the tautomeric equilibrium. The low

${E}_{\mathrm{max}}$ value itself may be due to the peculiarities of the chromophore system. For instance, the molar absorptivities of HR

^{−} and R

^{2−} anions of thiofluorescein in water–ethanol and water–acetone mixtures are ca. 5-fold lower as compared with those of fluorescein and related dyes [

48,

75], but their dependence on the solvent composition is practically not expressed. For thioeosin, thioerythrosin, and 4,5-dinitrothiofluorescein, the

${E}_{\mathrm{max}}$ values in 50 mass % ethanol of anions are 2-fold lower than for eosin, erythrosin, and 4,5-dinitrofluorescein, but for all these sulfur-containing dyes, no fundamental changes in the spectra were observed on going to 80% ethanol or acetone, as well as to a CTAC micellar solution with or without 4.0 KCl [

48]. Hence, for these dyes there are no reasons to suspect the substantial fractions of lactonic anions.

In the case of 4,5-dibromo-2,7-dinitrofluorescein anions, the shift of the tautomeric equilibrium is much more expressed. If the value of (90–100) × 10

^{3} M

^{−1} cm

^{−1} is chosen as a tentative standard of molar absorptivity for X

^{2−} and HX

^{−} species, then the

${\alpha}_{{\mathrm{X}}^{2-}}$ and

${\alpha}_{{\mathrm{HX}}^{-}}$ values are

$\approx $0.2 and

$\approx $0.5, respectively. Accordingly,

${\alpha}_{{\mathrm{L}}^{2-}}$ $\approx $ 0.8 and

${\alpha}_{{\mathrm{HL}}^{-}}$ $\approx $ 0.5. In general, the expressions for the tautomerization constants of anions look like this:

Generally speaking, chain-ring tautomeric equilibria in the fluorescein series can be considered as an intramolecular reaction of an anionic carboxylate group with a central carbon atom acting as a Lewis acid.

#### 4.5. Dependence of the Ratio of the Values of the Stepwise Ionization Constants on the Character of Tautomerism

**Fluorescein type:** The

$\mathrm{p}{K}_{\mathrm{a}2}^{\mathrm{a}}$ values are equal to

$\mathrm{p}{k}_{2,\mathrm{OH}}$ and are similar for dyes with identical xanthene moiety, namely, fluorescein, 3′,4′,5′,6′-tetrabromofluorescein, and sulfonefluorescein. The average value is 7.15, while replacing of the oxygen heteroatom by sulfur atom or introduction of a nitro group result in increase and decrease by 0.6 units, respectively. The

$\mathrm{p}{K}_{\mathrm{a}1}^{\mathrm{a}}$ values are complicated, and thus the difference between the

$\mathrm{p}{K}_{\mathrm{a}}$s of stepwise dissociation can be represented as follows:

With the exception of sulfonefluorescein, where the neutral form exists as zwitter-ion, other ($\mathrm{p}{K}_{\mathrm{a}2}^{\mathrm{a}}-\mathrm{p}{K}_{\mathrm{a}1}^{\mathrm{a}}$) values are very small because of the substantial contribution of the $\mathrm{log}{\alpha}_{{\mathrm{H}}_{2}\mathrm{Q}}$ item. The increase in the dissociation constant ${k}_{1,\mathrm{COOH}}$ of 3′,4′,5′,6′-tetrabromofluorescein is evidently compensated by the less expressed formation of the lactonic cycle of the neutral molecule.

**Eosin type:** The

$\mathrm{p}{K}_{\mathrm{a}2}^{\mathrm{a}}$ values are equal to

$\mathrm{p}{k}_{2,\mathrm{COOH}}$. They are similar to eosin and thioeosin, but are ca. a unity lower for 4,5-dinitro derivatives. This reflects strong inductive effect of nitro groups. By contrast, the

$\mathrm{p}{K}_{\mathrm{a}1}^{\mathrm{a}}$ values are quite different within this group of dyes. The

$\mathrm{p}{k}_{1,\mathrm{OH}}$ value of eosin and, probably, for thioeosin should be equated to the

$\mathrm{p}{K}_{\mathrm{a}1}^{\mathrm{a}}$ of ethyl eosin or n-decyl eosin, which are 1.11 and 1.18, respectively. On the other hand, the comparison of the

$\mathrm{p}{K}_{\mathrm{a}}$s of ethyl fluorescein, sulfonefluorescein, ethyl eosin, and 4,5-dinitrosulfonefluorescein in water [

7,

76] allows concluding that two NO

_{2} groups in ortho-position to the OH group display ca. the same effect as four Br atoms. Analogous conclusion may be made when comparing the

$\mathrm{p}{K}_{\mathrm{a}2}^{\mathrm{a}}$ values of 3,3′,5,5′-tetrabromo sulfonephthalein (indicator bromophenol blue) and 3,3′-dinitro-sulfonephthalein (nitrophenol violet) both in water and dimethyl sulfoxide [

77]. Therefore, the dramatic increase in the

$\mathrm{p}{K}_{\mathrm{a}1}^{\mathrm{a}}$ and decrease in the (

$\mathrm{p}{K}_{\mathrm{a}2}^{\mathrm{a}}-\mathrm{p}{K}_{\mathrm{a}1}^{\mathrm{a}}$) of 4,5-dinitro derivatives (

Table 3) as compared with eosin dyes is caused by the expressed shift of the tautomeric equilibrium H

_{2}Q ⇄ H

_{2}L toward the right.

As result, the negative contribution of the term

$\mathrm{log}{\alpha}_{{\mathrm{H}}_{2}\mathrm{Q}}$ is substantial. For example, the

${\alpha}_{{\mathrm{H}}_{2}\mathrm{Q}}$ = 0.036 value was estimated for the dye 4,5-dinitrofluorescein, which allows to estimate the value

$\mathrm{p}{k}_{1,\mathrm{OH}}$ = 2.6. 4,5-dinitro-2,7-dibromofluorescein is an exception, because of the presence of both two nitro groups and two bromine atoms, which results in dramatic drop of the

$\mathrm{p}{k}_{1,\mathrm{OH}}$ value and hence increasing in

$\mathrm{p}{K}_{\mathrm{a}2}^{\mathrm{a}}-\mathrm{p}{K}_{\mathrm{a}1}^{\mathrm{a}}$. Besides, in the case of this dye, the intensity of the absorption band of R

^{2−} is ca. 30% lower as compared with that of the monoanion HR

^{−}. Therefore, this dye may be (partly) referred to the lactoid anions type (

Table 3).

**Intervening type:** For dihalogen derivatives, the concentrations of tautomers HQ

^{−} and HX

^{−} are commensurable, and the

$\mathrm{p}{k}_{\mathrm{OH}}$ values lower than those of fluorescein.

As result, the

$\mathrm{p}{K}_{\mathrm{a}1}^{\mathrm{a}}$ and

$\mathrm{p}{K}_{\mathrm{a}2}^{\mathrm{a}}$ values approach each other, although the

${\alpha}_{{\mathrm{H}}_{2}\mathrm{Q}}$ values are not as small as for the un-substituted fluorescein. First of all, the thermodynamic

$\mathrm{p}{K}_{\mathrm{a}1}$ values of 4,5-dibromo- und 2,7-dichlorofluorescein in water are equal to 4.32 and 4.00 [

7,

62], and ongoing to CTAC media (

Table 1) they increase by 1.0–1.5 units largely thanks to the pronounced shift of the tautomeric equilibrium H

_{2}Q ⇄ H

_{2}L toward the right. By contrast, the

$\mathrm{p}{K}_{\mathrm{a}1}^{\mathrm{a}}$ of eosin even drops on going to CTAB medium (1.83) to water, where

$\mathrm{p}{K}_{\mathrm{a}1}$ = 2.81 [

69]. This is due to a well-known regularity: for the molecular form of eosin, the transition from water to non-aqueous media weakly shifts the position of the tautomeric equilibrium [

7,

57].

For 4,5-dibromofluorescein, the above assumptions about the absorption spectra of tautomers allow us to estimate the values

${\alpha}_{{\mathrm{H}}_{2}\mathrm{Q}}$ = 0.067 and

${\alpha}_{{\mathrm{HX}}^{-}}$ = 0.47. Then

$\mathrm{p}{k}_{1,\mathrm{OH}}$ = 4.5;

$\mathrm{p}{k}_{1,\mathrm{COOH}}$ = 4.45;

$\mathrm{p}{k}_{2,\mathrm{OH}}$ = 5.72;

$\mathrm{p}{k}_{2,\mathrm{COOH}}$ = 5.67. These, as well as the above data, allow us to compose the following series (

Table 4).

Thus arranged data clearly demonstrate the huge effect displayed by the nitro groups.

Data in

Table 4 may be supplemented with

$\mathrm{p}{k}_{2,\mathrm{OH}}$ values 7.00–7.27 of fluorescein, sulfonefluorescein, and 3′,4′,5′,6′-tetrabromofluorescein, on the one hand, and 5.14–5.72 of 2,7-dichloro- and 4,5-dibromofluorescein. As can be seen, these

$\mathrm{p}{k}_{2,\mathrm{OH}}$ values are always more or less higher than the corresponding

$\mathrm{p}{k}_{1,\mathrm{OH}}$s. The effect may be semi-quantitatively explained by the Bjerrum–Kirkwood–Westheimer equation [

57]

Here,

$e$,

${N}_{A}$, R, and T have their usual meanings, r is the distance between the negatively charged group and the ionizing group (here expressed in nm; T = 298.15 K),

${\epsilon}_{eff}$ is the effective relative permittivity of the space permeated by the electric field lines. For more details, see the book by Vereshchagin [

78].

**Lactonic anions type:** Most complicated is the equilibrium scheme in the case of the dyes inclined to formation of anionic lactones. Introduction of nitro groups in 2- and 7-positions favors the lactone formation owing to the decrease in the electronic density at the nodal C_{9}. However, the resulting effects are not so obvious. For example, in the case of 2,4,5,7-tetranitrofluorescein the dianion R^{2−} exists almost in the form of a lactone. Note, that the last is not colorless but yellow, owing to nitrophenolate absorption.

Let us consider the protolytic equilibrium of 4,5-dibromo-2,7-dinitrofluorescein in more detail. Tamburello-Luca et al. [

46] studied the ionization of this dye on the water/air interface using the surface second harmonic generation; the values

$\mathrm{p}{K}_{\mathrm{a}1}$ = 4.0 and

$\mathrm{p}{K}_{\mathrm{a}2}$ = 4.2 were reported. These authors considered only the deeply colored anionic structures HX

^{−} and X

^{2−}, ignoring the possibility of their lactonization. However, this was before the appearance of our publications [

47,

48].

Using our values determined in CTAC micellar solution,

$\mathrm{p}{K}_{\mathrm{a}1}^{\mathrm{a}}$ = 1.83 and

$\mathrm{p}{K}_{\mathrm{a}2}^{\mathrm{a}}$ = 4.35 (

Table 1), and the above estimated fractions of the tautomers, the following indices of microscopic ionization constants can be calculated:

$\mathrm{p}{k}_{1,\mathrm{L}}$ = 1.5,

$\mathrm{p}{k}_{2,\mathrm{L}}$ = 4.1, and

$\mathrm{p}{k}_{2,\mathrm{COOH}}$ = 4.05. The last value is in line with the aforementioned inductive effect of the NO

_{2} group, because the conjugation between the xanthenes moiety and phthalic acid residue is absent. In 50 mass % aqueous ethanol [

47], the corresponding values are as follows:

$\mathrm{p}{k}_{1,\mathrm{L}}$ = 3.5,

$\mathrm{p}{k}_{2,\mathrm{L}}$ = 5.1, and

$\mathrm{p}{k}_{2,\mathrm{COOH}}$ = 5.3.

It is of common knowledge that for statistical reasons the difference

$\mathrm{p}{k}_{2,\mathrm{L}}$ −

$\mathrm{p}{k}_{1,\mathrm{L}}$ should include the log 4 contribution. In addition, the abovementioned

$\Delta \mathrm{p}{k}_{\mathrm{a}}^{\mathrm{el}}$ should be taken into account:

Therefore, the last-named value in CTAC micelles may be estimated as $\Delta \mathrm{p}{k}_{\mathrm{a}}^{\mathrm{el}}$ = 4.1 − 1.5 − 0.602 = 2.0. In 50 mass % ethanol, the corresponding value is equal to 1.0.

Now consider also the protolytic equilibrium of 2,4,5,7-tetranitrofluorescein. From the molar absorptivities given in

Section 4.3, the

${\alpha}_{{\mathrm{HX}}^{-}}$ = 0.65 and

${\alpha}_{{\mathrm{HL}}^{-}}$ = 0.35 values can be estimated as for 4,5-dibromo-2,7-dinitrofluorescein was done. This leads to the values

$\mathrm{p}{k}_{1,\mathrm{L}}$ = 0.62,

$\mathrm{p}{k}_{2,\mathrm{L}}$= 0.99 (

Scheme 6). In 50 mass % aqueous ethanol [

47], the corresponding values equal to

$\mathrm{p}{k}_{1,\mathrm{L}}$ = 1.6 and

$\mathrm{p}{k}_{2,\mathrm{L}}$= 2.1. Batistela et al. [

29] reported for 2,4,5,7-tetranitrofluorescein in water the values

$\mathrm{p}{K}_{\mathrm{a}1}$ = 0.38 and

$\mathrm{p}{K}_{\mathrm{a}1}$ = 2.48. Using these data and their

${E}_{\mathrm{max}}$ = 25 × 10

^{3} value for the HR

^{−} form, we have calculated approximate estimates of

$\mathrm{p}{k}_{1,\mathrm{L}}$ and

$\mathrm{p}{k}_{2,\mathrm{L}}$ to be 0.9 and 1.9, respectively. Therefore, the difference here is also very small.

In the micellar system,

$\mathrm{p}{k}_{2,\mathrm{L}}$ −

$\mathrm{p}{k}_{1,\mathrm{L}}$ = 0.37, and after subtracting the statistical difference of 0.602 we receive even a negative value of −0.23, which seems to contradict the physical meaning. Indeed, the

$\Delta \mathrm{p}{k}_{\mathrm{a}}^{\mathrm{el}}$ must be substantially positive. In 50 mass % ethanol the situation is similar. Possible ionic association in the Stern layer can further stabilize the dianion, but such effects are less likely in aqueous ethanol. Probably, in this case we are dealing with an increased stabilization of the dianion-lactone structure due to the maximum delocalization of negative charges on nitro groups. Such effects are known for compounds of porphyrin series where they may cause even an inversion of the stepwise dissociation constants [

79,

80]. Hence, the advantage of maximum charge delocalization in the aromatic system outweighs the electrostatic factor described by Equation (26).

Note, that in the lactonic structure L^{2−}, which absolutely dominates in the case of the tetranitrofluorescein dianion R^{2−}, the conjugated aromatic system is split into two almost isolated rings. The character of the tautomerism of 2,4,5,7-tetranitrofluorescein anions is rather instructively. Indeed, for the monoanion HR^{−} of the dye, the HX^{−} structure is preferable. This is an argument in favor of the importance of the symmetry of the chromophore system for the stabilization of the corresponding tautomer.

Lactone formation is much more expressed for phthalein dyes. Indeed, in the case of the un-substituted phenolphthalein in water with 8 mass % ethanol, the tautomer of HL

^{−} type predominates whereas the fraction of the L

^{2−} tautomer is about 0.54 [

81]. Again, the thermodynamic values of

$\mathrm{p}{k}_{1,\mathrm{L}}$ = 9.3 and

$\mathrm{p}{k}_{2,\mathrm{L}}$ = 10.3 are very close [

72,

81]. For chloro-, bromo- and nitro-derivatives of phenolphthalein, the tendency of anions to form lactone is even stronger [

71].

#### 4.6. Solvation Properties of the CTAC–4.0 M KCl System

Table 1 contains 45

$\mathrm{p}{K}_{\mathrm{a}}^{\mathrm{a}}$ values, which characterize the protolytic equilibria of 22 fluorescein dyes. In addition, there are

$\mathrm{p}{K}_{\mathrm{a}}^{\mathrm{a}}$s of eight sulfonephthalein indicators, four dinitrophenols, 2,6-diphenyl-4-(2,4,6-triphenylpyridinium-1-yl) phenolate, and

N,

N′-di-

n-octadecyl rhodamine. These 59 values cover the range from −0.5 to 10.47. To compare the solvation properties of the CTAC + 4.0 M KCl system with those of some non-aqueous solvents, we chose a 1:1 mixture of water and ethanol (by mass). This (or similar) mixed solvent is often used not only in our studies [

39,

40,

47,

48], but also in works of other authors [

28,

82].

The polarity of the above mixed solvent is much higher in respect to the micellar pseudophase studied in this paper; the corresponding

${E}_{\mathrm{T}}^{\mathrm{N}}$ values are 0.75 [

83] and 0.623 (see above). Consequently, the Stern layer in this micellar system is somewhat less polar with respect to cationic micelles at a low bulk ionic strength. The reason probably lies in the weaker hydration of the Stern layer in the presence of 4.0 M KCl. For the last-named cationic micelles at low ionic strength,

${E}_{\mathrm{T}}^{\mathrm{N}}$ = 0.69–0.70 [

8]. At the same time, the

$\mathrm{p}{K}_{\mathrm{a}}$ values in 50 mass % ethanol are always higher as compared with the

$\mathrm{p}{K}_{\mathrm{a}}^{\mathrm{a}}$s of the same dyes. The correlation is depicted in

Figure 5.

However, a more detailed analysis requires taking into account the differences in the type of these dissociation constants. Indeed, for the

$\mathrm{p}{K}_{\mathrm{a}}$ values in the solvent “s” the following expression is valid:

Here

${}^{\mathrm{w}}{\gamma}_{{\mathrm{H}}^{+}}^{\mathrm{s}}$ stands for activity coefficient of proton transfer from water to the given solvent; for 50 mass % ethanol,

$\mathrm{log}{}^{\mathrm{w}}{\gamma}_{{\mathrm{H}}^{+}}^{\mathrm{s}}$ = −0.66 [

84]. In the case of the

$\mathrm{p}{K}_{\mathrm{a}}^{\mathrm{a}}$ values, there is no such contribution, since the pH values are determined in the bulk phase and not in the pseudophase. On the other hand, the indices of the apparent constants contain the item

$-\mathrm{\Psi}F/2.303RT$. For the colloidal system under study, it was estimated above as −0.26. Strictly speaking, both

${}^{\mathrm{w}}{\gamma}_{{\mathrm{H}}^{+}}^{\mathrm{s}}$ and

$\mathrm{\Psi}$ values are extra-thermodynamic quantities, but using them shows that the

${}^{\mathrm{w}}{\gamma}_{\mathrm{B}}^{\mathrm{m}}/{}^{\mathrm{w}}{\gamma}_{\mathrm{HB}}^{\mathrm{m}}$ and

${}^{\mathrm{w}}{\gamma}_{\mathrm{B}}^{\mathrm{s}}/{}^{\mathrm{w}}{\gamma}_{\mathrm{HB}}^{\mathrm{s}}$ values approach each other.

Electrostatic interactions between the cationic head groups of the surfactant and dye anions may additionally stabilize the latter. However, as was shown earlier [

7], such interactions should not be considered as neutralization of negative charges. Rather, they should be viewed as the formation of “loose” ionic associates that (latent) influence the

${}^{\mathrm{w}}{\gamma}_{\mathrm{i}}^{\mathrm{m}}$ values.

Finally, it should be noted that these transfer activity coefficients include the influence of the shift of the tautomeric equilibrium (if any) on going from one medium to another. For the fluoresceins with free carboxylic group, these equilibria were considered above.