Understanding the differences between cocrystal and salt aqueous solubilities

Abstract

This work challenges the popular notion that pharmaceutical salts are more soluble than cocrystals. There are cocrystals that are more soluble than salt forms of a drug and vice-versa. It all depends on the interplay between the chemistry of both the solid and solution phases. Aqueous solubility, pH_max, and supersaturation index (SA = S_CC/S_D or S_salt/S_D) of cocrystals and salts of a basic drug, Lamotrigine (LTG), were determined, and mathematical models that predict the influence of cocrystal/salt K_sp and K_a were derived. K_sp and SA followed the order LTG-Nicotinamide cocrystal (18) > LTG-HCl salt (12) > LTG-Saccharin salt (5) > LTG-Methylparaben cocrystal (1) > LTG-Phenobarbital cocrystal (0.2). The values in parenthesis represent SA under non-ionizing conditions. Cocrystal/salt solubility and thermodynamic stability are determined by pH and will drastically change with a single unit change in pH. pH_max values ranged from 5.0 (Saccharin salt) to 6.4 (Methylparaben cocrystal) to 9.0 (Phenobarbital cocrystal). Cocrystal/salt pH_max dependence on pK_sp and pK_a shows that cocrystals and salts exhibit different behavior. Solubility and pH_max are as important as supersaturation index in assessing the stability and risks associated with conversions of supersaturating forms.

Introduction

Cocrystals constitute an important class of pharmaceutical materials that have the ability to enhance and fine-tune solubility. This property enables cocrystals to solve absorption and bioavailability problems of poorly water-soluble drugs. Cocrystals are thus receiving significant attention and numerous cocrystals have been reported.^1–8 In spite of their promise to solve solubility problems, there is a wide gap between the principles that explain cocrystal solution behavior and their application to cocrystal characterization and development.

Unlike other supersaturating delivery systems, cocrystal stoichiometric nature predisposes them to huge and predictable changes in solubility and thermodynamic stability as solution conditions change (pH, complexation, solubilization, among others). Cocrystals are therefore characterized not only by their solubility but also by the supersaturation that they generate. For cocrystals whose constituents may ionize in solution, understanding the influence of pH on cocrystal solubility and supersaturation is essential to correctly evaluate their stability and potential for conversion to less soluble forms. The purpose of the work presented here is to develop mathematical relationships and determine thermodynamic parameters that explain the stability and solubility-pH dependence of cocrystals and salts of weakly basic drugs. We also wish to address the commonly held notion that salts are more soluble than cocrystals. To this end, we have studied the solubility behavior of salts and cocrystals of lamotrigine (LTG), a weakly basic drug of equimolar composition. The LTG cocrystal and salt constituents studied are summarized in Table 1.

Table 1.

pK_a values of cocrystal and salt constituents.

Compound	Abbreviation	pKa
Lamotrigine	LTG	5.7a
Saccharin	SAC	1.6b
Nicotinamide	NCT	3.4c
Phenobarbital	PB	7.5d, 11.8e

^aReference^9,10

^bDetermined at 25°C in water¹¹

^cDetermined at 20°C and 0.01 M ionic strength¹²

^dDetermined at 25°C and 0.02 M ionic strength¹³

^eReference⁹

Materials and Methods

Materials

Cocrystal and Salt Constituents

LTG was purchased from Jai Radhe Sales, India with a purity of 99.6% w/w and was used as received. Nicotinamide (NCT) and saccharin (SAC) were purchased from Sigma-Aldrich and used as received. X-ray powder diffraction (XRPD) and differential scanning calorimetry (DSC) analyses were performed on all materials to confirm phase purity prior to use. Lamotrigine monohydrate (LTG·H₂O) was prepared by suspending anhydrous LTG for 72 hours in water at 25±0.1°C. The slurry was vacuum filtered and the solid phase was confirmed by XRPD and DSC.

Solvents and Buffer Components

HPLC grade methanol was purchased from Fisher Scientific (Pittsburgh, PA). Trifluoroacetic acid spectrophometric grade 99% was purchased from Aldrich Company (Milwaukee, WI). All water used in this study was filtered through a double deionized purification system (Milli Q Plus Water System) from Millipore Company (Bedford, MA).

pH 2.0 phosphate buffer was prepared using sodium phosphate dibasic heptahydrate from Acros Organics, potassium dihydrogen phosphate from Sigma-Aldrich, and phosphoric acid from Acros Organics. pH 4.5 acetate buffer was prepared using acetic acid purchased from Sigma-Aldrich and sodium acetate purchased from Sigma Chemical Company. pH 6.8 phosphate buffer was prepared using monobasic potassium phosphate purchased from Sigma- Aldrich and sodium hydroxide pellets (NaOH) from J.T. Baker (Philipsburg, NJ).

Methods

Buffer Preparation

All buffers were prepared according to the pharmacopeial protocol.^14,15 pH 2.0 phosphate buffer was prepared by dissolving 1.41 g sodium phosphate dibasic heptahydrate and 0.85 g potassium dihydrogen phosphate in 250 mL of water. pH was adjusted to 2.0 using phosphoric acid (1.8 mL total). pH 4.5 acetate buffer was prepared by dissolving 147.5 mg sodium acetate and 3.5 mL of 2 M acetic acid in 246.5 mL of water. 2 M acetic acid was prepared adding 28.8 mL of acetic acid to 250 mL of water. pH 6.8 phosphate buffer was prepared by adding 22.4 mL of 0.2 M NaOH solution to 50 mL of 0.2 M monobasic potassium phosphate solution. 0.2 M NaOH solution was prepared by dissolving 0.8 g NaOH pellets in 100 mL of water. 0.2 M monobasic potassium phosphate solution was prepared by dissolving 2.7 g monobasic potassium phosphate in 100 mL of water. All buffers were prepared by stirring at room temperature.

Cocrystal and Salt Synthesis

LTG-NCT·H₂O was synthesized by reaction crystallization method (RCM)¹⁶. An aqueous solution of 2% w/w SLS and 3.5 M NCT was prepared, to which anhydrous LTG was added and stirred for 72 hours at ambient temperature. Solid phases were isolated, dried, and analyzed by XRPD, DSC, and HPLC to confirm crystal form and phase purity. LTG-SAC salt was synthesized by adding stoichiometric ratio of anhydrous LTG to a SAC solution. The solid phase was filtered after approximately 24 hours and confirmed to be LTG-SAC salt by XRPD and DSC.

Drug Solubility Measurement

Intrinsic LTG·H₂O solubility (S_0,LTG·H2O) was measured in water by adding excess solid to solution. Solutions were magnetically stirred and maintained at 25.0 ± 0.1°C using a water bath for 72 hours. At 24 hour intervals, 0.50 mL aliquots were collected and filtered through a 0.45 µm pore membrane. After dilution with mobile phase, solution concentrations were analyzed by HPLC. LTG·H₂O was confirmed as the equilibrium solid phase by XRPD and DSC.

Cocrystal and Salt Solubility Measurements

Cocrystal equilibrium solubilities were measured in pH 2.0 phosphate buffer, pH 4.5 acetate buffer, pH 6.8 phosphate buffer, and water at the eutectic point, where LTG·H₂O and LTG-NCT·H₂O were in equilibrium with solution. The eutectic point between LTG-NCT·H₂O and LTG·H₂O was approached by equilibrating both solid phases in aqueous media. LTG-SAC solubilities were measured by suspending salt in aqueous media, adjusting pH with pH 2 phosphate buffer or 0.1 M NaOH and allowing suspensions to equilibrate. Suspensions were stirred for 72 hours under constant temperature of 25.0 ± 0.1°C using a water bath. At 24 hour intervals, 0.50 mL aliquots were collected and filtered through a 0.45 µm pore membrane. Solid phases were analyzed by XRPD and DSC to characterize the solid phases at equilibrium. The equilibrium pH of the solution media was measured prior to dilution with mobile phase for concentration measurement of LTG cocrystal and salt constituents by HPLC. Solutions were considered to have reached equilibrium with solid phases when less than 5% change in concentration was detected in either component of the cocrystal or salt.

Stoichiometric solubility of the 1:1 cocrystal was calculated according to

$${\mathrm{S}}_{\text{LTG}-\text{NCT}·{\mathrm{H}}_2\mathrm{O}}=\sqrt{{[\text{LTG}]}_{\mathrm{T},\text{eu}}{[\text{NCT}]}_{\mathrm{T},\text{eu}}}$$ (1)

from measured drug and coformer concentrations at the eutectic point ([LTG]_T,eu and [NCT]_T,eu).^17–19

Stoichiometric solubility of the 1:1 salt was calculated by a similar expression according to

$${\mathrm{S}}_{\text{LTG}-\text{SAC}}=\sqrt{{[\text{LTG}]}_{\mathrm{T}}{[\text{SAC}]}_{\mathrm{T}}}$$ (2)

K_sp for LTG-NCT·H₂O and LTG-SAC was calculated from solubility determinations from the above equations, as described in the results section.

X-ray Powder Diffraction (XRPD)

XRPD patterns of solid phases were recorded with a Rigaku MiniFlex X-ray diffractometer (Danvers, MA) using Cu Ka radiation (λ = 1.5418 Å), a tube voltage of 30 kV, and a tube current of 15 mA. The intensities were measured at 2θ values from 2° to 35° with a continuous scan rate of 2.5°/min.

Thermal Analysis

Crystalline samples of 2–4 mg were analyzed by DSC using a TA instrument (Newark, DE) 2910 MDSC system equipped with a refrigerated cooling unit. DSC experiments were performed by heating the samples at a rate of 10°C/min under a dry nitrogen atmosphere. Temperature and enthalpy calibration of the instruments was achieved by using a high purity indium standard. Standard aluminum sample pans were used for all measurements.

High Performance Liquid Chromatography (HPLC)

Solution concentrations of drug and coformer were analyzed by Waters HPLC (Milford, MA) equipped with a UV/vis spectrometer detector. A reversed phase C18 Atlantis column (5 µm, 4.5 × 250 mm) at ambient temperature was used to separate the drug and the coformer or counterion. An isocratic method of 55% methanol, 45% water, and 0.1% trifluoroacetic acid mobile phase was used with a flow rate of 1 mL/min. Sample injection volume was 20µL. Absorbance of the drug and coformer or counterion analytes was monitored between 210–300nm. The peak areas were integrated using Empower™ software.

Results and Discussion

Solubility-pH dependence and supersaturation index

Figure 1 shows the solubility-pH dependence of the weakly basic drug LTG, a salt with a moderately strong acid, SAC, and two cocrystals, with a weakly basic coformer, NCT, or with a weakly acidic drug, phenobarbital (PB). We recently published the solubility-pH dependence of LTG-PB cocrystal and include it here for comparison.¹ These results demonstrate that pH has a huge influence on solubility and that both cocrystal and salt can exhibit a pH_max where their solubility curves intersect with the drug solubility curve. Furthermore, the cocrystal and salt solubility behaviors differ as a result of the ionization properties of their constituents.

Figure 1.

Solubility values for cocrystals and salt were determined under equilibrium conditions and calculated according to equations 1 and 2. Some of the solubility values in Figure 1 represent supersaturated conditions with respect to drug free base and are useful as a measure of the supersaturation index (SA=S_CC/S_D) that a cocrystal or a salt may generate, as presented in Figure 2.

Figure 2.

SA is the driving force for conversions from cocrystal to the less soluble drug. The change in Gibbs free energy for this conversion is

$$\mathrm{\Delta }{G}_{\mathit{\text{CC}}\to D}=-\mathit{\text{RT}}\text{ln}\left(\frac{S_{\mathit{\text{CC}}}}{S_D}\right)=-\mathit{\text{RT}}\text{ln}\left(\mathit{\text{SA}}\right)$$ (3)

where S is solubility and subscripts CC and D refer to cocrystal and drug phases. In this equation S_CC is expressed in terms of moles of drug. A phase conversion from cocrystal to drug is favorable when ΔG is negative, or when S_CC>S_D, SA>1. A similar analysis applies to salts and S_CC can be substituted for S_salt in equation 3. When S_CC=S_D, SA=1, and ΔG = 0, the system is at equilibrium and the pH corresponding to this equilibria is pH_max.

Supersaturation can be sustained for some time until nucleation occurs, which is the reason for the importance of supersaturating drug delivery systems. The higher supersaturation is, the more negative is the free energy for conversion, the shorter is the time for nucleation to occur, and the higher is the nucleation rate. This means, that cocrystals with higher SA values may experience lower supersaturations and shorter induction times before conversion. In the context of the work presented here, SA is used to quantify the propensity of cocrystal conversions as their SA changes with pH.

The utility of SA vs pH plot (Figure 2) in assessing the risk of cocrystal and salt conversions to drug is shown by considering reported dissolution results for LTG-NCT·H₂O cocrystal and LTG-SAC salt.^3,20 The cocrystal was reported to transform to the drug whereas the salt did not transform during dissolution in aqueous unbuffered media at 25°C. The dissolution media pH was reported to be 6.6 for the cocrystal and 5 for the salt. Considering the SA for cocrystal (18 at pH 6.6) and salt (1 at pH 5), one would expect the salt to be stable (as the dissolution pH is at pH_max) whereas the cocrystal will have a risk of conversion. In fact, the cocrystal was reported to transform to the less soluble drug as an SA of 18 was not sustainable and the salt did not transform and was reported to be stable.

A common mistake in cocrystal solubility and stability studies is that solution conditions are not considered. Even when initial pH conditions are known, in aqueous or buffered solutions, the pH during cocrystal dissolution can change considerably, causing huge errors in data interpretation.

A word of caution about kinetically obtained C_max values during cocrystal/salt dissolution studies is in order. C_max is a result of two opposing kinetic processes, cocrystal/salt dissolution and drug precipitation, and is not proportional to solubility. C_max is a kinetic parameter and its values are variable due to its kinetic nature and to the differences in changing experimental conditions. Integrating dissolution and thermodynamic data provides a useful conceptual context to assess the risks associated with changing factors and conditions.

Relationships between solubility, pK_a, and pH

LTG-NCT·H₂O is composed of two weakly basic components, which means the change in slope of the solubility-pH profile (Figure 1) is determined by the ionization behavior of both the drug (pK_a = 5.7) and the coformer (pK_a = 3.4). Cocrystal solubility remains constant above the drug pK_a as both components are predominantly nonionized. However, as the components become increasingly ionized, cocrystal solubility increases quite substantially as pH approaches the drug pK_a and even more so as pH approaches the coformer pK_a.

A multidrug cocrystal of basic LTG and acidic PB (pK_a,1 = 7.5, pK_a,2 = 11.8), exhibits a U-shaped solubility curve due the different ionization ranges of LTG and PB. Cocrystal solubility increases with LTG ionization and PB ionization. A pH of minimum solubility occurs between the pK_a of the basic and acidic constituents. The cocrystal and drug solubility curves intersect at a pH_max, which for this system is pH 9.

LTG-SAC salt with the acidic counterion SAC (pK_a = 1.6) also exhibits a U-shaped curve, including a plateau region between pH values of 2.5 and 5.0. Salt solubility increases below pH 2.5 and above pH 5.0 as ionization of the basic and acidic constituents change. A pH_max is observed at pH 5.

Solubilities of these four forms of LTG as a function of pH were predicted according to the following equations using pK_a values shown in Table 1. The drug solubility (S_LTG·H2O) was predicted from

$${\mathrm{S}}_{\text{LTG}·{\mathrm{H}}_2\mathrm{O}}={\mathrm{S}}_{0,\text{LTG}·{\mathrm{H}}_2\mathrm{O}}(1+{10}^{\text{pKa},\text{LTG}-\text{pH}})$$ (4)

where S_0,LTG·H2O represents the solubility of LTG monohydrate under nonionizing conditions, also referred to as intrinsic drug solubility. S_0,LTG·H2O was evaluated to be 6.6 × 10⁻⁴ M by fitting the above equation to the data.

For LTG-NCT·H₂O cocrystal the solubility expression is given by

$${\mathrm{S}}_{\text{LTG}-\text{NCT}·{\mathrm{H}}_2\mathrm{O}}=\sqrt{{\mathrm{K}}_{\text{sp}}(1+{10}^{\text{pKa},\text{LTG}-\text{pH}})(1+{10}^{\text{pKa},\text{NCT}-\text{pH}})}$$ (5)

where K_sp is the cocrystal solubility product. This equation was derived by considering the mass balance of all cocrystal species in solution and expressing them in terms of the equilibrium constants that correspond to cocrystal dissociation (K_sp) and ionization (K_a)

Cocrystal K_sp was evaluated from Equation 5 and cocrystal solubility (S_CC) values obtained from equation 1 by measurement of cocrystal component concentrations in equilibrium with cocrystal and drug phases at specific pH equilibrium values and pK_a values in Table 1.

The salt solubility-pH relationship is

$${\mathrm{S}}_{\text{LTG}-\text{SAC}}=\sqrt{{\mathrm{K}}_{\text{sp}}(1+{10}^{\text{pH}-\text{pKa},\text{LTG}})(1+{10}^{\text{pKa},\text{SAC}-\text{pH}})}$$ (6)

This well recognized equation is analogous to that of the cocrystal (Equation 5) as it considers dissociation and ionization equilibrium reactions.^21–23 In this case, however, the salt K_sp is the product of activities of ionized constituents, whereas for a cocrystal, it is the non-ionized constituents. As a result of the different ionization states in the dissociation and ionization reactions, the ionization terms in the solubility equations for cocrystal and salt also have different signs.

Fig. 1 shows excellent agreement between predicted and experimental solubility behavior. LTG-NCT cocrystal is more soluble than drug at pH > 3 and reaches solubilities 18 times the drug solubility at pH ≥ 6. The cocrystal is also more soluble than the SAC salt at pH < 7, and is orders of magnitude more soluble than the salt at pH < 3. The SAC salt has a pH_max around pH 5, below which it is less soluble than the drug. Experimental measurement of salt solubility above pH_max was not possible as the equilibrium pH decreased to pH 5 due to salt conversion to the less soluble drug at initial pH values of about 6.

The above results are compared with those recently reported for LTG-PB cocrystal.¹ The cocrystal solubility dependence on pH is given by

$${\mathrm{S}}_{\text{LTG}-\text{PB}}=\sqrt{{\mathrm{K}}_{\text{sp}}(1+{10}^{\text{pKa},\text{LTG}-\text{pH}})(1+{10}^{\text{pH}-\text{pKa},\text{PB}1}+{10}^{2\text{pH}-\text{pKa}1,\text{PB}-\text{pKa}2,\text{PB}})}$$ (7)

The cocrystal solubility curve generated by this equation²⁴ (Figure 1) predicts a pH_max of 9 and a solubility minimum between the pK_a of LTG and the first pK_a of PB.^19,24,25 Another pH_max with PB occurs at pH 2.6 (not shown in this plot). The PB cocrystal is the least soluble of the four forms considered between pH 3 and 9. PB is also the least soluble constituent among the cocrystals. In fact, its intrinsic solubility is only about 10 times higher than the drug. The ratio of coformer to drug solubilites (S_CF/S_D) ≤ 10 has been generally observed to result in cocrystals that are less soluble than drug.^17,26 Solubility is however determined by pH and these trends will change with the ionization of cocrystal and salt constituents as demonstrated in Figure 1.

Solubility product, K_sp

Whereas solubility is a conditional constant and dependent on pH, the solubility product, K_sp, is not. K_sp is the constant associated with the equilibrium between cocrystal or salt and a solution phase. It involves dissociation of cocrystal and salt into its constituents according to

$$A_y{B}_z{}_{\mathit{\text{solid}}}\stackrel{K_{\mathit{\text{sp}}}}{\rightleftharpoons }{\mathit{\text{yA}}}_{\mathit{\text{soln}}}+{\mathit{\text{zB}}}_{\mathit{\text{soln}}}$$ (8)

for a cocrystal, and

$$A_y^{-}{\mathit{\text{BH}}}_z^{+}{}_{\mathit{\text{solid}}}\stackrel{K_{\mathit{\text{sp}}}}{\rightleftharpoons }{\mathit{\text{yA}}}_{\mathit{\text{soln}}}^{-}+{\mathit{\text{zBH}}}_{\mathit{\text{soln}}}^{+}$$ (9)

for a salt. A and B represent cocrystal constituents (or ionized constituents A⁻ and BH⁺ for a salt), y and z are the stoichiometric coefficients. The forward reaction is dissociation and represents dissolution, while the reverse reaction is association and represents precipitation. K_sp for a cocrystal is

$$K_{\mathit{\text{sp}}}=\frac{a_A^y{a}_B^z}{a_{A_y{B}_z}}$$ (10)

and for a salt

$$K_{\mathit{\text{sp}}}=\frac{a_{A^{-}}^y{a}_{{\mathit{\text{BH}}}^{+}}^z}{a_{A_y^{-}{\mathit{\text{BH}}}_z^{+}}}$$ (11)

where a represents activities, and subscripts represent cocrystal or salt constituents. Since the activity of the solid phase is assumed to be constant and equal to 1, K_sp is an activity product. Activities are approximated by concentrations under the assumption of ideality, and K_sp becomes

$$K_{\mathit{\text{sp}}}={[A]}^y{[B]}^z$$ (12)

for a cocrystal, and

$$K_{\mathit{\text{sp}}}={[A^{-}]}^y{[{\mathit{\text{BH}}}^{+}]}^z$$ (13)

for a salt.

K_sp values for several salts and cocrystals of LTG are presented in Table 2. The K_sp expression for LTG-NCT cocrystal is

$${\mathrm{K}}_{\text{sp}}=[\text{LTG}][\text{NCT}]$$ (14)

For the saccharin salt, K_sp is

$${\mathrm{K}}_{\text{sp}}=[{\text{LTGH}}^{+}][{\text{SAC}}^{-}]$$ (15)

Similar equations with the corresponding coformers or counterions were used to evaluate K_sp of other LTG forms as they were all of equimolar stoichiometry.

Table 2.

Solubility product (K_sp), intrinsic solubility (S_0,CC), and solubility advantage ( $\mathit{\text{SA}}=\frac{S_{0,\mathit{\text{CC}}}\mathit{\text{ or }}{S}_{0,\mathit{\text{Salt}}}}{S_{0,\mathit{\text{LTG}}}}$) of LTG cocrystals and salts.

Solid Phase	Ksp (M2)	S0,CC or S0,Salt (M)	SA
LTG-NCT Cocrystal	(1.4±0.4) ×10−4	1.2 × 10−2	18
LTG-HCl Salt	(6.7±0.53) × 10−5 a	8.2 × 10−3	12
LTG-SAC Salt	(1.1±0.2) × 10−5	3.3 × 10−3	5
LTG-MP Cocrystal	(5.3±0.47) × 10−7 b	7.3 × 10−4	1.1
LTG-PB Cocrystal	(1.2±0.5) × 10−8	1.1 × 10−4	0.2

^aK_sp of LTG-HCl was calculated from reported solubility of 0.46 mg/mL at 37°C (pH 1.2) from reference²⁷. K_sp of the salt was estimated at 25°C from [LTGH⁺] and [Cl⁻] concentrations calculated from the dissolved salt and HCl concentrations, using a heat of solution value of 30 kJ/mol.

^bSteady state concentration from dissolution data in reference (3) was used to calculate the K_sp of lamotrigine-methylparaben (LTG-MP) cocrystal, where cocrystal was reported to be stable.

Results in Table 2 show that NCT cocrystal K_sp is higher than that of SAC and HCl salts. The PB cocrystal has the lowest K_sp among these forms. These findings challenge the popular notion that salts are more soluble than cocrystals. In fact, NCT cocrystal intrinsic solubility is 18 times higher than drug and even higher than the HCl and SAC salts.

It is important to note that K_sp is the product of only the cocrystal or salt constituents in the non-ionized or ionized state, respectively. K_sp ≠ [A]_T [B]_T when there are molecular species in solution different from those in the corresponding solid phase. The reader should be cautious of incorrect K_sp values calculated from total analytical concentrations of cocrystal or salt constituents that do not correspond to the K_sp definition according to the equilibrium in Equations 12 and 13.

K_sp values for cocrystals of several drugs in aqueous media are presented in Table 3 in terms of pK_sp. The low values of K_sp make use of pK_sp = −log K_sp more reasonable. Higher pK_sp values refer to lower K_sp values. The range of values is similar to those reported for pharmaceutical salts.^28–30 pK_sp values for CBZ cocrystals are in the range of 2 to 9, indicating increases in K_sp by orders of magnitude. When solubility is determined by solvation and not by solid-state lattice energy,^17,31 cocrystal solubility is dependent on the solubility of its components. Nicotinamide and glutaric acid are among the most soluble coformers and generally correspond to cocrystals with higher K_sp values for a given drug. The highest 1:1 cocrystal K_sp corresponds to theophylline-nicotinamide with a pK_sp of 0.7, among the most soluble combination of cocrystal constituents.

Table 3.

Cocrystal and Salt pK_sp

Cocrystal (drug-coformer) or Salt (drug-counterion)	Solid Form	Stoichiometry (drug:coformer or drug:counterion)	pKsp
Caffeine-Salicylic acid	Cocrystal	1:1	3.117
Carbamazepine-Nicotinamide	Cocrystal	1:1	2.317
Carbamazepine-Glutaric acid	Cocrystal	1:1	2.517
Carbamazepine-Salicylic acid	Cocrystal	1:1	5.924
Carbamazepine-Saccharin	Cocrystal	1:1	6.032
Carbamazepine-Malonic acida	Cocrystal	2:1b	6.117
Carbamazepine-Oxalic acid	Cocrystal	2:1b	8.017
Carbamazepine-Succinic acid	Cocrystal	2:1	8.233
Carbamazepine-4-aminobenzoic acid hydrate	Cocrystal	2:1	8.924
Danazol-Hydroxybenzoic acid	Cocrystal	1:1	8.034
Danazol-Vanillin	Cocrystal	1:1	8.534
Gabapentin Lactam-4-aminobenzoic acid	Cocrystal	1:1	3.119
Gabapentin Lactam-Fumaric acid	Cocrystal	2:1	3.419
Gabapentin Lactam-Benzoic acid	Cocrystal	1:1	3.519
Gabapentin Lactam-4-hydroxybenzoic acid	Cocrystal	1:1	3.719
Gabapentin Lactam-Gentisic acid	Cocrystal	1:1	3.919
Indomethacin-Saccharin	Cocrystal	1:1	8.932
Ketoconazole-Oxalic acid	Salt	1:1	5.9c
Ketoconazole-Adipic acid	Cocrystal	1:1	7.535
Ketoconazole-Succinic acid	Cocrystal	1:1	7.635
Ketoconazole-Fumaric acid	Cocrystal	1:1	8.835
Lamotrigine-Nicotinamide	Cocrystal	1:1	3.9
Lamotrigine-Hydrochloride	Salt	1:1	4.2d
Lamotrigine-Saccharin	Salt	1:1	5.0
Lamotrigine-Methylparaben	Cocrystal	1:1	6.3e
Lamotrigine-Phenobarbital	Cocrystal	1:1	7.91
Nevirapine-Maleic acid	Cocrystal	1:1	4.725
Nevirapine-Saccharin	Cocrystal	2:1	10.025
Nevirapine-Salicylic acid	Cocrystal	2:1	10.425
Pterostilbene-Caffeine	Cocrystal	1:1	5.336
Pterostilbene-Piperazine	Cocrystal	2:1	6.337
Piroxicam-Saccharin	Cocrystal	1:1	7.134
Theophylline-Nicotinamide	Cocrystal	1:1	0.717
Theophylline-Salicylic acid	Cocrystal	1:1	3.817

^aForm B (hydrated cocrystal).³⁸

^bDisordered crystal structure that does not provide definitive stoichiometry.²⁶

^cCalculated from reported solubility of 0.90 mg/mL at 25°C and pH 3.4.³⁹

^dCalculation described in Table 2 footnote a.

^eCalculated from steady state concentration during reported cocrystal dissolution as reported in reference (3).

Comparing the pK_sp values of salts and cocrystals of the same drug (Table 3) shows that some cocrystals are more soluble than salts, or less soluble depending on the coformers and counterions. Cocrystals with higher ratio of the less soluble drugs also have higher pK_sp values, as observed for 2:1 vs 1:1 cocrystals.

pH_max of cocrystals and salts

Knowledge of pH_max is important to determine phase stability regions. In this article, we are concerned with the LTG and cocrystal or salt pH_max, where LTG is the least soluble constituent under the conditions studied.

The pH_max of cocrystals is expected to vary with coformers over a wider pH range than that of salts due to the range of ionization properties of cocrystal constituents. Cocrystals can be composed of all possible combinations of acidic, basic, and nonionized constituents, unlike salts. For instance, binary cocrystals can be composed of two basic, two acidic, one basic and one acidic, or one or both nonionizable constituents.

We derived equations that predict cocrystal/salt pH_max values from K_a, K_sp, and S_0,D. Since at the pH_max the solution is doubly saturated with two solid phases, cocrystal or salt and drug, pH_max equations were derived by setting the cocrystal solubility equal to drug solubility and solving for pH_max. This approach is similar to that described for salts.^40–42

pH_max values for cocrystals and salts with the ionization properties of the LTG solid forms studied here are shown in Table 4. These were calculated from the below relationships. Equations are presented in terms of [H⁺]_max and K as they are simpler than in terms of pH or pK.

Table 4.

pH_max^a for LTG cocrystals and salts

Solid Phase	pHmax	SpHmax (M)
LTG-NCT·H2O Cocrystal	Noneb	−
LTG-MP Cocrystal	6.4	8.0 × 10−4
LTG-PB Cocrystal	9.0	6.5 × 10−4
LTG-SAC Salt	5.0	3.7 × 10−3

^aCalculated from equations 16, 17, 18, and 19 with K_a and K_sp values in tables 1 and 2.

^bEquation 16 gives an unreal solution for [H⁺]_max, confirming that there is no pH_max.

For cocrystals with a basic drug and a basic coformer, such as LTG-NCT·H₂O, [H⁺]_max is

$${[{\mathrm{H}}^{+}]}_{\text{max}}=\frac{{\mathrm{K}}_{\mathrm{a},\text{LTG}}{\mathrm{K}}_{\mathrm{a},\text{NCT}}({\mathrm{S}}_{0,\text{LTG}·{\mathrm{H}}_2\mathrm{O}}^2-{\mathrm{K}}_{\text{sp}})}{{\mathrm{K}}_{\mathrm{a},\text{LTG}}{\mathrm{K}}_{\text{sp}}-{\mathrm{K}}_{\mathrm{a},\text{NCT}}{\mathrm{S}}_{0,\text{LTG}·{\mathrm{H}}_2\mathrm{O}}^2}$$ (16)

where S_0,D is the drug intrinsic solubility and K_sp is the cocrystal or salt solubility product.

For cocrystals with a basic drug and a nonionic coformer, such as LTG-MP, [H⁺]_max is

$${[{\mathrm{H}}^{+}]}_{\text{max}}=-\frac{{\mathrm{K}}_{\mathrm{a},\text{LTG}}({\mathrm{S}}_{0,\text{LTG}·{\mathrm{H}}_2\mathrm{O}}^2-{\mathrm{K}}_{\text{sp}})}{{\mathrm{S}}_{0,\text{LTG}·{\mathrm{H}}_2\mathrm{O}}^2}$$ (17)

For cocrystals with a basic drug and an acidic coformer, such as LTG-PB [H⁺]_max is

$${[{\mathrm{H}}^{+}]}_{\text{max}}=\frac{{\mathrm{K}}_{\mathrm{a},\text{LTG}}{\mathrm{K}}_{\mathrm{s}\mathrm{p}}-{\mathrm{K}}_{\mathrm{a},\text{LTG}}{\mathrm{S}}_{0,\text{LTG}·{\mathrm{H}}_2\mathrm{O}}^2+\sqrt{4{\mathrm{K}}_{\mathrm{a},\text{LTG}}{\mathrm{K}}_{\mathrm{a}1,\text{PB}}{\mathrm{K}}_{\text{sp}}{\mathrm{S}}_{0,\text{LTG}·{\mathrm{H}}_2\mathrm{O}}^2+{({\mathrm{K}}_{\mathrm{a},\text{LTG}}{\mathrm{K}}_{\text{sp}}-{\mathrm{K}}_{\mathrm{a},\text{LTG}}{\mathrm{S}}_{0,\text{LTG}·{\mathrm{H}}_2\mathrm{O}}^2)}^2}}{2{\mathrm{S}}_{0,\text{LTG}·{\mathrm{H}}_2\mathrm{O}}^2}$$ (18)

Equation 18 is for a monoprotic acid. While PB is a diprotic acid, the second pK_a is 11.8 and the assumption of only using the lower pK_a is justified at pH values below 10.

For salts with a basic drug and an acidic counterion, such as LTG-SAC, [H⁺]_max is

$${[{\mathrm{H}}^{+}]}_{\text{max}}=\frac{{\mathrm{K}}_{\mathrm{a},\text{LTG}}^2{\mathrm{K}}_{\text{sp}}-{\mathrm{K}}_{\mathrm{a},\text{LTG}}{\mathrm{K}}_{\mathrm{a},\text{SAC}}{\mathrm{S}}_{0,\text{LTG}·{\mathrm{H}}_2\mathrm{O}}^2+\sqrt{4{\mathrm{K}}_{\mathrm{a},\text{LTG}}^2{\mathrm{K}}_{\mathrm{a},\text{SAC}}^2{\mathrm{K}}_{\text{sp}}{\mathrm{S}}_{0,\text{LTG}·{\mathrm{H}}_2\mathrm{O}}^2+{({\mathrm{K}}_{\mathrm{a},\text{LTG}}^2{\mathrm{K}}_{\text{sp}}-{\mathrm{K}}_{\mathrm{a},\text{LTG}}{\mathrm{K}}_{\mathrm{a},\text{SAC}}{\mathrm{S}}_{0,\text{LTG}·{\mathrm{H}}_2\mathrm{O}}^2)}^2}}{2{\mathrm{K}}_{\mathrm{a},\text{SAC}}{\mathrm{S}}_{0,\text{LTG}·{\mathrm{H}}_2\mathrm{O}}^2}$$ (19)

Results in Table 4 show the range in pH_max and solubility at pH_max, S_pHmax, for the cocrystals and salts studied. Of forms that exhibit a pH_max, the salt has the lowest pH_max and highest S_pHmax. This is consistent with SAC having the lowest pK_a and higher solubility than PB and MP. The NCT cocrystal approaches the drug solubility as pH approaches the NCT pK_a (3.4) at a solubility of about 0.6 M, although a pH_max is not achieved (Figure 1).

How pH_max changes with pK_sp for basic drugs and acidic coformers/counterions is shown in Figures 3 and 4 by using the above equations. The pK_a values for the simulations were selected for the purpose of understanding the influence of pK_sp and pK_a on cocrystal/salt pH_max and S_pHmax, even though it is generally accepted that salts may form when ΔpK_a (ΔpK_a = pK_a(base) - pK_a(acid)) is greater than 2 or 3.^43–45

Figure 3.

Figure 4.

Figure 3 illustrates the influence of coformer/counterion pK_a on cocrystal/salt pH_max dependence on pK_sp. Both cocrystal and salt pH_max values increase with pK_sp. Cocrystals have lower pH_max values than salts. Cocrystal pH_max values also show higher sensitivity to changes in counterion pK_a values.

Figure 4 shows how the pH_max dependence on pK_sp varies with pK_a of a basic drug when the acidic coformer/counterion pK_a = 2.0. At the same drug pK_a, salts have higher pH_max values. Salt pH_max changes by about one unit when drug pK_a is varied by one unit, and this trend appears to be almost constant throughout the studied pK_sp range. However, changes in cocrystal pH_max are smaller than those for salts, and they are not constant with changes in drug pK_a for all pK_sp values. While one unit change in drug pK_a results in about one unit change in pH_max at pK_sp 2, pH_max varies by 0.5 units at pK_sp 6 and by less than 0.2 units at pK_sp 10.

These findings are consistent with the fact that salt pH_max values typically occur in the salt solubility plateau region where the counterion is almost completely ionized.^21,41,46,47 Changes in counterion pK_a (Figure 3) have a small effect on pH_max dependence on pK_sp when ΔpK_a is large enough for the counterion to be fully ionized at pH_max. However, changes in drug pK_a will result in greater variability in pH_max vs pK_sp dependence as the solubility-pH dependencies of both the drug and salt shift. Unlike salts, the pH_max of cocrystals of basic drugs and acidic coformers can occur on either side of the solubility minimum depending on pK_sp and S_0,D. pH_max occurs above minimum solubility for LTG-PB (Figure 1),¹ but has been shown to occur below minimum solubility for some ketoconazole and nevirapine cocrystals.^25,31 For cocrystals with the same S_0,D, high pK_sp values show greater pH_max variability with changes in coformer pK_a (Figure 3), but low pK_sp show greater pH_max variability with changes in drug pK_a (Figure 4).

The analysis presented shows that cocrystals and salts exhibit different dependencies of pH_max on pK_sp. These cocrystal/salt properties are critical for selection, stability, and solubility assessments.

Conclusions

This work shows that cocrystals can be more soluble than salts or vice-versa. The stoichiometric nature of cocrystals and salts predisposes them to huge, yet predictable changes in solubility, supersaturation index, and thermodynamic stability as solution pH changes. Supersaturation index is as important as solubility and pH_max in anticipating the potential for phase conversions. Cocrystal and salt solubility/supersaturation dependence on pH as well as pH_max, can be predicted from knowledge of K_sp and pK_a.