Solubility of Pharmaceuticals and Their Salts As a Function of pH

Article pubs.acs.org/IECR

Solubility of Pharmaceuticals and Their Salts As a Function of pH Jan Cassens, Anke Prudic, Feelly Ruether, and Gabriele Sadowski* Laboratory of Thermodynamics, Department of Biochemical and Chemical Engineering, TU Dortmund, Emil-Figge Straße 70, D-44227 Dortmund, Germany S Supporting Information *

ABSTRACT: In this work, the solubilities of lidocaine, thiabendazole, and terfenadine and their salts were measured and modeled as a function of pH. The aqueous solubilities of lidocaine and thiabendazole were measured in the pH range between 0.5 and 9.8 using hydrochloric acid or phosphoric acid. The solubility was modeled using the ePC-SAFT equation of state. The model parameters of the nonionized pharmaceuticals were determined from their solubilities in pure organic solvents (acetone, ethanol, 2-propanol, n-hexane, n-heptane, and toluene), which were also measured. Depending on the pH value, the ionization of the pharmaceutical and the identity of the pH-changing agent were considered during the modeling. The charge of the ionized pharmaceutical was explicitly taken into account. All other model parameters were deduced from those of the nonionized pharmaceutical. Furthermore, the precipitation of the pharmaceutical salt upon a pH change was described by its solubility product. The latter was fitted to one experimental data point at a low pH value at which the pharmaceutical salt precipitated. Using this information, the solubility at any pH and the influence of ionization resulting in an increase in solubility with decreasing pH were nearly in agreement with the experimental data.

1. INTRODUCTION The solubility of pharmaceuticals is an important property that needs to be known for the formulation of pharmaceuticals and the design of production and purification processes. Furthermore, it is important to provide pharmaceuticals with good bioavailability, meaning good absorption into the human body at the desired location in the body. Various approaches can be used to influence the bioavailability of a pharmaceutical, such as the use of amorphous formulations1 and encapsulation materials.2 Furthermore, bioavailability can be improved by the formulation of pharmaceutical salts.3 For poorly soluble acidic or basic pharmaceuticals, the addition of bases or acids, respectively, leads to salt formation and thus ionization, which usually causes a strong increase in solubility. Therefore, models that describe the pH dependence of solubility are of great interest for the production and formulation of pharmaceuticals. Different approaches have already been applied for this purpose. Hansen et al.4 used a simple approach based on the Henderson−Hasselbalch equation to describe pH-dependent solubility. This approach was further investigated by Bergstrom et al.,5 who demonstrated that, in several cases, the model provided only a rough estimation of the pH-dependent solubility profile. Bergstrom et al.5 further developed a method to describe the pH-dependent solubilities of several pharmaceuticals in a phosphoric acid buffer solution. For this purpose, the solubility of the nonionized pharmaceutical must be known. Furthermore, the pH value corresponding to 50% maximum solubility and a slope factor describing the increase in solubility must be fitted to experimental data. Fuchs et al.6 calculated the solubilities of the nonionized species of different amino acids with the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state7,8 and applied a simplified approach to model pH-dependent solubility using dissociation constants. © 2013 American Chemical Society

In all of these approaches, only the nonionized pharmaceuticals were considered; additional components were neglected, including acids, bases, and, in particular, the resulting salts. However, the influence of neither the pH-modifying agents nor salt formation can be disregarded, as indicated by Streng et al.9 and others. Streng et al. demonstrated that the precipitation of the salt causes limited overall solubility with pH changes. This effect depends on the interactions of the pH-modifying agent and its released ions with the pharmaceutical and its ionized species. In their modeling approach, Streng et al.10 used equilibrium constants for the dissociation; the solubility product of the precipitating salt; and the Davies equation, an empirical expression for ion-activity coefficients. In this article, a novel approach to model pH-dependent solubility based on the electrolyte PC-SAFT (ePC-SAFT) equation of state is proposed. In this approach, the ionic species in the system are explicitly considered. The ionic interactions are described without adjusting for additional pure-component parameters, and the precipitation of pharmaceutical salts is considered.

2. THEORY The solubility of pharmaceutical i in a solvent or a solvent mixture can be described by the simplified thermodynamic phase-equilibrium relationship xiL =

⎡ Δh SL ⎛ 1 T ⎞⎤ exp⎢ − 0i ⎜1 − SL ⎟⎥ ⎢⎣ RT ⎝ γi T0i ⎠⎥⎦

Received: Revised: Accepted: Published: 2721

(1)

August 2, 2012 January 16, 2013 January 24, 2013 January 24, 2013 dx.doi.org/10.1021/ie302064h | Ind. Eng. Chem. Res. 2013, 52, 2721−2731

Industrial & Engineering Chemistry Research

Article

In eq 1, xLi is the mole fraction of pharmaceutical i in the liquid phase (i.e., its solubility), T is the temperature in Kelvin, ΔhSL 0i is the enthalpy of fusion of pharmaceutical i in joules per mole, TSL 0i is the melting temperature of pharmaceutical i in Kelvin, and γi is the mole-fraction-based activity coefficient of the pharmaceutical. If a pharmaceutical has acidic or basic functional groups, these groups can be ionized in aqueous solutions by pH changes. Because of the strong interactions of the ionized molecules with water, the solubility of the pharmaceutical usually increases. The ionization of acids is caused by the dissociation of the acid AH into its ionized form A− and a proton that forms a hydronium ion (H3O+) in aqueous solution AH + H 2O ⇆ A− + H3O+

(2)

For the dissociation in eq 2, the equilibrium constant Ka can be defined as a function of the activity a of each component a A−a H3O+ Ka = aAHa H2O (3)

Figure 1. Schematic development of the pH-dependent solubility of a pharmaceutical base B upon the addition of an acid AH.

sparingly soluble pharmaceutical base B dissolved in aqueous solution. When the pharmaceutical base B is dissolved, a small amount of the ionized species BH+ is also formed, according to eq 7. The addition of an acid AH to the solution decreases the pH value by increasing the hydronium ion concentration and, thereby, the amount of the ionized base BH+. The solubility then strongly increases because of the stronger interactions between water and the ionized species of the pharmaceutical base BH+. The pH at which this strong solubility increase occurs is mainly determined by the Ka value of the pharmaceutical base. Because the undissolved solid still is the nonionized base B, the solubility in this pH range is mainly determined by the solid−liquid equilibrium of this species and can be described by eq 1. Therefore, the melting enthalpy and the melting temperature of the pharmaceutical base must be known. The addition and dissociation of the acid AH increases the number of ionic species. The amounts of the undissociated acid and its anion in solution must be considered based on the dissociation equilibrium described by eq 4. At lower pH values, the numbers of both acid anions and ionized species BH+ of the pharmaceutical base increase. At a certain pH, the salt BHA precipitates, causing solubility limitations at low pH. This effect is illustrated by the dashed lines in Figure 1. Depending on the solubility of the salt formed, the solubility might further decrease as the pH value decreases further. Salt precipitation can be described as an equilibrium between the salt BHA in its solid state (index s) and the ionized pharmaceutical base BH+ and acid anion A− in solution (index aq). Assuming that the salt dissociates completely in solution, which is a common simplification for these systems,14 the equilibrium can be described as

Assuming that the ratio of the molality-based activity coefficients is 1 and including the molal concentration of water into the equilibrium constant, the acid constant Kac can then be expressed as a function of the various molalities m as follows m A−m H3O+ K ac = mAH (4) The acid constants, or often their negative logarithms denoted as pKa, are usually known for many acids (including pharmaceutical acids) and can be found in the literature. These values can also be determined by titration methods.11,12 In most cases, the Kac values are given on a molarity scale. However, using Kac on a molality scale is advantageous13 for extrapolations to other concentrations, and therefore, it is also used here. At infinite dilution, where the density of the solution can be assumed to be equal to the density of pure water, Kac on a molarity scale and Kac on a molality scale become the same. A base B dissolved in water can accept a proton and form an ionized base BH+. This process can also be described by the dissociation equilibrium BH+ + H 2O ⇆ B + H3O+

(5)

The equilibrium constant, again expressed in terms of activities, is defined according to the equation aBa H3O+ Ka = a BH+a H2O (6) Analogously to eq 4, the equilibrium constant can be expressed as an acid constant that is a function of the various molalities m as follows mBm H3O+ K ac = m BH+ (7)

[A−]aq + [BH+]aq ⇆ [BHA]s

(8)

If the salt precipitates as pure a component, the solubility product, KSP, is defined as follows

As for the acids, the Kac values (or the respective pKa values) are also known for pharmaceutical bases and can be directly used for modeling. To model the pH-dependent solubility of a pharmaceutical, the ionization of the pharmaceutical and the ionization of the pH-altering agent must be considered. Figure 1 schematically presents the pH-dependent solubility of a

KSP = a A−a BH+

(9)

The definition of KSP in eq 9 is not valid in cases of hydrate formation. For pharmaceutical salts, hydrates are often formed and must be considered in the model. Hydrate formation can be treated as a result of a chemical reaction between water and 2722

dx.doi.org/10.1021/ie302064h | Ind. Eng. Chem. Res. 2013, 52, 2721−2731


Article

volume κAiBi, are applied to describe association. Therefore, each nonionized component is described by three parameters if it does not comprise associating sites. If the component is an associating component, two additional parameters must be determined. The pure-component parameters for solvents are usually fitted to the vapor-pressure and density data of the pure component. However, for pharmaceutical solids, these data are not available. In these cases, the pure-component parameters can be fitted to the solubility data of binary systems.6,19 If binary or higher systems are considered, the Berthelot− Lorentz mixing rules are applied to calculate the segment diameter and the dispersion-energy parameter, according to the relationships

the pharmaceutical salt.15 Hence, the effect of hydrate formation can be taken into account by including the water activity in eq 9, which yields KSP,hydrate = a A−a BH+a H2O

(10)

Within this work, the salt precipitation was calculated according to eq 9 or 10, as appropriate. However, the solubility product is often unknown, so in this work, one experimental solubility data point at low pH at which salt precipitation occurred was used to adjust the solubility product. Because ions do not exist as pure components, the reference state for ions is usually defined as a 1 m solution exhibiting interactions as at infinite dilution. Because the activity coefficients must be unity at the reference state, the asymmetric activity coefficient γ*i was used in those cases16 γi γi* = ∞ γi (11)

εij = (1 − kij) εiεj

σij =

1 A iBi (ε + ε A jBj) 2

A iBj

A iBi A jBj ⎢

=

κ

κ

⎤3 ⎥ ⎢⎣ (σii + σjj) ⎥⎦

(16)

⎡ 2σiiσjj

(17)

For ions and ionized components, electrostatic interactions must be taken into account in the model. Small ions are modeled as spheres characterized by two parameters. The ion segment diameter σ describes the size of the hydrated ionic sphere. The interaction between the ions and water is described by a dispersion-energy parameter ε. The interaction between two ions is assumed to result only from repulsive and electrostatic forces. For many small ions, the ionic parameters have already been determined and can be found in the literature.16 2.2. Modeling of Ionized Pharmaceuticals. The use of a spherical geometry for modeling ionized species is not physically meaningful for large pharmaceuticals. Therefore, only one sphere of the molecule was defined as being charged. Figure 2 depicts a schematic of a pharmaceutical base that is ionized by the addition of hydrochloric acid to the solution.

(12)

Depending on the pH value, the nature of the precipitating solid changes. Hence, eq 1 applies for pH values where the pharmaceutical base is the precipitating component, and eq 9 or 10 applies for pH values where the salt or its hydrate is the precipitating component. To solve eqs 1, 9, and 10, the activity coefficients of the corresponding components must be known. For this purpose, the ePC-SAFT equation of state17 was utilized in this work. 2.1. ePC-SAFT. ePC-SAFT17 determines the residual Helmholtz energy, ares, as a sum of different contributions, namely, hard-chain repulsion (ahc), dispersive attraction (adisp), and associative interaction (aassoc). An additional contribution aelec, based on Debye−Hückel theory,18 accounts for ionic interactions. Using these contributions, the ePC-SAFT equation of state describes the residual Helmholtz energy as a res = a hc + adisp + aassoc + aelec

(15)

2

ε A iBj =

κ

N i=1

σi + σj

In eqs 14 and 15, σij is the segment diameter resulting from the combination of components i and j; εij is the dispersion-energy parameter between components i and j; and kij describes the binary interaction parameter, which must be determined for each binary mixture. The cross-association between two molecules is described by the combining rules of Wolbach and Sandler20 (no additional parameters are required) as follows

In eq 11, γi and γ∞ i are the activity coefficients in the solution at a finite concentration and at infinite dilution, respectively. This asymmetric activity coefficient and the molal ion concentrations were used to calculate the activities in eqs 9 and 10. It should be noted that, for the calculation of the solubility of the nonionized pharmaceutical using eq 1, the reference state for the activity coefficient was still the pure (liquid) component; hence, the activity coefficient γi was utilized in eq 1. For a known pH value and, therefore, for a known amount of hydronium ions in solution, the amounts of nonionized acid and its ionized species, as well as the amounts of pharmaceutical base and its ionized species, can be calculated using the dissociation equilibria for acids and bases described by eqs 4 and 7, respectively. In addition, electroneutrality must be satisfied in all calculations; this condition accounts for the ion balance of all N ion species, each with a point charge of qi, according to

∑ qimi = 0

(14)

Figure 2. Model for an ionized pharmaceutical base.

(13)

The acid dissociates into a proton and the acid anion, and the proton then charges the pharmaceutical base. The chloride is a single ion and was modeled as a sphere, whereas the protonation of the pharmaceutical base was modeled assuming one positive charge at one segment. If the pharmaceutical base is ionized, its molar mass is only slightly altered because the addition of the proton does not alter the size of the molecule

Nonionized components i are modeled as chains of mi tangentially connected spheres, each with segment diameter of σi. Furthermore, modeling the dispersive interactions between the chains requires a dispersion-energy parameter εi. In the case of associating molecules, two additional parameters, the association-energy parameter εAiBi and the association 2723



Article

0.45 μm) was used for sampling. After being weighed, the samples were dried until the solvent was removed, and the remaining quantity of the sample (pharmaceutical) was determined by weighing. For each temperature, three samples were measured to obtain reproducible solubility values. 3.3. Solubility Measurements of Terfenadine in Toluene. Because of its high solubility and the small amount of available solid, the solubility of terfenadine in toluene was determined by differential scanning calorimetry (DSC), which allowed for small sample volumes. The DSC measurements to determine solubility were performed as described in the literature.23 Homogeneous solutions containing different concentrations of terfenadine were prepared. Samples of the solution were placed in a closable aluminum crucible with a volume of 40 μL. This crucible was sealed with a collet chuck and then weighed, with an accuracy of 10−5 g. To obtain a supersaturated solution, the aluminum crucible was cooled at 280 K for 12 h. Afterward, DSC measurements were performed. The measurements were conducted with a DSC Q100 apparatus (TA Instruments), using a constant heating rate of 5 K/min. An empty aluminum crucible was used as a reference for the measurements. To ensure that there was no loss of solvent during the DSC measurements, the crucible was also weighed after the measurement. The temperature corresponding to the solubility of the component was defined as the offset value of the peak in the heating curve. 3.4. Measurement of pH-Dependent Aqueous Solubilities. To determine pH-dependent solubilities in aqueous solutions, a 100 mL glass vessel with a heating jacket was used. A PT100 probe (accuracy ±0.1 K) and a Qph 70 pH-electrode probe from VWR International were integrated into the cap through septa. The temperature (298.15 K) was controlled with a LAUDA Ecoline Star Edition RE304 thermostat. An additional septum in the cap was used to sample the solution or to add acids with a syringe. The solution was stirred for 24 h and considered equilibrated when there were no further changes in the pH value. Samples (5 mL) were removed from the saturated solution with a syringe equipped with a syringe-mounted filter (pore size of 0.45 μm). The concentration of the pharmaceutical in the sample was measured using a high-performance liquid chromatograph (HPLC) from Agilent Technologies (1200 Series). The HPLC was equipped with an Agilent Zorbax SB-C18 column and operated with a mobile phase consisting of 50 mM phosphate buffer at pH 3 and acetonitrile (80:20 v/v). Phosphate buffer was added to the sample to obtain a pH of 2 before the HPLC separation. After the solubility had been determined, DSC measurements of the solid samples were conducted to characterize the precipitated solutes. Each solubility point was measured at least three times, and the values were averaged over these three measurements. The experimental data points, including the standard deviations, are reported in Tables S1 and S2 in the Supporting Information.

significantly. For this reason, the segment number and the segment diameter of the ionized pharmaceutical base were assumed to be identical to the corresponding values for the nonionized pharmaceutical base. The dispersion-energy parameter of the pharmaceutical base was also assumed to remain the same. Thus, no additional pure-component parameters need to be adjusted for the ionized pharmaceutical base. Using an approach accounting for different types of segments within one molecule,21,22 the ionized and nonionized segments were explicitly considered in the model. Only the number of ionized segments (one molecule segment carrying a single charge was used for the molecules within this work) had to be known, and no additional parameters were required. The electrostatic interactions between the ionized segments and the ions (from the added acid) in the solution were described by Debye−Hückel theory. In addition, the formation of the hydration sphere was taken into account by the dispersive interactions between the ionized molecule and water. Therefore, the binary interaction parameter between the ionized molecule and water was adjusted to experimental solubility data from aqueous solution. To determine the associative contribution to the Helmholtz energy, the number of proton-donor and proton-acceptor sites on a molecule must be defined. In this work, the sites of association and the association parameters for the nonionized molecules were also used for the ionized species.

3. EXPERIMENTAL METHODS 3.1. Materials. Lidocaine, thiabendazole, and terfenadine were purchased as crystalline powders from Sigma-Aldrich Gmbh, Munich, Germany. Phosphoric acid, also purchased from Sigma-Aldrich Gmbh, was used as a crystalline solid with a purity of 99.9%. Acetone, ethanol, toluene, 2-propanol, nhexane, and n-heptane (of analytical-grade purity) were supplied by Merck, Darmstadt, Germany. Hydrochloric acid (37%) and phosphoric acid (99.99%) were also purchased from Merck. Millipore ultrapure water was used in the experiments. All substances were used as purchased from the manufacturers without additional purification steps. 3.2. Solubility Measurements of Lidocaine and Thiabendazole in Organic Solvents. The solubilities of lidocaine and thiabendazole in organic solvents were measured gravimetrically. A supersaturated solution of the pharmaceutical bases was used in each solvent system in a 40 mL vial. The vial was equilibrated in a rotary kiln for 24 h at a turning rate of 4 rpm. For solubility measurements of thiabendazole at temperatures below 298.15 K, a 100 mL glass vessel with a heating jacket was used. The temperature of the glass vessel was measured with a PT100 probe (accuracy ±0.1 K). For each temperature, the sample was equilibrated for 24 h. Because of the high solubility of lidocaine in the tested solvents, the solubility measurements of lidocaine below 298.15 K were performed in a 15 mL vial that was filled with a supersaturated solution. The vial was placed in the 100 mL glass vessel filled with water to temper the sample. The supersaturated solution was stirred with a magnetic stirrer to ensure sample equilibration. The vials were incubated at the specified temperature for 24 h. In each experiment, a 2 mL sample of the saturated solution was removed after the magnetic stirrer had been turned off and the system had been given enough time to settle. A tempered syringe equipped with a syringe-mounted filter (pore size of

4. RESULTS 4.1. Solubilities of Nonionized Pharmaceutical Bases. 4.1.1. Experimental Data. The solubility of lidocaine was measured in acetone, ethanol, heptane, and hexane. The results of these experiments are shown in Figures 3 and 4. Furthermore, the solubilities of thiabendazole in ethanol, 2propanol, and acetone were measured, and the results are depicted in Figure 5. The experimental solubility data for terfenadine in toluene are given in Figure 6. All experimental 2724



Article

Figure 3. Solubilities of lidocaine in acetone (squares) and ethanol (circles). The symbols represent experimental data, and the lines are correlations using the parameters from Tables 2 and 3.

Figure 6. Solubility of terfenadine in toluene. The symbols represent experimental data, and the lines are correlations using the parameters from Tables 2 and 3.

Table 1. Melting Temperatures and Melting Enthalpies of the Considered Pharmaceutical Bases pharmaceutical

T0iSL (K)

Δh0iSL(J/mol)

ref(s)

lidocaine thiabendazole terfenadine (polymorph II)

341.65 573.15 420.65

16090 35190 51900

26, 27 28 24

k, the association-energy parameter εAiBi, and the association volume κAiBi, must be determined. The parameters were fitted to the experimental solubility data obtained for the neutral pharmaceutical bases dissolved in several pure solvents, as shown in Figure 3−6, using the software SolCalc.25 Binary interaction parameters kij for each solution were fitted to the corresponding experimental binary solubility data. It has been previously demonstrated19 that the use of linearly temperature-dependent binary interaction parameters can improve the modeling results for some pharmaceuticals according to the equation

Figure 4. Solubilities of lidocaine in n-heptane (squares) and n-hexane (circles). The symbols represent experimental data, and the lines are correlations using the parameters from Tables 2 and 3.

kij = kij ,slopeT + kij ,int

(18)

For lidocaine, the pure-component parameters and the temperature-dependent binary interaction parameters between lidocaine and the corresponding solvents were fitted simultaneously to the experimental data for all organic solutions considered within this work. Because lidocaine was described as being associating, at least five experimental data points were required to fit the five pure-component parameters. Two additional data points for each solvent system were necessary to fit the binary interaction parameters between lidocaine and the respective solvents. Using more data points than required for the parameter fitting (as in this case) allows for faster convergence of the fitting process, but it is not generally necessary. A similar procedure was applied for thiabendazole. However, in this case, the binary interaction parameters were considered to be temperature-independent, meaning that only five data points for the pure-component parameters of thiabendazole and one additional data point for each solvent system were required for parameter fitting. Nevertheless, again, all available data points were considered for the parameter fitting. To demonstrate that pure-component parameters of a pharmaceutical can also be fitted to solubility data points in only a single solvent, the parameters for terfenadine were determined based solely on its experimental toluene solubility data. Because of the high molar mass and complex structure of the terfenadine molecule, it was assumed that steric effects

Figure 5. Solubilities of thiabendazole in ethanol (circles), 2-propanol (triangles), and acetone (squares). The symbols represent experimental data, and the lines are correlations using the parameters from Tables 2 and 3.

data will be discussed, along with the modeling results, in the following section. Notably, for terfenadine, three polymorphic structures that can be characterized by different melting temperatures and melting enthalpies are known.24 To identify the polymorphic form, DSC measurements of the terfenadine samples were performed. Furthermore, terfenadine crystallized from toluene was analyzed by DSC. The observed melting points were compared to literature values. The terfenadine that crystallized from toluene was identified as form II, with a melting point of 420.65 K. The melting properties of the analyzed pharmaceutical bases are listed in Table 1. 4.1.2. Modeling. For each associating pharmaceutical base, five pure-component parameters, namely, the segment number m, the segment diameter σ, the dispersion-energy parameter ε/ 2725



Article

Table 2. Pure-Component ePC-SAFT Parameters for the Pharmaceuticals and Solvents Used component

M

σ (Å)

ε/k (K)

εAiBi/k (K)

κAiBi

ndonors/nacceptors

ref

lidocaine thiabendazole terfenadine acetone ethanol n-heptane n-hexane 2-propanol phosphoric acid

5.2935 13.9820 18.3646 2.8913 2.3827 3.4831 3.0576 3.0929 5.960

2.5851 3.5203 2.2461 3.2279 3.1771 3.8049 3.7983 3.2085 2.252

155.97 420.63 242.95 247.42 198.24 238.4 236.77 208.42 176.13

1830.73 1645.64 0 0 2653.4 − − 2253.9 5137.78

0.02 0.00197 iBi κAsolvent iBi κApharmaceutical 0.032384 − − 0.024675 0.2

2/2 2/2 2/2 1/1 1/1 − − 1/1 1/1

this work this work this work 28 8 29 7 8 13

hexane with the experimental data obtained. Lidocaine is the most soluble in acetone. The solubility data of lidocaine in acetone and ethanol exhibit an almost linear dependence on temperature. The solubilities of lidocaine in hexane and heptane are low at temperatures below 300 K and strongly increase at higher temperatures. As can be seen, the ePC-SAFT model accurately reproduces the experimental solubility data. Thiabendazole is only slightly soluble in ethanol, 2-propanol, and acetone, as shown in Figure 5. The solubility data exhibit a moderate increase with increasing temperature. Again, the comparison between the correlated results and the experimental data demonstrates the applicability of ePC-SAFT for modeling the thiabendazole solubility in various solvents and verifies the fitted pure-component parameters for thiabendazole. The experimental solubility data for terfenadine in toluene and the calculated correlation are shown in Figure 6. The pure-component parameters for terfenadine were adjusted to the experimental data. As observed with the other pharmaceutical bases, the measured terfenadine solubility was accurately correlated by the model. It should be noted that the pure-component parameters were not influenced by the polymorphism of the solid phase, as the parameters describe only the components in the liquid solution. Table 4 summarizes the absolute relative deviations (ARDs) of the calculated solubilities from the experimental data for all considered systems.

prevent the associative compartments from converging. Therefore, the association-energy parameter of the terfenadine molecule was set equal to zero. However, small associating molecules such as water can approach the associating compartments of the terfenadine molecule and form hydrogen bonds. Hence, terfenadine was modeled as an inducedassociating component,30 meaning that terfenadine molecules can form hydrogen bonds with other associating molecules (e.g., water) but not with each other. Based on that assumption, the association-energy parameter of terfenadine was set equal to zero, and the association volume was set equal to the association volume of the associating solvent. This reduced the number of fitted pure-component parameters for terfenadine from five to three. In the first fitting step, the binary interaction parameter was considered to be temperature-independent, and it was fitted along with the pure-component parameters to the solubility data in toluene only. In the second step, the pure-component parameters were kept constant, and kij was readjusted as a function of temperature by fitting again to the same solubility data in toluene. This procedure also allowed the modeling of the solubilities in other solvents such as water by fitting only the binary interaction parameters to the solubility data in these solvents. All pure-component parameters determined for the tested pharmaceuticals and the other model parameters are reported in Table 2. It should be noted that the approach of induced association was also applied to acetone, meaning that the associationenergy parameter was set equal to zero and that the association volume was set as the volume of the pharmaceutical base (0.02 for lidocaine and 0.00197 for thiabendazole). The binary interaction parameters used in this work are summarized in Table 3. Figures 3 and 4 compare the modeling results for the solubilities of lidocaine in acetone, ethanol, heptane, and

Table 4. Average Absolute Relative Deviation (ARD) of the Correlated Predicted Solubilities from the Experimental Data pharmaceutical base lidocaine

thiabendazole

Table 3. Binary Interaction Parameters of Pharmaceutical Bases and Solvents Calculated As a Linear Function of the Temperature, According to Eq 18

terfenadine pharmaceutical base lidocaine

thiabendazole

terfenadine

solvent

kij,slope

kij,int

acetone ethanol n-hexane n-heptane acetone 2-propanol ethanol toluene

−4.57 × 10−6 7.74 × 10−7 1.80 × 10−6 −4.91 × 10−5 0 0 0 4.90 × 10−4

−0.01916 0.01152 0.01323 0.03522 −0.04230 −0.07158 −0.08697 −0.18346

solvent

ARD (%)

acetone ethanol n-hexane n-heptane acetone 2-propanol ethanol toluene

1.9 3.2 3.6 1.3 11.4 9.1 4.4 4.9 × 10−4

The deviations range from 1.3% for lidocaine in n-heptane to 3.6% for lidocaine in n-hexane. For the solubility of thiabendazole, the deviations are between 4.4% and 11.4%. However, it should be noted that the concentrations of thiabendazole in the tested solvents were very low [in the range of 10 mg/(g of solvent)], which resulted in high relative errors even though the absolute deviations were reasonable. Overall, the correlation results demonstrate the applicability of the 2726



Article

modeling approach to describe the solubilities of the tested pharmaceutical bases in organic solvents. 4.2. pH-Dependent Solubilities of Ionized Pharmaceutical Bases. In the previous section, the solubility data for the pharmaceutical bases in organic solvents were used to determine the pure-component parameters of the pharmaceutical bases. In the next section, these parameters are used to predict the solubilities of the pharmaceutical bases in aqueous solutions at different pH values. 4.2.1. Experimental Data. The aqueous solubilities of lidocaine and thiabendazole were measured as a function of pH. In each case, hydrochloric acid or phosphoric acid was used to alter the pH. The experimental data points, including the standard deviations, are reported in Table S2 in the Supporting Information. To characterize the solid phase, DSC measurements of the precipitated solids were performed. These measurements demonstrated that the solid phase changed as the pH decreased below the pH at maximum solubility. These results affirmed the formation of salt in this pH region. The experimental data presented in Figures 7−11 are indicated by solid symbols when the nonionized pharmaceutical base precipitated as a pure solid and as open symbols when the salt form precipitated.

Figure 8. Measured pH-dependent solubility of thiabendazole. The circles denote the use of hydrochloric acid as the pH-changing agent, whereas the squares denote the use of phosphoric acid as the pHchanging agent. The solid symbols represent the nonionized pharmaceutical base in the solid phase, and open symbols indicate when salt precipitates formed. Error bars are shown only when larger than the symbol size.

upon the addition of an acid, and a maximum solubility was reached. In contrast to the pH-dependent solubility of lidocaine, the solubility of thiabendazole salt at low pH decreased rapidly for pH values smaller than the maximum solubility. The maximum solubility was slightly higher when hydrochloric acid, rather than phosphoric acid, was used. The results again clearly demonstrate that the maximum solubility strongly depends on the type of acid that is used to alter the pH value. Thus, the effect of the acid anion is important and must be considered explicitly in the solubility model. 4.2.2. Modeling. The pure-component parameters for the ionized species of the pharmaceutical bases were set to be identical to those of the nonionized species, which were fitted to experimental solubility data in organic solvents as described earlier. Only the binary interaction parameters between the nonionized species and water and between the ionized species and water had to be determined. These parameters were considered to be independent of temperature, and both were adjusted to experimental data obtained using hydrochloric acid as the pH-changing agent and in the pH range where the salt did not precipitate. In this range, the ionized species of the pharmaceutical bases were taken into account using the acid constants listed in Table 5.

Figure 7. Measured pH-dependent solubility of lidocaine. The circles denote the use of hydrochloric acid as the pH-changing agent, whereas the squares denote the use of phosphoric acid as the pH-changing agent. The solid symbols represent the pure nonionized pharmaceutical base in the solid phase, and the open symbols indicate when salt precipitates formed. For each experimental data point, the error bars are smaller than the symbol size.

Figures 7 and 8 show the measured pH-dependent solubilities of lidocaine and thiabendazole, respectively. Figure 7 presents a hyperbolic increase in solubility upon the addition of an acid. At a certain pH value, a maximum solubility is observed; further decreasing the pH results in a solubility plateau. This behavior was previously described for a solution of lidocaine5 in which the pH was modified by the addition of phosphate buffer. The maximum solubility depended on whether hydrochloric acid or phosphoric acid was used in the experiments. The maximum concentration was approximately 500 mg/(g of water) when hydrochloric acid was used, compared to approximately 350 mg/(g of water) when phosphoric acid was used. This clearly indicates that that the maximum solubility depends on the acid used. In both cases, the addition of acid caused a hyperbolic increase in solubility and the formation of a solubility plateau. The experimental pH-dependent solubility data for thiabendazole are shown in Figure 8. As observed for the other compounds, a hyperbolic increase in the solubility was observed

Table 5. Acid Constants (pKa) for Ionizable Components at 298.15 K

a

component

pKa

ref

lidocaine thiabendazole terfenadine phosphoric acid

8.01 4.64 9.5 2.16a 7.21b

5 5 31 32

First dissociation step. bSecond dissociation step.

Hydrochloric acid is considered to be a strong electrolyte that completely dissociates in aqueous solution. In the case of phosphoric acid as the pH-changing agent, the dissociation of phosphoric acid and the presence of its different ionized forms were taken into account. The literature values for the acid constants of phosphoric acid used in this work are included in Table 5. The amounts of the various phosphate species were 2727



Article

Table 6. Pure-Component Parameters for the Ions and Ionized Pharmaceuticalsa and Binary Interaction Parameters for the Interaction with Water

a

component

M

σ (Å)

ε/k (K)

εAiBi/k (K)

κAiBi

ndonors/nacceptors

kij,water

ref

ionized lidocaine ionized thiabendazole ionized terfenadine H3O+ Cl− H2PO4− HPO42−

5.2935 13.9820 18.3646 1 1 1 1

2.5851 3.5203 2.2461 2.2740 3.0575 3.7026 4.4608

155.97 420.63 242.95 1616.49 47.29 0 0

1830.73 1645.63 0 0 0 0 0

0.02 0.00197 iBi κAsolvent

2/2 2/2 2/2 0/0 0/0 0/0 0/0

−0.064 0.127 −0.180 0 0 0 0

this work this work this work 16 16 16 16

0 0 0 0

Identical to the pure-component parameters for the nonionized pharmaceuticals.

determined based on the dissociation equilibrium described by eq 4. As demonstrated by Reschke et al.,34 the phosphate ion is present only at pH values higher than 10, so the dissociation of the dihydrogen phosphate ion into the phosphate ion was neglected in the modeling. Table 6 lists the pure-component parameters for the ionized species (taken from the literature) and the binary interaction parameters between the ionized species and water. Table 7 summarizes the binary interaction parameters between the nonionized species and water. Table 7. Binary Interaction Parameters between the Nonionized Pharmaceutical Bases and Water pharmaceutical base

kij,water

lidocaine thiabendazole terfenadine

0.0640 −0.0115 0.0130

Figure 9. pH-dependent solubilities of lidocaine in aqueous solutions containing hydrochloric acid (circles) or phosphoric acid (squares). The solid symbols represent experimental data for the solubility of the nonionized pharmaceutical base, and the open symbols indicate the solubility of the salt. The modeling results are depicted as lines. For each experimental data point, the error bars are smaller than the symbol size.

To model the pH-dependent solubility and salt precipitation at low pH values, knowledge of the solubility product (eq 9 for the salt or eq 10 for the hydrated salt) is required. Because these values were not available from the literature, they were fitted for each salt from one experimental data point at a low pH at which the salt or hydrate salt precipitated. The values for the solubility products used in this work are listed in Table 8.

reported in the literature5 and observed experimentally within this work. Upon further decreases in the pH, the predicted solubility decreased significantly. Also, the modeling results for the case of phosphoric acid as the pH-changing agent are in a good accordance with the experimental data, as shown in Figure 9. It should be noted that no additional binary interaction parameters were fitted for the pH-dependent solubility modeling with phosphoric acid, as all required parameters were already determined. Only the solubility product of the lidocaine salt was fitted to one experimental data point at a low pH where the salt precipitated. The expected plateau formation at low pH values is well described by the model. The slope of the hyperbola representing the experimental solubility profile at pH values between 6 and 7 differs slightly, depending on which acid was used. This difference is also captured by the model. As in the aqueous system with hydrochloric acid, the solubility decreases rapidly at lower pH values when more acid is added. This behavior can be ascribed to the common-ion effect, meaning that the precipitating salt and the acid have one ion (i.e., the anion of the dissociating acid) in common. The further addition of acid causes an increase in the amount of acid anions in the system. If the solubility of the acid in the solution is greater than the solubility of the pharmaceutical salt, the salt begins to precipitate at a certain pH value in order to satisfy the equilibrium condition given in eq 9. This common-ion effect is also well captured by the model. The second tested system was thiabendazole in aqueous solutions with hydrochloric acid or phosphoric acid. For this

Table 8. Solubility Products of the Considered Pharmaceutical Salts and of Lidocaine Hydrochloride Hydrate component

KSP, KSP,hydrate

lidocaine hydrochloride hydrate lidocaine dihydrogen phosphate thiabendazole hydrochloride thiabendazole dihydrogen phosphate terfenadine hydrochloride

4.1 1.37 1.13 × 10−3 4.1 × 10−6 2 × 10−5

Figure 9 compares the experimental and modeled pHdependent solubility data for lidocaine in an aqueous solution containing either hydrochloric acid or phosphoric acid. The chloride salt of lidocaine forms a monohydrate that precipitates at low pH.33 This monohydrate was taken into account using eq 10, whereas the precipitation of lidocaine dihydrogen phosphate was described by eq 9. The solubility product for the lidocaine salts was fitted to the solubility data point at the lowest pH value. The modeling results for the aqueous system with hydrochloric acid are in good agreement with the experimental data and describe a solubility plateau at low pH, as was previously 2728



Article

compound, the solubility decreases significantly when the pH value is reduced beyond the optimal pH for maximum solubility. To model this system, the pure-component parameters for nonionized and ionized thiabendazole were calculated in the previous section. The binary interaction parameters between water and the ionized form of thiabendazole and between water and thiabendazole’s nonionized form were fitted to the experimental solubility data obtained with hydrochloric acid in a pH range where no salt precipitated. The parameter values are listed in Tables 6 and 7. As before, the solubility products of thiabendazole hydrochloride and thiabendazole dihydrogen phosphate were fitted to a data point in the pH region where the corresponding salt precipitated (at pH 2). These values are listed in Table 8. Figure 10 compares the modeling results with the experimental data when hydrochloric acid was used. The

Figure 11. pH-dependent solubility of thiabendazole in an aqueous solution with phosphoric acid as the pH-changing agent. The solid symbols mark experimental solubility data for the nonionized pharmaceutical base, and open symbols indicate the solubility of the salt. The modeling results are depicted as lines. For each experimental data point, the error bars are smaller than the symbol size.

solubility curve at low pH values is calculated in qualitative agreement with the experimental observation. The solubility of terfenadine was also investigated. The experimental pH-dependent solubility data for an aqueous system with hydrochloric acid as the pH-changing agent were taken from the literature.9 The solubility of terfenadine decreases slightly at pH values lower than the pH at maximum solubility and decreases rapidly when the pH is further decreased. The same modeling procedure as described previously was applied. The pure-component parameters for nonionized terfenadine were independently determined by fitting to binary solubility data in toluene. The pure-component parameters of ionized terfenadine were again set to be identical to those of nonionized terfenadine. Both the binary interaction parameters between nonionized terfenadine and water and between ionized terfenadine and water were fitted to the experimental data at pH 7.3, at which no salt precipitated. Terfenadine hydrochloride precipitates as a pure salt;9 hence, the solubility product was fitted to one experimental data point at pH 4.9, at which the salt precipitated. Figure 12 shows good

Figure 10. pH-dependent solubility of thiabendazole in an aqueous solution with hydrochloric acid as the pH-changing agent. The solid symbols represent experimental solubility data for the nonionized pharmaceutical base, and the open symbols indicate the solubility of the salt. The modeling results are depicted as lines. The error bars are given only when they are larger than the symbol size.

comparison again exhibits good agreement between the experimental data and solubility modeling. The experimentally observed hyperbolic increase in solubility at high pH values is well predicted by the model. Furthermore, the spontaneous decrease in solubility when the pH is below the value for maximum solubility is also correctly described. The solubility profile of thiabendazole differs greatly from the solubility profile of lidocaine, in which a solubility plateau was observed. Obviously, the presented modeling approach is able to describe this difference. Figure 11 depicts the result of the modeled pH-dependent solubility of thiabendazole when phosphoric acid was used. No additional binary interaction parameters were fitted to model this system, and only the solubility product for thiabendazole dihydrogen phosphate was determined from one experimental data point at low pH. The modeling results are again in good agreement with the experimental data. The hyperbolic increase in the solubility at pH values greater than 2.3 (at which the nonionized species of thiabendazole precipitated) is well captured by the model. Furthermore, the model is able to quantitatively describe the experimentally observed significant decrease in solubility at very low pH values. Figure 10 also shows that the calculated solubility at pH 1.5 deviates from the experimental value by approximately 50%. The activity coefficient for thiabendazole in this system seems to be overestimated, but it should be noted that the slope of the

Figure 12. pH-dependent solubility of terfenadine in aqueous solution with hydrochloric acid as the pH-changing agent: comparison of the experimental data9 (symbols) and modeling results (lines).

agreement between the experimental data and the modeling results, which again verifies the applicability of the proposed modeling approach to describe the solubility of pharmaceuticals and their salts at different pH values. 2729



■

5. CONCLUSIONS In this work, an approach to model the solubility of pharmaceuticals and their salts as a function of pH was developed. The ionization of the pharmaceuticals and the precipitation of their salts were explicitly taken into account. The activity coefficients were determined with the ePC-SAFT model. The model parameters of the nonionized pharmaceutical bases lidocaine, thiabendazole, and terfenadine were fitted to solubility data in pure organic solvents. These parameters were used in the subsequent step to model the solubilities of the pharmaceuticals in water as a function of pH. The pH-dependent solubilities were measured for lidocaine and thiabendazole using hydrochloric acid and phosphoric acid as pH-changing agents. At high pH values, the nonionized pharmaceutical bases precipitated as solids, allowing the determination of the solubility profile in this pH range. Upon a decrease in the pH, a maximum solubility was observed; this maximum concentration was strongly influenced by the type of acid added to the solution. At low pH values, at which the salt of the pharmaceutical base precipitated, further addition of the acid caused either a plateau or a rapid decrease in solubility. A similar behavior was also found in the literature for the pHdependent solubility of terfenadine with hydrochloric acid as the pH-changing agent. To model the pH-dependent solubilities of pharmaceutical bases, the ionic species of the pharmaceutical bases and the ionic species of the pH-changing acids were explicitly considered. For this purpose, all of the model parameters of the ionized pharmaceutical bases were deduced from those of the nonionized molecules. The only parameter that needed to be fitted to an experimental data point was the solubility product of the pharmaceutical salts. Using these parameters, the pH-dependent solubilities of lidocaine, thiabendazole, and terfenadine could be predicted in very good agreement with the experimental data. The solubility at high pH and the influence of ionization caused an increase in solubility with decreasing pH, and this effect was modeled in almost quantitative agreement with the experimental data. By explicitly accounting for salt precipitation, the maximum solubility and the decreases in solubility at lower pH values could be well captured. The proposed approach allows the solubilities of pharmaceuticals and their salts to be described in the pH range of interest and the influence of the acid used to be taken into account.

■

ACKNOWLEDGMENTS The authors thank BASF, DSM, Lonza, Novartis, and Solvay for funding the project within the “Consortium of Modeling and Prediction of Solute Solubility and Oiling Out”. All calculations were performed using the software SolCalc25 developed at TU Dortmund.

■

REFERENCES

(1) Hancock, B. C.; Parks, M. What is the true solubility advantage for amorphous pharmaceuticals? Pharm. Res. 2000, 17, 397. (2) Khamkar, G. S.; Pede, P. V.; Mali, D. K.; Kadam, M. V. A review 2011: Methods for enhancing boavailability of drug. Int. J. Pharm. Technol. 2011, 3, 912. (3) Newton, D. W. Drug incompatibility chemistry. Am. J. Heal. Sys. 2009, 66, 348. (4) Hansen, N. T.; Kouskoumvekaki, I.; Jorgensen, F. S.; Brunak, S.; Jonsdottir, S. O. Prediction of pH-dependent aqueous solubility of druglike molecules. J. Chem. Inf. Model. 2006, 46, 2601. (5) Bergstrom, C. A. S.; Luthman, K.; Artursson, P. Accuracy of calculated pH-dependent aqueous drug solubility. Eur. J. Pharm. Sci. 2004, 22, 387. (6) Fuchs, D.; Fischer, J.; Tumakaka, F.; Sadowski, G. Solubility of amino acids: Influence of the pH value and the addition of alcoholic cosolvents on aqueous solubility. Ind. Eng. Chem. Res. 2006, 45, 6578. (7) Gross, J.; Sadowski, G. Perturbed-chain SAFT: An equation of state based on a perturbation theory for chain molecules. Ind. Eng. Chem. Res. 2001, 40, 1244. (8) Gross, J.; Sadowski, G. Application of the perturbed-chain SAFT equation of state to associating systems. Ind. Eng. Chem. Res. 2002, 41, 5510. (9) Streng, W. H.; His, S. K.; Helms, P. E.; Tan, H. G. H. General treatment of pH solubility profiles of weak acids and bases and the effects of different acids on the solubility of a weak base. J. Pharm. Sci. 1984, 73, 1679. (10) Butler, J. N. Ionic Equilibrium: A Mathematical Approach; Addison-Wesley Publishing Company: Reading, MA, 1964. (11) Levy, R. H.; Rowland, M. Dissociation constants of sparingly soluble substances: Nonlogarithmic linear titration curves. J. Pharm. Sci. 1971, 60, 1155. (12) Kramer, S. F.; Flynn, G. L. Solubility of organic hydrochlorides. J. Pharm. Sci. 1972, 61, 1896. (13) Reschke, T.; Naeem, S.; Sadowski, G. Osmotic coefficients of aqueous weak electrolyte solutions: Influence of dissociation on data reduction and modeling. J. Phys. Chem. 2012, 116, 7479. (14) Stahl, H. P., Wermuth, C. G., Eds. Handbook of Pharmaceutical Salts; Helvetica Chimica Acta: Zürich, Switzerland, 2008. (15) Tumakaka, F.; Prikhodko, I. V.; Sadowski, G. Modeling of solid−liquid equilibria for systems with solid-complex phase formation. Fluid Phase Equilib. 2007, 260, 98. (16) Held, C.; Cameretti, L. F.; Sadowski, G. Modeling aqueous electrolyte solutions: Part 1. Fully dissociated electrolytes. Fluid Phase Equilib. 2008, 270, 87. (17) Cameretti, L. F.; Sadowski, G.; Mollerup, J. M. Modeling of aqueous electrolyte solutions with perturbed-chain statistical associated fluid theory. Ind. Eng. Chem. Res. 2005, 44, 3355. (18) Debye, P. H.; Hueckel, E. Zur Theorie der Elektrolyte. Phys. Z. 1923, 9, 185. (19) Ruether, F.; Sadowski, G. Modeling the solubility of pharmaceuticals in pure solvents and solvent mixtures for drug process design. J. Pharm. Sci. 2009, 98, 4205. (20) Wolbach, J. P.; Sandler, S. I. Using molecular orbital calculations to describe the phase behavior of cross-associating mixtures. Ind. Eng. Chem. Res. 1998, 37, 2917. (21) Tumakaka, F.; Gross, J.; Sadowski, G. Modeling of polymer phase equilibria using perturbed-chain SAFT. Fluid Phase Equilib. 2002, 194, 541. (22) Schäfer, E.; Brunsch, Y.; Sadowski, G.; Behr, A. Hydroformylation of 1-dodecene in the thermomorphic solvent system

ASSOCIATED CONTENT

S Supporting Information *

Experimental data points, including the standard deviations, for solubility measurements. This material is available free of charge via the Internet at http://pubs.acs.org.

■

Article

AUTHOR INFORMATION

Corresponding Author

*Tel. : +49-231-755-2635. Fax: +49-231-755-2572. E-mail: g. [email protected]. Notes

The authors declare no competing financial interest. 2730



Article

DMF/decane. Phase behavior−reaction performance−catalyst recycling. Ind. Eng. Chem. Res. 2012, 51, 10296. (23) Mohan, R.; Lorenz, H.; Myerson, A. S. Solubility measurement using differential scanning calorimetry. Ind. Eng. Chem. Res. 2002, 41, 4854. (24) Canotilho, J.; Costa, F. S.; Sousa, A. T.; Redinha, J. S.; Leitao, M. L. P. Melting curves of terfenadine crystallized from different solvents. J. Therm. Anal. Calorim. 1998, 54, 139. (25) SolCalc is property of TU Dortmund. Please contact the corresponding author for further information. (26) Corvis, Y.; Negrier, P.; Lazerges, M.; Massip, S.; Leger, J. M.; Espeau, P. Lidocaine/L-menthol binary system: Cocrystallization versus solid-state immiscibility. J. Phys. Chem. B 2010, 114, 5420. (27) Abildskov, J. Organic Solutes Ranging from C2 to C41; DECHEMA: Frankfurt, Germany, 2005. (28) Bustamante, P.; Muela, S.; Escalera, B.; Pena, A. Solubility behavior and prediction for antihelmintics at several temperatures in aqueous and nonaqueous mixtures. Chem. Pharm. Bull. 2010, 58, 644. (29) Tumakaka, F.; Sadowski, G. Application of the perturbed-chain SAFT equation of state to polar systems. Fluid Phase Equilib. 2004, 217, 233. (30) Kleiner, M.; Sadowski, G. Modeling of polar systems using PCPSAFT: An approach to account for induced-association interactions. J. Phys. Chem. C 2007, 111, 15544. (31) Bergstrom, C. A. S.; Wassvik, C. M.; Johansson, K.; Hubatsch, I. Poorly soluble marketed drugs display solvation limited solubility. J. Med. Chem. 2007, 50, 5858. (32) Sillen, L. G. Stability Constants of Metal-Ion Complexes; Chemical Society: London, 1964. (33) Koehler, H. M.; Hefferren, J. J. Mineral acid salts of lidocaine. J. Pharm. Sci. 1964, 53, 1126. (34) Reschke, T.; Neaeem, S.; Sadowski, G. Osmotic coefficients of aqueous weak electrolyte solutions: Influence of dissociation on data reduction and modeling. J. Phys. Chem. B 2012, 116, 7479.

2731


Solubility of Pharmaceuticals and Their Salts As a Function of pH

Recommend Documents