Date of Submission | May 25, 2010 |

Date of Revision | April 27, 2012 |

Date of Acceptance | May 5, 2012 |

Indian J Pharm Sci, 2012, 74 (3): 254-258 |

## Abstract

The solubility of satranidazole in several water-N,N-dimethylformamide mixtures was analysed in terms of solute-solvent interactions and data were treated on the basis of extended Hildebrand solubility approach. The solubility profile of satranidazole in water-N,N-dimethylformamide mixtures shows a curve with a solubility maxima well above the ideal solubility of drug. This is attributed to solvation of the drug with the water-N,N-dimethylformamide mixture, and indicates that the solute-solvent interaction energy (W) is larger than the geometric mean (δ1δ2 ) of regular solution theory. The new approach provides an accurate prediction of solubility once the interaction energy (W ) is obtained. In this case, the energy term is regressed against a polynomial in δ1 of the binary solvent mixture. A quartic expression of W in terms of solvent solubility parameter was found for predicting the mole fraction solubility of satranidazole in the studied mixtures. The method has potential usefulness in preformulation and formulation studies during which solubility prediction is important for drug design.

## Keywords

Extended Hildebrand solubility approach, N, N‑dimethylformamide, satranidazole, solubility

Extended Hildebrand solubility approach is applied to predict the solubility of satranidazole in mixtures of water and N,N‑dimethylformamide (DMF). DMF is a very interesting cosolvent to study the interrelation between drug solubility and medium polarity because it is aprotic and completely miscible with water [1]. Water‑DMF mixtures are strongly non ideal and can act in the solute‑solvation process via hydrophobic interactions and preferential solvation [2,3]. In terms of polarity, water–DMF mixtures cover a wide range of Hildebrand solubility parameters from 12.1 (pure DMF) to 23.4 (pure water)[4,5].

The extended Hildebrand solubility approach enables us to predict the solubility of semipolar crystalline drugs in irregular solutions involving self‑association and hydrogen bonding in pure solvents or in solvent blends. The key relationship may be written as[6,7]

where W is an interaction term for estimating energy
between solute and solvent for an irregular solution.
This interaction parameter W accurately quantifies the
cohesive energy density between solute and solvent.
When W = δ_{1}δ_{2}, the solution is said to be regular.
W>δ_{1}δ_{2} appears when the blended solvents are able
to hydrogen bond with each other but not with their
own kind. The case of W<δ_{1}δ_{2} occurs when like
molecules associate and unlike molecules do not, such
as for nonpolar media in water. Although W cannot be
theoretically evaluated, it is assumed that when a range
of similar solvents are used for dissolving a fixed solute,
W = K δ_{1}δ_{2}, where K is a proportionality constant [8].

Interaction energy (W) values were evaluated as
a power series in δ_{1} utilizing mixed solvents by
polynomial regression[9‑11]. By using these polynomial
fits, the mole fraction solubility of solutes may
be predicted that is in good agreement with the
experimental values. This procedure may be applied
for calculating solubilities of missing data by
interpolation. When the solvent studied is a mixed
one, there are a series of parameters to be calculated
such as: the solubility parameter, the volume fraction
and the mean molar volume of mixed solvents.

The solubility parameter (δ_{1}) for the mixture of two
solvents DMF and water, W, is averaged in terms of
volume fractions using the expression[12],

where Ф_{1}=Ф_{DMF}+Ф_{W} is the total volume fraction of
two solvents which can be calculated from[13],

(3)

where X_{2} is the mole fraction solubility of the solute
in the mixed solvent and V_{1} is the molar volume of
the binary solvent. For each mixed solvent composed
of water and DMF in various proportions[14]:

Here, X_{i} and M_{i} are the mole fraction and the
molecular weight of the particular solvent in the
mixture, respectively and d_{1} is the density of the
solvent mixture at the experimental temperature.

Satranidazole, 1–methylsulphonyl-3-(1-methyl-5-nitro-
2-imidazolyl)-2-imidazolidinone, is one of the large
series of nitroimidazoles with a potent antiprotozoal
activity against *E. hystolytica*, *T. vaginalis* and *Giardia*.
Satranidazole is not official in IP, USP and BP till
date. Though the molecule is found to be effective
against these microorganisms, its therapeutic efficacy
is hindered due to its poor aqueous solubility (0.01
mg/ml). The poor aqueous solubility and wettability of
satranidazole give rise to difficulties in pharmaceutical
formulations meant for oral or parenteral use, which
may lead to variation in bioavailability[15-18].

As such, no solubility reports are found for its estimation and prediction by any of the method till date. Hence, the aim of this communication is to report the solubility behaviour of satranidazole in individual solvents (water and DMF) and different concentrations of water‑DMF mixtures, predict it theoretically by applying the Extended Hildebrand Solubility Approach.

Satranidazole, obtained as gift sample from Erika Pharmaceuticals, Mumbai, India, was purified by recrystallization process. The solvent used for recrystallization of satranidazole was acetone. DMF and acetone both were obtained as gift samples from Qualigens Fine Chemicals, Mumbai, India.

Throughout the study, double distilled water was used for experimental purpose. 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 were used to measure absorbance of the resulting solutions. Citizen balance, CX‑100, was used for weighing of satranidazole. Differential scanning calorimeter, Shimadzu TA‑60 WS, was used for the determination of melting point and heat of fusion of satranidazole.

Solubilities of satranidazole (δ_{2}=11.34) were
determined in mixed solvent consisting of DMF
(δ_{DMF}=12.1) and water (δ_{W}=23.4). Solvent blends were
made covering 0-100% DMF (v/v). About 25 ml of
DMF, water, or mixed solvents were placed into
screw‑capped vials (Thermostated at 25° and under
continuous magnetic stirring) containing an excess
amount of satranidazole and agitation was maintained
at 150 rpm for 24 h in a constant‑temperature bath.
Preliminary studies showed that this time period was
sufficient to ensure saturation at 25°[19].

After equilibration, the solution was 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 satranidazole
(λ_{max}‑319.80 nm). Calibration graphs of satranidazole
in each solvent blend were previously established
with correlation coefficients greater than 0.9978. The
working concentration range was from 10 to 50 μg/
ml satranidazole. The densities of the blends as well
as the filtrates of saturated solutions were detefrmined
by using 25‑ml specific gravity bottle at 25°. Once
the densities of solutions are known, the solubilities
can be expressed in mole fraction scale.

The molar volume (V_{2}) and the solubility parameter
of satranidazole were previously estimated by using
the Fedor’s group contribution method [20,21] giving
235.6 cm^{3}/mol and 11.3928 (cal/cm^{3})^{0.5}. The ideal
solubility of satranidazole was calculated by using
the equation [22],

where, ΔS_{f} is the entropy of fusion of the crystalline drug molecule at its melting point T_{0} and T is the
temperature in Kelvin at which the solubility was
determined. The value of ΔS_{f} was evaluated by [23],(ΔH_{f}=7763.838 cal/mol, T_{0}=461.83°K) giving
16.811 cal/mol/°K. Thus, the ideal mole fraction
solubility of satranidazole (X_{2}^{
i}) is 0.024561.

The mole fraction solubility of satranidazole in
water‑DMF mixtures and other parameters of interest
(δ_{1}, Φ_{1}, V_{1}) are collected in **Table 1**. The plot of
these experimental solubilities versus the solubility
parameter of mixtures, Δ_{1} is shown in **fig. 1**. The
solubility of satranidazole was far from its ideal value
in both pure solvents (DMF, water) as well as in the
mixtures. The maximum solubility, although higher
than ideal occurred at a δ_{1}=12.10, very close to the
calculated δ_{2} for satranidazole.

ΦDMF | X2(obs) | δ1 | F1 | V1 | δ1δ2 | W(obs) |
---|---|---|---|---|---|---|

0 | 3.8119E‑05 | 23.40 | 0.99950 | 18.00 | 265.36 | 330.51 |

0.1 | 7.5836E‑05 | 22.27 | 0.99925 | 23.90 | 252.54 | 305.57 |

0.2 | 1.3239E‑04 | 21.14 | 0.99895 | 29.80 | 239.73 | 281.74 |

0.3 | 2.1919E‑04 | 20.01 | 0.99856 | 35.70 | 226.91 | 259.12 |

0.4 | 4.2637E‑04 | 18.88 | 0.99759 | 41.60 | 214.10 | 237.97 |

0.5 | 5.9677E‑04 | 17.75 | 0.99705 | 47.50 | 201.29 | 217.70 |

0.6 | 1.4499E‑03 | 16.62 | 0.99363 | 53.40 | 188.47 | 199.38 |

0.7 | 3.7972E‑03 | 15.49 | 0.98508 | 59.30 | 175.66 | 182.42 |

0.8 | 1.4453E‑02 | 14.36 | 0.94967 | 65.20 | 162.84 | 167.23 |

0.9 | 2.3516E‑02 | 13.23 | 0.92610 | 71.10 | 150.03 | 152.32 |

1.0 | 4.3502E‑02 | 12.10 | 0.87784 | 77.00 | 137.22 | 139.00 |

δ_{1}=Solubility parameter of solvent blend, δ_{2}=Solubility parameter of drug,
V_{1}=Molar volume of solvent blend, and Φ_{1}=Total volume fraction of solvent
blend. The values for δ_{1}, Φ_{1} and V_{1} are calculated from Eqs. 2‑4, respectively
and W is calculated from Eq. 1

**Table 1:** Mole fraction solubility of
Satranidazole

Observed solubility data were then subjected to the
evaluation of interaction energy. The interaction term
W can be calculated from Eq.1 at each experimental
point (X_{2}, δ_{1}). The results are also presented in
**Table 1**. Experimental values of interaction energy
(W_{obs}) were regressed against solubility parameter
to obtain W_{cal} (**fig. 2**), which was then used to
back‑calculate the mole fraction solubility (X_{2cal}).
A mathematical model is proposed for individual
system as fourth power polynomial. The W values
may also be expanded in a power series of δ_{1} from
fourth degree polynomial regression.

In our case, the following fit was obtained:

If we insert this equality in Eqn. 1, we can predict
the solubility of satranidazole. The back‑calculated
logarithmic solubilities, log X_{2cal} are recorded in
**Table 2**, together with the experimental values of log
X2 and their differences. The plot of log X_{2cal} against
log X_{2obs} gives a straight line passing through the
origin with very high degree of correlation coefficient
(R^{2}) 0.9912 and negligible intercept (0.00009) equal to
zero as shown in **fig. 3**.

-log X_{(2 obs)} |
-log X_{(2 cal)} |
Residual (∆) |
Percent difference |
|||
---|---|---|---|---|---|---|

4.418857 |
4.434688 |
+0.035796 |
3.58E+00 |
|||

4.120125 |
4.091550 |
‑0.068009 |
‑6.80E+00 |
|||

3.878144 |
3.865188 |
‑0.030281 |
‑3.03E+00 |
|||

3.659178 |
3.671673 |
+0.028360 |
2.84E+00 |
|||

3.370217 |
3.449925 |
+0.167680 |
1.68E+01 |
|||

3.224190 |
3.168771 |
‑0.136110 |
‑1.36E+01 |
|||

2.838657 |
2.808556 |
‑0.071768 |
‑7.18E+00 |
|||

2.420537 |
2.385907 |
‑0.083003 |
‑8.30E+00 |
|||

1.840041 |
1.936473 |
+0.199120 |
1.99E+01 |
|||

1.628638 |
1.577837 |
‑0.124090 |
‑1.24E+01 |
|||

1.361490 |
1.368473 |
+0.015951 |
1.60E+00 |

Residuals obtained from quartic regression Eq. 7, for satranidazole in water‑DMF
mixtures at 25°. Residuals can also be obtained from (X_{2 obs‑}X_{2 cal})/X_{2 obs}

**Table 2:** Experimental and calculated mole
Fraction solubilities

**Figure 3: **Comparison of observed and calculated mole fraction
solubility.
Comparison of 11 observed satranidazole solubilities in water‑DMF
mixtures at 25° with solubilities predicted by the extended
Hildebrand approach. The intercept of the line is 0.00009, and the
slope is 0.9912. The correlation coefficient, r^{2}, is 0.9912 for n = 11.

A careful scrutiny of the behaviour of the solutions
of satranidazole in water‑DMF mixtures may be performed, comparing the value of the interaction
term W at each experimental point with the regular
value W=δ_{1}δ_{2}. This comparison is presented also in
**Table 1**. As can be observed, for volume fractions of
DMF from 0 to 1, W>δ_{1} δ_{2}. But, for volume fractions
of DMF from 0 to 0.5, W is far greater than δ_{1}δ_{2}
and for volume fractions of DMF from 0.6 to 0.9,
W is nearby closer to δ_{1}δ_{2}. It may be assumed that
satranidazole solutions can behave as regular solutions
at some point (W=δ_{1}δ_{2}) with 1.0 DMF volume
fraction.

Thus, in water‑rich mixtures (0-0.5) there seems to be
some kind of association between satranidazole and
the solvent mixture according to W>δ_{1}δ_{2}. This finding
could be explained considering the hydrophobic
hydration (HH). HH is featured by an enhanced
hydrogen bonding between water molecules in the
neighbourhood of nonpolar groups in water. When
adding DMF, HH breaks down. The endothermic shift
of the enthalpies of solution upon small additions of
aprotic cosolvent to water is known to appear for
hydrophobic solutes like satranidazole.

Conversely, in water poor mixtures (0.6-1.0)
self‑association of solvent, solute or both is not
obtained because W is still far greater than δ_{1}δ_{2}.
This behaviour may remain as such in rich DMF
blends, and therefore, the corresponding satranidazole
solubilities are still higher than regular one.

The extended Hildebrand approach applied to
the solubility data of satranidazole in water‑DMF
mixtures leads to an expansion of the W interaction
term as a fourth degree power series in δ_{1} which
reproduces the satranidazole solubility within the accuracy ordinarily achieved in such measurements.
The procedure can be used to predict the solubility
of satranidazole in pure water or DMF and in any
water‑DMF mixtures.

## Acknowledgements

The authors wish to express their gratitude to M/S Erika Pharmaceuticals, Mumbai, India for providing the gift sample of satranidazole. The authors are also thankful to Qualigens Fine Chemicals, Mumbai, India for providing the gift sample of DMF and Acetone.

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