Article pubs.acs.org/IECR
Partition Coefficients of Pharmaceuticals as Functions of Temperature and pH Franziska Laube, Timo Klein, and Gabriele Sadowski* Laboratory of Thermodynamics, Technische Universität Dortmund, Emil-Figge-Straße 70, 44227 Dortmund, Germany S Supporting Information *
ABSTRACT: Liquid−liquid extraction is a potential separation process for the purification of active pharmaceutical ingredients (APIs). The design of an extraction step requires knowledge of the API partition coefficient, which strongly depends on the solvent system and process conditions. Usually, cost-intensive experiments have to be performed to select the most suitable solvent system and the best process conditions. The number of experiments can be reduced by predicting the partition coefficient using perturbed chain statistical associating theory (PC-SAFT). In this work, modeling results and experimental data were compared for the partition coefficients of the APIs nicotinamide and salicylamide in different solvent systems at temperatures from 293.15 to 328.15 K and at pH values varying between 5.2 and 10.3. The results show that PC-SAFT is able to predict the API partition coefficients for different solvent systems as functions of temperature and pH.
1. INTRODUCTION Liquid−liquid extraction of an active pharmaceutical ingredient (API) is based on the different solubilities of the API in two demixing solvents. The advantage (as well as a disadvantage) of liquid−liquid extraction is the large number of potential solvents that can (need to) be considered. Because of this versatility, significant experimental effort is required to choose the best solvent system. For that reason, liquid−liquid extraction is rarely used in the pharmaceutical industry. Moreover, partition coefficients are not only influenced by the solvent system but also depend on the process conditions, such as the concentration, temperature, and pH. However, applying a thermodynamic model to predict the partition coefficients of APIs substantially decreases the experimental effort needed to select suitable solvents and the most appropriate process conditions for liquid−liquid extraction. Several approaches exist in the literature for the prediction of partition coefficients, particularly 1-octanol/water partition coefficients. These are semiempirical approaches, such as quantitative structure property relationships (QSPRs), XlogP,1 ClogP,2 or group-contribution methods [e.g., universal functional activity coefficient (UNIFAC)3]. However, the accuracy of these methods depends on the number of data points used for parametrization. Furthermore, these methods fail to predict partition coefficients at different temperatures and API concentrations or for solvent systems other than 1octanol/water. More recently, several thermodynamic models have been applied to predict partition coefficients in other solvent systems, such as the conductor-like screening model for real solvents (COSMO-RS)4 and the nonrandom two-liquid segment activity coefficient (NRTL−SAC) model.5 However, the application of the NRTL−SAC model was not purely predictive, as experimentally determined partition coefficients were used to fit the API parameters. According to previous work by our group,6 the perturbedchain statistical associating fluid theory (PC-SAFT) is able to © 2015 American Chemical Society
successfully predict the extraction behavior of APIs based on binary data only, that is, based on API solubilities in pure solvents and on the demixing behavior of the API-free solvent system. This approach is now extended to predict API partition coefficients at different temperatures and pH values based solely on binary data. Because experimental data for API partitioning are rarely available, API partition coefficients were measured in this work to allow for validation of the predictions. The predictions and experiments were performed for nicotinamide, which is a weak base, and salicylamide, which is a weak acid. The structural formulas of these APIs are shown in Figure 1.
Figure 1. Structures of the APIs nicotinamide (left) and salicylamide (right).
The partition coefficients of these APIs were experimentally determined and predicted for different solvent 1/solvent 2 systems and at different temperatures and pH values. In all cases, one solvent was water, and the other one was an organic solvent. The organic solvents were FDA-approved solvents of class 2 or class 37 or 1-octanol. All parameters required for predicting the partition coefficients were fitted to binary data only. Specifically, API solid solubility data were used to fit the API pure-component parameters and the binary API/organic solvent and API/water parameters. The solid solubility data of Received: Revised: Accepted: Published: 3968
January 8, 2015 March 30, 2015 March 30, 2015 March 30, 2015 DOI: 10.1021/acs.iecr.5b00068 Ind. Eng. Chem. Res. 2015, 54, 3968−3975
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Industrial & Engineering Chemistry Research
As most APIs are capable of accepting (bases) or releasing (acids) H+ ions in the aqueous phase, the partition coefficient of a partially ionized API, KpH, is different from that of the nonionized one, K0. KpH is defined as the ratio of the total amount of API (ionized and nonionized) in the organic phase to the total amount of API in the aqueous phase (ionized and nonionized)
the APIs are easy to measure and are always available because they are necessary for the licensing and registration of APIs. Binary liquid−liquid equilibrium (LLE) data were used to fit the binary organic solvent/water interaction parameters. These data can easily be found in the literature. The pure-component parameters of water and all organic solvents considered in this work are also available in the literature. After estimation of the parameters, the partition coefficients (LLE in the ternary system) in the API/organic solvent/water systems were fully predicted and validated by comparison with experimental data.
K pH =
1 γAPI −
Ka =
i = 1, ..., n
org wAPI aq wAPI
3
aq cAPI
(6)
can be used to substitute the weight fraction in eq 5. Because the molar mass of the nonionized API, MAPI, and the molar mass of the ionized API, MAPI,ionized, are about the same, eq 6 can be transformed into the expression
(1)
Ka =
aq c HaqO+wAPI,ionized 3
aq wAPI
caq H3O+
(7) −pH
−pKa
Using = 10 and Ka = 10 , for an acidic API, eq 5 can be transformed into the expression wAPI,total = wAPI(1 + 10 pH − pKa)
(8)
worg API,total
Inserting eqs 8 and 3 into eq 4 and using = worg API yields the following equation for the calculation of the pHdependent partition coefficient KpH of an acidic API K pH =
K0 1 + 10 pH − pKa
(9)
Analogously, eqs 10 and 11 can be derived for an alkaline API wAPI,total = wAPI(1 + 10 pKa − pH)
(2)
where xIi and xIIi are the mole fractions of component i in liquid phases I and II, respectively. γIi and γIIi are the corresponding activity coefficients of component i, which were again calculated using PC-SAFT. The input parameters for the calculation of the activity coefficients were the PC-SAFT parameters of all components considered. The partition coefficient K0 of an API is defined as the weight-fraction ratio of the nonionized API in the two phases of an LLE according to the equation
K0 =
aq c HaqO+cAPI,ionized
waq API,ionized
where T is the temperature of the system and R is the ideal gas constant. γAPI is the activity coefficient of the API, as calculated SL using PC-SAFT. TSL 0API and Δh0API are the melting temperature and the melting enthalpy of the API, respectively, and ΔcSL p,0API is the difference in the heat capacities of the solid and liquid API at its melting point. These calorimetric pure-component properties were taken from the literature or, if not available, determined using differential scanning calorimetry (DSC) measurements. The solid solubility of an API in terms of mole fraction, xLAPI, obtained from eq 1 can also be transformed into solubility in terms of mass fraction, wLAPI. 2.2. LLE Calculations. LLE calculations were performed to fit the binary organic solvent/water interaction parameters (binary LLE) and to predict the partition coefficients of the APIs (ternary LLE). The basic relationship used to calculate an LLE with n components is given by xiIγi I = xiIIγi II
(5)
The acid constant Ka of an acidic API
SL ⎡ Δc p,0API
R
(4)
aq aq aq wAPI,total = wAPI + wAPI,ionized
⎧ SL ⎛ ⎪ Δh0API T ⎞ ⎜1 − SL ⎟ − exp⎨ ⎪ RT ⎝ T0API ⎠ ⎩ ⎤⎫ ⎛ T SL ⎞ T SL ⎪ ⎢ln⎜ 0API ⎟ − 0API + 1⎥⎬ ⎢⎣ ⎝ T ⎠ T ⎦⎥⎪ ⎭
aq wAPI,total
Assuming that the API does not ionize in the organic phase, the total amount of API in the organic phase, worg API,total, is equal to the amount of nonionized API in the organic phase, worg API. The total amount of API in the aqueous phase is defined as the sum of the weight fractions of the ionized API, waq API,ionized, and the nonionized API, waq API, according to the equation
2. THEORY 2.1. Solid Solubility Calculations. In this work, solid solubility data were used to fit the pure-component parameters of the APIs as well as the binary API/organic solvent and API/ water interaction parameters. The solid solubility in terms of mole fraction, xLAPI, of an API component is expressed as L = xAPI
org wAPI,total
K pH =
(10)
K0 1 + 10 pKa − pH
(11)
Equations 9 and 11 depend only on the partition coefficient of the nonionized API, KpH, the pH, and the pKa value of the API. Equation 9 can be transformed into eq 3 for high pH, whereas eq 11 can be transformed into eq 3 for low pH. The partition coefficient of the nonionized API, K0, can be obtained from a thermodynamic model, such as PC-SAFT. The pKa value of an API is always available because it is required for the licensing of the API. 2.3. PC-SAFT. PC-SAFT8,9 is based on a thermodynamic perturbation theory, which uses a hard chain as a reference system. All other contributions are considered as independent perturbations of the reference system. In this work, the residual Helmholtz energy (ares) is calculated as the sum of the
(3)
which indicates whether the API is hydrophilic and prefers to concentrate in the aqueous phase (K0 < 1) or hydrophobic and prefers to be in the organic phase (K0 > 1). 3969
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Industrial & Engineering Chemistry Research Table 1. Chemical Compounds Used in This Work, Including Suppliers, Purities, and Calorimetric Properties TSL 0API (K)
component
ΔhSL 0API (kJ/mol)
ΔcSL p,0API [J/(mol K)]
pKa
purity
supplier
3.3515 8.3618
≥99.5 ≥99.0
Sigma-Aldrich Merck KGaA
≥99.9 ≥99.9 ≥99.9
Sigma-Aldrich Merck KGaA Merck KGaA
APIs 401.1514 413.1516
nicotinamide salicylamide
28.0214 29.0016
78.12 192.317 Organic Solvents
1-octanol butyl acetate n-heptane
3.2. Measurement of API Partition Coefficients. The partition coefficients of the nonionized APIs, K0, in the organic solvent/water systems were measured at temperatures between 293.15 and 328.15 K. To determine K0, a 20 mL vial with a heating jacked was filled with a mixture of the API, organic solvent, and water. The temperature of the mixture was controlled with a Pt100 temperature sensor with an accuracy of ±0.1 K. The mixture was stirred for 2 h. To achieve sharp phase separation, the mixture was equilibrated afterward for another 12 h. Three samples from each the organic phase and the aqueous phase were collected using a tempered syringe. Each sample was analyzed by UV spectroscopy to determine the weight fraction of the API in that sample. For that purpose, calibration curves were determined beforehand based on a series of solutions with known amounts of API in the organic solvent (to determine the weight fraction of API in the organic phase) and in Sørensen’s phosphate buffer (to determine the weight fraction of API in the aqueous phase). The pH of the buffer was set to 5.0 for nicotinamide and to 6.5 for salicylamide to allow the same calibration curve to be used for ionized and nonionized systems (see below). As an example, the calibration curve of salicylamide in butyl acetate at 304 nm is shown in Figure 2.
contributions resulting from repulsion (hard chain), attraction (dispersion), and association a res = a hard‐chain + adispersion + aassociation
(12)
Every component is described using physically meaningful pure-component parameters. These are the number of segments (miseg ), the segment diameter (σ i), and the dispersion-energy parameter (ui/k). For associating compounds, such as water and almost all APIs, two additional pure-component parameters are required, namely, the association-energy parameter (εAiBi) and the association-volume parameter (κAiBi). To calculate the thermodynamic properties of mixtures of two substances i and j, Berthelot−Lorentz combining rules10 are applied for the segment diameter (eq 13) and the dispersion-energy parameter (eq 14). A binary interaction parameter kij is introduced in eq 14 to correct for the dispersion energy in the mixture. σij =
1 (σi + σj) 2
(13)
uij = (1 − kij) uiuj
(14)
To account for association between two different species, mixing rules as suggested by Wolbach and Sandler11 are used to calculate the mixture association energy (eq 15) and association volume (eq 16) ε A iBj =
1 A iBi (ε + ε A jBj) 2
A iBj
A iBi A jBj ⎢
κ
⎡
=
κ
κ
(15)
⎤3 ⎥ ⎢⎣ (1/2)(σi + σj) ⎥⎦ σσ i j
(16)
Induced association in a mixture of a polar but non-selfassociating component and a self-associating component is taken into account by applying the approach proposed by Kleiner and Sadowski.12 In this approach, the εAiBi value of the non-self-associating component is set to zero, whereas the κAiBi value of the non-self-associating component is assumed to be the same as that of the self-associating component. Additionally, for associating compounds, the numbers of association sites, Ndonors and Nacceptors, have to be defined. Association schemes from Huang and Radosz13 were used to define the possible site−site interactions of different compounds.
Figure 2. Absorbance of salicylamide at 304 nm versus the weight fraction of salicylamide in butyl acetate. The symbols are experimental data points, and the line is the best-fit straight line.
The samples taken from the organic and aqueous phases of the ternary API/organic solvent/water mixture were diluted to achieve API weight fractions within the calibration range. The organic phase was diluted with organic solvent, whereas the aqueous phase was diluted with Sørensen’s phosphate buffer. The maximum relative standard deviation of the API weight fraction was 4.05% in the organic phase and 12.58% in the aqueous phase. After the weight fractions of the API in both phases had been determined, the partition coefficient K0 was calculated according to eq 3.
3. EXPERIMENTAL METHODS 3.1. Materials. All chemicals used in this work, along with their calorimetric properties, purities, and suppliers, are listed in Table 1. Ultrapure water was received from the laboratory water system (Milli Q-Synthesis A10 from Merck Millipore). 3970
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Industrial & Engineering Chemistry Research Table 2. Pure-Component Parameters of the APIs, Water, and Organic Solvents Considered in This Work component
M (g/mol)
mi
σi (Å)
nicotinamide salicylamide
122.12 137.14
4.6485 7.4775
1.7143 4.0650
1-octanol butyl acetate ethyl acetate n-heptane toluene water 2B water 4C
130.23 116.16 88.11 100.20 92.14 18.02 18.02
4.3555 3.9608 3.5375 3.4831 2.8149 1.2047 2.5472
3.7145 3.5427 3.3079 3.8049 3.7169 b 2.1054
ui (K) APIs 166.25 419.14 Solvents 262.74 242.52 230.80 238.40 285.69 353.94 138.63
εAiBi (K)
κAiBi
Ndonors/Nacceptors
ref
1056.2 1194.9
0.00200 0.02000
1/1 3/3
this work this work
2754.8 0 0 0 0 2425.7 1718.2
0.00220 a a 0 0 0.04509 0.29122
1/1 1/1 1/1 − − 1/1 2/2
9 8 8 8 8 21 22
a For mixtures with associating components, the κAiBi value of the respective associating component was used. bσi = 2.7927 + 10.11 exp(−0.01775T) − 0.417 exp(−0.01146T).21
cell. A continuous flow of nitrogen (50 mL/min) was maintained through the sample and reference holders of the calorimeter. To determine cSp,0API, the sample and reference were equilibrated at 303.15 K. Afterward, they were heated at a constant heating rate of 2 K/min to 323.15 K. To determine cLp,0API, the sample and reference were equilibrated at 413.15 K and then heated to 428.15 K at a constant heating rate of 2 K/ min. The heat capacities cSp,0API and cLp,0API were determined at different temperatures using TA Universal Analysis software as the average of three measurements at each temperature. Linear correlations of the measured heat capacities, cSp,0API and cLp,0API, with temperature were used to extrapolate the heat capacitates to the melting point as described by Neau et al.19 Afterward, ΔcSL p,0API was calculated according to the equation
To measure the partition coefficients of the partially ionized APIs, KpH, a known amount of nicotinamide or salicylamide was dissolved in a known amount of water. In the case of nicotinamide, the pH of this solution was changed by adding acetic acid. In the case of salicylamide, the pH of the solution was changed by adding sodium hydroxide or ammonium hydroxide. In the latter case, two different bases were used to determine whether the type of base also influences the value of KpH. It was found that the experimental results depended not on the type of base but only on the pH. The resulting solution was mixed with the organic solvent in a 20 mL vial for 2 h and then equilibrated for 12 h. The temperature was again controlled with a Pt100 temperature sensor. Additionally, the pH of the aqueous phase at equilibrium was measured in all experiments. As before, three samples were collected from each the aqueous phase and the organic phase using a tempered syringe. The samples from the aqueous phase were again diluted with Sørensen’s phosphate buffer. The pH was set to pH 5.0 for nicotinamide and pH 6.5 for salicylamide to ensure that the API was completely nonionized and, thus, that the measured API weight fraction corresponds to the sum of both the ionized and nonionized forms (total weight fraction). The samples from the organic phase were diluted with pure organic solvent. The (total) API weight fractions in both phases were determined by UV spectroscopy. The maximum relative standard deviations of the API weight fraction were 9.29% in the organic phase and 5.17% in the aqueous phase. Afterward, the partition coefficient KpH was calculated according to eq 4. 3.3. Measurement of the Calorimetric Properties of the Pure Components. The melting temperature (TSL 0API); the melting enthalpy (ΔhSL 0API); the difference in heat capacities of the solid and liquid API (cSp,0API and cLp,0API); and, therefore, the difference in heat capacities at the API melting point (ΔcSL p,0API) can be measured using differential scanning calorimetry (DSC). As observed from eq 1, these calorimetric properties of the pure components are required for the calculation of the solid solubility of an API. In this work, these properties were taken from the literature (see Table 1), except for the ΔcSL p,0API value of nicotinamide. The ΔcSL p,0API value of nicotinamide was determined by performing DSC measurements on a Q2000 differential scanning calorimeter from TA Instruments. For this purpose, 6−15 mg of nicotinamide was placed in a hermetically sealed aluminum pan. This sample pan and an empty reference pan were placed in the sample and reference holders of the DSC
SL L S Δc p,0API = c p,0API − c p,0API
The standard deviation for
ΔcSL p,0i
(17)
was 4.72 J/(mol K).
4. RESULTS AND DISCUSSION 4.1. PC-SAFT Parameters. To predict the partition coefficients of APIs in organic solvent/water systems, the pure-component parameters of the APIs, water, and all organic solvents considered as well as the corresponding binary API/ water, API/organic solvent, and organic solvent/water interaction parameters must be known. Because the pure-component parameters of water and all of the organic solvents considered in this work were available in the literature, only the pure-component parameters of the APIs and the binary interaction parameters had to be determined. The pure-component parameters of the APIs were fitted to the solid solubility data for each API in different pure organic solvents or water as described earlier by Ruether and Sadowski.20 Simultaneously, the temperature-dependent API/ organic solvent and API/water interaction parameters [kij(T)] were also fitted to the binary solid solubility data according to the equation kij(T ) = kij ,slopeT + kij ,int
(18)
The organic solvent/water binary parameters were fitted to binary LLE data. All pure-component parameters of the APIs and the purecomponent parameters of water and all organic solvents considered in this work are summarized in Table 2. The corresponding binary interaction parameters can be found in Table 3. 3971
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Industrial & Engineering Chemistry Research Table 3. Binary Interaction Parameters for the Binary Subsystems Considered in This Work binary parameters
a
kij,slope
kij,int
nicotinamide/1-octanol nicotinamide/ethyl acetate nicotinamide/toluene salicylamide/1-octanol salicylamide/butyl acetate salicylamide/n-heptane
5.81 × 10−4 1.45 × 10−3 9.63 × 10−4 −8.09 × 10−9 1.06 × 10−4 −4.46 × 10−6
0.11048 −0.13075 0.31207 0.02390 −0.05190 0.00142
salicylamide/water 2B salicylamide/water 4C nicotinamide/water 2B nicotinamide/water 4C
1.56 × 10−4 −1.01 × 10−4 −1.57 × 10−4 −1.70 × 10−3
−0.03416 0.17826 0.06364 0.37980
1-octanol/water 2B butyl acetate/water 2B ethyl acetate/water 2B n-heptane/water 4C toluene/water 4C
5.50 × 10−4 4.50 x10−4 0 0 0
−0.14976 −0.161 −0.04700a 0.17400 0.06000a
temperature range of experimental data (K) API/Organic Solvent 298−328 283−302 291−321 288−303 288−303 288−303 API/Water 283−323 283−323 298−328 298−328 Organic Solvent/Water 288−333 273−332 280−340 273.15−423.6 270−330
reference for the binary data used in the fitting 23 23 23 23 23 23 16 16 23 23 24 25 26 27 28
Binary interaction parameters taken from ref 6.
Two different parameter sets for water were used in this work. For systems containing nonpolar organic solvents, such as n-heptane and toluene, the 4C association scheme of water was used. In all other systems, the 2B association scheme was used for water. As shown in our previous work,6 use of these association schemes provides the best modeling results for the respective binary organic solvent/water systems. 4.2. Partition Coefficients of Nonionized APIs (K0). The K0 value of nicotinamide was investigated in toluene/water and ethyl acetate/water at 298.15 K and in 1-octanol/water at 298.15 and 328.15 K. The K0 value of salicylamide was investigated in n-heptane/water at 293.15 K and in 1-octanol/ water and butyl acetate/water at 293.15 and 323.15 K. In all of the following figures, the partition coefficient of the API, K0, is plotted versus the total weight fraction of the API in the aqueous phase. All modeling results included in the same figures are predictions from PC-SAFT performed without any further parameter fitting. Figure 3 shows the partition coefficients K0 of nicotinamide in toluene/water, ethyl acetate/water, and 1-octanol/water at 298.15 K. The K0 value of nicotinamide in 1-octanol/water is the highest for both the predicted results and the experimental data, followed by the K0 value in the ethyl acetate/water system. The K0 value is lowest in the toluene/water system. For all three organic solvents, the predicted K0 values follow the same trend as the experimental data. Nicotinamide is hydrophilic and prefers to concentrate in the aqueous phase; therefore, for all three organic solvents, namely, 1-octanol, ethyl acetate, and toluene, the K0 value at 298.15 K is less than 1. The partition coefficients K0 of salicylamide in n-heptane/ water, butyl acetate/water, and 1-octanol/water are shown in Figure 4. As can be observed from Figure 4, the K0 value of salicylamide in the n-heptane/water system is again less than 1. Therefore, in the salicylamide/n-heptane/water system, salicylamide prefers to concentrate in the aqueous phase. However, the K0 values of salicylamide in the butyl acetate/water and 1octanol/water systems are greater than 1, indicating that salicylamide prefers to concentrate in the organic phases in these cases. This behavior is correctly predicted by PC-SAFT.
Figure 3. Partition coefficients K0 of nicotinamide in toluene/water (dashed black line and white square, experimental data from ref 29), ethyl acetate/water (solid black line and circles, experimental data from ref 29), and 1-octanol/water (gray line and triangles) at 298.15 K. The symbols are experimental data points, and the lines were predicted using PC-SAFT.
Figure 4. Partition coefficients K0 of salicylamide in n-heptane/water (gray line and triangles), 1-octanol/water (solid black line and circles), and butyl acetate/water (dashed black line and white squares) at 293.15 K. The symbols are experimental data points, and the lines were predicted using PC-SAFT.
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Industrial & Engineering Chemistry Research For both nicotinamide and salicylamide, the predicted orders of the partition coefficients K 0 are the same as the experimentally determined results. It can therefore be concluded that the partition coefficients can be correctly predicted using PC-SAFT, which confirms our previous results for the pharmaceutical intermediate cis-2-(2,4-dichlorophenyl)2-(1H-1,2,4-triazol-1-ylmethyl)-1,3-dioxolane-4-methanol and its impurity cis-2-(2,4-dichlorophenyl)-2-(4H-1,2,4-triazol-4ylmethyl)-1,3-dioxolane-4-methanol.6 To investigate the effect of the temperature on K0, the partition coefficient of nicotinamide in the 1-octanol/water system was also predicted and measured at 328.15 K. The predicted results and the experimental data at 298.15 and 328.15 K are shown in Figure 5.
Figure 7. Partition coefficients K0 of salicylamide in butyl acetate/ water at 293.15 K (black line and circles) and 323.15 K (gray line and squares). The symbols are experimental data points, and the lines were predicted using PC-SAFT.
were measured and predicted at 293.15 and 323.15 K. As shown in Figures 6 and 7, the K0 values of salicylamide in 1octanol/water and butyl acetate/water depend strongly on temperature. A comparison of the experimental data points and the predicted results shows good agreement for both systems and at both temperatures. In contrast to the K0 value of nicotinamide in 1-octanol/ water, the 1-octanol/water and butyl acetate/water partition coefficients of salicylamide decrease with increasing temperature. This behavior can be correctly predicted using PC-SAFT. 4.3. Partition Coefficients of Partially Ionized APIs (KpH). The partition coefficients of the partially ionized APIs, KpH, were experimentally determined and modeled for the nicotinamide/1-octanol/water and salicylamide/butyl acetate/ water systems at different pH values. As shown in Figure 8, the partition coefficient of nicotinamide in the 1-ocatnol/water system changed only
Figure 5. Partition coefficients K0 of nicotinamide in 1-octanol/water at 298.15 K (black line and circles) and 328.15 K (gray line and squares). The symbols are experimental data points, and the lines were predicted using PC-SAFT.
For both temperatures, the predicted results and experimental data points are in good agreement. As shown in Figure 5, the K0 value of nicotinamide in 1-octanol/water increases with increasing temperature, although the effect of temperature is very small. At both temperatures, the partition coefficient is less than 1, and nicotinamide prefers to concentrate in the aqueous phase. The effect of temperature on K0 was also investigated for the salicylamide systems. The K0 values of salicylamide in 1octanol/water (Figure 6) and butyl acetate/water (Figure 7)
Figure 8. Partition coefficients of nonionized nicotinamid, K0, in 1octanol/water (dashed black line and circles) and partially ionized nicotinamide KpH in 1-octanol/water at pH 5.2 (solid gray line and squares) at 298.15 K. The symbols are experimental data points, and the lines were predicted using PC-SAFT. The predicted lines overlap and, therefore, are difficult to distinguish.
slightly as the pH was changed. This finding is the same for the experimental data points and the predicted results. Figure 9 shows partition coefficients K0 and KpH of salicylamide in butyl acetate/water at different pH values. A higher pH results in a higher degree of ionization of salicylamide. Therefore, the partition coefficient decreases
Figure 6. Partition coefficients K0 of salicylamide in 1-octanol/water at 293.15 K (black line and circles) and 323.15 K (gray line and squares). The symbols are experimental data points, and the lines were predicted using PC-SAFT. 3973
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their maxima for the nonionized forms of the APIs, and the solubility of the API in the aqueous phase increases with increasing ionization. Changing the pH enhances the degree of ionization of the API and, thus, decreases the partition coefficient of the partially ionized API. This result was found in the experimental data and the PC-SAFT predictions. For all considered API/solvent/water systems, the PC-SAFT predictions and experimental data were in qualitative or even quantitative agreement. In all cases, the predicted sequence of the partition coefficients in the considered organic solvent/ water systems agreed with the experimentally determined results. Moreover, the effects of temperature and pH on the partition coefficients could be correctly predicted at all investigated temperatures and pH values. All of the PC-SAFT parameters used to predict the partition coefficients were fitted to only binary data, that is, to the solid solubility of the APIs in pure solvents and to API-free LLE data for the organic solvent/water systems. The solubility data of the solid APIs in pure solvents are usually available because they need to be known for API licensing, or if they are not available, they are easy and inexpensive to measure. The LLE data of the solvent systems have been measured extensively over many years and are now available in various databases. Therefore, PC-SAFT is a powerful tool for the prediction of API partition coefficients in ternary liquid−liquid systems at varying temperatures and pH values. In general, it is applicable to any solvent system; however, because of the lack of experimental data, it has thus far been validated for only a limited number of systems. The prediction of partition coefficients can dramatically reduce the experimental effort needed in the design of liquid−liquid extractions and could lead to increasing application of this separation technique in the pharmaceutical industry.
Figure 9. Partition coefficients of nonionized salicylamide, K0, in butyl acetate/water (black line and circles) and of partially ionized salicylamide, KpH, in butyl acetate/water at pH 8.5 (dotted line and white squares), pH 8.7 (gray line and triangles), and pH 10.3 (dashed line and white stars) at 293.15 K. The symbols are experimental data points, and the lines were predicted using PC-SAFT.
with increasing pH. This result was found in both the experiments and the predictions. For both the experimental data and the predictions, K0 and KpH at pH 8.5 and 8.7 are greater than 1. At these pH values, salicylamide is hydrophobic and prefers to concentrate in the organic phase. Further increases in the pH increase the degree of ionization of salicylamide and, therefore, the water solubility. Thus, the experimentally determined and predicted partition coefficients KpH decrease to less than 1, which is correctly predicted by the PC-SAFT modeling.
5. CONCLUSIONS The partition coefficients of the APIs nicotinamide and salicylamide were experimentally determined and predicted for different organic solvent/water systems in the temperature range from 293.15 to 328.15 K and at pH values varying between 5.2 and 10.3. The partition coefficients of nonionized nicotinamide were compared for the toluene/water, 1-octanol/water, and ethyl acetate/water systems at 298.15 K. The experimentally determined and predicted partition coefficients of these systems both increased in the following order: toluene/water < ethyl acetate/water
