Hansen parameters fine-tune the total Hildebrand value (δt) into three contributions: a dispersion-force component (δd); a polar component (δp); and a hydrogen-bonding component (δh) (15) as expressed in the following equation:
Dispersion forces are the induced attractions by the random polarities of two molecules in proximity. They are called London dispersion forces or induced dipole-induced dipole forces, and the number of temporary dipoles increases with the molecule's size. Polar forces are created when electrons are unequally
shared between the individual atoms in a molecule. The charge distribution is related to the atomic composition, geometry,
and size of a molecule. When polar molecules arrange themselves head-to-tail and positive-to-negative, the molecular network
leads to a further increase in intermolecular interaction. These temperature-dependent dipole–dipole forces collectively create
the Keesom orientation effect. A particularly strong type of polar interaction occurs when hydrogen's sole electron is drawn
toward such electronegative atoms as oxygen, nitrogen, and fluorine, leaving the positively charged hydrogen nucleus exposed.
The exposed positive nucleus exerts a considerable attraction on electrons in other molecules, forming a proton bridge, which
is called hydrogen bonding.
Materials and methods
Solvents. Table I lists the 23 solvents from five different classes in the ascending order of Hildebrand parameters (13). Two other
solvents n-propanol (CH3(CH2)2OH, ACS grade, 99.98%, boiling point of 97 °C, molecular weight of 60.1 g/mole, Lot 909065 Tedia Company, Fairfield, NJ)
and cyclohexane (C6H12, ACS grade, 99.9%, boiling point of 80.7 °C, molecular weight of 84.16 g/mol, Lot k24470166, Merck KGaA, Darmstadt, Germany)
were used to verify the solubility sphere in the three-dimensional (3-D) Hansen plot.
Table I: Total Hildebrand value and Hansen parameters for solvents at 25 8C.
Active pharmaceutical ingredient. Ibuprofen sodium salt (C13H17NaO2, molecular weight of 228.29 g/mol, batch number 015K0586) purchased from Sigma-Aldrich Corporation (St. Louis, MO) was a
dihydrate of racemic (R, S)-(±)-sodium 2-(4-isobutylphenyl) propionate with a molecular formula of C13H17NaO2•2H2O and a molecular weight of 264.29 g/mol. The amount of the stoichiometric water was determined by the thermogravimetric-use
test showing about 13% water loss by weight near the boiling point of water (see Figure 2).