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Solubility of Clonazepam and Diazepam in Polyethylene Glycol 200, Propylene Glycol, N‑Methyl Pyrrolidone, Ethanol, and Water at (298.2 to 318.2) K and in Binary and Ternary Mixtures of Polyethylene Glycol 200, Propylene Glycol, and Water at 298.2 K Shahla Soltanpour,*,† Zahra Bastami,† Shayan Sadeghilar,† Morteza Kouhestani,† Farid Pouya,† and Abolghasem Jouyban‡,§ †

Faculty of Pharmacy, Zanjan University of Medical Sciences, Zanjan 45139, Iran Drug Applied Research Center and Faculty of Pharmacy, Tabriz University of Medical Sciences, Tabriz 51664, Iran § Pharmaceutical Engineering Laboratory, School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11155/4563, Tehran, Iran ‡

ABSTRACT: Experimental molar solubility of clonazepam and diazepam in binary and ternary mixtures of polyethylene glycol 200 (PEG 200), propylene glycol (PG), and water (116 data points) along with the density of saturated solutions at 298.2 K were reported. Also, the experimental solubilities of clonazepam and diazepam in the monosolvents of PEG 200, PG, N-methyl pyrrolidone (NMP), ethanol (EtOH), and water at five different temperatures, (298.2, 303.2, 308.2, 313.2, and 318.2) K (50 data points), have been reported. The Jouyban−Acree model was used to fit to the measurements for providing a computational method. Employing the solubilities in the neat solvents, the measured solubilities were backcalculated, and the overall mean percentage deviations (OMPDs) of the model were 21.4 % and 19.5 % for clonazepam and diazepam, respectively. An addition of the Hansen solubility parameters to the model helps us to train all of the data sets (clonazepam and diazepam) at once, and the back-calculated OMPD was 20.7 %.

■

INTRODUCTION

them by a useful technique and controlling their biodistribution. There are several methods to increase the aqueous solubility of drugs such as cosolvency, complexation, using the surfaceactive agents, using prodrugs, and salt formation.3−5 When the aqueous solubility of a drug is below its therapeutic dose, a cosolvent or a mixture of the cosolvents is added to water to achieve sufficient solubility; also it must be noticed that these used cosolvents must be safe for use in pharmaceutical fields. The common and safe cosolvents which are used in the pharmaceutical industry are ethanol (EtOH), propylene glycol (PG), glycerine, and polyethylene glycols (PEGs).6 Cosolvents can increase the solubility of a nonpolar drug up to several orders of aqueous solubility. The cosolvency phenomenon has a wide range of applications in different fields. Sometimes it has clinical usage such as tert-butyl ether which was used for dissolving cholesterol gallstones.7 Our intent was to measure the solubilities of clonazepam and diazepam in a series of aqueous and nonaqueous solvent systems

Solubility is defined as the maximum amount of a solute dissolved in a given volume of the solution phase when equilibrium exists between the residual solid phase and the solution phase.1 In the pharmaceutical industry, it is important to choose the best solvent or solvent mixture for dissolving a drug or combination of the drugs, so having knowledge about the solubility is necessary for scientists. Measuring the purity of drug bulks, preparing a liquid formulation, and extracting the ingredients from the synthetic or natural sources all can be done by using the solutions. Investigations on the drug solubilities and related properties can give useful information about the structure such as the functional groups. Despite the importance of the aqueous solubility of the drugs in the pharmaceutical sciences, nearly 40 % of the drug candidates have a low aqueous solubility, so they cannot reach the market place and fail to pass the initial tests and show inadequate or variable bioavailability and unanticipated side effects which limit their applicability in drug formulations. A large number of low soluble pharmaceuticals, which are classified in the class II of the Biopharmaceutics Classification System (BCS),2 are widely used in clinical practices, so it is necessary to solubilize © 2013 American Chemical Society

Received: August 6, 2012 Accepted: January 3, 2013 Published: January 14, 2013 307

dx.doi.org/10.1021/je3009842 | J. Chem. Eng. Data 2013, 58, 307−314

Journal of Chemical & Engineering Data

Article

where CSat m,T is the molar solubility of the solute in the solvent mixtures at temperature T, w1, and w2 are the mass fractions of the solvents 1 and 2 in the absence of the solute, Sat respectively. CSat 1,T and C2,T are the molar solubility of the solute in the neat solvents 1 and 2, respectively, and Ji terms are the constants of the model computed by a regression analysis. The model for representing the solubility of drugs in ternary solvent mixtures based on sub-binary interaction terms is:

containing PG and PEG 200 at 298.2 K which extends the available database of drug solubilities in mixed solvents,8 fitting the data to the Jouyban−Acree model that relates the solubilities in solvent mixtures to the fractions of the solvent components and constants computed by a regression analysis.9 In previous reports, the solubility of clonazepam and diazepam in aqueous solutions of EtOH, PG, and NMP,10,11 in binary mixtures of PEG 600 with water and ethanol, and ternary mixtures of PEG 600-EtOH-water12 at 298.2 K was discussed. In this work, the solubility of clonazepam and diazepam in aqueous and nonaqueous binary mixtures of PG, PEG 200, and their aqueous ternary mixtures at 298.2 K are reported.

log CmSat, T = w1 log C1,SatT + w2 log C2,SatT + w3 log C3,SatT

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EXPERIMENTAL SECTION Chemicals. Clonazepam (purity of 99.8 w/w) and diazepam (99.8 w/w) were purchased from Sobhan Pharmaceutical Company (Tehran, Iran). PEG 200 (99.5 w/w), methanol (99.8 w/w), and PG (99.5 w/w) were purchased from Merck (Germany), and double-distilled water was used for preparation of the solutions. Apparatus and Procedure. The determined mass fractions of the solvents in binary and ternary mixtures have been prepared with the accuracy of 0.001 mass fractions. The solubilities of clonazepam and diazepam were determined using the saturation shake-flask method of Higuchi and Connors.14 Briefly, excess amounts of the drugs were added to the solvent mixtures separately. Then the solutions were equilibrated for at least 72 h on a shaker (Behdad, Tehran, Iran), which was placed in an incubator equipped with a temperature maintained constant at 298.2 (± 0.2) K. The saturated solutions were centrifuged with the speed of 13 000 rpm for 10 min and diluted with methanol. Diluted samples were then assayed at 309 nm for clonazepam and 250 nm for diazepam, using a UV−vis spectrophotometer (Beckman DU-650, Fullerton, USA). The concentration of each solution was determined with an absorbance versus concentration calibration curve (clonazepam: Absorbance = 25458*Conc + 0.007; diazepam: Absorbance = 30193*Conc + 0.101) after appropriate dilution. Each experimental data point measurement has been repeated three times, and the final data are the average of the repeated experiments which were reproducible within ± 2.7 %. A 5 mL calibrated pycnometer was used for determining the densities of the saturated solutions.

i=0

⎡w w +⎢ 2 3 ⎢⎣ T

i=0

⎤

⎡w w

⎥⎦

⎢⎣ T

1 3

2

⎤

∑ Ji′(w1 − w3)i ⎥ i=0

⎥⎦

2

(2)

2

⎤

⎡w w

⎥⎦

⎢⎣ T

∑ Ji (w1 − w2)i ⎥ + ⎢ i=0

1 3

2

⎤

∑ Ji′(w1 − w3)i ⎥ i=0

⎥⎦

⎤

2

∑ Ji″(w2 − w3)i ⎥ ⎥⎦

i=0

⎡w w w +⎢ 1 2 3 ⎢⎣ T

2

⎤

∑ Ji‴(w1 − w2 − w3)i ⎥ i=0

⎥⎦

(3)

Sat Sat The J‴ i terms are computed by {log Cm,T − w1 log C1,T − w2 Sat Sat 2 log C2,T − w3 log C3,T − [(w1w2/T)∑i=0Ji(w1 − w2)i] − [(w1w3/T)∑2i=0J′i (w1 − w3)i] − [(w2w3/T)∑2i=0J″i (w2 − w3)i]} regressing against (w1w2w3/T), (w1w2w3(w1 − w2 − w3)/T), and (w1w2w3(w1 − w2 − w3)2/T). In the Jouyban−Acree model when there is one solute in Sat binary solvent mixtures, w1 log CSat 1,T and w2 log C2,T terms represent the ideal mixing behavior of the saturated solutions composed of solvent 1 and 2 without any additional interactions, and for describing the interactions between the solute and the solvents in the mixtures, the Ji terms are used. So the model can cover the probable interactions which occur in the mixture. But for covering the physicochemical properties of the solute or solvents, we can combine this model with the parameters which are used for determining the properties of the substances. With combining the Jouyban−Acree model and the Hansen solubility parameters eq 1 could be obtained as:

⎤ ⎥⎦

⎤ ∑ Ji″(w2 − w3)i ⎥ ⎥⎦ i=0

⎡w w +⎢ 1 2 ⎢⎣ T

log CmSat, T = w1 log C1,SatT + w2 log C2,SatT 2

⎡w w +⎢ 2 3 ⎢⎣ T

2

log CmSat, T = w1 log C1,SatT + w2 log C 2,SatT + w3 log C3,SatT

COMPUTATIONAL METHOD For correlating and predicting the solubility of drugs in mixed solvents, several models have been produced. The Jouyban− Acree model is one of these models which has the most accurate results in correlating and predicting the data.9 The solubilities of clonazepam and diazepam in the mixed solvents are calculated using the Jouyban−Acree model, and its accuracies are discussed by comparing the percentage deviations between calculated and experimental solubilities. The Jouban−Acree model produces very exact mathematical descriptions for variety of the solute solubility with both temperature and solvent composition:9

∑ Ji (w1 − w2)i ⎥

∑ Ji (w1 − w2)i ⎥ + ⎢

where CSat 3,T is the molar solubility of the solute in the neat solvent 3 (water in this work) at temperature T, and w3 is the mass fraction of the solvent 3 in the absence of the solute. The J′i and J″i terms are computed using the same procedure of Ji terms. The solvents’ numbers Sat Sat are defined as CSat 1,T ⟩ C2,T ⟩ C3,T. This model is a predictive version and is able to predict the solubility of solutes in ternary solvents based on sub-binary data. To provide more accurate data, it is possible to include ternary interaction terms as:

■

⎡w w +⎢ 1 2 ⎢⎣ T

⎡w w +⎢ 1 2 ⎢⎣ T

(1) 308



Article

In the numerical analysis I, the model constants of eq 1 for clonazepam and diazepam were calculated by fitting the experimental solubility data of each drug in binary solvents to eq 1, and then the back-calculated solubilities were used to calculate the MPD values. In the second part of the numerical analysis I, for predicting the solubility of the drugs in ternary mixtures the determined model constants of eq 1 were included in eq 2. The ternary interaction terms of eq 3 were calculated using a linear regression analysis, for providing better computations. In the numerical analysis II, the combined form of the Jouyban−Acree model and the Hansen solubility parameters was used for training all of the data sets at once. In the second part of analysis II, the Jouyban−Acree model was used for training all data, and the produced OMPDs from these two parts were compared. In a previous paper,15 for PG (1)−water (2) binary mixtures, a trained version of Jouyban−Acree model has been introduced:

log CmSat, T = w1 log C1,SatT + w2 log C2,SatT ww + 1 2 [W0 + W1δds(δd1 − δd 2)2 T + W2δps(δp1 − δp2)2 + W3δhs(δh1 − δh2)2 ] w1w2(w1 − w2) [W 0′ + W1′δds(δd1 − δd 2)2 T + W 2′δps(δp1 − δp2)2 + W3′δhs(δh1 − δh2)2 ] +

w1w2(w1 − w2)2 [W 0″ + W1″δds(δd1 − δd 2)2 T + W 2″δps(δp1 − δp2)2 + W3″δhs(δh1 − δh2)2 ] +

(4)

where δds, δps, and δhs are the Hansen solubility parameters for the solute, δd1, δp1, δh1 and δd2, δp2, and δh2 are the Hansen parameters for solvent 1 and 2, respectively. For ternary solvent mixtures, eq 4 could be modified as: log

CmSat, T

C1,SatT

C2,SatT

= w1 log + w2 log + w3 log w1w2 [W0 + W1δds(δd1 − δd 2)2 + T

log CmSat, T = w1 log C1,SatT + w2 log C2,SatT ww + 1 2 [37.030 + 319.490(w1 − w2)] T

C3,SatT

In the numerical analysis III, the obtained model constants for binary mixtures of PEG 200 (1)−water (3) and PEG 200 (1)− PG (2) by fitting a minimum number of experimental solubility data (five data points with the mass fractions of PEG 200 + cosolvent: 0.00 + 1.00, 0.30 + 0.70, 0.50 + 0.50, 0.70 + 0.30, 1.00 + 0.00) to eq 1, and the model constants of eq 8 are included in eq 3. Then for calculating the ternary interaction terms, that is, Ji‴, a minimum number of experimental data (six data points with the mass fractions of PEG 200 + PG + water: 0.80 + 0.10 + 0.10, 0.10 + 0.80 + 0.10, 0.10 + 0.10 + 0.80, 0.30 + 0.50 + 0.20, 0.20 + 0.50 + 0.30, 0.20 + 0.30 + 0.50) in ternary solvents, were fitted to eq 3. After producing the trained versions of the Jouyban−Acree model for binary and ternary mixtures of PEG 200, PG, and water for clonazepam and diazepam, these are used for predicting the solubility of clonazepam and diazepam in binary and ternary mixtures, and the applicability of the Jouyban−Acree model was discussed. In numerical analysis IV, the solubility data points of clonazepam and diazepam in five monosolvents at five different temperatures, are used for calculating the A and B values of eq 6 for each solvent. Then by using the determined A and B values, clonazepam and diazepam solubility in monosolvents at different temperatures were predicted by a back-calculation method. For converting the molar solubilities into the mole fraction solubilities, the density of the saturated solutions is required. With introducing a way to predict the density of the saturated solutions, one can save time and cost of the experimental efforts. The applicability of the Jouyban−Acree model for prediction of the density of liquid mixtures at various temperatures was shown in our previous papers.16,17 In the numerical analysis V, for showing the model’s applicability in predicting the density of the saturated solutions, first the densities of the solute free binary and ternary solutions were fitted to the Jouyban−Acree model. Then the model constants (sub-binary and ternary) were computed and with these produced trained versions of the Jouyban−Acree model and the densities of the saturated monosolvents. The densities of the saturated solutions were predicted in which the produced prediction errors were within an acceptable range.18 Then one can use the experimental and calculated densities for converting the molar solubilities to mole fraction data.

+ W2δps(δp1 − δp2)2 + W3δhs(δh1 − δh2)2 ] w1w2(w1 − w2) [W 0′ + W1′δds(δd1 − δd 2)2 T + W 2′δps(δp1 − δp2)2 + W3′δhs(δh1 − δh2)2 ] +

w1w2(w1 − w2)2 [W 0″ + W1″δds(δd1 − δd 2)2 T + W 2″δps(δp1 − δp2)2 + W3″δhs(δh1 − δh2)2 ] +

w1w2w3(w1 − w2 − w3)2 T × [W 0‴ + W1‴δds(δd1 − δd 2 − δd3)2

+

+ W 2‴δps(δp1 − δp2 − δp3)2 + W3‴δhs(δh1 − δh2 − δh3)2 ]

(5)

where δd3, δp3, and δh3 are the Hansen solubility parameters for the solvent 3. For correlation of experimental solubility data of clonazepam and diazepam in neat solvents at different temperatures, the van’t Hoff equation is used. The van’t Hoff equation can be written as:13 log CTSat = A +

B T

(6)

where A and B are the model constants computed using a leastsquares method. Equation 6 was used for predicting clonazepam and diezepam solubility in monosolvents at different temperatures by back-calculation method. The mean percentage deviation (MPD) was used to check the accuracy of the fitted and predicted values and was calculated using: MPD =

100 N

Sat ⎤ ⎡ |(C Sat) pred − (C )| ⎢ ⎥ ∑ ⎢⎣ ⎥⎦ (C Sat)

(8)

(7)

where N is the number of data points in each set. 309



Article

Table 1. Experimental Molar and Mole Fraction Solubilities (CSat m,T) of Clonazepam and Diazepam in Binary and Ternary Mixtures of PEG 200, PG and Water (Mass Fractions, w) at 298.2 K and Atmospheric Pressurea along with the Density of the Saturated and Solute Free Solutions (ρSat m,T) PEG 200

PG

water

density of the solute-free solutions

w1

w2

w3

g·cm‑3

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.6 0.5 0.4 0.3 0.2 0.1 0.5 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 0.3 0.2 0.1

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.1 0.2 0.3 0.4 0.5 0.6 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.1 0.2 0.3

0.9999 1.0155 1.0332 1.0647 1.0863 1.0981 1.1119 1.0273 1.0548 1.0627 1.0686 1.0883 1.0962 1.1021

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.5 0.5 0.5 0.5 0.6 0.6 0.6

1.1119 1.1100 1.0942 1.0765 1.0588

1.0844 1.0765 1.0627

1.0883 1.0726 1.0548 1.0724 1.0706 1.0686 1.0647 1.0548

1.0470

diazepam CSat m,T mol·L−1 0.00007 0.00011 0.00030 0.00044 0.00082 0.00202 0.00412 0.01355 0.07144 0.08138 0.08786 0.02696 0.03386 0.04380 0.05042 0.05705 0.06229 0.06828 0.07325 0.07766 0.08014 0.08786 0.04703 0.05299 0.02583 0.02185 0.03974 0.03245 0.02782 0.01788 0.01081 0.00861 0.02119 0.02384 0.01921 0.01656 0.01457 0.00828 0.00761 0.00695 0.00623 0.00546 0.00496 0.00430 0.00370 0.00344 0.00324 0.00298 0.00145 0.00173 0.00124 0.00165 0.00069 0.00096 0.00062

density of the saturated solutions

mole fraction

g·cm‑3

0.000001 0.000012 0.000032 0.000046 0.000084 0.000205 0.000413 0.001346 0.007123 0.008070 0.015696 0.002009 0.004503 0.005768 0.006597 0.007431 0.008044 0.008667 0.009304 0.009780 0.010096 0.015696 0.004117 0.004729 0.002314 0.001974 0.003636 0.002987 0.002583 0.001666 0.000955 0.000769 0.001916 0.002174 0.001760 0.001528 0.001351 0.000739 0.000684 0.000630 0.000568 0.000503 0.000460 0.000387 0.000336 0.000314 0.000299 0.000277 0.000132 0.000159 0.000115 0.000154 0.000064 0.000090 0.000058

1.0030 1.0100 1.0300 1.0350 1.0600 1.0740 1.0870 1.1000 1.1080 1.1160 1.1300 1.0300 1.0440 1.0560 1.0640 1.0700 1.0800 1.0997 1.0998 1.1100 1.1100 1.1200 1.1300 1.1100 1.1000 1.0900 1.0800 1.0720 1.0620 1.0560 1.1120 1.1000 1.0890 1.0800 1.0740 1.0660 1.0600 1.1000 1.0930 1.0830 1.0760 1.0660 1.0580 1.0900 1.0800 1.0740 1.0640 1.0570 1.0770 1.0660 1.0570 1.0490 1.0620 1.0510 1.0450 310

clonazepam


CSat m,T mol·L−1 0.00001 0.00006 0.00009 0.00010 0.00021 0.00057 0.00135 0.00387 0.01506 0.03135 0.05575 0.00857 0.00981 0.01047 0.01499 0.01630 0.01701 0.02526 0.03102 0.03508 0.04496 0.05575 0.01976 0.01622 0.01426 0.01112 0.00962 0.00922 0.00733 0.00458 0.01151 0.00752 0.00582 0.00523 0.00406 0.00376 0.00353 0.00343 0.00251 0.00259 0.00226 0.00198 0.00178 0.00136 0.00120 0.00110 0.00083 0.00072 0.00883 0.00337 0.00102 0.00069 0.00023 0.00019 0.00014

mole fraction 0.000000 0.000013 0.000014 0.000019 0.000022 0.000058 0.000138 0.000386 0.001497 0.003091 0.010049 0.000641 0.001299 0.001379 0.001965 0.002127 0.002211 0.003263 0.003989 0.004497 0.005736 0.010049 0.001738 0.001450 0.001278 0.001004 0.000876 0.000846 0.000679 0.000428 0.001021 0.000672 0.000524 0.000476 0.000372 0.000348 0.000329 0.000306 0.000226 0.000235 0.000207 0.000182 0.000165 0.000123 0.000109 0.000101 0.000077 0.000067 0.000807 0.000310 0.000095 0.000065 0.000021 0.000018 0.000013

g·cm‑3 b

1.0160 1.0230 1.0280 1.0380 1.0470 1.0640 1.0700 1.0950 1.1000 1.1120 1.1160 1.0289 1.0370 1.0553 1.0614 1.0630 1.0690 1.0890 1.0970 1.1056 1.0830 1.1135 1.1190 1.1000 1.0970 1.0880 1.0790 1.0700 1.0600 1.0500 1.1080 1.0990 1.0900 1.0790 1.0700 1.0600 1.0520 1.0990 1.0900 1.0800 1.0720 1.0640 1.0550 1.0860 1.0790 1.0720 1.0600 1.0520 1.0750 1.0660 1.0550 1.0430 1.0590 1.0500 1.0430



Article

Table 1. continued

a

diazepam

clonazepam

PEG 200

PG

water

density of the solute-free solutions

w1

w2

w3

g·cm‑3

mol·L−1

mole fraction

g·cm‑3

mol·L−1

mole fraction

g·cm‑3

0.2 0.1 0.1

0.1 0.2 0.1

0.7 0.7 0.8

1.0352 1.0194

0.00046 0.00038 0.00015

0.000043 0.000036 0.000014

1.0470 1.0370 1.0260

0.00012 0.00010 0.00003

0.000011 0.000009 0.000003

1.0420 1.0340 1.0250

CSat m,T



CSat m,T

b Sat Sat Standard uncertainties u are u(T) = 0.2 K, u(w) = 0.001, u(CSat m,T) = 0.027·Cm,T, u(ρm,T) = 0.01, u(p) = 10 kPa. For accurate values see Table 3.

Table 2. Constants of the Jouyban−Acree Model (eqs 1 and 3) and the Mean Percentage Deviations (MPDs) of the BackCalculation for Solubility of Clonazepam and Diazepam in Binary and Ternary Solvent Mixtures of PEG 200, PG, and Water drug

a

solvent system

N

J0

J1

J2

MPD

1151.291 b 782.295 overall MPD b overall MPD 913.295 b b overall MPD b overall MPD

15.4 1.0 6.6 7.7 31.4 19.5 6.9 4.6 10.8 7.4 35.4 21.4

diazepam diazepam diazepama

PEG 200−water PG−PEG 200 PG−water

11 11 11

−162.105 133.791 −615.248

654.304 −82.081 −423.762

diazepam

PEG 200−PG−water

36

1061.623

b

clonazepam clonazepam clonazepama

PEG 200−water PG−PEG 200 PG−water

11 11 11

−778.055 −59.675 141.684

531.855 b 876.534

clonazepam


36

2166.057

6987.294

Data are taken from a previous paper.11 bNot significant.

■

RESULTS AND DISCUSSION Table 1 lists the experimental solubility of clonazepam and diazepam in the binary and ternary solvent mixtures along with the measured density of the saturated solution and solute-free solvent mixtures at 25 °C. The minimum solubilities of clonazepam (0.00010 M) and diazepam (0.00007 M) are observed for aqueous solutions, and the maximum solubilities of clonazepam (0.055752 M) and diazepam (0.087868 M) for the solvent mixtures studied are observed in PEG 200. Table 2 shows the model constants and MPD values which were produced by fitting the solubility data of clonazepam and diazepam to eqs 1 and 3 in numerical analysis I. Including the Sat experimental solubility in monosolvents, that is, CSat 1,T, C2,T, and , and these produced constants, one can predict the solubility CSat 3,T of clonazepam and diazepam in all composition ranges of the solvents at various temperatures. In the binary mixtures of clonazepam the lowest and highest MPD values belong to PG− PEG 200 and PG−water mixtures with 4.6 % and 10.8 %, respectively. The overall MPD (OMPD) values are 7.4 % and 35.4 %, respectively, for binary and ternary mixtures. For diazepam the lowest and highest MPD values are observed for PG−PEG 200 and PEG 200−water mixtures with 1.0 % and 15.4 %, respectively. The overall MPD (OMPD) values are 7.7 % and 31.4 %, respectively, for binary and ternary mixtures. All of the MPD values along with the set detail are listed in Table 2. In numerical analysis II, eqs 4 and 5, which are the combined form of Jouyban−Acree model with Hansen solubility parameters, were used for fitting the experimental solubilities. The back-calculated OMPD for all data of clonazepam and diazepam was 20.7 %. In the second part of this analysis, eq 3 was used for training all of the data sets, and the back-calculated OMPD was 34.3 %. In numerical analysis III, with employing a minimum number of experimental data the constants of the model were calculated.

For calculating the ternary interaction terms, model constants of eq 8 and the calculated constants for PEG 200−PG and PEG 200−water binary mixtures were included in eq 3. The obtained equation for clonazepam and in PEG 200 (1)−PG (2)−water (3) mixtures is: log CmSat, T = w1 log C1,SatT + w2 log C2,SatT + w3 log C3,SatT ww − 1 2 [129.954 + 16.630(w1 − w2) T ww − 759.252(w1 − w2)2 ] − 1 3 T × [741.344 − 907.632(w1 − w3) ww + 637.030(w1 − w3)2 ] + 2 3 T × [37.030 + 319.490(w2 − w3)]

(9)

Equation 9 was used for predicting the solubility data of binary and ternary solvents, and the obtained prediction OMPD was 37.5 %. For diazepam in PEG 200 (1)−PG (2)−water (3) mixtures the trained model is: log CmSat, T = w1 log C1,SatT + w2 log C2,SatT + w3 log C3,SatT ww + 1 2 [127.779 − 76.409(w1 − w2) T ww + 57.050(w1 − w2)2 ] − 1 3 T × [296.025 − 513.604(w1 − w3) ww − 759.916(w1 − w3)2 ] + 2 3 T × [37.030 + 319.490(w2 − w3)] 311

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Article

The prediction OMPD for solubility data in binary and ternary solvents was 40.0 %. In numerical analysis IV, the solubility data of clonazepam and diazepam in five monosolvents (NMP, EtOH, PG, PEG 200, and water) at five different temperatures (see Table 3) are used for

Table 4. Experimental Mole Fraction Solubilities, Experimental (expt.) and Correlated (cor) Molar Solubilities of Diazepam in NMP, PEG 200, PG, ETOH, and Water at (298.2, 303.2, 308.2, 313.2, and 318.2) K and Atmospheric Pressurea, A and B Values of eq 6, and IPD, MPD, and OMPD Values

Table 3. Experimental Mole Fraction Solubilities, Experimental (expt.) and Correlated (cor.) Molar Solubilities of Clonazepam in NMP, PEG 200, PG, ETOH, and Water at (298.2, 303.2, 308.2, 313.2, and 318.2) K and Atmospheric Pressurea, A and B Values of eq 6, and IPD, MPD, and OMPD Values T/K 298.2 303.2 308.2 313.2 318.2

298.2 303.2 308.2 313.2 318.2

298.2 303.2 308.2 313.2 318.2

298.2 303.2 308.2 313.2 318.2

298.2 303.2 308.2 313.2 318.2

mole fraction

T/K 298.2 303.2 308.2 313.2 318.2

−1 CSat T /mol·L

CSat T expt.

cor.

NMP: A = 3.804, B = −1377.999 0.01321938 0.153783 0.1523855 0.01415158 0.169495 0.1816136 0.01871486 0.230183 0.2152190 0.02067468 0.261607 0.2536639 0.02218022 0.285176 0.2974360 MPD 4.3 PEG 200: A = −6.271, B = 1591.197 0.01004913 0.055752 0.0494177 0.01001495 0.055909 0.0627378 0.01340466 0.075222 0.0790337 0.01684867 0.094862 0.0988312 0.02385817 0.134143 0.1227226 MPD 8.2 PG: A = 2.743, B = −1416.834 0.00064059 0.008570 0.0098110 0.00104159 0.013958 0.0117507 0.00108304 0.014625 0.0139918 0.00116354 0.015830 0.0165678 0.00138230 0.018920 0.0195141 MPD 8.4 ETOH: A = 2.406, B = −1379.015 0.00034775 0.005951 0.0060470 0.00040910 0.007025 0.0072077 0.00053334 0.009198 0.0085425 0.00057999 0.010075 0.0100697 0.00065211 0.011450 0.0118087 MPD 2.9 Water: A = −1.373, B = −1063.462 0.00000019 0.000011 0.0000115 0.00000024 0.000014 0.0000132 0.00000026 0.000015 0.0000150 0.00000029 0.000017 0.0000170 0.00000032 0.000019 0.0000193 MPD 2.4 overall MPD 5.3

−1 CSat T /mol·L

CSat T

IPDb 0.9 7.1 6.5 3.0 4.3

298.2 303.2 308.2 313.2 318.2

11.3 12.2 5.0 4.1 8.5

298.2 303.2 308.2 313.2 318.2

14.4 15.8 4.3 4.6 3.1

298.2 303.2 308.2 313.2 318.2

1.6 2.6 7.1 0.0 3.1

298.2 303.2 308.2 313.2 318.2

4.5 5.9 0.0 0.2 1.4

mole fraction

expt.

cor.

NMP: A = 4.701, B = −1419.967 0.07740180 0.761766 0.8693725 0.12615480 1.189017 1.0416733 0.13793523 1.324810 1.2408214 0.15257119 1.490412 1.4698099 0.16311335 1.600813 1.7318153 MPD 8.4 PEG 200: A = 17.629, B = −5555.996 0.01569662 0.087860 0.099363 0.03965402 0.225218 0.201593 0.08046480 0.455200 0.399722 0.15129761 0.844567 0.775442 0.17278831 0.966008 1.473316 MPD 11.3 PG: A = 7.147, B = −2593.987 0.00200915 0.026960 0.0280662 0.00275033 0.037095 0.0390512 0.00464030 0.062928 0.0537563 0.00535269 0.072865 0.0732477 0.00678724 0.092737 0.0988406 MPD 6.1 ETOH: A = 2.216, B = −990.131 0.00486389 0.081973 0.078640 0.00521375 0.088155 0.089206 0.00553419 0.094006 0.100780 0.00662620 0.112774 0.113413 0.00774169 0.132481 0.127156 MPD 3.4 Water: A = 4.323, B = −2529.928 0.00000126 0.000070 0.000069 0.00000165 0.000093 0.000095 0.00000239 0.000136 0.000130 0.00000287 0.000165 0.000176 0.00000420 0.000244 0.000236 MPD 3.6 overall MPD 6.6

IPD 14.1 12.3 6.3 1.3 8.1

12.8 4.5 12.2 10.0 17.1

3.7 5.2 14.5 0.5 6.5

4.1 1.2 7.2 0.6 4.0

1.4 2.4 4.3 6.6 3.4

a

Standard uncertainties u are u(T) = 0.2 K, u(w) = 0.001, u(CSat m,T) = 0.027·CSat m,T, u(p) = 10 kPa.

clonazepam and diazepam are shown in Tables 3 and 4, respectively. For clonazepam the lowest IPD is 0.0 % for EtOH and water at (313.2 and 308.2) K, respectively; the highest IPD value (15.8 %) belongs to PG at 303.2 K, and the back-calculation OMPD for 25 monosolvent solubility data points of clonazepam is 5.3 %. For diazepam the lowest IPD is 0.5 % for PG at 313.2 K, and the highest one is 17.1 % which is for PEG 200 at 318.2 K; the back-calculation OMPD for 25 monosolvent solubility data points of diazepam is 6.6 %. In the numerical analysis V, the densities of the solute free solutions (ρm,T) were measured and fitted to eq 11.

a

Standard uncertainties u are u(T) = 0.2 K, u(w) = 0.001, u(CSat m,T) = Sat , u(p) = 10 kPa. bIPD is calculated using: IPD = 0.027·Cm,T Sat Sat 100{(|(CSat m,T)pred − (Cm,T)|)/(Cm,T)}.

calculating the A and B values of eq 6 for each solvent. Then, by using the determined A and B values, clonazepam and diazepam solubilities in monosolvents at different temperatures were backcalculated. The numerical values of A and B for each solvent, the individual percentage deviations (IPD) and MPD values for 312



Article

preparation of other formulations such as softgels. In addition, the systematic solubility measurements and suggesting the trained models for predicting the solubility data could facilitate the solvent selection process in the pharmaceutical area. In modeling part, the small MPD values of the fitting and the predicting of the experimental solubility data show that the Jouyban−Acree model fits well to the experimental solubility data of clonazepam and diazepam in binary and ternary mixtures with the obtained mass fractions of the cosolvents. Producing the model constants with these very low MPDs especially for subbinary solvent mixtures help one to save the time and cost, because computing the constants of the model need experimental efforts. Generally, because of the low OMPDs observed in these predictions, the Jouyban−Acree model is one of the more accurate cosolvency models which can predict the solubility of the drugs in the presence of one or two cosolvents.

log ρm , T = w1 log ρ1, T + w2 log ρ2, T + w3 log ρ3, T ⎡w w +⎢ 1 2 ⎢⎣ T ⎡w w +⎢ 2 3 ⎢⎣ T

2

⎤

⎡w w

⎥⎦

⎢⎣ T

∑ Ji (w1 − w2)i ⎥ + ⎢ i=0

1 3

⎤

2

∑ Ji′(w1 − w3)i ⎥ ⎥⎦

i=0

⎤

2

∑ Ji″(w2 − w3)i ⎥ ⎥⎦

i=0

(11)

where ρm,T is the density of the solute free solvent mixtures, ρ1,T, ρ2,T, and ρ3,T are the densities of the solute free monosolvents of 1 to 3 at temperature T, respectively.19 Then by using these calculated sub-binary constants, the ternary constants of eq 12 were obtained. log ρm , T = w1 log ρ1, T + w2 log ρ2, T + w3 log ρ3, T ⎡w w +⎢ 1 2 ⎢⎣ T

∑ Ji (w1 − w2)i ⎥ + ⎢

⎡w w +⎢ 2 3 ⎢⎣ T

⎤ ∑ Ji″(w2 − w3)i ⎥ ⎥⎦ i=0

2 i=0

⎤

⎡w w

⎥⎦

⎢⎣ T

1 3

⎤

2

■

∑ Ji′(w1 − w3)i ⎥ ⎥⎦

i=0

2

⎡w w w +⎢ 1 2 3 ⎢⎣ T

Corresponding Author

*E-mail: [email protected]. Tel.: +98 241 4273635. ⎤

2

Funding

∑ Ji‴(w1 − w2 − w3)i ⎥ ⎥⎦

i=0

The authors are grateful for financial support from Zanjan University of Medical Sciences, Iran (No. A-11-387-1).

(12)

Table 5 lists the model constants of the Jouyban−Acree model (after excluding the constants with p > 0.10) for all studied data

Notes

The authors declare no competing financial interest.

■

Table 5. Model Constants and the MPD Values Using the Density of the Solute-Free Binary and Ternary Solvent Mixtures J0

J1

J2

MPD

PEG 200−water PEG 200−PG PG−water

−2.150 5.722 −0.460

a −54.630 −3.252


86.180

−70.490

a a 2.831 overall MPD a overall MPD

0.1 2.3 0.1 0.8 0.4 0.6

solvent system

a

AUTHOR INFORMATION

REFERENCES

(1) Lio, R. Water-Insoluble Drug Formulation. 2nd ed.; CRC Press: Boca Raton, FL, 2006. (2) Lindenberg, M.; Kopp, S.; Dressman, J. B. Classification of orally administered drugs on the world health organization model list of essential medicines according to the biopharmaceutics classification system. Eur. J. Pharm. Biopharm. 2004, 58, 265−278. (3) Serajuddin, A. T. M.; Pudipeddi, M. Salt selection strategies. In Handbook of pharmaceutical salts: Properties, selection and use; Stahl, P. H., Wermuth, C. G., Eds.; Wiley-VCH: Weinheim, 2002; pp 135−160. (4) Dressman, J.; Reppas, C. Drug solubility: How to measure it, how to improve it. Adv. Drug Delivery Rev. 2007, 59, 531−532. (5) Blagden, N.; de Matas, M.; Gavan, P. T.; York, P. Crystal engineering of active pharmaceutical ingredients to improve solubility and dissolution rates. Adv. Drug Delivery Rev. 2007, 59, 617−630. (6) USP 23rd Revision; US Pharmacopeial Convention: Rockville, MD, 1995. (7) Allen, M. J.; Borody, T. J.; Bugliosi, T. F. Rapid dissolution of gallstones by methyl tert-butyl ether preliminary observations. New Eng. J. Med. 1985, 312, 217−220. (8) Jouyban, A. Handbook of solubility data for pharmaceuticals; CRC Press, Boca Raton, FL, 2009. (9) Jouyban, A. Review of the cosolvency models for predicting solubility of drugs in water-cosolvent mixtures. J. Pharm. Pharmaceut. Sci. 2008, 11, 32−58. (10) Shayanfar, A.; Acree, W. E., Jr.; Jouyban, A. Solubility of clonazepam, diazepam, lamotrigine, and phenobarbital in N-methyl-2pyrrolidone + water mixtures at 298.2 K. J. Chem. Eng. Data 2009, 54, 2964−2966. (11) Shayanfar, A.; Acree, W. E., Jr.; Jouyban, A. Solubility of lamotrigine, diazepam, clonazepam, and phenobarbital in propylene glycol + water mixtures at 298.15 K. J. Chem. Eng. Data 2009, 54, 1153− 1157. (12) Soltanpour, Sh.; Acree, W. E., Jr.; Jouyban, A. Solubility of 5-(2chlorophenyl)-7-nitro-1,3-dihydro-1,4-benzodiazepin-2-one, 7-chloro1-methyl-5-phenyl-3H-1,4-benzodiazepin-2-one, and 6-(2,3-dichlorophenyl)-1,2,4-triazine-3,5-diamine in the mixtures of poly(ethylene glycol) 600, ethanol, and water at a temperature of 298.2 K. J. Chem. Eng. Data 2010, 55, 1727−1731.

Not significant.

sets. Using the densities of the saturated solutions in monosolvents and the obtained model constants, it is possible to predict the densities of the saturated solvent mixtures.16,17 For converting the molar solubility to the mole fraction solubility, the experimental and calculated densities were used, and the OMPD value for the difference of mole fraction solubilities obtained from experimental and predicted densities was 1.6 %.

■

CONCLUSIONS For extending the solubility database of drugs in solvent mixtures8 the experimental solubilities of clonazepam and diazepam in PEG 200, PG, NMP, ethanol, and water at (298.2 to 318.2) K and in binary and ternary mixtures of PEG 200, PG, and water at 298.2 K are reported. In developing the liquid formulations and improving their bioavailability the solubility of drugs is a limiting factor. The main purpose of this investigation was to determine the solubility of clonazepam and diazepam. Clonazepam and diazepam are poorly soluble in water, so it is important to find some suitable solvent mixtures for producing their solution forms or modifying the available solution forms. The generated solubility data in aqueous mixtures could be used in preparation of oral liquid drug formulations, whereas nonaqueous mixtures could be used in 313



Article

(13) Grant, D. J. W.; Mehdizadeh, M. Non-linear Van’t Hoff solubility−temperature plots and their pharmaceutical interpretation. Int. J. Pharm. 1984, 18, 25−38. (14) Higuchi, T.; Connors, K. A. Phase solubility diagram. Adv. Anal. Chem. Instrum. 1965, 4, 117−212. (15) Jouyban, A. Prediction of drug solubility in water-propylene glycol mixtures using Jouyban-Acree model. Pharmazie 2007, 62, 365−367. (16) Soltanpour, Sh.; Jouyban, A. Solubility of acetaminophen and ibuprofen in polyethylene glycol 600, N-methyl pyrrolidone and water mixtures. J. Solution Chem. 2011, 40, 2032−2045. (17) Soltanpour, Sh.; Jouyban, A. Solubility of pioglitazone hydrochloride in binary mixtures of polyethylene glycol 400 with ethanol, propylene glycol, N-methyl-2-pyrrolidone, and water at 25 °C. Chem. Pharm. Bull. 2010, 58, 1132−1135. (18) Soltanpour, Sh.; Jouyban, A. Solubility of acetaminophen and ibuprofen in binary and ternary mixtures of polyethylene glycol 600, ethanol and water. Chem. Pharm. Bull. 2010, 58, 219−224. (19) Jouyban, A.; Fathi-Azarbayjani, A.; Khoubnasabjafari, M.; Acree, W. E., Jr. Mathematical representation of the density of liquid mixtures at various temperatures using Jouyban-Acree model. Indian J. Chem. A 2005, 44, 1553−1560.

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