Anomalous salting-out, self-association and pKa effects in the practically-insoluble bromothymol blue doi: https://doi.org/10.5599/admet.1822 1 ADMET & DMPK 0(0) (2023) 000-000; doi: https://doi.org/10.5599/admet.1822 Open Access : ISSN : 1848-7718 http://www.pub.iapchem.org/ojs/index.php/admet/index Communication Anomalous salting-out, self-association and pKa effects in the practically-insoluble bromothymol blue Alex Avdeef in-ADME Research, New York, NY 10128 USA E-mail: alex@in-ADME.com; Tel.: +1-646-678-5713 Received: April 17, 2023; Revised: May 17, 2023; Published: May 23, 2023 Abstract Background and Purpose: The widely-used and practically insoluble diprotic acidic dye, bromothymol blue (BTB), is a neutral molecule in strongly acidic aqueous solutions. The Schill (1964) extensive solubility-pH measurement of bromothymol blue in 0.1 and 1.0 M NaCl solutions, with pH adjusted with HCl from 0.0 to 5.4, featured several unusual findings. The data suggest that the difference in solubility of the neutral-form molecule in 1M NaCl is more than 0.7 log unit lower than the solubility in pure water. This could be considered as uncharacteristically high for a salting-out effect. Also, the study reported two apparent values of pKa1, 1.48 and 1.00, in 0.1 M and 1.0 M NaCl solutions, respectively. The only other measured value found for pKa1 in the literature is -0.66 (Gupta and Cadwallader, 1968). Experimental Approach: It was reasoned that the there can be only a single pKa1 for BTB. Also, it was hypothesized that salting-out alone might not account for such a large difference in solubility observed at the two levels of salt. A generalized mass action approach incorporating activity corrections for charged species using the Stokes-Robinson hydration equation and for neutral species using the Setschenow equation, was selected to analyze the Schill solubility- pH data to seek a rationalization of these unusual results. Key Results: BTB reveals complex speciation chemistry in saturated aqueous solutions which had been poorly understood for many years. The appear - ance of two different values of pKa1 at different levels of NaCl and the anomalously high value of the empirical salting-out constant could be rationalized to normal values by invoking the formation of a very stable neutral dimer (log K2 = 10.0 ± 0.1 M-1). A ‘normal’ salting-out constant, 0.25 M-1 was then derived. It was also possible to estimate the ‘self-interaction’ constant. The data analysis in the present study critically depended on the pKa1 = -0.66 reported by Gupta and Cadwallader. Conclusion: A more reasonable salting- out constant and a consistent single value for pKa1 have been determined by considering a self-interacting (aggregation) model involving an uncharged form of the molecule, which is likely a zwitterion, as suggested by literature spectrophotometric studies. ©2023 by the authors. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/). Keywords Salting-out effect; self-interaction; aggregation; solubility-pH; intrinsic solubility; ionization constant; dimerization constant Introduction The intrinsic (i.e., neutral form) solubility of an ionizable substance in water generally decreases when a ‘water-structure maker’ salt (e.g., NaCl) is added to the solution. The phenomenon is known as ‘salting-out’ [1-5]. The decrease in solubility seldom exceeds 0.3 log unit per molar salt. Such changes in magnitude are https://doi.org/10.5599/admet.1822 https://doi.org/10.5599/admet.1822 http://www.pub.iapchem.org/ojs/index.php/admet/index mailto:alex@in-ADME.com http://creativecommons.org/licenses/by/4.0/ Alex Avdeef ADMET & DMPK 00(0) (2023) 000-000 2 comparable to those seen between different polymorphs of a drug substance [6] and in solubility differences between racemates and individual isomers of an optically-active drug substance [7-9]. In a simple view of the salting-out phenomenon, ions introduced from the salt (e.g., Na+, Cl–) become strongly hydrated, thus tying up a significant portion of the available water. The added neutral organic solute, effectively deprived of the water molecules associated with the salt ions, dissolves to a lesser extent in terms of the total solution volume, thus appearing to be less soluble. Many studies of the salting effect had focused on relatively simple organic nonelectrolytes, including gases and water-immiscible organic solvents [2-4,10-12]. The more soluble the nonelectrolyte, the larger is the salting effect [11]. However, there appear to be very few reported salting studies of practically-insoluble (e.g., intrinsic solubility, S0 < 10-5 M) nonelectrolytes, particularly of drug-like molecules, or substances of similar complexity. In this communication, we re-examine the saturation solution-pH behavior of bromothymol blue (BTB, Fig. 1), which is practically insoluble in its zero net-charge form in strongly acidic solutions (left-most structure in Fig. 1). The molecule may be used as an indicator (yellow for pH <6, blue for pH >7.6, and green in between) to follow pH-dependent cellular processes. It can function as a complexing agent, and has been used in textiles, paints, cleaning products, detergents, and photovoltaic cells [13]. In cases of prolonged general exposure or if absorbed through the skin, BTB can be harmful. Because of its low solubility and high stability, BTB can be a persistent environmental pollutant [13]. BTB is a diprotic acid (H2A), with ionization reactions shown in Figure 1. In strongly acidic solution (pH <1), the molecule is plausibly a zwitterion forming a red solution. In mildly acidic/neutral and alkaline solutions, BTB exists as the anionic species HA– and A2–. The second ionization constant (pKa2) has the reported value of 7.12 at ionic strength, I = 0.1 M [14]. In contrast, the value of pKa1 has been unresolved for many years, with values reported as low as -0.66 [15] and as high as 1.48 [14]. There has also been a long-standing controversy about the structure of the uncharged species in aqueous solution (pH <1). Figure 1. Ionization equilibria for the diprotic weak acid bromothymol blue in water. Although the value of pKa2 is confidently established, the value of pKa1 has been elusive. Schill [14] extensively studied the solubility-pH behavior of BTB in 0.1 M and 1.0 M NaCl solutions at 20 °C. In a series of publications, Schill applied BTB as a sensitive ion-pair extraction reagent to determine the concentrations of amines and quaternary ammonium compounds by spectrophotometry. The reported BTB solubility-pH data, along with the originally-determined constants are shown in Figure 2. We found three points of interest in Schill’s study, which appeared in need of additional examination. • The study indicated surprising departures from the expected salting behavior of neutral electrolytes. The difference between the apparent intrinsic solubility in pure water and in solutions containing 1.0 M NaCl was reported to be greater than 0.7 log unit for BTB, which is inexplicably high [1-5]. ADMET & DMPK 00(0) (2023) 000-000 Polyvinyl alcohol nanoparticles loaded with propolis extract doi: https://doi.org/10.5599/admet.1822 3 • Also, two significantly different values of the first ionization constant were reported by Schill in saturated solutions: pKa1 = 1.48 in 0.1 M NaCl and pKa1 = 1.00 in 1.0 M NaCl (cf. Fig. 2). The Stokes-Robinson hydration equation [16] (a) includes the Debye-Hückel expression (ion-ion electrostatic interactions), (b) incorporates decrease in activity of water (work done in immobilizing some of the bulk water to hydrate ions), and (c) accounts for the free energy change of ions (as their concentrations increase when the volume of bulk water decreases upon hydration of ions). From the Stokes-Robinson hydration equation, the difference between the apparent pKa1 values is expected to be near 0.02, far less than the above 0.48 implied value [14]. • Schill’s examination of the UV spectra of BTB in sub-saturated solutions suggested that (AH–)2 and (AH–)4 aggregates might be forming in the pH region where the BTB anion prevails. They reported association constants from analysis of the spectroscopic data in the absence of visible signs of precipitation. In saturated solutions in the same region, micelles appeared to form. The reported limiting slope in Figure 2 in the pH 1-3 region is +1, which is not compatible with the aggregation models proposed by Schill. If aggregation comprised solely of the HA– species, the slopes in the acid region would have been +2 (dimer) or +4 (tetramer), rather than +1 [17]. If mixed-charge aggregates (H2A.HA–)n were to form, the slope would be +1 [17], but such models cannot resolve the unusual salting-out magnitude reported by Schill. So, the stoichiometry of the observed aggregation may need to be further examined. pH Figure 2. Bromothymol blue solubility-pH profiles reported by Schill [14], with data collected at 20 oC, after 24 h equilibration time. The upper saturated solutions profile contained 0.1 M NaCl, while the lower profile contained 1.0 M NaCl. The pH electrode was calibrated by Schill for the concentration scale, using solutions of known [H+] concentrations. The various listed equilibrium constants are those reported by Schill. In the present communication, an attempt is made to rationalize the apparently excessive salting behavior, the lack of consistency regarding the value of pKa1, and the formation of aggregates by applying a mass action model, using the program pDISOL-XTM (in-ADME Research) [16-26], to analyze the saturation solubility-pH data published by Schill [14]. It was hypothesized that the critical aggregation, which could explain some of the above-mentioned anomalies in acidic solutions (pH <3), is due to the self-association of the zero net-charge species, H2A. Method Mass action equilibrium model Consider a diprotic acid, H2A, with the dissociation constants pKa1 and pKa2. Let’s assume it is prone to form zero net-charge dimers, (H2A)2, in aqueous solutions. The equilibrium reactions of relevance in saturated solutions (pH <6) are H2A  HA– + H+ Ka1 = [HA–][H+]/[H2A] (1a) lo g ( S / M ) https://doi.org/10.5599/admet.1822 Alex Avdeef ADMET & DMPK 00(0) (2023) 000-000 4 HA–  A2– + H+ Ka2 = [A2–][H+]/[HA–] (1b) 2H2A  H4A2 K2 = [H4A2]/[H2A]2 (1c) H2A(s)  H2A S0 = [H2A] (1d) Na.HA(s)  Na+ + HA– Ksp = [Na+][HA–] (1e) where S0 is the intrinsic solubility of the uncharged (monomeric free acid) form of the molecule. Based on the above relations, the total concentration of the weak acid in the saturated aqueous phase, Atotaq, is the total solubility, ST, which can be expressed solely in terms of equilibrium constants and pH: Atotaq = ST = [H2A] + [HA–] + [A2–] + 2 [H4A2] (2a) = [H2A] + [H2A] Ka1 / [H+] + [H2A] Ka1 Ka2 / [H+]2 + 2 K2 [H2A]2 (2b) = S0 (1 + Ka1 / [H+] + Ka1 Ka2 / [H+]2 + 2 S0 K2) (2c) In logarithmic form, base 10, log ST = log S0 + log (1 + 10–pKa1 + pH + 10–pKa1 –pKa2 + 2pH + 210–pS0 +log K2 ) (3) In the thermodynamically valid constant ionic medium (CIM) activity scale [17], the reference ionic strength may be set to Iref > 0. In such a framework, all equilibrium constants are expressed in terms of concentrations. In the multiple-pH solubility data analysis, all constants are adjusted for local deviations from Iref, using the Stokes-Robinson hydration equation [16,17]. In the case of uncharged species, similar adjustments for local deviations from Iref are made using the salting out equation approach described below. In the CIM framework, the operational paH scale (pH meter readings) is standardized to the concentration scale, pcH, using the four-parameter equation [27] paH = α + k pcH + jH [H+] + jOH Kw / [H+] (4) where Kw is the ionization constant of water [28]. The jH term corrects paH readings for the nonlinear pH electrode response due to liquid junction and asymmetry potentials in highly acidic solutions (pH <2), while the jOH term corrects for high-pH nonlinear effects [17]. Since Schill standardized the electrode to read on the concentration scale and since all saturation data were for pH <6, it was assumed here that α = jOH = 0 and k = 1. The jH was adjusted during the regression analysis since many pH values were <1 in the 1 M NaCl set (Fig. 2). In the analysis of the Schill data, pKa2 was selected as 7.12. (Since most of the data are in the acidic range, pKa2 is of minor role here.) The rest of the constants in Eq. (3) were determined by nonlinear regression analysis (i.e. mass action model), the details of which are described elsewhere [16,17]. The data were first evaluated as Schill had done, and essentially the same constants were determined as those listed in Figure 2. For those constants, self-interaction (aggregation) was not included (as per Schill’s assumption). Salting activity model for uncharged species The Setschenow equation [1,2,10-15] describes the salting effect on nonelectrolyte (i.e. H2A) total aqueous solubility, ST, as log (ST(0) / ST(s)) = KCs (5) where K is the empirical Setschenow coefficient (M−1) and Cs is the concentration (M) of the added salt. ST(0) and ST(s) are the neutral solute total solubility values in pure water and in water containing salt, respectively. K is positive in the case of salting-out and negative in the case of salting-in processes. Generally, the equilibrium constants in Eq. (5) can represent a solute partitioning process between different phases. If self-interaction (aggregation) is hypothesized, then a modified form of the Setschenow equation may need to be invoked [2,4,11]: ADMET & DMPK 00(0) (2023) 000-000 Polyvinyl alcohol nanoparticles loaded with propolis extract doi: https://doi.org/10.5599/admet.1822 5 log (ST(0) / ST(s) ) = ksCs + ki (ST(s) – ST(0)) (6) where ks and ki are nonelectrolyte salting and self-interaction parameters, respectively. Only for low ST or in the absence of nonelectrolyte self-interaction will the empirical Setschenow constant, K, be equal to the salting parameter, ks. Usually ks is determined from oil-water partition data using small volumes of water-immiscible oil, where aggregates would not be expected to enter the oil phase [11]. Eq. (5), cast in the form of partition coefficients, may be used to determine ks. The concentration of the monomer is measured in the oil phase and the corres- ponding value in the water phase is calculated from mass balance to determine the partition coefficient. Once ks is known, then ki can be calculated form Eq. (6). This is the approach used by Al-Maaieh and Flanagan [11] to determine the self-interaction parameter for caffeine, theophylline, and theobromine (e.g., ki = -2.06 M-1 for caffeine in 1 M Na2SO4 solution, indicating less aggregation with increasing salt concentration [11]). A different approach was used presently: ks was determined by substituting into Eq. (5) the intrinsic (mono- mer) solubility, S0 (cf. Eq. (1d)), determined by regression analysis. In Eq. (5), K was taken to be ks; ST(0) and ST(s) were substituted with S0(0) *and S0(s), respectively. Once ks was so determined, then ki was calculated from Eq. (6). Abraham linear free energy descriptors used to predict the salting-out constant of BTB Abraham’s five linear free energy solvation descriptors (A, B, Sπ, E, V) have been used to describe the distribution of nonelectrolytes between two phases [29,30]. A is the H-bond acidity and B is the H-bond basicity of the solute. Sπ is the dipolarity/polarizability, E is an excess molar refractivity in units of (cm3/mol)/10, and V is the McGowan characteristic molar volume in units of (cm3/mol)/100. Endo et al. [4] used the Abraham model to predict salting-out constants (M-1): ks = a0 + a1A + a2B + a3Sπ + a4E + a5V (7) The a0-a5 coefficients in Eq. (7) were determined by multi-linear regression (MLR): 0.112, -0.047, -0.060, -0.042, -0.020, and 0.171, respectively [4]. Evidently, large molecules increase the salting-out behavior, and polar molecules act in the opposite direction. Presently, the a-coefficients were re-determined by partial least squares (PLS) regression (open-source package from https://cran.r-project.org/web/packages/pls), using 142 ks values as the training set (136 values compiled/measured by Endo et al. [4] and six derived here from the data of Furia et al. [12]) to predict the ks value of bromothymol blue. Values of the Abraham descriptors for bromothymol blue were calculated from its 2D structure using the ABSOLV algorithm [30] (cf. www.acdlabs.com). Results and discussion of data re-analysis The nature of the structure of the BTB free acid species in saturated solutions is still controversial and has been discussed for many decades. Several different monomeric structures for the H2A species may exist/co- exist (two zwitterion tautomers and a closed sultone ring uncharged form) in saturated solutions below pH 3, each with its own associated ‘micro-constant’ for pKa1. An electrostatically-bound dimer based on two zwitterions oriented with opposite-charge groups at contact distances may be feasible. Other structures are possible for a BTB dimer. A further complication is that the structural form of the BTB free acid in the crystal lattice may undergo tautomeric re-arrangement upon dissolution, posing a challenge to the canonical definition of intrinsic solubility, since the form of the substance would be different between the solid state and the solution phases. Definitive support for structures of BTB species in saturated aqueous solutions is sketchy and is mostly inferred from spectrophotometric measurements in sub-saturated solutions. https://doi.org/10.5599/admet.1822 https://cran.r-project.org/web/packages/pls http://www.acdlabs.com/ Alex Avdeef ADMET & DMPK 00(0) (2023) 000-000 6 The speciation analysis of solubility-pH data is based on thermodynamic principles, formulated in terms of ‘macro-constants.’ Structural questions can only be addressed indirectly. In this communication, three different model strategies were hypothesized and tested against Schill’s solubility-pH data. MODEL A. Dimer-free, single pKa1 model, based on an unusually-high salting-out factor Our first strategy was to be open to the possibility of an unusually high K, to assume that (i) dimers did not form in the pH <3 region, and (ii) one of Schill’s pKa values was more reliable (but both values could not be simultaneously ‘correct’). We selected (and refined) pKa1 = 1.43 ±0.09 (0.1M NaCl) since its value would be least affected by the salting-out effect of bromothymol blue. A fit of the two apparent intrinsic solubility values to Cs (Eq. (5)), yielded intercept salt-free value of pS0 = 5.10 and the slope factor K = 0.778. The refinement of the model in the case of 0.1 M NaCl (keeping pKa1 fixed at 1.43) yielded at Iref = 0.1 M: pS0 = 5.17±0.02 (using the high K to correct for the activity of the net zero charge H2A species) and pKsp = 4.41±0.03 (goodness-of-fit, GOF = 0.50). However, when the above model was applied to the 1.0 M NaCl case, it was not feasible to adhere to the above assumption (i) at the high salt level. It was not possible to fit the Schill data without invoking the mixed- charge dimer, H2A.HA–, since such a species would account for the apparently lower pKa1 in 1 M NaCl solutions reported by Schill, while maintaining the slope in the 1-3 pH region at +1 [17]. Also, it was necessary to invoke two salt species, with the new addition being Na.H2A.HA(s), needed to explain the data in the pH 2.5-3.5 region. In the refinement of the data, pKa1 and pS0 were kept fixed at 1.43 and 5.17 (since the 0.1 M NaCl data defined these values). The refined constants, also with reference to Iref = 0.1 M, were log KH3A2 = 5.87±0.03, pKps (NaH3A2) = 4.93 ±0.02, and pKsp(NaHA) = 4.33 ±0.02 (GOF = 0.35) for the case of 1.0 M NaCl. MODEL B. Fitting a single pKa1 to Schill’s data, assuming a neutral dimer forms In our next strategy, it was hypothesized that there can only be a single pKa1 for bromothymol blue and its value would not likely be either 1.48 or 1.00, as Schill had reported. We hypothesized that a neutral dimer formed. It was reasoned that this caused the ST near pH 0 to be different in the 0.1 and 1.0 M NaCl solutions. This was hypothesized to be the explanation for the two values of the reported pKa1. Since there appeared to be less self-association in the 1 M NaCl solutions, the new value for the pKa1 was sought in that medium, with Iref was set to 1.0 M. Starting with the Schill pKa1 = 1.00 as a fixed constant, the pS0, log K2, and pKsp constants were determined iteratively by nonlinear regression. Next, these three refined values were fixed, and pKa1 was subjected to regression. Its value decreased steadily. It was then fixed, and the process was repeated with the first three constants. After several cycles of this ‘block-diagonalization’ refinement, the minimum errors in all four constants were reached, and the overall goodness-of-fit (GOF) [17] settled at its minimum value. The excessive correlations between the pKa1 and the other three constants did not permit their simultaneous determination, so the ‘block-diagonalization’ approach was used. The pKa1 so determined (+0.217) was then applied to the 0.1 M NaCl set. The same iterative process led to convergence. It soon became evident that a range of reasonable pKa1 values could be proposed and the fitting of the Schill data (Fig. 2) would be equally good (as indicated by the minimum GOF reached). Since the correlation between pKa1 and the other constants was extreme, the ‘block-diagonalization’ minimum lay over a very shallow well, and normal experimental errors in solubility measurement caused havoc to pin down the ‘best’ pKa1 value. MODEL C. Applying an independently-measured single pKa1 to Schill’s data, assuming a neutral dimer forms Attention was then directed to finding an independently determined value of pKa1 for the further analysis of the Schill solubility data. The only value found was reported by Gupta and Cadwallader [15]: pKa1 = -0.66. The authors collected UV-visible spectroscopic data in the pH interval from 0.92 to -1.08 (concentration ADMET & DMPK 00(0) (2023) 000-000 Polyvinyl alcohol nanoparticles loaded with propolis extract doi: https://doi.org/10.5599/admet.1822 7 scale), where the pH of distilled water was adjusted using 12 M HCl. At -log [H+] = -0.662, the concentration of the anion was found to be equal to the concentration of the uncharged species. This defines the value of the pKa1 at ionic strength 10+0.662 = 4.59 M. The Stokes-Robinson hydration equation was then used to harmonize this value to the CIM activity scale (Iref = 1.0 M), to obtain pKa1 = -1.18, the value ultimately to be used as a fixed contribution in the regression analysis of the Schiff solubility data. Model selection Model A described above, with the single pKa1 = 1.43 (although it could not support a dimer-free case for both 0.1 and 1.0 M NaCl media), is consistent with the ‘red’ species in Figure 1 as shedding a proton from a protonated carbonyl group in the cyclohexadienone zwitterion. Also, Model A supports a more soluble ‘red’ zwitterion with pS0 = 5.17, compared to 8.02 in Model C (Table 1). However, pKa1, derived from Schill’s data, depends on two assumptions that could not be fully supported since it was necessary to invoke the presence of a mixed dimer, H2A.HA–, as well as a salt based on the dimer, in 1.0 M NaCl solutions. The latter two species could not be fit to the data in 0.1 M solutions. Model A was also dependent on an unusually high value of the empirical constant, K = 0.778. Model B can be dismissed since a specific value of pKa1 could not be determined definitively from the solubility data by the ‘block diagonalization’ refinement procedure. Model C is attractive since the pKa1 value was derived from an independent study using UV/Vis data taken in sub-saturated solutions [15]. The so-determined value, adjusted to Iref = 1.0 M is -1.18, a much lower value than either of the two apparent values reported by Schill. It may represent the shedding of the proton from a protonated sulfonic acid group in an open sultone ring form of BTB, possibly present in the sub-saturated solution used by Gupta and Cadwallader [15]. However, structural issues cannot be directly addressed by the thermodynamic speciation analysis presented here. It was decided in this communication to focus further discussion on Model C. Also, the Setschenow constant based on Model C is much more in line with values taken from the literature for many molecules. Mass action equilibrium model The results of the final re-analysis of Schill’s two sets of saturation solubility-pH data (in 0.1 and 1.0 M NaCl media), employing the Gupta-Cadwallader [15] pKa1 (transformed to the CIM activity scale), are listed in Table 1 and depicted in Figure 3. Table 1. Refined constants - bromothymol blue, 20 °C, 0.1 and 1.0 M NaCl Media (Iref = 1.0 M) [NaCl] / M pKa1 pS0 log K2 pKsp Iavg / Ma nb GOFc 0.10 -1.18 d 8.03 ±0.03 10.11 ±0.10 4.41 ±0.02 0.11 10 0.48 1.00 -1.18 d 8.02 ±0.01 9.94 ±0.02 4.31 ±0.01 1.07 15 0.18 aAverage ionic strength. To minimize dilution effects, 12 M HCl titrant was used in the refinement model. bNumber of pH points. cGOF = goodness-of-fit [16], based on assigned individual log S errors of 0.1 log unit. dpKa1 = -0.66 at I = 4.59 M from Gupta and Cadwallader [15] was transformed to Iref = 1.0 M here, using the Stokes-Robinson hydration equation. Dependence of equilibrium constants on ıonic strength (Stokes-Robinson hydration equation corrections) When the ionic strength for a given point in a log S-pH titration is calculated to stray from the designated Iref value (1.0 M here), it is beneficial to adjust the equilibrium constants in Eqs. (1a), (1b), and (1e). The Debye- Hückel equation is often used for this adjustment. However, the latter equation becomes less accurate as ionic strength exceeds about 0.3 M [17]. Since the Gupta-Cadwallader [15] pKa1 was measured at I = 4.59 M, it was not expected that the simple Debye-Hückel equation would be suitable in correcting for activity changes. https://doi.org/10.5599/admet.1822 Alex Avdeef ADMET & DMPK 00(0) (2023) 000-000 8 (a) (b) pH pH Figure 3. Summary of the re-analysis of bromothymol blue solubility-pH data reported by Schill [14], incorporating the pKa1 reported by Gupta and Cadwallader [15] (adjusted to Iref used here). The points in the green solid curves were calculated after correcting for salting-out effects of the uncharged saturated species. The curves decrease with pH <0 since salt concentrations are elevated due to addition of titrant. Ionic strength, M Ionic strength, M Figure 4. (a) Dependence of pKa1 and pKa2 on ionic strength, according to the Stokes-Robinson hydration model. (b) Dependence of the negative logarithm of the solubility product, Ksp = [Na+][HA–] on ionic strength. A more comprehensive correction scheme, which may still be useful for I < 5 M, involves the application of the Stokes-Robinson hydration theory [16,17]. The scheme is coded into pDISOL-X. Figure 4 shows how the ionization constants and the solubility product depend on ionic strength in the Stokes-Robinson model. The Gupta-Cadwallader reported pKa1 = -0.66 (unfilled square in Fig. 4a) was adjusted to -1.18 at Iref = 1.0 M (solid red circle in the upper curve in Fig. 4a). The solubility product, Ksp (cf., Eq. (1e) and Fig. 4b), has a less steep ionic strength dependence, compared to those of pKa1 and pKa2. Since ionic strength is not defined for uncharged species, the Stokes-Robinson scheme is not directly applicable to the intrinsic solubility (Eq. (1c)) and dimerization of uncharged species (Eq. (1d)) equilibrium constants. However, the next section addresses how salt levels can affect the activity of uncharged species. Salting model The application of Eq. (5) to the total solubility values in Figure 2 resulted in the linear relationship, pST(s) = 5.10 + 0.778 Cs, where the slope factor is K = 0.778. Figure 5a shows the equivalent of Eq. (5) based on intrinsic (monomer) solubility values. The slope factor listed in the figure corresponds to the true salting- out parameter, ks = 0.250. When this salting-out value is substituted into Eq. (6) for the case of Cs = 1.0 M, lo g ( S / M ) lo g ( S / M ) p K a 2 p K sp p K a 1 ADMET & DMPK 00(0) (2023) 000-000 Polyvinyl alcohol nanoparticles loaded with propolis extract doi: https://doi.org/10.5599/admet.1822 9 ki = (pST(s) – pST(0) – ksCs) / (ST(s) – ST(0)) = (5.865 – 5.094 – 0.250)/(1.364·10-6 – 8.056·10-6) = -7.787·104 (7) Its magnitude exceeds that of any other reported ki values, as far as we could find. Once ks and ki were determined, Eq. (6) can be used to calculate the intrinsic and dimerization equilibrium constants of BTB over a range of salt concentrations. This is evident in the green solid curves in Figure 3 for pH values below zero, where titrant additions to achieve very low pH increase the salt content in the saturated solutions. CS / M (of added NaCl) CS / M (of added NaCl) Figure 5. (a) Salting-out and (b) dimerization effects in bromothymol blue saturated solutions, as a function of the amount of added salt, NaCl. These are the apparent refined constants when ks was set to zero. Two salt points preclude the possibility to test nonlinear relationships, as seen in cases of substituted phenolic acids covering a wide range of salt concentrations [12]. Distribution of aqueous-phase species in saturated solutions of bromothymol blue The equilibrium model developed using Schill’s solubility-pH data and Gupta-Cadwallader pKa1 (Table 1) allows for the calculation of the distribution of species at the two levels of salts considered, as illustrated in Figure 6. It is evident that the monomer concentration (green dash-dot curve in Fig. 6) is dwarfed by that of the dimer (red dash-dot-dot curve in Fig. 6). pcH pcH Figure 6. Distribution of species in (a) 0.1 M NaCl and (b) 1.0 M NaCl containing solutions, based on the constants in Table 1; pKa1 = -1.18 (Iref = 1.0 M). p S 0 (S ) lo g K 2 (S ) https://doi.org/10.5599/admet.1822 Alex Avdeef ADMET & DMPK 00(0) (2023) 000-000 10 In the 0.1 M NaCl medium at pH 1.28 (Fig. 6a), 50% of the total bromothymol blue is in the monoanionic form and half is essentially in the dimeric form. So, in Figure 2, the Schill-proposed ionization constant, 1.48, appears to be indicating the equilibrium between anionic HA– and the dimeric (H2A)2 species (and not the monomer). Similarly, in the 1.0 M NaCl medium at pH 0.60 (Fig. 6b), 50 % of BTB is in the monoanionic form and half is essentially in the dimeric form. The Schill-proposed ionization constant, 1.00, again appears to be indicating the equilibrium between anionic HA– and the dimeric (H2A)2 species. At the half-point pH1/2, [HA–] ≈ [H4A2]. From Eq. (2c), the estimate of pKa1 ≈ -log 2 + pcH + pS0 – log K2. For the 0.1 M and 1.0 M NaCl cases, the resulting approximate pKa1 values are -1.3 and -1.4, respectively, compared to the -1.18 used (Fig. 3). The slight differences may indicate the shortcomings in attempts to standardize the pH electrode in such low pH regions, as per Eq. (4), given the uncertainty over junction potentials and the uncertainty in adjusting the pKa1 = -0.66 (at 4.59 M ionic strength) from Gupta and Cadwallader [15] to the selected reference ionic strength of 1.0 M. Comparison of bromothymol blue (BTB) to thymol blue (TB) equilibrium speciation The ‘Flexible‑Acceptor’ GSE consensus model [31] predicts the intrinsic solubility values of thymol blue (TB) and BTB as 6.67 and 7.68, respectively. Given the similarity of structures, it might be anticipated that TB and BTB would possess similar equilibrium reactions. Shimada et al. [32] analyzed the spectral changes (300 to 650 nm) of TB solutions in the pH -0.02 to 4.35 interval. Solutions of TB gradually change from red to yellow as pH is raised in the interval studied. One prominent and two minor isosbestic points were evident in the spectra. Using principal components analysis (PCA) and alternative least-square (ALS) regression, the authors concluded that two major species accounted for the TB equilibria in the strong acid solutions. The apparent pKa1 of TB was determined to be 1.54 in 0.1 M and 1.45 at 1.0 M ionic strength solutions [32]. The red species was most plausibly the zwitterionic form of TB, possibly a carbocation or its resonance equivalent, like the left structure in Figure 1 of BTB. The colorless uncharged sultone closed ring form was not expected to be stable in the polar medium of water (although it is present in the crystal structure reported by Yamaguchi et al. [33]). Since the bromine atoms in BTB are electron withdrawing substituents, the pKa1 value of BTB was suggested (without reference) to be -1.3 (compared to +1.6 of BT), and the red form was anticipated to be dominant in highly acidic aqueous medium [32]. From the rigorous analysis of spectrophotometric, potentiometric, and conductimetric data at 25 oC of TB in 1.1 M ionic strength (NaCl) aqueous solutions, Balderas-Hernández et al. [34] reported pKa2 = 8.90 and the constants for the reactions H2A + HA–  H3A2– KH3A2 = [H3A2 –]/[H2A][HA–] = 10+11.48 (8) 2H2A  H4A2 KH4A2 = [H4A2]/[H2A] 2 = 10+11.41 (9) The above two constants were originally reported on the cumulative ‘stability’ basis. The conversions to the step-wise basis [17] in Eqs. (8) and (9) employed pKa1 = 1.45 for TB from Shimada et al. [32]. The latter constant taken with those from Eqs. (8) and (9) suggest that the proton dissociation constant of the H4A2 dimeric species has a dimeric ionization constant of 1.38, as indicated in Eq. (10). H4A2  H3A2– + H+ Ka” = [H3A2–][H+]/[H4A2] = 10-1.38 (10) Hence, the anionic dimer in TB is expected to be dominant above pH 1.38, while the zero net-charge dimer is expected to prevail below pH 1.38. Attempts to incorporate the above model into the Schill data for BTB were not successful. Given the BTB pKa1 = -1.18, Schill’s solubility-pH data did not support the inclusion of the H3A2– species in both the 0.1 and 1.0 M NaCl solutions, as discussed earlier in the context of Model A. It is quite remarkable that the uncharged dimeric species from the Balderas-Hernández et al. [34] TB study is so close in value to that reported here for the BTB. The predicted TB intrinsic solubility is an order of ADMET & DMPK 00(0) (2023) 000-000 Polyvinyl alcohol nanoparticles loaded with propolis extract doi: https://doi.org/10.5599/admet.1822 11 magnitude higher than that of BTB. It is reasonable to view the TB and BTB system as being similar, with ionizations shifted to lower values of pH in the case of BTB because of the bromine substituents. Prediction of ks using the Abraham model and literature values of salting-out constants The 142 ks values mentioned earlier (including the provided Abraham descriptors) [4,12] were used to re-determine the Abraham coefficients in Eq. (7) by PLS regression. The a0-a5 coefficients were determined as 0.090, -0.073, -0.064, -0.039, -0.002, +0.188, respectively. The regression coefficients are comparable to those reported by Endo et al. [4]. Highly-polar molecules are predicted to have weak salting-out effects (a1- a4 factors). On the other hand, large molecules are expected to be highly sensitive to salting-out. The ABSOLV- calculated values of the Abraham descriptors for bromothymol blue (left-most structure in Fig. 1) are A = 0.33, B = 1.28, Sπ = 2.48, E = 2.94, and V = 3.99. The polar terms contribute 21 % (negative) to the predicted effect and the volume term contributes 75 % (positive). Using the coefficients reported by Endo et al. [4], predicted ks = 0.54 for BTB. Using the PLS-derived coefficients here, the predicted ks = 0.63. The two predictions are substantially higher than the ks = 0.25 value determined from the data of Schill [14] using Model C. It may be that the training set of 142 ks values did not cover the chemical space of molecules like bromothymol blue or molecules that form very stable water-soluble oligomers. Limitation of the bromothymol blue equilibrium model As discussed elsewhere [9, 17-23], it is not possible to determine the exact degree of aggregation of neutral species solely from the solubility-pH data (Case 1a in Fig. 6.6 in ref. [17]). It is necessary to use other stoichiometry-sensitive methods, such as ESI-Q-TOF-MS/MS [25]. The simplest stoichiometry (dimer) was modeled here, but the actual species may be a tetramer, a higher-order/mixture of (H2A)n oligomers [14,15]. Any of such species can fit the solubility data equally well for low sample concentrations. The pH1/2 values in Figure 6 would remain unchanged for low sample concentrations. The pKa1 value is not easy to measure independently since its value is negative, and aggregation is a confounding complication. Standardization of the pH electrode is likely to be a challenge. The measurement of the ionization constant in cosolvent mixtures (e.g., methanol-water) is expected to increase the pKa1 value, perhaps making the determination more reliable. Potentiometric titrations, which can simultaneously determine both the solubility and the pKa can be effective [17, 35]. Additional measurements of the saturation solubility of bromothymol blue for pH >6 might possibly support some of the suggestions proposed by Schill regarding the nature of self-association he studied by UV-vis spectrophotometry in sub-saturated solutions. Conclusion Bromothymol blue reveals complex speciation chemistry in saturated aqueous solutions, which is influenced strongly by the presence of high concentrations of NaCl. Schill’s [14] extensive saturation solubility-pH measurements (pH from 0 to 5 in 0.1 and 1.0 M NaCl solutions) of the practically-insoluble diprotic weak acid, bromothymol blue (6 ng/mL monomer solubility), was re-analyzed and harmonized using a general mass action approach. A ‘normal’ salting-out constant, ks = +0.25 M-1 was derived. The formation of self-aggregates (here treated as dimers, with zero-salt log K2 = 10.0 ± 0.1 M-1) in strongly acidic solutions raised the total solubility of bromothymol blue nearly 500-fold to zero-salt log ST = -5.10. The data analysis in the present study critically depended on the pKa1 = -0.66 (at 4.59 M ionic strength) reported by Gupta and Cadwallader [15]. It was possible to estimate the self-interaction constant, ki = -7.787·10+4 M-1, an unusually high value, reflecting the tendency of bromothymol blue to form oligomers in strongly acidic solutions. https://doi.org/10.5599/admet.1822 Alex Avdeef ADMET & DMPK 00(0) (2023) 000-000 12 Acknowledgements: We are grateful to Drs. Abu Serajuddin (St. John’s Univ., NYC) and Tatjana Verbić, Miloš Pešić, Olivera Marković, Dušan Veljković (University of Belgrade, Serbia), and Kin Tam (University of Macau) for the critical discussions regarding determinations of ionization constants of practically-insoluble molecules which can self-aggregate (e.g., clofazimine) in saturated solutions [35]. Also, I thank the reviewer for a stimulating discussion of the structural nature of the BTB free acid, and for suggesting a new reference. References [1] J.Z. Setschenow. Über die konstitution der salzlosungen auf grund ihres verhaltens zu kohlensaure. Z. Physik. Chem. 4 (1889) 117-125. https://doi.org/10.1515/zpch-1889-0409. [2] F.A. Long, W.F. McDevit. Activity coefficients of nonelectrolyte solutes in aqueous salt solutions. Chem. Rev. 51 (1952) 119-169. https://doi.org/10.1021/cr60158a004. [3] N. Ni, M.M. El-Sayed, T. Sanghvi, S.H. Yalkowsky. Estimation of the effect of NaCl on the solubility of organic compounds in aqueous solutions. J. Pharm. Sci. 89 (2000) 1620-1625. https://doi.org/10.1002/1520-6017(200012)89:12. [4] S. Endo, A. Pfennigsdorff, K.-U. Goss. Salting-out effect in aqueous NaCl solutions: trends with size & polarity of solute molecules. Environ. Sci. Technol. 46 (2012) 1496-1503. https://doi.org/10.1021/ es203183z. [5] S.H. Lubbad, B.K.A. Al-Roos, F.S. Kodeh. Adsorptive–removal of bromothymol blue as acidic–dye probe from water solution using Latvian sphagnum peat moss: thermodynamic assessment, kinetic & isotherm modeling. Curr. Green Chem. 6 (2019) 53-61. https://doi.org/10.2174/2452273203666 190114144546. [6] M. Pudipeddi, A.T.M. Serajuddin. Trends in solubility of polymorphs. J. Pharm. Sci. 94 (2005) 929-939. https://doi.org/10.1002/jps.20302. [7] P. Friberger, G. Åberg. Some physicochemical properties of the racemates and optically active isomers of two local anaesthetic compounds. Acta Pharm. Suec. 8 (1971) 361-364. [8] S.K. El-Arini, D. Giron, H. Leuenberger. Solubility properties of racemic praziquantel and its enantiomers. Pharm. Dev. Tech. 3 (1998) 557-564. https://doi.org/10.3109/10837459809028638. [9] A. Avdeef, E. Fuguet, A. Llinas, C. Ràfols, E. Bosch, G. Völgyi, T. Verbić, E. Boldyreva, K. Takács-Novák. Equilibrium solubility measurement of ionizable drugs − consensus recommendations for improving data quality. ADMET DMPK 4 (2016) 117−178. https://doi.org/10.5599/admet.4.2.292. [10] W.H. Xie, W.Y. Shiu, D. Mackay. A review of the effect of salts on the solubility of organic compounds in seawater. Mar. Environ. Res. 44 (1997) 429-444. [11] A. Al-Maaieh, D.R. Flanagan. Salt effects on caffeine solubility, distribution, & self-association. J. Pharm. Sci. 91 (2002) 1000-1008. https://doi.org/10.1002/jps.10046. [12] E. Furia, A. Beneduci, L. Malacaria, A. Fazio, C. La Torre, P. Plastina. Modeling the solubility of phenolic acids in aqueous media at 37 oC. Molecules 26 (2021) 6500. https://doi.org/10.3390/molecules262 16500. [13] S.H. Lubbad, B.K.A. Al–Roos, F.S. Kodeh. Adsorptive–removal of bromothymol blue as acidic–dye probe from water solution using Latvian sphagnum peat moss: thermodynamic assessment, kinetic & isotherm modeling. Curr. Green Chem. 6 (2019) 53-61. https://doi.org/10.2174/24522732036661 90114144546. [14] G. Schill. Photometric determination of amines and quaternary ammonium compounds with bromothymol blue. Part 2. Association of bromothymol blue in aqueous solutions. Acta Pharm. Suec. 1 (1964) 101-122. [15] V.D. Gupta, D.E. Cadwallader. Determination of first pKa’ value & partition coefficients of bromothymol blue. J. Pharm. Sci. 57 (1968) 2140-2142. https://doi.org/10.1002/jps.2600571224. [16] G. Völgyi, A. Marosi, K. Takács-Novák, A. Avdeef. Salt solubility products of diprenorphine hydrochloride, codeine and lidocaine hydrochlorides and phosphates – novel method of data analysis https://doi.org/10.1515/zpch-1889-0409 https://doi.org/10.1021/cr60158a004 https://doi.org/10.1002/1520-6017(200012)89:12 https://doi.org/10.1021/es203183z https://doi.org/10.1021/es203183z https://doi.org/10.2174/2452273203666190114144546 https://doi.org/10.2174/2452273203666190114144546 https://doi.org/10.1002/jps.20302 https://doi.org/10.3109/10837459809028638 https://doi.org/10.5599/admet.4.2.292 https://doi.org/10.1002/jps.10046 https://doi.org/10.3390/molecules26216500 https://doi.org/10.3390/molecules26216500 https://doi.org/10.2174/2452273203666190114144546 https://doi.org/10.2174/2452273203666190114144546 https://doi.org/10.1002/jps.2600571224 ADMET & DMPK 00(0) (2023) 000-000 Polyvinyl alcohol nanoparticles loaded with propolis extract doi: https://doi.org/10.5599/admet.1822 13 not dependent on explicit solubility equations. ADMET DMPK 1 (2013) 48-62. https://doi.org/ 10.5599/admet.1.4.24. [17] A. Avdeef. Absorption and Drug Development, 2nd Ed., John Wiley & Sons, Inc., Hoboken, NJ, 2012. ISBN 978-1-118-05745-2. [18] A. Avdeef. Anomalous Solubility Behavior of Several Acidic Drugs. ADMET DMPK 2 (2014) 33-42. https://doi.org/10.5599/admet.2.1.30. [19] A. Avdeef. Phosphate precipitates and water-soluble aggregates in re-examined solubility-pH data of twenty-five basic drugs. ADMET DMPK 2 (2014) 43-55. https://doi.org/10.5599/admet.2.1.31. [20] A. Avdeef. Suggested improvements for measurement of equilibrium solubility-pH of ionizable drugs. ADMET DMPK 3 (2015) 84-109. https://doi.org/10.5599/admet.3.2.193. [21] G. Butcher, J. Comer, A. Avdeef. pKa-critical Interpretations of solubility–pH profiles: PG-300995 and NSC-639829 case studies. ADMET DMPK 3 (2015) 131-140. https://doi.org/10.5599/admet.3.2.182. [22] A. Pobudkowska, C. Ràfols, X. Subirats, E. Bosch, A. Avdeef. Phenothiazines solution complexity – determination of pKa and solubility-pH profiles exhibiting sub-micellar aggregation at 25 and 37 oC. Eur. J. Pharm. Sci. 93 (2016) 163-176. https://doi.org/10.1016/j.ejps.2016.07.013. [23] C.A.S. Bergström, A. Avdeef. Perspectives in solubility measurement and interpretation. ADMET DMPK 7 (2019) 88-105. http://dx.doi.org/10.5599/admet.686. [24] O.S. Marković, M.P. Pešić, A.V. Shah, A.T.M. Serajuddin, T.Ž. Verbić, A. Avdeef. Solubility-pH profile of desipramine hydrochloride in saline phosphate buffer: enhanced solubility due to drug-buffer aggregates. Eur. J. Pharm. Sci. 133 (2019) 264–274. https://doi:10.1016/j.ejps.2019.03.014. [25] E. Fuguet, X. Subirats, C. Ràfols, E. Bosch, A. Avdeef. Ionizable drug self-associations and the solubility dependence on pH: detection of aggregates in saturated solutions using mass spectrometry (ESI-Q- TOF-MS/MS). Mol. Pharmaceutics 18 (2021) 2311-2321. https://doi.org/10.1021/acs.molpharma ceut.1c00131. [26] O.S. Marković, N.G. Patel, A.T.M. Serajuddin, A. Avdeef, T. Ž. Verbić. Nortriptyline hydrochloride solubility-pH profiles in a saline phosphate buffer: drug-phosphate complexes and multiple pHmax domains with a Gibbs Phase Rule "soft" constraints. Mol. Pharmaceutics 19 (2022) 710-719. https://doi.org/10.1021/acs.molpharmaceut.1c00919. [27] A. Avdeef, J.J. Bucher. Accurate measurements of the concentration of hydrogen ions with a glass electrode: calibrations using the Prideaux and other universal buffer solutions and a computer-con- trolled automatic titrator. Anal. Chem. 50 (1978) 2137-2142. https://doi.org/10.1021/ac50036a045. [28] F.H. Sweeton, R.E. Mesmer, C.F. Baes, Jr. Acidity measurements at elevated temperatures. 7. Dissociation of water. J. Solut. Chem. 3 (1974) 191-214. https://doi.org/10.1007/BF00645633. [29] M.H. Abraham, J. Le. The correlation and prediction of the solubility of compounds in water using an amended solvation energy relationship. J. Pharm. Sci. 88 (1999) 868-880. https://doi.org/10.1021/ js9901007. [30] J.A. Platts, D. Butina, M.H. Abraham, A. Hersey. Estimation of molecular linear free energy relation descriptors using a group contribution approach. J. Chem. Inf. Comput. Sci. 39 (1999) 835-845. https://doi.org/10.1021/ci980339t. [31] A. Avdeef, M. Kansy. Predicting solubility of newly-approved drugs (2016–2020) with a simple ABSOLV and GSE (Flexible-Acceptor) consensus model outperforming Random Forest regression. J. Solution Chem. 51 (2022) 1020-1055. https://doi.org/10.1007/s10953-022-01141-7. [32] T. Shimada, K. Tochinai, T. Hasegawa. Determination of pH dependent structure of thymol blue revealed by cooperative analytical method of quantum chemistry and multivariate analysis of electronic absorption spectra. Bull. Chem. Soc. Jpn. 92 (2019) 1759-1766. https://doi.org/10.1246/ bcsj.20190118. [33] K. Yamaguchi, Z. Tamura, M. Maeda. (1997). Molecular structure of bromophenol blue having a γ- sultone ring. Anal. Sci. 13 (1997) 1057-1058. https://doi.org/10.2116/analsci.13.1057. https://doi.org/10.5599/admet.1822 https://doi.org/10.5599/admet.1.4.24 https://doi.org/10.5599/admet.1.4.24 https://doi.org/10.5599/admet.2.1.30 https://doi.org/10.5599/admet.2.1.31 https://doi.org/10.5599/admet.3.2.193 https://doi.org/10.5599/admet.3.2.182 https://doi.org/10.1016/j.ejps.2016.07.013 http://dx.doi.org/10.5599/admet.686 https://doi:10.1016/j.ejps.2019.03.014 https://doi.org/10.1021/acs.molpharmaceut.1c00131 https://doi.org/10.1021/acs.molpharmaceut.1c00131 https://doi.org/10.1021/acs.molpharmaceut.1c00919 https://doi.org/10.1021/ac50036a045 https://doi.org/10.1007/BF00645633 https://doi.org/10.1021/js9901007 https://doi.org/10.1021/js9901007 https://doi.org/10.1021/ci980339t https://doi.org/10.1007/s10953-022-01141-7 https://doi.org/10.1246/bcsj.20190118 https://doi.org/10.1246/bcsj.20190118 https://doi.org/10.2116/analsci.13.1057 Alex Avdeef ADMET & DMPK 00(0) (2023) 000-000 14 [34] P. Balderas-Hernández, M.T. Ramírez, A. Rojas-Hernández, A. Gutiérez. Determination of pKa’s for thymol blue in aqueous medium: evidence of dimer formation. Talanta 46 (1998) 1439-1452. https://doi.org/10.1016/S0039-9140(98)00015-0. [35] T.Ž. Verbić, K.Y. Tam, D.Ž. Veljković, A.T.M. Serajuddin, A. Avdeef. Clofazimine pKa determination by potentiometry and spectrophotometry – reverse cosolvent dependence as an indicator of presence of dimers in aqueous solutions. Mol. Pharmaceutics (2023) https://doi.org/10.1021/acs.molphar maceut.3c00172. ©2023 by the authors; licensee IAPC, Zagreb, Croatia. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/) https://doi.org/10.1016/S0039-9140(98)00015-0 https://doi.org/10.1021/acs.molpharmaceut.3c00172 https://doi.org/10.1021/acs.molpharmaceut.3c00172 http://creativecommons.org/licenses/by/3.0/