Article pubs.acs.org/jced
Solubility of (S)-3-(Aminomethyl)-5-Methylhexanoic Acid in Pure and Binary Solvent Mixtures Giuseppe Cogoni, Brian de Souza,* Denise M. Croker, and Patrick J. Frawley Synthesis and Solid State Pharmaceutical Centre (SSPC), Materials and Surface Science Institute (MSSI), University of Limerick, Limerick, V94 T9PX, Ireland ABSTRACT: The solubility of (S)-3-(aminomethyl)-5-methylhexanoic acid in both 2-propanol and water and methanol and water mixtures, as well as in pure solvents, is reported across the temperature range of 283.15−338.15 K, as determined gravimetrically under atmospheric conditions. The experimental data is correlated using the empirical Apelblat and (CNIBS)/Redlich− Kister equations to describe the influence of temperature and solvent composition on solubility, respectively. A maximum solubility is observed between x2/(x2 + x3) = 0.15 and x2/(x2 + x3) = 0.25 for 2-propanol and water mixtures and between x2/(x2 + x3) = 0.35 and x2/(x2 + x3) = 0.5 for methanol and water mixtures. The solubility data is then used to estimate the binary activity coefficient using the Wilson and NRTL activity coefficient models, as well as the coefficients of the Jouyban−Acree empirical solubility model, as a function of temperature and composition. The goodness of fit is determined using the mean square error as a metric in which the Jouyban−Acree model provides the best fit to the solubility data. The modified Apelblat equation is also used to calculate enthalpies of solution under standard conditions.
1. INTRODUCTION Pain is the most common symptom for which patients seek medical attention.1 The prevalence of chronic pain the United States alone is estimated to be 30.7% of the population2 or approximately 105 million people. Modern pain management relies upon the use of analgesic agents such as gabapentinoids, which are widely prescribed in neurology, psychiatry, and primary healthcare. (S)-3-(aminomethyl)-5-methylhexanoic acid, also known as Pregabalin (PRG) (see Figure 1 for chemical
States. Additionally, in Europe it is indicated for the treatment of generalized anxiety disorder.7 The molecule is often prescribed off-label for a heterogeneous range of indications such as pain related to inflammatory arthritis,8 chronic prostatitis,9 and restless leg syndrome10 among others. The solubility of bioactive compounds, such as PRG, is of critical importance to the pharmaceutical manufacturing industry, impacting on such areas as separation, liquid extraction, crystallization, and drug formulation design. Accurate solubility data is essential to process modeling and development, directly impacting on yield, throughput, and solvent usage. To date, there has been no published solubility data for PRG in pure solvents, nor in solvent mixtures. Furthermore, the thermodynamic properties of PRG in mixed solvents have not been reported until now. A variety of empirical, correlative thermodynamic and predictive thermodynamic models are commonly used for solubility estimation. In population balance modeling of cooling crystallization, it has previously been shown that the determination of crystal size properties is highly sensitive to the selection of solubility model.11 Incorrect prediction of supersaturation leads to inaccuracy in the resultant particle size distribution (PSD). Hence, a requirement exists to examine and quantify the accuracy of fit of the most prevalent models. This paper reports the equilibrium solubility measurements of PRG in both 2-propanol and water and methanol and water
Figure 1. Chemical structure of Pregablin.
structure) and registered with the Chemical Abstracts Service No. 148553-50-8, is one such analgesic agent. It is normally characterized as a white crystalline powder, which is freely soluble in water and both basic and acidic aqueous solutions. PRG, which was first approved for use in July 2004, has become a blockbuster bioactive compound. Globally, it ranks among the top 20 prescription medications in terms of sales value in recent years.3,4 It has multiple approved indications; for instance, it is used in the treatment of central and peripheral neuropathic pain and as an adjunctive treatment of partial onset epilepsy (partial seizures).5 It has been further approved for use in the treatment of fibromyalgia,6 the first drug accepted for such, and for the treatment of post therapeutic neuralgia in the United © XXXX American Chemical Society
Received: August 31, 2015 Accepted: December 25, 2015
A
DOI: 10.1021/acs.jced.5b00736 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
filtered into a preweighed dry glass vial using a 0.2 μm, PTFE membrane (15 mm diameter) syringe filter. Caps were placed on the vials immediately after solution addition in order to prevent solvent evaporation. The combined mass of vials and sample was measured without undue delay. The caps were removed, and the solvents were allowed evaporate in a vacuum oven at 323.15 K over 10 h until only the solid residue of PRG was found to remain in the vials. All the masses were weighed using an analytical balance (Mettler Toledo AX054, weighing capacity up to 520 g, sensitivity ±0.1 mg). Triplicate measurements were performed under the same conditions and the arithmetic average value was calculated. According to the repeated experiments, the estimated relative standard uncertainty (calculated as 100% standard deviation/ average value) of the solubility measurement was less than 8% for methanol and (methanol and water) mixtures. For 2-propanol and 2-propanol and water mixtures the estimated uncertainty is increased by a factor of 5 due in particular to increased relative error, as the solubility of PGB in 2-propanol is very small. Further verification measurements were taken 24 h after the initial mass measurements. All cases that showed negligible change in mass were noted thus indicating that the samples were completely dry. The mole fraction solubility was calculated as
mixtures, as well as in pure solvents from 283.15 to 338.15 K using the gravimetric approach under atmospheric conditions. PRG contains one chiral center but is synthesized from racemic mixture as the single enantiomer S. PRG is known to have four polymorphs. In this work, the pharmacologically active and commercially marketed form 1 is considered, as verified by X-ray powder diffraction with characteristic peaks (2Θ): 9.5 ± 0.2, 12.3 ± 0.2, 16.7 ± 0.2, 19.1 ± 0.2, and 19.8 ± 0.2. In order to correlate the effects of temperature and solvent composition on solubility, the modified Apelblat and (CNIBS)/ Redlich−Kister equations are utilized, respectively. In addition, the coefficients extracted from the modified Apelblat equation are used to calculate the properties of the dissolution process, such as enthalpy. Wilson and non-random two-liquid (NRTL) binary coefficient models in addition to the widely applied Jouyban−Acree solubility model are imposed and their fit to the underlying experimental data is assessed.
2. MATERIALS AND METHODS 2.1. Materials. Pregabalin (>97% NMR) was obtained directly from Sigma-Aldrich. The 2-propanol [CAS 67-63-0] and methanol [CAS 67-56-1] employed in this paper was of HPLC grade and was also supplied by Sigma-Aldrich with purity greater than 99.9%, in mass fraction. The water used was prepared in our lab and distilled, deionized, and filtered (0.2 μm filters from the Millipore Corp.) before use. The description about these chemicals is summarized in Table 1.
x1 =
methanol 2-propanol water (S)-3-(aminomethyl)-5methylhexanoic acid
source SigmaAldrich SigmaAldrich distilled SigmaAldrich
mass purity as supplied
analysis method
additional purification
≥ 0.999
HPLC
none
≥ 0.999
HPLC
none
≥ 0.970
NMR
none none
+
+
m3 M3
(1)
where the subscripts 1, 2, and 3 is referred to the ith compound used, PRG (1), 2-propanol (2), or methanol (2) and water (3), respectively. The terms mi, Mi, and xi indicate the mass, the molecular weight, and the molar fraction of the ith compound, respectively.
Table 1. Source and Mass Fraction Purity of the Materials Used in This Work chemical name
m1 M1
m1 M1 m2 M2
3. EXPERIMENTAL RESULTS AND LOCAL COMPOSITION MODELS The experimentally derived mole fraction solubility data (x1) for PRG in (2-propanol and water) and (methanol and water) mixtures at temperatures ranging from 298.15 to 338.15 K are presented in Table 2. Each experimental data point represents the average of a triplicate solubility measurement at a set temperature and solvent composition. X-ray diffraction of PRG samples was utilized in order to eliminate the possibility of polymorphic transformation. Powder diffraction data were collected on a Philips X’Pert-MPD PRO diffractometer (PW3064 sample spinner) with nickel-filtered copper Cu Kα radiation (λ = 1.5418 Å), run at 40 kV and 35 mA, 2θ = 5−50°, with a step size of 0.02° 2θ and a scan speed of 0.02° s−1. Samples were prepared by light grinding prior to placement in a sample holder and flattening with a glass slide. The possibility of a polymorph transformation occurring during grinding was eliminated by analyzing the sample before and after this step. Analysis of the spectra indicated no polymorphic transformation, with consistent peaks before and after equilibration. An empirical model was used to fit the solubility data as a function of temperature as can be seen from Figure 2. The empirical model used is described by the modified Apelblat equation15−17
All chemicals were used as received without undergoing further purification. 2.2. Solubility Determination. Equilibrium solubility measurements of Pregabalin in (2-propanol and water) and (methanol and water) mixtures at temperatures from 283.15 to 338.15 K were performed using the gravimetric method.12−14 A thermostatic stainless steel water bath (Grant GR150; 38L; stability ±0.005 K and uniformity ±0.02 K) with a serial magnetic stirrer plate placed on the base was employed for the gravimetric tests. A further verification reading of temperature was obtained using a calibrated PT-100 resistance thermometer. The predetermined binary solvent mixtures were prepared by adding the required mass fractions of the solvents to glass vials. In order to reach the solid−liquid equilibrium, excess PRG was added to each solvent mixture tube. The tubes were sealed to prevent solvent loss due to evaporation, following which the solution was stirred at 500 rpm for a minimum of 72 h using a Teflon coated magnetic stirrer. The remaining solid residue was left to settle for at least 12 h at constant temperature and without stirring until the saturated solution was observed to be visibly clear. This was further verified using a laser light of 532 nm. The clear solution was then sampled using a preheated syringe and
ln x1 = A +
B + C ln T T
(2)
A, B, and C are indicated as the three adjustable parameters of the empirical solubility model. The values of these parameters were B
DOI: 10.1021/acs.jced.5b00736 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Table 2. Experimental Solubility of PRG in Two Binary Solvent Mixtures at Different Temperaturesa (p = 0.1 MPa) 103x1 x2/(x2+x3)
283.15
298.15
0.000 0.032 0.070 0.114 0.166 0.229 0.308 0.411 0.546 1.000
3.492
3.729
1.598
2.626
1.855 2.049 1.829
3.579 3.648 3.526
0.774 0.025
1.625 0.069
0.000 0.059 0.123 0.194 0.273 0.360 0.457 0.568 0.694 1.000
3.492 2.852 2.155 1.991 1.858 1.804 1.842 1.721 1.578 0.864
3.729 3.383 3.046 2.787 2.810 3.005 2.905 2.584 1.899 1.085
308.15
315.65
2-Propanol (2) and Water (3) 3.974 4.465 4.283 3.427 4.786 5.932 5.035 6.790 5.268 7.047 4.859 6.440 5.019 2.107 3.037 0.128 0.116 Methanol (2) and Water (3) 3.974 4.465 3.804 4.449 3.717 4.466 3.680 4.726 3.829 4.919 3.987 5.091 3.994 5.085 3.715 4.789 2.795 4.054 1.713 1.986
323.15
328.15
338.15
4.860
3.423 0.092
5.311 5.615 7.179 9.050 10.426 10.469 9.368 7.148 3.959 0.068
6.408 7.445 9.969 12.581 14.331 13.634 12.599 9.396 4.908 0.000
4.860 5.250 5.391 5.732 6.193 6.558 6.546 6.026 5.065 2.662
5.311 5.714 6.049 6.651 7.209 7.702 7.571 7.107 5.800 2.906
6.408 7.110 7.818 8.947 9.099 10.494 10.416 9.658 7.807 3.229
6.200 8.636 8.932 8.128
a
Standard uncertainty of T is u(T) = 0.05 K, u(p) = 2 KPa. The relative standard uncertainties of ur(x1) of the solubility measurement is 8%, for methanol and methanol and water mixtures. For 2-propanol and 2-propanol and water mixtures, the estimated uncertainty is increased by a factor of 5. The uncertainty in solvent composition u(SC) is less than 0.3% for both binary solvent mixtures.
Figure 2. Mole fraction solubility of PRG in (a) 2-propanol and water and (b) methanol and water binary solvent mixtures correlated by the modified Apelblat equation.
found through regression and are summarized in Table 3. The empirical model shows good agreement with the underlying
experimental data in the case of all compositions tested. For each of the fixed solvent compositions, solubility is seen to increase C
DOI: 10.1021/acs.jced.5b00736 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
solubility of PRG increases with the alcohol addition, reaching a maximum, and then declining. The maximum solubility values were obtained with the use of approximately between x2/(x2 + x3) = 0.15 and x2/(x2 + x3) = 0.25 for 2-propanol and water mixtures and between x2/(x2 + x3) = 0.35 and x2/(x2 + x3) = 0.5 for methanol and water mixtures, varying slightly with the change of temperature. Table 4 summarizes the optimized results of the parameters of (CNIBS)/Redlich−Kister equation.
Table 3. Parameters of the Modified Apelblat Equation for PRG in Two Binary Solvent Mixtures x2/(x2+x3)
A
0.000 0.032 0.070 0.114 0.166 0.229 0.308 0.411 0.546 1.000
−258.19 −489.06 −157.34 7.55 −0.73 −1.89 66.46 −817.53 −30.82 7518.76
0.000 0.059 0.123 0.194 0.273 9 0.457 0.568 0.694 1.000
−275.54 −247.65 −148.96 −209.11 −98.22 −122.09 −145.92 −157.77 −321.82 −30.94
B
C
2-Propanol and Water 10715.00 38.03 21050.00 72.45 4200.50 24.10 −3616.40 −0.21 −3222.79 1.03 −3058.00 1.15 −6131.55 −9.05 36423.00 121.09 −1595.00 5.21 −341184.00 −1120.31 Methanol and Water 11502.88 40.61 9749.49 36.73 4683.37 22.37 7087.15 31.50 1831.81 15.13 2748.84 18.79 3865.33 22.31 4385.25 24.07 11954.99 48.37 −1033.29 4.87
MSE 4.38 × 10−9 1.21 × 10−10 2.35 × 10−7 1.81 × 10−9 5.80 × 10−9 1.46 × 10−6 5.00 × 10−9 7.25 × 10−8 1.21 × 10−7 4.69 × 10−9
4. ACTIVITY COEFFICIENT MODELS Activity coefficient models such as Wilson and Non-Random Two-Liquid (NRTL) model offer a more thermodynamically rigorous approach than empirical models, accounting for deviation from ideal solubility. In order to calculate the binary interaction parameters utilized by these models, it was first necessary to calculate the experimental activity coefficients, based on the solubility data. The experimental activity coefficients were calculated using a nonideal solid−liquid equilibrium equation defined as follows20
1.54 × 10−9 3.18 × 10−9 9.50 × 10−10 4.18 × 10−9 2.02 × 10−8 1.99 × 10−9 1.40 × 10−9 5.85 × 10−9 7.97 × 10−8 2.63 × 10−8
ln(x1γ1) =
2 i=0
(3)
eq 3 was further simplified by substituting (1-x2) for x3, thus giving: ln x1 = B0 + B1x 2 + B2 x 22 + B3x 23 + B4 x 24
(5)
Here the exchange of enthalpy has been assumed constant with value ΔHf = 122.32 kJ/mol and melting temperature specified as Tm = 464.32 K.21 Inserting the enthalpy and melting temperature with known experimental solubility values x1 and temperatures into eq 5, it is possible to evaluate the experimental activity coefficients by rewriting eq 5 for γ1. The ideal solubility of PRG may also be estimated (setting γ1 = 1). Having established the experimental activity coefficients, activity coefficient models could be fitted to the experimental data. In practice, selection of model can be influenced by factors such as complexity and the inherent nature of the temperature dependency. For a ternary system, the Wilson and NTRL models are expressed as per Table 5. Where R is the ideal gas constant expressed in J/mol/K, vi or vj are the molar volumes of the ith or jth component, respectively, in cm3/mol, T is the absolute temperature in Kelvin, and α is the nonrandomness parameter chosen equal to 0.3 as recommended by Renon and Prausnitz.22
with increasing temperature, thus indicating that the dissolution process of PRG is endothermic. In order to quantitatively express the relationship between the solubility and binary solvent compositions, at fixed temperatures the (CNIBS)/Redlich−Kister equation18,19 was used. It can be expressed as follows ln x1 = x 2 ln(x1)2 + x3 ln(x 2)1 + x 2x3 ∑ Si(x 2 − x3)i
ΔHf |Tm ⎛ 1 1⎞ − ⎟ ⎜ R ⎝ Tm T⎠
(4)
where B0, B1, B3, and B4 are coefficients tthat were determined using nonlinear least-squares. Figure 3 shows the correlated results of solubility data with (CNIBS)/Redlich−Kister equation. In general, it is seen that the
Figure 3. Mole fraction solubility of PRG in (a) 2-propanol and water and (b) methanol and water binary solvent mixtures, correlated by (CNIBS)/ Redlich−Kister equation. D
DOI: 10.1021/acs.jced.5b00736 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Table 4. (CNIBS)/Redlich-Kister Model Parameters for PRG in Two Binary Solvent Mixtures T/K
B0
B1
B2
B3
B4
MSE
−497.48 159.29 34.82 −8.54 −1.54 16.36 31.12
447.60 −135.42 −14.44 6.42 3.14 −7.00 −14.51
7.69 × 10−10 7.25 × 10−7 1.99 × 10−10 7.08 × 10−8 3.56 × 10−8 8.12 × 10−8 1.33 × 10−7
−18.92 −27.22 −21.09 −10.34 −7.94 −8.95 −7.06
7.36 13.16 10.50 4.80 3.64 4.42 3.31
2-Propanol and Water 283.15 298.15 308.15 315.65 323.15 328.15 338.15
−5.66 −6.63 −6.25 −5.49 −5.34 −5.31 −5.10
−20.66 14.18 10.46 3.73 5.19 7.23 9.17
283.15 298.15 308.15 315.65 323.15 328.15 338.15
−5.64 −5.56 −5.51 −5.41 −5.32 −5.23 −5.04
−5.39 −3.78 −1.98 −0.41 0.55 0.87 1.48
170.98 −71.87 −33.55 −5.17 −10.72 −20.88 −30.20 Methanol and Water 15.67 16.57 11.71 5.26 3.03 3.01 1.57
2
Table 5. Activity Coefficient Models Used in the Present Work Complete with Their Respective Number of Parameters and Temperature Dependency Information model
ln x1 = x 2 ln(x1)2 + x3 ln(x1)3 + x 2x3 ∑ i=0
n j=1
where with
Λij = i≠j
υj υi
ln γi = where
∑ j = 1 τjiGjixj n ∑k = 1 Gkixk
T ln x1 = A 0 + A1T + A 2Tx 2 + A3x 2 + A4 x 22 + A5x 23 + A 6x 24
n
+
⎛
Gijxj ⎜τij n ∑ G x ⎜ k = 1 kj k ⎝ j=1
∑
∑l = 1 τljGljxl ⎞ ⎟ n ∑k = 1 Gkjxk ⎟⎠ n
−
Gij = exp(− αijτij)
τij = (gij − gjj)/RT = Δgij /RT with
i≠j
and
i , j = 1, 2, 3
The values of model parameters shown in Table 5 were estimated by minimizing the following objective function with experimental solubility data in the ternary system N
Φobj =
∑ (ln γ1,expk − ln γ1,calk )2
(6)
k=1
γ1,kexp
(8)
where A0−A6 represent adjustable parameters and are obtained by least-square analysis. Tables 6, 7, and 8 show the optimized results of model parameters correlated by the two local composition models (i.e., Wilson model and NRTL model) and the Jouyban-Acree model together with the mean square error (MSE) of each model. The Jouyban-Acree model achieves the best correlation results with a mean square error of 1.30 × 10−5 and 2.63 × 10−8 for 2propanol and water and methanol and water, respectively. The modified Apelblat equation and (CNIBS)/Redlich− Kister equation produces a better correlation accuracy than local composition models (i.e., Wilson and NRTL) and Jouyban− Acree model, but more adjustable parameters are required. 4.1. Enthalpy of Solution. The van’t Hoff enthalpy ΔH0sol can be extracted from the modified Apelblat equation26 through the use of eq 9
i , j = 1, 2, 3
n
NRTL
Λkixk n ∑ j = 1 Λkjxj k=1
∑
⎛ λij − λii ⎞ υj ⎛ Δλij ⎞ exp⎜− ⎟ = exp⎜− ⎟ RT ⎠ υi ⎝ ⎝ RT ⎠
and
T
where Ji is the model constant and T denotes the absolute temperature in Kelvin. Substituting (1 − x2) for x3, eq 7 can be further simplified as
n
ln γi = 1 − ln(∑ Λijxj) −
Ji (x 2 − x3)i (7)
equation
Wilson
4.49 × 10−9 6.79 × 10−9 4.15 × 10−9 6.28 × 10−9 1.09 × 10−8 3.63 × 10−9 3.57 × 10−8
⎛ B⎞ 0 ΔHsol = RT ⎜C − ⎟ ⎝ T⎠
γ1,kcal
where and refer to the experimental and calculated activity coefficients of PRG, respectively, and N is the number of data points. The regression procedure was performed with the “lsqnonlin” function, a nonlinear regression method in the MATLAB software package. A further model, the Jouyban− Acree model23−25 was used in order to describe the dependence of PRG solubility on both temperature and solvent composition. It can be described as follows
(9)
where A, B, and C are, as before, the parameters of modified Apelblat equation. The temperature selected for this analysis was 298.15 K, thus in standard conditions. The calculated values of ΔH0sol are listed in Table 9 and have the physical meaning of representing the slope of the solubility curve
Table 6. Wilson Model Parameters for PRG in Two Binary Solvent Mixtures Δλ12
Δλ13
Δλ21
2.00 × 1008
−3.10 × 1003
−3.70 × 1003
−6.36 × 1003
−1.88 × 1003
6.75 × 1006
Δλ23 2-Propanol and Water 8.67 × 1003 Methanol and Water 1.52 × 1005 E
Δλ31
Δλ32
MSE
−1.09 × 1004
4.57 × 1005
5.43 × 10−4
−1.11 × 1004
6.83 × 1003
3.11 × 10−4
DOI: 10.1021/acs.jced.5b00736 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Table 7. NRTL Model Parameters for PRG in Two Binary Solvent Mixtures Δg12
Δg13
Δg21
Δg23
−5.80 × 1003
−1.20 × 1004
9.25 × 1005
−9.02 × 1003
−1.18 × 1003
6.61 × 1005
Δg31
2-Propanol and Water 1.41 × 1004 2.26 × 1004 Methanol and Water 2.00 × 1004 2.10 × 1005
Δg32
αij
MSE
−2.75 × 1004
0.3
5.52 × 10−4
−2.44 × 1004
0.3
5.51 × 10−4
Table 8. Parameters of the Jouyban-Acree Model for PRG in Two Binary Solvent Mixtures A0
A1
A2
−2.98 × 1003
4.044
−1.709
−2.08 × 1003
1.262
3.456
A3
A4
2-Propanol and Water 1.15 × 1003 1.31 × 1003 Methanol and Water −1.43 × 1003 2.44 × 1003
ΔH0sol/kJ/mol 2-Propanol and Water
0.000 0.032 0.070 0.114 0.166 0.229 0.308 0.411 0.546 1.000
■
5.17 4.58 24.81 29.54 29.35 28.27 28.54 −2.65 26.17 59.56
MSE
−8.21 × 1003
5.03 × 1003
1.30 × 10−5
−4.42 × 1003
2.05 × 1003
2.63 × 10−8
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Tel: +353 (0)61 213134. Fax: +353 (0)61 202944. URL:. http://www.ul.ie/sspc. Funding
This research has been conducted within the Synthesis and Solid state Pharmaceutical Centre (SSPC) with financial support provided by Science Foundation Ireland (SFI) through Grant 07/SRC/B1158.
Methanol and Water 0.000 0.059 0.123 0.194 0.273 0.360 0.457 0.568 0.694 1.000
A6
Wilson or NRTL models, requiring the optimized specification of only six parameters. The modified Apelblat equation was further used to calculate enthalpies of solution for PGB in both binary solvent mixtures, physically representative of the slope of the solubility curves.
Table 9. Van’t Hoff Enthalpies of Solution As Calculated for PGB in Two Binary Solvent Mixtures at 298.15 K x2/(x2 + x3)
A5
5.02 9.98 16.50 19.16 22.29 23.71 23.17 23.21 20.50 20.65
Notes
The authors declare no competing financial interest.
■
REFERENCES
(1) Melnikova, I. Pain Market. Nat. Rev. Drug Discovery 2010, 9, 589− 590. (2) Johannes, C. B.; Kim Le, T.; Zhou, X.; Johnston, J. A.; Dworkin, R. H. The Prevalence of Chronic Pain in United States Adults: Results of an Internet-Based Survey. J. Pain 2010, 11, 1230−1239. (3) Lindsley, C. W. 2013 Trends and Statistics for Prescription Medications in the United States: CNS Highest Ranked and Record Number of Prescriptions Dispensed. ACS Chem. Neurosci. 2015, 6, 356− 357. (4) Lindsley, C. W. The Top Prescription Drugs of 2012 Globally: Biologics Dominate, But Small Molecule CNS Drugs Hold on to Top Spots. ACS Chem. Neurosci. 2013, 4, 905−907. (5) Dworkin, R.; Kirkpatrick, P. Pregabalin. Nat. Rev. Drug Discovery 2005, 4, 455−456. (6) Federal Drug Administration (FDA). Living with Fibromyalgia, drugs approved to manage pain; FDA: Washington, DC, 2008. (7) Wensel, T.; Powe, K.; Cates, M. Pregabalin for the treatment of generalized anxiety disorder. Ann. Pharmacother. 2012, 46, 424−429. (8) Richards, B.; Whittle, S.; van der Heijde, D.; Buchbinder, R. Efficacy and safety of neuromodulators in inflammatory arthritis: a Cochrane systematic review. J. Rheumatol., Suppl. 2012, 90, 28−33. (9) Aboumarzouk, O.; Nelson, R. Pregabalin for chronic prostatitis.Cochrane Database Systematic Reviews; John Wiley and Sons: Chichester, U.K., 2012; Vol. 8, pp 1−16. (10) Aurora, R.; Kristo, D.; Bista, S.; Rowley, J.; Zak, R.; Casey, K.; Lamm, C.; Tracy, S.; Rosenberg, R. The treatment of restless legs syndrome and periodic limb movement disorder in adults - an update for 2012: practice parameters with an evidence-based systematic review and meta-analyses: an American Academy of Sleep Medicine clinical practice guideline. Sleep (N. Y.) 2012, 35, 1039−1062.
5. CONCLUSIONS The solubilities of PRG in both 2-propanol and water and methanol and water mixtures, as well as pure solvents, were gravimetrically determined at temperatures from 283.15 to 338.15 K. The experimental data was correlated using the empirical Apelblat and (CNIBS)/Redlich−Kister equations to describe the influence of temperature and solvent composition on solubility, respectively. The solubility of PRG in water reaches a peak value with the addition of alcohol and decreases thereafter. For the binary solvent mixtures of 2-propanol and water, maximum solubility was seen between x2/(x2 + x3) = 0.15 and x2/(x2 + x3) = 0.25. For methanol and water mixtures, the maximum was found to occur between x2/(x2 + x3) = 0.35 and x2/(x2 + x3) = 0.5, approximately. The thermodynamically correlative models of Wilson and NRTL in addition to the Jouyban−Acree models were selected to correlate solubility data. The mean square error metric was chosen to access fit. The Jouyban−Acree model achieved the best fitting results with a mean square error smaller than either the F
DOI: 10.1021/acs.jced.5b00736 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
(11) Widenski, D. J.; Abbas, A.; Romagnoli, J. A. Comparison of different solubility equations for modelling in cooling crystallization. Chem. Eng. Process. 2010, 49, 1284−1297. (12) Maher, A.; Croker, D.; Rasmuson, A. C.; Hodnett, B. K. Solubility of Form III Piracetam in a Range of Solvents. J. Chem. Eng. Data 2010, 55, 5314−5318. (13) Rodriguez, G. A.; Delgado, D. R.; Martinez, F.; Jouyban, A.; Acree, W. E., Jr. Solubility of naproxen in ethyl acetate + ethanol mixtures at several temperatures and correlation with the Jouyban-Acree model. Fluid Phase Equilib. 2012, 320, 49−55. (14) Granberg, R. A.; Rasmuson, A. C. Solubility of Paracetamol in Pure Solvents. J. Chem. Eng. Data 1999, 44, 1391−1395. (15) Apelblat, A.; Manzurola, E. Solubility of oxalic, malonic, succinic, adipic, maleic, malic, citric and tartaric acids in water from 278.15 to 338.15 K. J. Chem. Thermodyn. 1987, 19, 317−320. (16) Qingzhu, J.; Peisheng, M.; Shouzhi, Y.; Qiang, W.; Chang, W.; Guiju, L. Solubilities of benzoic acid, p-methylbenzoic acid, mmethylbenzoic acid, o-methylbenzoic acid, p-hydroxybenzoic acid, and o-nitrobenzoic acid in 1-octanol. J. Chem. Eng. Data 2008, 53, 1278− 1282. (17) Feng, Y.; Dai, H.; Gao, W.; Huang, Y.; Tang, W.; Zhang, C.; Luo, H.; Yuan, Y.; Chen, L.; Li, Y. Measurement and correlation of solubility of tetraphenyl piperazine-1,4-diyldiphosphonate in mixed solvents. J. Chem. Eng. Data 2015, 60, 561−567. (18) Ren, G.; Wang, J.; Li, G. Solubility of paroxetine hydrochloride hemi-hydrate in (water + acetone). J. Chem. Thermodyn. 2005, 37, 860− 865. (19) Buchowski, H.; Khiat, A. Solubility of solids in liquids: Oneparameter solubility equation. Fluid Phase Equilib. 1986, 25, 273−278. (20) Prausnitz, J. M.; Lichtenthaler, R. N.; Azevedo, E. G. Molecular Thermodynamics of fluid-Phase Equilibria, 3rd ed.; Prentice Hall PTR: New York, 1998. (21) Marras, G. Polymorphic Form alpha of (S)-Pregabalin and process for its preparation. Eur. Pat. Appl. 1977744A1, April 03, 2008. (22) Renon, H.; Prausnitz, J. M. Estimation of Parameters for the NRTL Equation for Excess Gibbs Energies of Strongly Non-Ideal Liquid Mixtures. Ind. Eng. Chem. Process Des. Dev. 1969, 8, 413−419. (23) Liu, B. S.; Sun, H.; Wang, J. K.; Yin, Q. X. Solubility of disodium 5′-guanylate heptahydrate in aqueous methanol mixtures. Food Chem. 2011, 128, 218−221. (24) Sun, H.; Li, M.; Jia, J.; Tang, F.; Duan, E. Measurement and Correlation of the Solubility of 2, 6-Diaminohexanoic Acid Hydrochloride in Aqueous Methanol and Aqueous Ethanol Mixtures. J. Chem. Eng. Data 2012, 57, 1463−1467. (25) Hasan, M.; Sawant, A. B.; Sawant, R. B.; Loke, P. G.Densities, viscosities, speed of sound, and IR spectroscopic studies of binary mixtures of tert-butyl acetate with benzene, methylbenzene, and ethylbenzene at T = (298.15 and 308.15) K. J. Chem. Thermodyn. 2011, 43, 1389−1394. (26) Li, T.; Jiang, Z. X.; Chen, F. X.; Ren, B. Z. Solubilities of d-xylose in water+ (acetic acid or propionic acid) mixtures at atmospheric pressure and different temperatures. Fluid Phase Equilib. 2012, 333, 13− 17.
G
DOI: 10.1021/acs.jced.5b00736 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
