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Solubility of silybin in aqueous poly(vinylpyrrolidone) solution
Fluid Phase Equilibria 238 (2005) 186–192
Solubility of silybin in aqueous poly(vinylpyrrolidone) solution H.-L. Zhang, T.-C. Bai ∗ , G.-B. Yan, J. Hu School of Chemistry and Chemical Engineering, Suzhou University, Suzhou 215006, China Received 3 February 2005; received in revised form 3 October 2005; accepted 4 October 2005
Abstract Silybin is a main component in silymarin, which is an antihepatotoxic polyphenolic substance isolated from the milk thistle plant, Silybum marianum. A major problem in the development of an oral solid dosage form of this drug is the extremely poor aqueous solubility. In present work, the solubility of silybin in aqueous poly(vinylpyrrolidone) (PVP k30) solution at the temperature range from 293.15 to 313.15 K was measured by a solid–liquid equilibrium method. Experimental results reveal that the solubility of silybin increases with the increase both in PVP’s concentration and temperature. With the increase in PVP’s concentration, the transfer enthalpy for silybin from water to aqueous PVP solution decreases within a negative region, and the transfer entropy increases slightly first in a positive region and then decreases to a negative region. The transfer enthalpy is lower than the entropy term. A modified UNIQUAC model was used to correlate solubility data. © 2005 Elsevier B.V. All rights reserved. Keywords: Silybin; Poly(vinylpyrrolidone) (PVP); Solubility; UNIQUAC model
1. Introduction The solubility of biologically active compounds is often a limiting factor for their applicability. Drugs are mainly hydrophobic organic compounds. Therefore, the solubility enhancement of drugs is an important task in pharmaceutical technology, because it leads to a better bioavailability. A broad variety of solubilization methods has been developed, reaching from changes of the physicochemical parameters of the solution, including pH adjustment and temperature variation, up to the application of cosolvents and excipients, like complexing agents or surfactants [1–4]. Silymarin is an antihepatotoxic polyphenolic substance isolated from the milk thistle plant, Silybum marianum. Derivatives of milk thistle have been used as herbal remedies for almost 200 years. Silymarin was considered as a pure compound with the structure of 7-chromanol-3-methyl-taxifolin, but after the introduction of more accurate methods of analysis and separation it was shown that silymarin consists of a large number of flavonolignans, including silybin, isosilybin, silydianin and silychristin. Among them, silybin is the main component and has been separated commercially as a pure substance. The molecular structure
∗
Corresponding author. Tel.: +86 512 65880363; fax: +86 512 65880089. E-mail address: [email protected] (T.-C. Bai).
0378-3812/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2005.10.004
of silybin is shown in Fig. 1. Currently, the most important medicinal application of milk thistle is its use as a hepatoprotectant and as supportive treatment of chronic inflammatory liver disorders, such as cirrhosis, hepatitis and fatty infiltration, due to alcohol and toxic chemicals [5]. Its use has been widespread since preparations became officially available for clinical use. A major problem in the development of an oral solid dosage form of this drug is the extremely poor aqueous solubility, possibly resulting in dissolution-limited oral absorption [6]. The solubility enhancement of poorly soluble compounds can be induced by changes of temperature, solvation properties using different cosolvent compositions [2]. Among the techniques to increase aqueous solubility/dissolution rate, the formulation of solid dispersions is one of the most popular ones, although few marketed products rely on this concept. Polymers, such as poly(ethylene glycol) (PEG) and poly(vinylpyrrolidone) (PVP), have frequently been used as a carrier in solid dispersion formulations [7]. Numerous attempts to understand the physicochemical principle behind the improvement of the dissolution of drugs by solid dispersion formulation with polymers have been reported [3]. Equilibrium solubilities of the drug in aqueous polymer solutions of different polymer concentrations reveal the solubilization capacity of a polymer for the drug. Several approaches have been used to explain the solubility of organic compounds as well as its temperature dependence [8]. Enthalpy of solution values can be measured directly
H.-L. Zhang et al. / Fluid Phase Equilibria 238 (2005) 186–192
187
Fig. 1. Chemical structure of silybin.
from the temperature dependence of the saturation concentration [2,3,9]. The prediction of the solubility of drugs in aqueous mixed solvents or even a reliable correlation of the available experimental data is of interest to the pharmaceutical science and industry. Many methods, mainly empirical and semiempirical, were suggested for the correlation and prediction of the solubility of solid drug in a mixed solvent [8,10–14]. The main difficulty in predicting the solid solubility in a mixed solvent consists of calculating the activity coefficient of a solute in a ternary mixture. In the present work, solubilities of silybin in aqueous PVP k30 solution at temperatures 293.15, 298.15, 303.15, 308.15 and 313.15 K were measured by a solid–liquid equilibrium method. The aim of this study is to investigate the possible effect of polymer concentration and temperature on the solubility of drug. A modified UNIQUAC model was used to correlate the solubility data. 2. Materials and methods
by DSC technique. (Instrument: Perkin-Elmer Dsc-7 differential scanning calorimeter, Norwalk, CT). Certified indium wire encapsulated in an aluminum crucible (supplied by instrument manufacturer) was used for temperature and heat flow calibration. An aluminum pan and lid without pinhole were used to contain the sample. An empty container of the same type was employed as a reference. Nitrogen gas of 99% purity was used as the purge gas for all the experiments performed at a rate of 20 mL min−1 . Samples 3–8 mg were weighed to ±0.1 mg. Balance model: FA 1004, Shanghai Balance Instrument Factory. A mass losing profile of pure silybin solid was measured by TG instrument. Instrument model, PEDELTA series 7, with N2 protection, flowing rate: 20 mL min−1 . The TG curve shows that silybin is decomposed above 473 K. In DSC measurement, samples were heated at a scanning rate of 5 K min−1 , over a temperature range from 303 to 473 K. Onset temperature and enthalpy of fusion were determined (using the software attached to DSC apparatus). The uncertainty of Tm and fus H was less than 1 K and 2 J g−1 , respectively.
2.1. Materials
2.3. Solubility measurements
Silybin was purchased from Panjin Green Biological Development Co. Ltd., Liaoning, China. Its purity was claimed to be 97% detected by a UV spectrometer at the wavelength 252–288 nm by the company. The drug was recrystallized in methanol and being dried under vacuum at 353 K over 24 h, and then analyzed by HPLC. Our HPLC measurement reveals that the mass percent of silybin is 96.8%, isosilybin is 1.1%, silycristin is 0.1%, silydianin is 0.8% and other impurities are 1.2%. Silycristin and silydianin are hydrophobic drug effective components. They have similar therapeutic effects as silybin. In a drug sample, the content of theses hydrophobic impurities is too small, and they hardly dissolve in water. In view of the fact that it is still difficult to separate more pure silybin, in solubility measurement the drug was used without further treatment. Poly(vinylpyrrolidone) k30 was received from Shanghai ChemReagent Co. Its purity was of analytical grade. Both reagents were stored over P2 O5 in a desiccator before use.
Binary solutions of PVP + water were prepared. Known masses of PVP were added into 250 cm3 volumetric flasks. The flasks were put into a thermostatic bath at the temperature 298.15 K, and water was added into the flask until the flask mark was reached. The polymer concentration was determined as g cm−3 . Because the temperature had effect on solvent volume, it was better to convert the polymer concentration from mass per unit volume into the mass fraction for equilibrium calculations. The densities of aqueous PVP solution were measured by a densimeter for converting the polymer concentration. Polymer concentration was controlled within a mass fraction of <2.0%. Solubility measurement of silybin was carried out by adding an excess amount to 100 mL of demineralized water or to an aqueous PVP k30 solution (mass fraction is from 0.1 to 2.0%)
2.2. Differential scanning calorimeter measurement Some physical properties of silybin are shown in Table 1. The melting temperature (Tm ) and enthalpy of fusion (fus H) of silybin are necessary in solubility correlation and were measured
Table 1 Physical properties of silybin Properties (g mol−1 )
M Tm (K) fus H (J g−1 )
Silybin 482.436 424 93
H.-L. Zhang et al. / Fluid Phase Equilibria 238 (2005) 186–192
188
in sealed glass containers. The stoppered tubes were rotated for 60 h in water baths at 293.15, 298.15, 303.15, 308.15 and 313.15 K, respectively. Preliminary experiments had shown that this time period was sufficient to ensure saturation. After 60 h, the rotation was stopped and the saturated solutions were kept still for 2 days at the equilibrium temperature to ensure that the solid was deposited. The solution was filtered through a 0.20 m membrane filter (Anpel Science Instrument Company, Shanghai, China), which was performed in the water bath at the equilibrium temperature, and then diluted with water or aqueous PVP solution to prevent crystallization. The known masses of saturated solution and dilution solvent were used to ensure that the drug concentration was calculable. Three tubes containing identical aqueous PVP solution were used for comparing test. Silybin concentration in each tube was detected in triplicate. An experimental uncertainty study for silybin in pure water at temperature from 293.15 to 313.15 K showed that the mean value of the relative standard deviation is 0.023. The concentration of silybin in the diluted solution was analyzed by UV–vis spectrometer at the wavelength 285– 288 nm.
added to dilute the sample to prevent solid deposition and to adjust the concentration of silybin to be within the linear response range of the UV absorption. For silybin + PVP + water solution, the wavelength used in the determination is at their maximum absorption, mostly at λ = 287 nm. To eliminate the solvent effect on absorbance, the blank was filled with the identical solvent with the sample cell.
2.4. UV spectrometer measurement
The solubility of a solid in a liquid (or a liquid mixture) is determined not only by the intermolecular forces between solute and solvent but also by the melting point and the enthalpy of fusion of the solute. The quantitative thermodynamic analysis is given in several texts [15,16]. For ternary solution in this work, component indexes are assigned for (1) silybin, (2) PVP and (3) water. At temperature T, the solubility (mole fraction) x1 of a solid solute (1) is given by Cp Tt − T fus Hm T + ln γ1 x1 = − 1− RT Tt R T
The UV spectrometry was used as an experimental analytical method; Model: TU-1800, Beijing Analysis Instrument Company. Silybin standard solutions were prepared in ethanol solvent. The concentration of the standard solution was limited within the mass fraction range from 1.0 to 6.0 × 10−5 . By considering the relationship between UV maximum absorbance and silybin’s concentration, a linear response range was found, where the maximum wavelength is from 288 to 285 nm. A correlation equation between the UV absorbance (A) at maximum wavelength and the mass fraction of silybin (S) is obtained. A = 0.00314 + 24410 × S
(1)
where the standard deviation is 0.002. In solubility analysis, silybin samples were taken from equilibrium bottles. Known masses of the aqueous PVP solution, with the same concentration as the equilibrium solvents, were
3. Results and discussions 3.1. Solubility The solubility of silybin in PVP k30 aqueous solution is determined at temperatures of 293.15, 298.15, 303.15 308.15 and 313.15 K, respectively. The data of solubility are presented in Table 2. The PVP concentrations are converted from mass per unit volume at 298.15 K to the mass percent. It can be found from Table 2 that the solubility of silybin increases with increasing PVP’s concentration and temperature. 3.2. Thermodynamic equations
−
Cp Tt ln R T
(2)
where fus Hm is the molar enthalpy of fusion of the solute (1) at the triple-point temperature Tt . The standard state of activity coefficient is pure (subcooled) liquid (1) at system temperature T. To a good approximation, we can substitute normal melting temperature Tm for Tt , and we can assume that fus Hm is essentially the same at the two temperature. In above equation, the
Table 2 Solubility (mass fraction, ×104 S) of silybin in aqueous PVP k30 solution, wPVP mass fraction of PVP 100wPVP
0 0.1021 0.2040 0.5008 0.8053 1.004 1.201 1.538 1.997
Solubility T = 293.15 K
T = 298.15 K
T = 303.15 K
T = 308.15 K
T = 313.15 K
0.4244 0.6200 0.7166 0.7851 0.9600 1.000 1.159 1.401 1.877
0.5401 0.7435 0.8026 1.014 1.146 1.251 1.285 1.707 2.231
0.6906 0.9502 1.109 1.201 1.525 1.500 1.605 1.986 2.632
0.8326 1.150 1.288 1.430 1.730 1.808 1.878 2.350 2.958
0.9965 1.425 1.610 1.854 2.009 2.082 2.252 2.685 3.230
H.-L. Zhang et al. / Fluid Phase Equilibria 238 (2005) 186–192
first term on the right hand is much more important than the remaining two terms, and therefore a simplified form of that equation is fus Hm T (3) ln γ1 x1 = − 1− RT Tm If we let γ 1 = 1, we can readily calculate the ideal solubility at temperature T. This ideal solubility depends only on properties of the solute (1); it is independent of the properties of solvent. fus Hm 1 1 id ln x1 = − (4) R Tm T By the data of fus Hm and Tm in Table 1, the value of x1id at 298.15 K is evaluated, x1id = 0.00467. Converting the x1id value into mass fraction, we have Sid = 0.1251. This value is much higher than the actual experiment data (0.5401 × 10−4 ). It reveals that for real solution, the effect of solute–solvent interaction, which is represented by γ 1 , must be considered. Dissolution process is occurred in experimental temperature T, which is not in Tm . The heat of dissolution, sol Hm , is connected with fus Hm by Eq. (5). Tm ¯ p dT sol Hm = fus Hm − C (5) T
¯p where T¯ is the mean value of experimental temperature and C is the mean value of heat capacity in the temperature range from T¯ to Tm . Within the experimental accuracy, the second term in Eq. (5) can be neglected. In general, solubility of drug is expressed in mass fraction (S). Silybin is a hydrophobic solute. The measured solubility (in Table 2) is very small. At very low solute concentrations, all concentration units become collinear with one another. Then we have M3+2 ≈ M3 , S × M3 /M1 1 and x2 = S × M3 /M1 , where M3 and M1 are molecular weights of water and silybin, respectively. By combining Eqs. (3) and (5), we have M1 1 fus Hm 1 − ln γ1 + ln − ln S = − R T Tm M3 =−
sol Hm +C RT
(6)
189
The enthalpy of solution (sol Hm ) is related to fus Hm and [∂ln γ 1 /∂(1/T)], and can be evaluated from the slopes of the Van’t Hoff plots by using Eq. (6). Parameter C is independent of temperature. On considering the transfer Gibbs free energy (tr G), enthalpy (tr H) and entropy (tr S) for silybin from pure water (3) to aqueous PVP solution (2 + 3), we have S(2 + 3) tr G = −RT ln (7) S(3) tr H = sol Hm (2 + 3) − sol Hm (3) tr S =
(8)
tr H − tr G T
(9)
where S(2 + 3) and S(3) are the solubilities of drug in aqueous PVP solution and water, respectively. sol Hm (2 + 3) and sol Hm (3) are the molar enthalpies of solution of silybin in aqueous PVP solution and water, respectively. 3.3. Heat of solution and transfer properties At fixed PVP concentration, the plots of ln S versus 1/T are approximately linear. The enthalpy of solution (sol Hm ) can be calculated from the slopes of Eq. (6). The values of sol Hm are presented in Table 3. The endothermic enthalpy of solution further explains the increase in solubility with temperature. With the increase in PVP concentration, sol Hm decreases, which leads to the solubility increase. The transfer entropy (tr S) of silybin from water to aqueous PVP solution can be calculated from Eq. (9). The values of tr H and tr G are calculated by Eqs. (7) and (8), respectively. The values of tr S are presented in Table 3. The comparison of enthalpy and entropy effect is shown in Fig. 2. Two characteristics can be found in Fig. 2. First, the temperature effect: for T tr S, the temperature effect is small. Second, the concentration effect: with the increase in PVP concentration, tr H decreases within a negative region; the T tr S term increases slightly in a positive region firstly, and then decreases to a negative region. In Fig. 2, the tr H term drops more rapidly than the T tr S term does. This phenomenon is an indication that, with the increase in PVP concentration, enthalpy effect causes drug dissolution to be more favorable, but the entropy effect leads to
Table 3 Enthalpy of solution of silybin (sol Hm ) and transfer entropy (tr S) for silybin from water to aqueous PVP solution 100wPVP
0 0.1021 0.204 0.5008 0.8053 1.004 1.201 1.538 1.997
sol Hm (kJ mol−1 )
32.7 32.1 31.9 31.5 28.9 28.0 26.1 24.8 20.9
tr S (J mol−1 ) T = 293.15 K
T = 298.15 K
T = 303.15 K
T = 308.15 K
T = 313.15 K
0.93 1.70 0.92 −6.24 −8.80 −14.3 −17.1 −27.8
0.48 0.68 1.11 −6.56 −8.68 −15.1 −17.0 −27.7
0.51 1.37 0.54 −6.02 −8.96 −14.9 −17.4 −27.7
0.57 1.10 0.51 −6.32 −8.71 −14.8 −17.1 −27.7
0.90 1.50 1.23 −6.37 −8.79 −14.4 −17.1 −27.8
H.-L. Zhang et al. / Fluid Phase Equilibria 238 (2005) 186–192
190
Table 5 Interaction parameters of modified UNIQUAC model, standard deviation (σ a ) and correlation coefficient (R) Parameter
Binary system silybin (1) + water (3)
Ternary system silybin (1) + PVP (2) + water (3)
σ R u13 (K) u11 (K) u33 (K) u22 (K) u12a (K) u12b (K) u12c (K) u23a (K) u23b (K)
0.027 0.9985 1.269 120.2 −221.1
0.078 0.9939 1.269 120.2 −221.1 −753.0 −105.2 −1859 × 102 1310 × 104 1329 −2032 × 102
1/2
Fig. 2. Transfer enthalpy (tr H, ) and entropy (T tr S) at T = () 293.15, (䊉) 298.15, () 303.15, () 308.15 and () 313.15 K, for silybin from water to PVP + water solution as a function of mass fraction of PVP (wPVP ).
σ = { j [104 Sj − 104 Sjmodel ] /(n − p)} , where n is the total number of experimental data and p is the total number of adjustable parameters used in the fitting.
the dissolution to be difficult, since tr H is more negative than T tr S.
parameter τ 13 plays in curve fitting is to adjust the intercept of the curve ln γ1res as a function of 1/T. To obtain parameters u13 , u11 and u33 , the solubility data of water in silybin solvent are needed, but this is difficult. Therefore, for the convenience of data fitting, τ 13 is assumed to be evaluated by τ13 = exp[−(u13 − u33 )/T0 ], where T0 is a reference temperature, here it is 293.15 K. By using a nonlinear least-squares fitting technique based on the Levenberg–Marquardt algorithm, which is performed by software of Origin 6.1 (OriginLab Corporation), the fitting results were obtained and presented in Table 5. For a ternary system, other parameters, such as u12 , u22 and u23 , should be regressed from ternary solubility data. But the fitting result is not satisfying. The standard deviation (σ) and the correlation coefficient (R) are 0.17 and 0.9665, respectively. Larsen et al. [17] had proposed a modified equation for the temperature dependence of interaction parameters. If we suppose the temperature effect on u23 is described by a linear dependence equation, and applying this modification to correlate the
3.4. Activity coefficient by UNIQUAC To correlate drug solubility, an important procedure is to calculate the activity coefficient of drug in aqueous solution. By the UNIQUAC model, the activity coefficient is composed of two parts, the combinatorial, γ1com , and residual part, γ1res . ln γ1 = ln γ1com + ln γ1res
(10)
In calculating γ1com , group parameters Rk and Qk are obtained from literature [15]. Parameters ri and qi for silybin and PVP are listed in Table 4. In Eq. (10), the term of ln γ1res is usually introduced to account for the contribution from molecule interaction. By UNIQUAC model, the term of ln γ1res is calculated by
θj τij
(11) ln γ1res = qi 1 − ln θj τji − k θk τkj j
a
exp
2
j
where
uji − uii τji = exp − T
(12)
and uij = uji . Parameters uji and uii can be obtained by fitting experimental solubility data via Eq. (3). For binary system of silybin dissolves in water, solubility were located within the infinite dilution region, the role of Table 4 UNIQUAC parameters Component
ri
qi
Silybin (1) PVP monomer unit (2) Water (3)
16.6032 4.2012 0.9200
12.384 3.124 1.400
Fig. 3. Mass fraction solubility (S) of silybin in aqueous PVP solution. xPVP , Mole fraction of PVP. Experimental: T = () 293.15, (䊉) 298.15, () 303.15, () 308.15 and () 313.15 K. Lines (—), modified UNIQUAC correlation.
H.-L. Zhang et al. / Fluid Phase Equilibria 238 (2005) 186–192
solubility data, then we have the fitting result of σ = 0.14 and R = 0.9758, respectively. To improve the fitting result, modification on UNIQUAC was introduced. In view of the interaction between solute and solvent is more complex with the addition of PVP, it was supposed that the interaction parameter (uij ) is concentration dependent. In this work, silybin’s concentration is supposed at infinite dilution. Therefore, uij is dependent on the ratio of PVP and water. Then we have uij = uija + (uijb + uijc θ2 )θ3 θ2
(13)
where uija , uijb and uijc are concentration effect parameters. Applying this modification to correlate the solubility data, the fitting result was improved significantly (σ = 0.078 and R = 0.9939), and graphically shown in Fig. 3. The interaction parameters and concentration effect parameters are listed in Table 5. 4. Conclusion The solubility of silybin is increased with the increase in both PVP’s concentration and temperature. At fixed PVP concentration, the enthalpy of solution, sol Hm , can be calculated from the slopes of the Van’t Hoff plots. The results of transfer enthalpy and entropy for silybin from water to aqueous PVP solution reveals that, with the increase in PVP’s concentration, the enthalpy effect causes drug dissolution to be more favorable, but the entropy effect causes the dissolution to be difficult. A modified UNIQUAC model was used to correlate drug solubility. By introducing concentration effect parameters, the model gives good quality correlation. List of symbols A UV spectra absorbance Cp heat capacity at constant pressure tr G transfer Gibbs free energy for silybin from water to aqueous PVP solution tr H transfer enthalpy for silybin from water to aqueous PVP solution fus Hm the molar enthalpy of fusion sol Hm enthalpy of solution li parameter in UNIQUAC model, li = (z/2)(ri − qi ) − (ri − 1) M mole weight (g mol−1 ) qi molecular surface area parameter for component i Qk surface area parameter for group k ri molecular volume parameter for component i R correlation coefficient Rk volume parameter for group k S solubility of silybin in mass fraction tr S transfer entropy for silybin from water to aqueous PVP solution T temperature (K) Tm melting temperature (K) Tt triple-point temperature (K) T0 reference temperature (K)
191
uija , uijb , uijc concentration effect parameters for modifying UNIQUAC parameter uji uji interaction parameters of UNIQUAC model xi mole fraction of component i Greek letters Φi volumetric fraction for component i γi activity coefficient of component i γ com the combinatorial term of activity coefficient γ res the residual term of activity coefficient νki the number of groups of type k in molecule i θi surface area fraction for component i σ standard deviation τ ji Boltzmann factor in UNIQUAC model Subscripts 1 silybin 2 PVP 3 water References [1] P. Kallinteri, S.G. Antimisiaris, Solubility of drugs in the presence of gelatin: effect of drug lipophilicity and degree of ionization, Int. J. Pharm. 221 (2001) 219–226. [2] H. Viernstein, P. Weiss-Greiler, P. Wolschann, Solubility enhancement of low soluble biologically active compounds—temperature and cosolvent dependent inclusion complexation, Int. J. Pharm. 256 (2003) 85– 94. [3] S. Verheyen, N. Blaton, R. Kinget, G. Van den Mooter, Mechanism of increased dissolution of diazepam and temazepam from polyethylene glycol 6000 solid dispersions, Int. J. Pharm. 249 (2002) 45–58. [4] J. Jinno, D.M. Oh, J.R. Crison, G.L. Amidon, Dissolution of ionisable water-insoluble drugs: the combined effect of pH and surfactant, J. Pharm. Sci. 89 (2000) 268–274. [5] F. Kvasnicka, B. Biba, R. Sevcik, M. Voldrich, J. Kratka, Analysis of the active components of silymarin, J. Chromatogr. A 990 (2003) 239– 245. [6] F.-Q. Li, J.-H. Hu, Y.-Y. Jiang, Preparation and characterization of solid dispersions of silymarin with polyethylene glycol 6000, J. Chin. Pharm. Sci. 12 (2) (2003) 76–81. [7] F. Damian, N. Blaton, L. Naesens, J. Balzarini, R. Kinget, P. Augustijns, G. Van den Mooter, Physicochemical characterization of solid dispersions of the antiviral agent UC-781 with polyethylene glycol 6000 and Gelucire 44/14, Eur. J. Pharm. Sci. 10 (2000) 311–322. [8] A. Jouyban-Gharamaleki, W.E. Acree Jr., Comparison of models for describing multiple peaks in solubility profiles, Int. J. Pharm. 167 (1998) 177–182. [9] G. Reinwald, I. Zimmermann, A combined calorimetric and semiempirical quantum chemical approach to describe the solution thermodynamics of drugs, J. Pharm. Sci. 87 (1998) 745–750. [10] A. Jouyban-Gharamaleki, L. Valaee, M. Barzegar-Jalali, B.J. Clark, W.E. Acree Jr., Comparison of various cosolvency models for calculating solute solubility in water–cosolvent mixtures, Int. J. Pharm. 177 (1999) 93–101. [11] A. Jouyban-Gharamaleki, P. York, M. Hanna, B.J. Clark, Solubility prediction of salmeterol xinafoate in water–dioxane mixtures, Int. J. Pharm. 216 (2001) 33–41. [12] E. Ruckenstein, I. Shulgin, Solubility of drugs in aqueous solutions. Part 1. Ideal mixed solvent approximation, Int. J. Pharm. 258 (2003) 193–201. [13] E. Ruckenstein, I. Shulgin, Solubility of drugs in aqueous solutions. Part 2. Binary nonideal mixed solvent, Int. J. Pharm. 260 (2003) 283–291.
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[14] G. Van den Mooter, P. Augustijns, R. Kinget, Application of the thermodynamics of mobile order and disorder to explain the solubility of temazepam in aqueous solutions of polyethylene glycol 6000, Int. J. Pharm. 164 (1998) 81–89. [15] R.C. Reid, J.M. Prausnitz, B.E. Poling, The Properties of Gases and Liquids, fourth ed., McGraw-Hill, New York, 1987, p. 372.
[16] W.E. Acree Jr., Thermodynamic Properties of Nonelectrolyte Solutions, Academic Press, Orlando, 1984. [17] B.L. Larsen, P. Rasmussen, A. Fredenslund, A modified UNIFAC groupcontribution model for prediction of phase equilibria and heat of mixing, Ind. Eng. Chem. Res. 26 (1987) 2274–2286.
Solubility of silybin in aqueous poly(vinylpyrrolidone) solution H.-L. Zhang, T.-C. Bai ∗ , G.-B. Yan, J. Hu School of Chemistry and Chemical Engineering, Suzhou University, Suzhou 215006, China Received 3 February 2005; received in revised form 3 October 2005; accepted 4 October 2005
Abstract Silybin is a main component in silymarin, which is an antihepatotoxic polyphenolic substance isolated from the milk thistle plant, Silybum marianum. A major problem in the development of an oral solid dosage form of this drug is the extremely poor aqueous solubility. In present work, the solubility of silybin in aqueous poly(vinylpyrrolidone) (PVP k30) solution at the temperature range from 293.15 to 313.15 K was measured by a solid–liquid equilibrium method. Experimental results reveal that the solubility of silybin increases with the increase both in PVP’s concentration and temperature. With the increase in PVP’s concentration, the transfer enthalpy for silybin from water to aqueous PVP solution decreases within a negative region, and the transfer entropy increases slightly first in a positive region and then decreases to a negative region. The transfer enthalpy is lower than the entropy term. A modified UNIQUAC model was used to correlate solubility data. © 2005 Elsevier B.V. All rights reserved. Keywords: Silybin; Poly(vinylpyrrolidone) (PVP); Solubility; UNIQUAC model
1. Introduction The solubility of biologically active compounds is often a limiting factor for their applicability. Drugs are mainly hydrophobic organic compounds. Therefore, the solubility enhancement of drugs is an important task in pharmaceutical technology, because it leads to a better bioavailability. A broad variety of solubilization methods has been developed, reaching from changes of the physicochemical parameters of the solution, including pH adjustment and temperature variation, up to the application of cosolvents and excipients, like complexing agents or surfactants [1–4]. Silymarin is an antihepatotoxic polyphenolic substance isolated from the milk thistle plant, Silybum marianum. Derivatives of milk thistle have been used as herbal remedies for almost 200 years. Silymarin was considered as a pure compound with the structure of 7-chromanol-3-methyl-taxifolin, but after the introduction of more accurate methods of analysis and separation it was shown that silymarin consists of a large number of flavonolignans, including silybin, isosilybin, silydianin and silychristin. Among them, silybin is the main component and has been separated commercially as a pure substance. The molecular structure
∗
Corresponding author. Tel.: +86 512 65880363; fax: +86 512 65880089. E-mail address: [email protected] (T.-C. Bai).
0378-3812/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2005.10.004
of silybin is shown in Fig. 1. Currently, the most important medicinal application of milk thistle is its use as a hepatoprotectant and as supportive treatment of chronic inflammatory liver disorders, such as cirrhosis, hepatitis and fatty infiltration, due to alcohol and toxic chemicals [5]. Its use has been widespread since preparations became officially available for clinical use. A major problem in the development of an oral solid dosage form of this drug is the extremely poor aqueous solubility, possibly resulting in dissolution-limited oral absorption [6]. The solubility enhancement of poorly soluble compounds can be induced by changes of temperature, solvation properties using different cosolvent compositions [2]. Among the techniques to increase aqueous solubility/dissolution rate, the formulation of solid dispersions is one of the most popular ones, although few marketed products rely on this concept. Polymers, such as poly(ethylene glycol) (PEG) and poly(vinylpyrrolidone) (PVP), have frequently been used as a carrier in solid dispersion formulations [7]. Numerous attempts to understand the physicochemical principle behind the improvement of the dissolution of drugs by solid dispersion formulation with polymers have been reported [3]. Equilibrium solubilities of the drug in aqueous polymer solutions of different polymer concentrations reveal the solubilization capacity of a polymer for the drug. Several approaches have been used to explain the solubility of organic compounds as well as its temperature dependence [8]. Enthalpy of solution values can be measured directly
H.-L. Zhang et al. / Fluid Phase Equilibria 238 (2005) 186–192
187
Fig. 1. Chemical structure of silybin.
from the temperature dependence of the saturation concentration [2,3,9]. The prediction of the solubility of drugs in aqueous mixed solvents or even a reliable correlation of the available experimental data is of interest to the pharmaceutical science and industry. Many methods, mainly empirical and semiempirical, were suggested for the correlation and prediction of the solubility of solid drug in a mixed solvent [8,10–14]. The main difficulty in predicting the solid solubility in a mixed solvent consists of calculating the activity coefficient of a solute in a ternary mixture. In the present work, solubilities of silybin in aqueous PVP k30 solution at temperatures 293.15, 298.15, 303.15, 308.15 and 313.15 K were measured by a solid–liquid equilibrium method. The aim of this study is to investigate the possible effect of polymer concentration and temperature on the solubility of drug. A modified UNIQUAC model was used to correlate the solubility data. 2. Materials and methods
by DSC technique. (Instrument: Perkin-Elmer Dsc-7 differential scanning calorimeter, Norwalk, CT). Certified indium wire encapsulated in an aluminum crucible (supplied by instrument manufacturer) was used for temperature and heat flow calibration. An aluminum pan and lid without pinhole were used to contain the sample. An empty container of the same type was employed as a reference. Nitrogen gas of 99% purity was used as the purge gas for all the experiments performed at a rate of 20 mL min−1 . Samples 3–8 mg were weighed to ±0.1 mg. Balance model: FA 1004, Shanghai Balance Instrument Factory. A mass losing profile of pure silybin solid was measured by TG instrument. Instrument model, PEDELTA series 7, with N2 protection, flowing rate: 20 mL min−1 . The TG curve shows that silybin is decomposed above 473 K. In DSC measurement, samples were heated at a scanning rate of 5 K min−1 , over a temperature range from 303 to 473 K. Onset temperature and enthalpy of fusion were determined (using the software attached to DSC apparatus). The uncertainty of Tm and fus H was less than 1 K and 2 J g−1 , respectively.
2.1. Materials
2.3. Solubility measurements
Silybin was purchased from Panjin Green Biological Development Co. Ltd., Liaoning, China. Its purity was claimed to be 97% detected by a UV spectrometer at the wavelength 252–288 nm by the company. The drug was recrystallized in methanol and being dried under vacuum at 353 K over 24 h, and then analyzed by HPLC. Our HPLC measurement reveals that the mass percent of silybin is 96.8%, isosilybin is 1.1%, silycristin is 0.1%, silydianin is 0.8% and other impurities are 1.2%. Silycristin and silydianin are hydrophobic drug effective components. They have similar therapeutic effects as silybin. In a drug sample, the content of theses hydrophobic impurities is too small, and they hardly dissolve in water. In view of the fact that it is still difficult to separate more pure silybin, in solubility measurement the drug was used without further treatment. Poly(vinylpyrrolidone) k30 was received from Shanghai ChemReagent Co. Its purity was of analytical grade. Both reagents were stored over P2 O5 in a desiccator before use.
Binary solutions of PVP + water were prepared. Known masses of PVP were added into 250 cm3 volumetric flasks. The flasks were put into a thermostatic bath at the temperature 298.15 K, and water was added into the flask until the flask mark was reached. The polymer concentration was determined as g cm−3 . Because the temperature had effect on solvent volume, it was better to convert the polymer concentration from mass per unit volume into the mass fraction for equilibrium calculations. The densities of aqueous PVP solution were measured by a densimeter for converting the polymer concentration. Polymer concentration was controlled within a mass fraction of <2.0%. Solubility measurement of silybin was carried out by adding an excess amount to 100 mL of demineralized water or to an aqueous PVP k30 solution (mass fraction is from 0.1 to 2.0%)
2.2. Differential scanning calorimeter measurement Some physical properties of silybin are shown in Table 1. The melting temperature (Tm ) and enthalpy of fusion (fus H) of silybin are necessary in solubility correlation and were measured
Table 1 Physical properties of silybin Properties (g mol−1 )
M Tm (K) fus H (J g−1 )
Silybin 482.436 424 93
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188
in sealed glass containers. The stoppered tubes were rotated for 60 h in water baths at 293.15, 298.15, 303.15, 308.15 and 313.15 K, respectively. Preliminary experiments had shown that this time period was sufficient to ensure saturation. After 60 h, the rotation was stopped and the saturated solutions were kept still for 2 days at the equilibrium temperature to ensure that the solid was deposited. The solution was filtered through a 0.20 m membrane filter (Anpel Science Instrument Company, Shanghai, China), which was performed in the water bath at the equilibrium temperature, and then diluted with water or aqueous PVP solution to prevent crystallization. The known masses of saturated solution and dilution solvent were used to ensure that the drug concentration was calculable. Three tubes containing identical aqueous PVP solution were used for comparing test. Silybin concentration in each tube was detected in triplicate. An experimental uncertainty study for silybin in pure water at temperature from 293.15 to 313.15 K showed that the mean value of the relative standard deviation is 0.023. The concentration of silybin in the diluted solution was analyzed by UV–vis spectrometer at the wavelength 285– 288 nm.
added to dilute the sample to prevent solid deposition and to adjust the concentration of silybin to be within the linear response range of the UV absorption. For silybin + PVP + water solution, the wavelength used in the determination is at their maximum absorption, mostly at λ = 287 nm. To eliminate the solvent effect on absorbance, the blank was filled with the identical solvent with the sample cell.
2.4. UV spectrometer measurement
The solubility of a solid in a liquid (or a liquid mixture) is determined not only by the intermolecular forces between solute and solvent but also by the melting point and the enthalpy of fusion of the solute. The quantitative thermodynamic analysis is given in several texts [15,16]. For ternary solution in this work, component indexes are assigned for (1) silybin, (2) PVP and (3) water. At temperature T, the solubility (mole fraction) x1 of a solid solute (1) is given by Cp Tt − T fus Hm T + ln γ1 x1 = − 1− RT Tt R T
The UV spectrometry was used as an experimental analytical method; Model: TU-1800, Beijing Analysis Instrument Company. Silybin standard solutions were prepared in ethanol solvent. The concentration of the standard solution was limited within the mass fraction range from 1.0 to 6.0 × 10−5 . By considering the relationship between UV maximum absorbance and silybin’s concentration, a linear response range was found, where the maximum wavelength is from 288 to 285 nm. A correlation equation between the UV absorbance (A) at maximum wavelength and the mass fraction of silybin (S) is obtained. A = 0.00314 + 24410 × S
(1)
where the standard deviation is 0.002. In solubility analysis, silybin samples were taken from equilibrium bottles. Known masses of the aqueous PVP solution, with the same concentration as the equilibrium solvents, were
3. Results and discussions 3.1. Solubility The solubility of silybin in PVP k30 aqueous solution is determined at temperatures of 293.15, 298.15, 303.15 308.15 and 313.15 K, respectively. The data of solubility are presented in Table 2. The PVP concentrations are converted from mass per unit volume at 298.15 K to the mass percent. It can be found from Table 2 that the solubility of silybin increases with increasing PVP’s concentration and temperature. 3.2. Thermodynamic equations
−
Cp Tt ln R T
(2)
where fus Hm is the molar enthalpy of fusion of the solute (1) at the triple-point temperature Tt . The standard state of activity coefficient is pure (subcooled) liquid (1) at system temperature T. To a good approximation, we can substitute normal melting temperature Tm for Tt , and we can assume that fus Hm is essentially the same at the two temperature. In above equation, the
Table 2 Solubility (mass fraction, ×104 S) of silybin in aqueous PVP k30 solution, wPVP mass fraction of PVP 100wPVP
0 0.1021 0.2040 0.5008 0.8053 1.004 1.201 1.538 1.997
Solubility T = 293.15 K
T = 298.15 K
T = 303.15 K
T = 308.15 K
T = 313.15 K
0.4244 0.6200 0.7166 0.7851 0.9600 1.000 1.159 1.401 1.877
0.5401 0.7435 0.8026 1.014 1.146 1.251 1.285 1.707 2.231
0.6906 0.9502 1.109 1.201 1.525 1.500 1.605 1.986 2.632
0.8326 1.150 1.288 1.430 1.730 1.808 1.878 2.350 2.958
0.9965 1.425 1.610 1.854 2.009 2.082 2.252 2.685 3.230
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first term on the right hand is much more important than the remaining two terms, and therefore a simplified form of that equation is fus Hm T (3) ln γ1 x1 = − 1− RT Tm If we let γ 1 = 1, we can readily calculate the ideal solubility at temperature T. This ideal solubility depends only on properties of the solute (1); it is independent of the properties of solvent. fus Hm 1 1 id ln x1 = − (4) R Tm T By the data of fus Hm and Tm in Table 1, the value of x1id at 298.15 K is evaluated, x1id = 0.00467. Converting the x1id value into mass fraction, we have Sid = 0.1251. This value is much higher than the actual experiment data (0.5401 × 10−4 ). It reveals that for real solution, the effect of solute–solvent interaction, which is represented by γ 1 , must be considered. Dissolution process is occurred in experimental temperature T, which is not in Tm . The heat of dissolution, sol Hm , is connected with fus Hm by Eq. (5). Tm ¯ p dT sol Hm = fus Hm − C (5) T
¯p where T¯ is the mean value of experimental temperature and C is the mean value of heat capacity in the temperature range from T¯ to Tm . Within the experimental accuracy, the second term in Eq. (5) can be neglected. In general, solubility of drug is expressed in mass fraction (S). Silybin is a hydrophobic solute. The measured solubility (in Table 2) is very small. At very low solute concentrations, all concentration units become collinear with one another. Then we have M3+2 ≈ M3 , S × M3 /M1 1 and x2 = S × M3 /M1 , where M3 and M1 are molecular weights of water and silybin, respectively. By combining Eqs. (3) and (5), we have M1 1 fus Hm 1 − ln γ1 + ln − ln S = − R T Tm M3 =−
sol Hm +C RT
(6)
189
The enthalpy of solution (sol Hm ) is related to fus Hm and [∂ln γ 1 /∂(1/T)], and can be evaluated from the slopes of the Van’t Hoff plots by using Eq. (6). Parameter C is independent of temperature. On considering the transfer Gibbs free energy (tr G), enthalpy (tr H) and entropy (tr S) for silybin from pure water (3) to aqueous PVP solution (2 + 3), we have S(2 + 3) tr G = −RT ln (7) S(3) tr H = sol Hm (2 + 3) − sol Hm (3) tr S =
(8)
tr H − tr G T
(9)
where S(2 + 3) and S(3) are the solubilities of drug in aqueous PVP solution and water, respectively. sol Hm (2 + 3) and sol Hm (3) are the molar enthalpies of solution of silybin in aqueous PVP solution and water, respectively. 3.3. Heat of solution and transfer properties At fixed PVP concentration, the plots of ln S versus 1/T are approximately linear. The enthalpy of solution (sol Hm ) can be calculated from the slopes of Eq. (6). The values of sol Hm are presented in Table 3. The endothermic enthalpy of solution further explains the increase in solubility with temperature. With the increase in PVP concentration, sol Hm decreases, which leads to the solubility increase. The transfer entropy (tr S) of silybin from water to aqueous PVP solution can be calculated from Eq. (9). The values of tr H and tr G are calculated by Eqs. (7) and (8), respectively. The values of tr S are presented in Table 3. The comparison of enthalpy and entropy effect is shown in Fig. 2. Two characteristics can be found in Fig. 2. First, the temperature effect: for T tr S, the temperature effect is small. Second, the concentration effect: with the increase in PVP concentration, tr H decreases within a negative region; the T tr S term increases slightly in a positive region firstly, and then decreases to a negative region. In Fig. 2, the tr H term drops more rapidly than the T tr S term does. This phenomenon is an indication that, with the increase in PVP concentration, enthalpy effect causes drug dissolution to be more favorable, but the entropy effect leads to
Table 3 Enthalpy of solution of silybin (sol Hm ) and transfer entropy (tr S) for silybin from water to aqueous PVP solution 100wPVP
0 0.1021 0.204 0.5008 0.8053 1.004 1.201 1.538 1.997
sol Hm (kJ mol−1 )
32.7 32.1 31.9 31.5 28.9 28.0 26.1 24.8 20.9
tr S (J mol−1 ) T = 293.15 K
T = 298.15 K
T = 303.15 K
T = 308.15 K
T = 313.15 K
0.93 1.70 0.92 −6.24 −8.80 −14.3 −17.1 −27.8
0.48 0.68 1.11 −6.56 −8.68 −15.1 −17.0 −27.7
0.51 1.37 0.54 −6.02 −8.96 −14.9 −17.4 −27.7
0.57 1.10 0.51 −6.32 −8.71 −14.8 −17.1 −27.7
0.90 1.50 1.23 −6.37 −8.79 −14.4 −17.1 −27.8
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Table 5 Interaction parameters of modified UNIQUAC model, standard deviation (σ a ) and correlation coefficient (R) Parameter
Binary system silybin (1) + water (3)
Ternary system silybin (1) + PVP (2) + water (3)
σ R u13 (K) u11 (K) u33 (K) u22 (K) u12a (K) u12b (K) u12c (K) u23a (K) u23b (K)
0.027 0.9985 1.269 120.2 −221.1
0.078 0.9939 1.269 120.2 −221.1 −753.0 −105.2 −1859 × 102 1310 × 104 1329 −2032 × 102
1/2
Fig. 2. Transfer enthalpy (tr H, ) and entropy (T tr S) at T = () 293.15, (䊉) 298.15, () 303.15, () 308.15 and () 313.15 K, for silybin from water to PVP + water solution as a function of mass fraction of PVP (wPVP ).
σ = { j [104 Sj − 104 Sjmodel ] /(n − p)} , where n is the total number of experimental data and p is the total number of adjustable parameters used in the fitting.
the dissolution to be difficult, since tr H is more negative than T tr S.
parameter τ 13 plays in curve fitting is to adjust the intercept of the curve ln γ1res as a function of 1/T. To obtain parameters u13 , u11 and u33 , the solubility data of water in silybin solvent are needed, but this is difficult. Therefore, for the convenience of data fitting, τ 13 is assumed to be evaluated by τ13 = exp[−(u13 − u33 )/T0 ], where T0 is a reference temperature, here it is 293.15 K. By using a nonlinear least-squares fitting technique based on the Levenberg–Marquardt algorithm, which is performed by software of Origin 6.1 (OriginLab Corporation), the fitting results were obtained and presented in Table 5. For a ternary system, other parameters, such as u12 , u22 and u23 , should be regressed from ternary solubility data. But the fitting result is not satisfying. The standard deviation (σ) and the correlation coefficient (R) are 0.17 and 0.9665, respectively. Larsen et al. [17] had proposed a modified equation for the temperature dependence of interaction parameters. If we suppose the temperature effect on u23 is described by a linear dependence equation, and applying this modification to correlate the
3.4. Activity coefficient by UNIQUAC To correlate drug solubility, an important procedure is to calculate the activity coefficient of drug in aqueous solution. By the UNIQUAC model, the activity coefficient is composed of two parts, the combinatorial, γ1com , and residual part, γ1res . ln γ1 = ln γ1com + ln γ1res
(10)
In calculating γ1com , group parameters Rk and Qk are obtained from literature [15]. Parameters ri and qi for silybin and PVP are listed in Table 4. In Eq. (10), the term of ln γ1res is usually introduced to account for the contribution from molecule interaction. By UNIQUAC model, the term of ln γ1res is calculated by
θj τij
(11) ln γ1res = qi 1 − ln θj τji − k θk τkj j
a
exp
2
j
where
uji − uii τji = exp − T
(12)
and uij = uji . Parameters uji and uii can be obtained by fitting experimental solubility data via Eq. (3). For binary system of silybin dissolves in water, solubility were located within the infinite dilution region, the role of Table 4 UNIQUAC parameters Component
ri
qi
Silybin (1) PVP monomer unit (2) Water (3)
16.6032 4.2012 0.9200
12.384 3.124 1.400
Fig. 3. Mass fraction solubility (S) of silybin in aqueous PVP solution. xPVP , Mole fraction of PVP. Experimental: T = () 293.15, (䊉) 298.15, () 303.15, () 308.15 and () 313.15 K. Lines (—), modified UNIQUAC correlation.
H.-L. Zhang et al. / Fluid Phase Equilibria 238 (2005) 186–192
solubility data, then we have the fitting result of σ = 0.14 and R = 0.9758, respectively. To improve the fitting result, modification on UNIQUAC was introduced. In view of the interaction between solute and solvent is more complex with the addition of PVP, it was supposed that the interaction parameter (uij ) is concentration dependent. In this work, silybin’s concentration is supposed at infinite dilution. Therefore, uij is dependent on the ratio of PVP and water. Then we have uij = uija + (uijb + uijc θ2 )θ3 θ2
(13)
where uija , uijb and uijc are concentration effect parameters. Applying this modification to correlate the solubility data, the fitting result was improved significantly (σ = 0.078 and R = 0.9939), and graphically shown in Fig. 3. The interaction parameters and concentration effect parameters are listed in Table 5. 4. Conclusion The solubility of silybin is increased with the increase in both PVP’s concentration and temperature. At fixed PVP concentration, the enthalpy of solution, sol Hm , can be calculated from the slopes of the Van’t Hoff plots. The results of transfer enthalpy and entropy for silybin from water to aqueous PVP solution reveals that, with the increase in PVP’s concentration, the enthalpy effect causes drug dissolution to be more favorable, but the entropy effect causes the dissolution to be difficult. A modified UNIQUAC model was used to correlate drug solubility. By introducing concentration effect parameters, the model gives good quality correlation. List of symbols A UV spectra absorbance Cp heat capacity at constant pressure tr G transfer Gibbs free energy for silybin from water to aqueous PVP solution tr H transfer enthalpy for silybin from water to aqueous PVP solution fus Hm the molar enthalpy of fusion sol Hm enthalpy of solution li parameter in UNIQUAC model, li = (z/2)(ri − qi ) − (ri − 1) M mole weight (g mol−1 ) qi molecular surface area parameter for component i Qk surface area parameter for group k ri molecular volume parameter for component i R correlation coefficient Rk volume parameter for group k S solubility of silybin in mass fraction tr S transfer entropy for silybin from water to aqueous PVP solution T temperature (K) Tm melting temperature (K) Tt triple-point temperature (K) T0 reference temperature (K)
191
uija , uijb , uijc concentration effect parameters for modifying UNIQUAC parameter uji uji interaction parameters of UNIQUAC model xi mole fraction of component i Greek letters Φi volumetric fraction for component i γi activity coefficient of component i γ com the combinatorial term of activity coefficient γ res the residual term of activity coefficient νki the number of groups of type k in molecule i θi surface area fraction for component i σ standard deviation τ ji Boltzmann factor in UNIQUAC model Subscripts 1 silybin 2 PVP 3 water References [1] P. Kallinteri, S.G. Antimisiaris, Solubility of drugs in the presence of gelatin: effect of drug lipophilicity and degree of ionization, Int. J. Pharm. 221 (2001) 219–226. [2] H. Viernstein, P. Weiss-Greiler, P. Wolschann, Solubility enhancement of low soluble biologically active compounds—temperature and cosolvent dependent inclusion complexation, Int. J. Pharm. 256 (2003) 85– 94. [3] S. Verheyen, N. Blaton, R. Kinget, G. Van den Mooter, Mechanism of increased dissolution of diazepam and temazepam from polyethylene glycol 6000 solid dispersions, Int. J. Pharm. 249 (2002) 45–58. [4] J. Jinno, D.M. Oh, J.R. Crison, G.L. Amidon, Dissolution of ionisable water-insoluble drugs: the combined effect of pH and surfactant, J. Pharm. Sci. 89 (2000) 268–274. [5] F. Kvasnicka, B. Biba, R. Sevcik, M. Voldrich, J. Kratka, Analysis of the active components of silymarin, J. Chromatogr. A 990 (2003) 239– 245. [6] F.-Q. Li, J.-H. Hu, Y.-Y. Jiang, Preparation and characterization of solid dispersions of silymarin with polyethylene glycol 6000, J. Chin. Pharm. Sci. 12 (2) (2003) 76–81. [7] F. Damian, N. Blaton, L. Naesens, J. Balzarini, R. Kinget, P. Augustijns, G. Van den Mooter, Physicochemical characterization of solid dispersions of the antiviral agent UC-781 with polyethylene glycol 6000 and Gelucire 44/14, Eur. J. Pharm. Sci. 10 (2000) 311–322. [8] A. Jouyban-Gharamaleki, W.E. Acree Jr., Comparison of models for describing multiple peaks in solubility profiles, Int. J. Pharm. 167 (1998) 177–182. [9] G. Reinwald, I. Zimmermann, A combined calorimetric and semiempirical quantum chemical approach to describe the solution thermodynamics of drugs, J. Pharm. Sci. 87 (1998) 745–750. [10] A. Jouyban-Gharamaleki, L. Valaee, M. Barzegar-Jalali, B.J. Clark, W.E. Acree Jr., Comparison of various cosolvency models for calculating solute solubility in water–cosolvent mixtures, Int. J. Pharm. 177 (1999) 93–101. [11] A. Jouyban-Gharamaleki, P. York, M. Hanna, B.J. Clark, Solubility prediction of salmeterol xinafoate in water–dioxane mixtures, Int. J. Pharm. 216 (2001) 33–41. [12] E. Ruckenstein, I. Shulgin, Solubility of drugs in aqueous solutions. Part 1. Ideal mixed solvent approximation, Int. J. Pharm. 258 (2003) 193–201. [13] E. Ruckenstein, I. Shulgin, Solubility of drugs in aqueous solutions. Part 2. Binary nonideal mixed solvent, Int. J. Pharm. 260 (2003) 283–291.
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