Solubility intrinsic

The concentrations of species in the solid phase, [HA(s)j, [B(s)j and [XH(s)], by convention are taken as unity. Hence, the quotients in Eqs. (10) reduce to the concentrations of the neutral species in the saturated solution, each called the intrinsic solubility of the compound, Sq. 

In Eqs. (11), [HA], [B] and [XH] are constant (intrinsic solubility), but the other concentrations are variable. The next step involves conversions of all variables into expressions containing only constants and [H j (as the independent variable). Substitution of Eqs. (2) and (10) into (11) produces the desired equations. 

There are other soUd states which sometimes confuse the measurement and definition of solubiUty. The dmg may crystaUize as a hydrate, i.e. under inclusion of water molecules. If the hydrate form is more stable than the pure form it may be difficult to measure the intrinsic solubility of the drug at all. Often drugs tend to precipitate in an amorphous form, often under the inclusion of impurities. As with metastable polymorphs, such amorphous precipitates may lead to erroneously high solubility measurements. CommerciaUy, drugs are often crystallized in salt form, e.g. as the hydrochloride salt, a cation with a chloride anion. In these co-crystallized salts, a much lower solubility than the intrinsic solubility will typi-... 

It is not only the solid state of a drug that suffers from ambiguities, but also the aqueous state. The state relevant for the intrinsic solubility is the state of the saturated solution of the neutral species. Since most aqueous drug solubilities are small, direct interactions of the drug molecules are usually rare. Hence, this state is usually very similar to the state of the drug at infinite dilution in water. Most computational methods disregard saturation effects. Usually this is a good approximation, but one should keep in mind that this approximation may result in some moderate, but systematic errors at the upper end of the solubility scale. 

Various models of SFE have been published, which aim at understanding the kinetics of the processes. For many dynamic extractions of compounds from solid matrices, e.g. for additives in polymers, the analytes are present in small amounts in the matrix and during extraction their concentration in the SCF is well below the solubility limit. The rate of extraction is then not determined principally by solubility, but by the rate of mass transfer out of the matrix. Supercritical gas extraction usually falls very clearly into the class of purely diffusional operations. Gere et al. [285] have reported the physico-chemical principles that are the foundation of theory and practice of SCF analytical techniques. The authors stress in particular the use of intrinsic solubility parameters (such as the Hildebrand solubility parameter 5), in relation to the solubility of analytes in SCFs and optimisation of SFE conditions. 

If the compound is virtually insoluble (< 1 pM), then a pH-metric mixed-solvent approach can be tried [112]. For example, the pKa of the antiarrhythmic amiodar-one, 9.06 0.14, was estimated from water-methanol mixtures, though the intrinsic solubility of the molecule is --0.008 pM (6 ng/mL) / ION. ... 

By convention, [HA(s)] = [B(s)] = 1. Eqs. (6.1) represent the precipitation equilibria of the uncharged species, and are characterized by the intrinsic solubility equilibrium constant, Sq. The zero subscript denotes the zero charge of the precipitating species. In a saturated solution, the effective (total) solubility S, at a particular pH is defined as the sum of the concentrations of all the compound species dissolved in the aqueous solution ... 

Figure 6.6 Empirical relationship between intrinsic solubility of ionizable molecules and their octanol water log P [pION]. [Avdeef, A., Curr. Topics Med. Chem., 1, 277-351 (2001). Reproduced with permission from Bentham Science Publishers, Ltd.]...

The procedure takes as input parameters the measured (or calculated) pKa and the measured (or calculated) octanol-water partition coefficient, log P. The latter parameter is used to estimate the intrinsic solubility So, using the Hansch-type expression [38], log So = 1.17 — 1.38 log P, or an improved version for ionizable molecules of moderate lipophilicity (Fig. 6.6) ... 

Figure 6.8 shows the Bjerrum plots for an weak acid (benzoic acid, pKa 3.98, log So — 1.55, log mol/L [474]), a weak base (benzydamine, pKa 9.26, log So —3.83, log mol/L [472]), and an ampholyte (acyclovir, pKa 2.34 and 9.23, log So — 2.16, log mol/L I/40N ). These plots reveal the pKa and pA pp values as the pcH values at half-integral % positions. By simple inspection of the dashed curves in Fig. 6.8, the pKa values of the benzoic acid, benzydamine, and acyclovir are 4.0, 9.3, and (2.3, 9.2), respectively. The pA pp values depend on the concentrations used, as is evident in Fig. 6.8. It would not have been possible to deduce the constants by simple inspection of the titration curves (pH vs. volume of titrant, as in Fig. 6.7). The difference between pKa and pA pp can be used to determine log So, the intrinsic solubility, or log Ksp, the solubility product of the salt, as will be shown below.

As can be seen in Fig. 6.8, the presence of precipitate causes the apparent pKa, pA jjPP, to shift to higher values for acids and to lower values for bases, and in opposite but equal directions for ampholytes, just as with octanol (Chapter 4) and liposomes (Chapter 5). The intrinsic solubility can be deduced by inspection of the curves and applying the relationship [472]... 

TABLE 6.1 Intrinsic Solubility S0, Corrected for the Drug DMSO/Drng Aggregation Effects... 

The working assumption is that the aggregates are water soluble, that they effectively make the compound appear more soluble. If ignored, they will lead to erroneous assessment of intrinsic solubility. It can be shown that Eq. (6.19) also applies to the case of aggregation. 

It can be shown that for such a case, the observed solubility-pH curve is shifted horizontally, not vertically, as with uncharged-compound DMSO/aggregation effects, and that the apparent intrinsic solubility is not affected by the phenomenon. 

Since the pKa values of the compounds studied are reliably known (Table 6.1), it was possible to calculate the A shifts (Table 6.2). These shifts were used to calculate the corrected aqueous intrinsic solubilities So, also listed in Table 6.2. 

There are obvious similarities in the derived relative flux expressions for the MMHS model and the precursor HWPH model. The second term on the right-hand side of Eq. (11) accounts for the increase in dissolution observed near the pKa of the acid. Addition of the ionization reaction [Eq. (9)] provides the added flexibility and accountability so that dissolution at low pH s can be accurately predicted. The agreement between theoretical predictions and experimental results for three carboxylic acids with intrinsic solubilities ranging from 10 2 to 10 M over a pH range of 2-12 was good (see Fig. 2). Computationally, the MMHS model was also quite reasonable to use the roots for a quadratic expres-... 

The derivation and experimental verification of the MMHS model represented a significant accomplishment and a natural plateau for film models. To be sure, there are general criticisms of film models and more specific criticisms of the MMHS model [6], However, overall the MMHS model should be recognized as a robust but simply applicable model which serves to demonstrate how factors such as intrinsic solubility of the acid drug, ionization and pA of the drug, and concentration of the reactive base all contribute to increasing the dissolution rate and mass transfer. 

The accelerated dissolution of soluble pure acidic or basic drugs, through the addition of acidic or basic components to the dissolution media, becomes significant when the concentration of added components approaches the intrinsic solubility of the drug. 

Logarithm of intrinsic solubility (mol L ) experimentally determined (pSOL) also logSexp Melting point Molecular weight... 

McFarland et al. recently [1] published the results of studies carried out on 22 crystalline compounds. Their water solubilities were determined using pSOL [21], an automated instrument employing the pH-metric method described by Avdeef and coworkers [22]. This technique assures that it is the thermodynamic equilibrium solubility that is measured. While only ionizable compounds can be determined by this method, their solubilities are expressed as the molarity of the unionized molecular species, the intrinsic solubility, SQ. This avoids confusion about a compound s overall solubility dependence on pH. Thus, S0, is analogous to P, the octanol/water partition coefficient in both situations, the ionized species are implicitly factored out. In order to use pSOL, one must have knowledge of the various pKas involved therefore, in principle, one can compute the total solubility of a compound over an entire pH range. However, the intrinsic solubility will be our focus here. There was one zwitterionic compound in this dataset. To obtain best results, this compound was formulated as the zwitterion rather than the neutral form in the HYBOT [23] calculations. 

We thank Professor Per Artursson of Uppsala University for allowing us to use the intrinsic solubilities reported in reference [28] prior to their publication, and Suzanne Tilton and Alexis Foreman of pION INC. for some of the pSOL solubility measurements. 

In general, the chiral ligands are water-soluble variants of those already studied in purely organic solvents (e.g., the sulfonated chiraphos, A, cyclobutane-diop, C, BDPP, F, MeOBIPHEP-TS, Q, BIFAPS, R and the quaternary ammonium derivatives of diop, D, BDPP, E). Solubility in water could also be achieved by attaching the parent phosphine molecule to a water-soluble polymer (J, M, P). The chiral phosphinites and phosphines derived from carbohydrates (e.g., K and L) have intrinsic solubility in water. During studies of one-phase... 

Figure 6 Typical solubility behavior for a poorly soluble weak base as a function of pH. The intrinsic solubility is 0.4 pg/mL. At pH values typical of the small intestine, solubility is minimally better than the intrinsic solubility (solubility of the free base form) but at gastric pH ( 2) the solubility is about 16 mg/mL.

For an acidic and basic drug, the solubility over the GI pH range varies depending on the intrinsic solubility (SD) of the compound (i.e., solubility of unionized or nonprotonated species), pfCa, and the solubility of the salt form.71 72... 

QMPRPlus predicts intrinsic solubility (the solubility of the unionized species) while we are measuring the actual solubility at pH 6.5. 

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