Document Type: Research Paper
Author
Department of Pharmaceutics, Shri Bhagwan College of Pharmacy, N6, CIDCO, Auranagabad431003, India
Abstract
Keywords
1. Introduction
Solubility data on drugs and pharmaceutical adjuncts in mixed solvents have wide applications in the drug sciences. Knowledge of interaction forces between solutes and solvents are of considerable theoretical and practical interest throughout the physical and biological sciences [1]. The theory of solution is one of the most challenging branches of physical chemistry. The HildebrandScatchard theory of regular solution is the pioneer approach in this field, used to estimate solubility only for relatively nonpolar drugs in nonpolar solvents [2]. An irregular solution is one in which selfassociation of solute or solvent, solvation of the solute by the solvent molecules, or complexation of two or more solute species are involved [3]. Polar systems exhibit irregular solution behaviour and are commonly encountered in pharmacy. Extended Hildebrand Solubility Approach (EHSA), modification of the HildebrandScatchard equation, permits calculation of the solubility of polar and non polar solutes in solvents ranging from non polar hydrocarbons to highly polar solvents such as water, ethanol, and glycols [4]. The solubility parameters of solute and solvent were introduced to explain the behavior of regular and irregular solutions [5]. EHSA has been developed to reproduce the solubility of drugs and other solids in the binary solvent systems [6].
The HildebrandScatchard Equation for the solubility of crystalline solids in a regular solution may be written as [7]:
The Extended Hildebrand Equation for the solubility of solids in an irregular solution may be written as [8]:
In pharmaceutical solutions, the geometric mean of δ12and δ22, that is δ1δ2= (δ,is too restrictive and ordinarily provides a poor fit to experimental data in irregular solutions. The assumption that the geometric mean of two geometric parameters δ(Eq.1) can be replaced by a less restrictive term 1 W(Eq. 2), interaction energy parameter, which is allowed to take on values as required to yield correct mole fraction solubilities X as [9],
K is the proportionality factor relating ‘W’ to the geometric mean of solubility parameter. In equation 1 and 2, X_{2} and X_{2}^{i} are the mole fraction solubility and ideal mole fraction solubility of the solute respectively. The terms δ_{1} and δ_{2} are the solubility parameters for the solvent and solute, respectively. The geometric mean, δ_{1}δ_{2}, provides a reasonable estimate of solvent solute interaction in regular (ordinarily nonpolar) mixtures, whereas W or Kδ_{1}δ_{2} is required to express solubility’s in nonregular systems (irregular solutions) of drugs in associating mixed solvents.
The term negative logarithm of the ideal solubility (–log X_{2}^{i}) can be taken as [10]
Where, ΔH_{f} is heat of fusion of the crystalline drug molecule, T0 is the melting point of solute in absolute degrees.
The term A in equations 1 and 2 is defined as [11]:
From the geometric mean:
Where, V_{2} is the molar volume of the solute
as a hypothetical supercooled liquid at solution temperature, R is the universal gas constant, T is the absolute temperature, 298.2 °K, of the experiment and Φ_{1}, the volume fraction of the
solvent, is [12]:
Where, V_{1} is the molar volume of the solvent
at 25 °C.
The term logarithmic solute activity coefficient (log γ_{2}) from Eq. 2 and Eq. 5 can
be written as [13],
A better approach is not to restrict the interaction term ‘W’ to a geometric mean but rather to evaluate it experimentally from the solubility of the solute in various solvent concentrations in a binary mixture employing Eq. 2. An empirical equation for ‘W’ as a function of solubility parameters of the solvent mixture remains to be discovered. Then, backcalculating ‘W’ and substituting into Eq. 2 permit the mole fraction solubility of a drug (solute) to be predicted in essentially any solvent mixture. Therefore, the present investigation pertains to the utility of EHSA in relation to the satranidazole solubility in waterPEG 400 binary solvent mixtures.
2. Materials and methods
2.1. Materials
Satranidazole was obtained as a gift sample from Alkem Laboratories Ltd., Baddi, India, and was purified by recrystallization process. The solvent used for recrystallization of Satranidazole was acetone. Polyethylene Glycol 400 and acetone were purchased from Research Laboratory; Mumbai, India and Qualigens Fine Chemicals, Mumbai, India, respectively. Freshly prepared double distilled water was used for experimental purpose throughout the study. All chemicals and reagents used in the study were of analytical grade and used as such. Double beam UV/Vis spectrophotometer, Shimadzu model 1601 with spectral bandwidth of 2 nm, wavelength accuracy ±0.5 nm and a pair of 10 mm matched quartz cells was used to measure absorbance of the resulting solutions. Citizen balance, CX100, was used for weighing of Satranidazole. Differential Scanning Calorimeter, Shimadzu TA60 WS, was used for determination of melting point and heat of fusion of satranidazole.
2.2. Methods
2.2.1. Solubility measurements
The solubility of satranidazole was determined in binary solvent mixtures of water and PEG 400. Double distilled water was used to prepare mixtures with PEG 400 in concentrations of 0100% by volume of PEG 400. About 10 ml of PEG 400, water, or binary solvent blends were introduced into screwcapped vials containing an excess amount of satranidazole. After being sealed with several turns of electrical tape, the vials were submerged in water at 25±0.4 °C and were shaken at 150 rpm for 24 h in a constanttemperature bath. Preliminary studies showed that this time period was sufficient to ensure saturation at 25 °C [14].
Figure 1. Mole fraction solubility of satranidazole in water, PEG 400, and waterPEG 400 mixtures at 25±0.4 °C.Key: (♦) represents experimental solubilities in waterPEG 400 binary solvent system and () backcalculated solubilities from Extended Hildebrand Eq. 2.
Table 1.Molar observed solubility and validation parameters of satranidazole in waterPEG 400 mixtures.








Water: PEG 400 
Solubility 
δ_{1} 

Density 
Mol. Wt 


(%v/v) 
(g/ml) 
(Cal/cm^{3})^{0.5} 
V_{1} 
of blend 
of blend 
^{X}2( obs) 
^{W}(obs) 
100:0 
0.0004700 
23.40 
18.00 
0.9980 
18.00 
2.9322E05 
330.18 
90:10 
0.0004484 
22.19 
68.70 
1.0110 
56.20 
8.6193E05 
303.96 
80:20 
0.0005207 
20.98 
119.40 
1.0240 
94.40 
1.6599E04 
278.66 
70:30 
0.0005930 
19.77 
170.10 
1.0370 
132.60 
2.6221E04 
254.58 
60:40 
0.0006725 
18.56 
220.80 
1.0500 
170.80 
3.7830E04 
231.85 
50:50 
0.0008895 
17.35 
271.50 
1.0630 
209.00 
6.0473E04 
210.72 
40:60 
0.0015186 
16.14 
322.20 
1.0760 
247.20 
1.2064E03 
191.32 
30:70 
0.0026395 
14.93 
372.90 
1.0890 
285.40 
2.3915E03 
173.38 
20:80 
0.0059660 
13.72 
423.60 
1.1020 
323.60 
6.0526E03 
157.21 
10:90 
0.0076654 
12.51 
474.30 
1.1150 
361.80 
8.5840E03 
141.78 
0:100 
0.0088224 
11.30 
525.00 
1.1280 
400.00 
1.0783E02 
127.67 
δ_{1}=Solubility parameter of solvent blend, V_{1}=molar volume of the solvent blend
After equilibration, the solutions were microfiltered (0.45 µm) and the filtrate was then diluted with double distilled water to carry out the spectrophotometric determination at the maximum wavelength of absorption of the satranidazole (λ_{max}319.80 nm). The solubility of the satranidazole was determined at least three times for this solvent mixture, and the average value was taken. The densities of the solvent mixtures and the filtrates of the saturated solutions of satranidazole were determined in triplicate at 25±0.4 °C using 10 ml specific gravity bottles. Once the densities of solutions are known, the solubilities can be expressed in mole fraction scale.
The solubility parameters of the solvents were obtained from the literature [15, 16]. The solubility parameter of satranidazole was calculated previously by the method of Fedor [17, 18] which was confirmed by solubility analysis in dioxanewater blend.
Figure 2. Plot of observed interaction energy versus solubility parameter of waterPEG 400 binary mixtures. Quartic expression provides relation between two variables (W obs and δ1), which has been used to back calculate Wcal.
Table 2. Comparison of observed and calculated mole fraction solubility’s of satranidazole in waterPEG 400 mixtures at 25 ±0.4 0C.









^{W}(obs) 
^{W}(cal) 
^{X}2(obs) 
^{X}2(cal) 
logγ_{2}/A_{(obs)} logγ_{2}/A_{(cal)} Residual 
Percent Difference 


330.180117 
330.170282 
2.9322E05 
2.9093E05 
16.931866 
16.951536 
7.7888E03 
7.79E01 
303.955691 
303.985923 
8.6193E05 
8.8290E05 
14.216819 
14.156353 
2.4331E02 
2.43E+00 

278.661628 
278.662736 
1.6599E04 
1.6614E04 
12.569244 
12.567028 
8.8160E04 
8.82E02 

254.582485 
254.538073 
2.6221E04 
2.5312E04 
11.420030 
11.508854 
3.4694E02 
3.47E+00 

231.853422 
231.854413 
3.7830E04 
3.7860E04 
10.498855 
10.496874 
7.8763E04 
7.88E02 

210.716801 
210.759363 
6.0473E04 
6.2553E04 
9.320999 
9.235875 
3.4407E02 
3.44E+00 

191.321541 
191.305657 
1.2064E03 
1.1913E03 
7.588618 
7.620387 
1.2537E02 
1.25E+00 

173.382081 
173.451155 
2.3915E03 
2.5262E03 
5.872838 
5.734689 
5.6320E02 
5.63E+00 

157.212832 
157.058847 
6.0526E03 
5.3591E03 
3.544835 
3.852806 
1.1458E01 
1.15E+01 

141.783405 
141.896847 
8.5840E03 
9.3876E03 
2.665390 
2.438505 
9.3613E02 
9.36E+00 

127.666283 
127.638398 
1.0783E02 
1.0549E02 
2.089535 
2.145303 
2.1731E02 
2.17E+00 
Calculation of interaction energy and mole fraction solubilities were obtained with the help of Eq. 2 and 10 as described in the text.
2.2.2. Differential scanning calorimetry
The thermogram of satranidazole was obtained with a differential scanning calorimeter [19]. The melting point and heat of fusion were measured. Sample of 8.8 mg in perforated pan was heated at a rate of 15 °C/min. under nitrogen purge. The temperature range studied was 25225 degrees.
3. Results and discussion
3.1. Mole fraction solubility and solubility parameter
The molar enthalpy of fusion of satranidazole was 112.30 J/g (7763.838 cal/mol) and the temperature of fusion is 461.83 °K. Neither decomposition nor polymorphic change was observed at the experimental temperature range. The ideal mole fraction solubility of satranidazole was calculated from these values (–logX_{2}^{i}=1.60974602). The mole fraction solubilities of satranidazole at 25±0.4 °C in waterPEG 400 binary mixtures which cover a large range of the solubility parameter scale, from 11.30 to 23.40 (Cal/cm^{3})0.5, are listed in Table 1. The experimental mole fraction solubility of satranidazole at 25±0.4 °C in waterPEG 400 mixtures is plotted in Figure 1 versus the solubility parameter, δ_{1}, of the various mixed solvent systems. The mole fraction solubility of satranidazole (δ_{2}=11.30) in pure PEG 400 (δ_{2}=11.30), pure water (δ_{1}=23.4), and in the mixture of the twosolvents is represented by the solid circles in Figure 1. The maximum solubility of satranidazole in the mixture is X_{2}=0.010783 mol/ lit and occurs at δ_{1}=11.30. This value is well below the ideal solubility, X_{2}^{i}=0.0245614 mol/lit, as predicted from regular solution theory. The discrepancy between the results using the original HildebrandScatchard equation and experimental points demonstrates that Eq 1a and 1b cannot be used to predict drug solubility in waterPEG 400 binary solvent systems. This behavior has been dealt with the theoretical replacement of mean geometric solubility parameters (δ_{1}δ_{2}) term with the interaction energy term (W).
Figure 3. Relationship of observed and calculated mole fraction solubility of satranidazole. Comparison of 11 observed satranidazole solubilities in waterPEG 400 systems at 25±0.4 °C with solubilities predicted by extended Hildebrand approach.
3.2. Solubility prediction using regression of W versus δ_{1}
Equation 2, differing from Equation 1 in that the geometric mean is not used provides an accurate prediction of solubility once ‘W’ is obtained. Although ‘W’ presently cannot be estimated based on fundamental physicochemical properties of the solute and solvent, ‘W’ may be regressed against a polynomial in δ1 of the water PEG 400 binary solvent mixtures (Figure 2). The following quadratic, cubic, and quartic equations were obtained using the experimental solubility data for satranidazole in waterPEG 400 mixtures:
W = 69.77056 – 0.45826 δ 
1 
+ 0.49572 δ 
2 


cal 


1 



(n=11, R^{2}= 0.9999847) 

(Eq.8) 


W 
=72.149470.89558 δ +0.52168 δ 
^{2}  0.00050 δ ^{3} 


cal 
1 

1 

1 

(n=11, R^{2}= 0.9999848) 

(Eq.9) 


W_{cal}=74.92073+35.28771 δ_{1}2.74156 δ_{1}^{2}+0.12749 


δ130.00185 δ14 






(n=11, R^{2}= 0.9999989) 

(Eq.10) 

The ‘W’ values calculated using these expressions compared favorably with the original ‘W’ values computed using Eq. 2. The solid line plotted in Figure 1 was obtained employing the quartic expression (Eq.10). This calculated solubility curve fits the experimental data points quite well (Figures 1 and 3), predicting the solubility of satranidazole in waterPEG 400 mixtures at most points within an error of ~2.17%, a value approximating the error in experimentally determined solubility values. These polynomials are used successfully for the calculation of ‘W’, at any value of solubility parameter (δ_{1}), which was
subsequently employed to calculate mole fraction solubility of solute (X_{2cal}) in a solvent blend using backward regression. Representative data along with validation parameters are summarized in Table 1. Wcal values are indicating significant interaction of satranidazole and solvent molecules at the peak of solubility profile.
Validation of Eq. 10 was done by comparing experimentally obtained and calculated values of mole fraction solubility by estimating residuals and percent difference (Table 2). The predictive capability of the model for satranidazole is represented in Figure 3, which indicates a very high degree of correlation coefficient (R^{2}) 0.992 and negligible intercept (0.00003) equal to zero.
4. Conclusion
The Extended Hildebrand Approach to solubility employs a power series(quartic) equation in δ_{1} to backcalculate ‘W’, which reproduces the solubility of satranidazole in waterPEG 400 mixtures within the accuracy ordinarily achieved in experimental solubility results.
On the basis of validation parameters, it can be expressed that the behavior of non regular solution can be quantified more precisely using EHSA. The procedure can be explored further to predict the solubility of satranidazole in pure water or PEG 400 and in any waterPEG 400 mixtures.Simultaneously, this tool may become useful in optimization problems of clear solution formulations. Thus the method has potential usefulness in preformulation and formulation studies during which solubility prediction is important for drug design.
Acknowledgement
The author wishes to express his gratitude to M/S Alkem Laboratories Limited, Baddi for providing gift sample of Satranidazole.