A crossover of the solid substances solubility in supercritical fluids: What is it in fact?

We investigate a well-known phenomenon of the appearance of the crossover points, corresponding to the intersections of the solubility isotherms of the solid compound in supercritical fluid. Opposed to the accepted understanding of the existence of two fixed crossover points, which confine the region of the inverse isobaric temperature dependence of the solubility, we have found that these points tend to shift with the change of the temperature and in the limit of the certain threshold value they converge to a single point. We demonstrate this analyzing the solubility data of a set of poorly soluble drug compounds, which have been computed in a wide area of the phase diagram via the approach, based on the classical density functional theory. Thorough analysis of the available in the literature experimental solubility data is found to be in an agreement with our conclusions, as one can find that the wider temperature region of the experimental study is, the more pronounced effect of the crossover points drift can be observed. There is a well-known phenomenon, observed when studying solid compounds’ solubility in supercrtitical fluids, where one can locate the region of the so-called ”retrograde vaporization” (RV), where the increase of the temperature at constant pressure leads to the decrease of the studied compound’s solubility [1, 2, 3]. The boundaries of this region are represented by two points, where all isotherms intersect and the solubility as a function of temperature has extremums, the corresponding pressure values are called the lower and upper crossover pressures [4, 5]. Described phenomenon is rather interesting for practical use, since one can easily adjust the solubility via the change of the state parameters to achieve the appropriate conditions for a number of supercritical procedures, including microand nanonization, cocrystallization, precipitation, extraction, chromatography, etc. [6, 7, 8, 9, 10, 11]. On the other hand, despite its practical importance and fundamental significance, the thorough investigation of the phenomenon of this area appearance is rather limited in literature [2, 3, 4, 5], where the occurrence of the crossover pressure was concluded to be a ∗Corresponding author Preprint submitted to Elsevier April 13, 2021 ar X iv :2 10 4. 04 77 6v 1 [ co nd -m at .s of t] 1 0 A pr 2 02 1 thermodynamic constraint in supercritical mixtures. It is also worth noting that the authors discussed only the upper crossover pressure, as they refer to it as a more important for the applications one. The variety of the experimental studies, devoted to the solubility measurements, also rarely demonstrate the location of the lower crossover pressure, partially for the same reason as mentioned above, but also due to the proximity of the lower point to the solvent critical point. Nevertheless the mentioned studies, describing the modeling of the position of the single point where all isotherms intersect, a careful investigation of the vast number of the available experimental solubility data for different chemical classes of the solutes [12, 13, 14, 15, 16, 17, 18, 19], especially in the cases of the studies demonstrating the broad temperature interval, leads one to the conclusion that either the accuracy of the experimental approaches and following correlation procedures leaves much to be desired, as the upper crossover point location often appears rather ”smeared”, or that in actual fact there is no sole specific point where all isotherms intersect. The fact that the experimental solubility data, depicting the position of the lower crossover pressure point, to our knowledge, is practically absent in literature does not help one to grasp the idea, underlying this inconsistency. In this communication, we share the results of our computational solubility study, which demonstrate that there are no two exact points in the concentration-pressure coordinates where all of the solubility isotherms intersect, allocating the region of the RV behavior. Instead, we observe that the points, corresponding to the temperature extremums of solubility, shift with the temperature change. Moreover, the increase of the temperature leads to the convergence of the lower and upper crossover pressure values to one point at certain temperature, after which the dependence of the solubility on temperature once again becomes direct for any pressure values. The computation of the solubility isotherms was conducted with the help of the developed methodology, based on the solvation free energy calculation via the classical density functional theory (cDFT), the thorough description of which can be found elsewhere [20, 21]. The results of the methodology approbation have shown a satisfactory agreement with the available experimental data for a number of solutes. Here we have obtained data for six poorlysoluble drug compounds of different chemical structure with analgesic, anti-inflammatory, anticonvulsive, antioxidant and neuroprotective properties [22, 23, 24, 25, 26, 27], namely diflunisal, ibuprofen, naproxen, aspirin, carbamazepine and thiadiazole derivative (1-[5-(3chloro-4-methyl-phenylamino)-1,2,4-thiadiazol-3-yl]-propan-2-ol). For each compound we have obtained a set of isotherms, corresponding to the temperatures from 313.15 K to 483.15 K with a step of 10 K, and several auxiliary ones to differentiate the areas where the region of the phenomenological behavior is supposed to vanish. The pressure increment of 5 bar and region from 75 bar to 330 bar allowed us to determine the position of both the upper and lower crossover region boundaries for each solute. We should note that obtained solubility values for each drug compound are in a satisfactory agreement with the available in the literature experimental data, and with the results of the solubility measurements, based on our infrared spectroscopy approach, for the thiadiazole derivative, for which there are no available in literature solubility data (see Appendix for the details of the experimental approach and the thorough comparison).