The values of (ΔHd) and (ΔSd) for (R, S)-(±)-sodium ibuprofen dihydrate are summarized in Table II for qualitative comparisons. The positive values of ΔHd in Table II indicate that the energy of attraction of (R, S)-(±)-sodium ibuprofen dihydrate with each other, and the energy of attraction of the solvent molecules with each other were
lower than the energy of attraction of (R, S)-(±)-sodium ibuprofen dihydrate and the solvent molecules in the solution. Heat was absorbed to make (R, S)-(±)-sodium ibuprofen dihydrate dissolve in the solvent. The solubility of (R, S)-(±)-sodium ibuprofen dihydrate increased with temperature. The positive values of (ΔSd) in Table II show that (R, S)-(±)-sodium ibuprofen dihydrate-solvent systems became less ordered as (R, S)-(±)-sodium ibuprofen dihydrate dissolved into the solution. The entropy gain of the whole system was the main driving force
Table II: Total Hildebrand values for solvents at 25 8C versus enthalpies and entropies of solution of (R, S)-(6)-sodium
Because of the symmetrical nature of the solvent miscibility table (see Table III), the number of boxes was divided by 2,
except for the diagonal boxes (13). Based on the solvent miscibility studies of the solvent pairs of the 23 solvents, 36 gray
boxes were divided by 2 to give 18 immiscible pairs in total (see Table III). The form space (i.e,. a possible location for discovering a new polymorph) of the pure-solvent systems for the initial solvent-screening was limited
to the number of good pure solvents (repesented by the yellow boxes). The form space for (R, S)-(±)-sodium ibuprofen dihydrate was 9. However, if the good cosolvent systems (i.e., binary miscible mixtures of good solvents) were taken into account, the form space would be extended to the total number
of blue boxes in the solvent miscibility table divided by 2 (see Table III), which was equal to 36. In addition, if the antisolvent
systems (i.e., binary miscible mixtures of a good and a bad solvent) also were considered, the form space of the antisolvent systems was
calculated as the number of green boxes in the solvent miscibility table divided by 2 (see Table III); this value was 109.
Table III. Solvent miscibility table, cosolvent, and antisolvent systems of (R,S)-(6)-sodium ibuprofen dihydrate.
Consequently, the total form space should then be at least equal to 9 + 36 + 109 =154. The total form space is expected to
expand dramatically if various solvent compositions of binary mixtures, temperatures, and ternary solvent systems also are
considered. Solid generation by temperature cooling only was applied in the yellow regions, yet the same crystallization mode
could be applied to the blue regions in the solvent-miscibility table (see Table III). For the green regions (see Table III),
solid generation is achieved isothermally by adding an antisolvent. Generally, no attempts are made for solid generation in
the regions of immiscible solvent pairs (represented by the purple boxes), bad solvents (represented by the red boxes), and
cosolvents of bad solvents (i.e., binary mixture of miscible bad solvents) (represented by the white boxes) in the solvent miscibility table (see Table III).
References of other miscible solvents pairs from organic solvents other than the 23 solvents listed in Table III are available
in the literature (19, 20).