Representing solute solubility in supercritical carbon dioxide: A novel empirical model

A comprehensive study of pharmaceutics solubility in supercritical solvent through diverse thermodynamic and hybrid Machine learning approaches

The pharmaceutical industry is increasingly drawn to the research of innovative drug delivery systems through the use of supercritical CO2 (scCO2)-based techniques. Measuring the solubility of drugs in scCO2 at varying conditions is a crucial parameter in this context. In this research, the supercritical solubility of two pharmaceutical ingredients, namely Febuxostat and Chlorpromazine, has been assessed theoretically using various thermodynamic approaches, including PR, SRK, UNIQUAC, and Wilson models. Additionally, hybrid machine learning models of PO-GPR, and PO-KNN were applied to anticipate the supercritical solubility of these medicines. Verification of the accuracy of each model for each pharmaceutical substance is conducted against previously reported experimental solubility data. In the comparison between the SRK and PR models, it is observed that the SRK model displays greater precision in correlating the solubility of both drugs. It consistently achieves a mean Radj value of 0.995 across all cases and mean AARD% values of 14.47 and 9.30 for Febuxostat and Chlorpromazine, respectively. Furthermore, the findings indicate that the UNIQUAC model surpasses the Wilson model in precisely representing the solubility of both medicines. It consistently achieves a mean Radj value higher than 0.985 across both cases and mean AARD% values of 11.39 and 7.08 for Febuxostat and Chlorpromazine, respectively. Additionally, the performance of both hybrid machine learning models proved to be excellent in anticipating the supercritical solubility of both compounds.

Determination of morphine sulfate anti-pain drug solubility in supercritical CO2 with machine learning method

Accurate solute solubility measuring and modeling in supercritical carbon dioxide (ScCO2) would address the best working conditions and thermodynamic boundaries for material processing with this type of fluid. Theory- and data-driven methods are two general modeling approaches. Using theory-driven methods, the solubility is estimated based on the principles of thermodynamics, while data-driven methods are developed by training the algorithms. Despite acceptance of each of these methods, more experimental solubility data are still needed to promote modeling performances. In this study, for the first time, solubility of morphine sulfate is determined and modeled by a set of 13 semi-empirical (theory-driven) and random forest (data-driven) models. Using a laboratory system with an ultraviolet-visible (UV-Vis) spectroscopy, the experimental solubilities including 48 data points were obtained at different temperatures (308-338 K) and pressures (12-27 MPa). The minimum (0.806 × 10-5) and maximum (5.902 × 10-5) equilibrium mole fractions were observed at working pressures of 12 and 27 MPa, respectively, both at the same temperature of 338 K. It was indicated that random forest model (with AARD% of 1.29%) had an excellent predictive performance against semi-empirical models (with AARD% from 9.33 to 19.76%). The results showed that solute molecular weight had the highest effect on random forest modeling. Using modeling results from Chrastil and Bartle models, total and vaporization enthalpies of dissolution of morphine sulfate in ScCO2 were found to be 35.12 and 59.04 kJ/mole, respectively.

Determination of Regorafenib monohydrate (colorectal anticancer drug) solubility in supercritical CO2: Experimental and thermodynamic modeling

In this study, the solubilities of Regorafenib monohydrate (REG), a widely used as a colorectal anticancer drug, in supercritical carbon dioxide (ScCO2) were measured under various pressures and temperature conditions, for the first time. The minimum value of REG in mole fraction was determined to be 3.06×10-7, while the maximum value was found to be 6.44×10-6 at 338 K and 27 MPa. The experimental data for REG were correlated through the utilization of two types of models: (1) a set of 25 existing empirical and semi-empirical models that incorporated 3-8 parameters according to functional dependencies, (2) a model that relied on solid-liquid equilibrium (SLE) and the newly improved association models. All of the evaluated models were capable of generating suitable fits to the solubility data of REG, however, the average absolute relative deviation (AARD) of Gordillo et al. model (AARD=13.2%) and Reddy et al. model (AARD=13.5%) indicated their superiority based on AARD%. Furthermore, solvation and sublimation enthalpies of REG drug were estimated for the first time.

Solubility of palbociclib in supercritical carbon dioxide from experimental measurement and Peng-Robinson equation of state

Palbociclib is a poorly water-soluble medicine which acts against metastatic breast cancer cells. Among various techniques to improve the solubility of this medicine, applying supercritical technologies to produce micro- and nano-sized particles is a possible option. For this purpose, extraction of solubility data is required. In this research, the solubility of palbociclib in supercritical carbon dioxide (ScCO₂) at different equilibrium conditions was measured at temperatures between 308 and 338 K and pressures within 12-27 MPa, for the first time. The minimum and maximum solubility data were found to be 8.1 × 10^-7 (at 338 K and 12 MPa) and 2.03 × 10^-5 (at 338 K and 27 MPa), respectively. Thereafter, two sets of models, including ten semi-empirical equations and three Peng-Robinson (PR) based integrated models were used to correlate the experimental solubility data. Bian's model and PR equation of state using van der Waals mixing rules (PR + vdW) showed better accuracy among the examined semi-empirical and integrated models, respectively. Furthermore, the self-consistency of the obtained data was confirmed using two distinct semi-empirical models. At last, the total and vaporization enthalpies of palbociclib solubility in ScCO₂ were calculated from correlation results of semi-empirical equations and estimated to be 40.41 and 52.67 kJ/mol, respectively.

Correlation of the solubility of solid hydrocarbons in supercritical CO2 using different equations of state and mixing rules

The supercritical extraction process is a technique that has increasingly been applied in various industries in recent years. Solubility determination in the supercritical region is the key feature for this process. However, high expenses and time consuming experiments for this task obligates the need for process modeling. In this study, a thermodynamic model is proposed to correlate the solubility of solid hydrocarbons, namely, 1-hexadecanol, 1-octadecanol, anthracene, benzoin, fluorene, hexamethylbenzene, mandelic acid, naphthalene, palmitic acid, phenanthrene, propyl 4-hydroxybenzoate, pyrene and stearic acid in supercritical conditions, using Peng?Robinson (PR) and Soave?Redlich?Kwong (SRK) equations of state with one-parameter van der Waals (vdW1) and two-parameters (vdW2) and covolume dependent (CVD) mixing rules. For the above combination of equations of state and mixing rules, binary interaction parameters were determined, utilizing the differential evolution optimization strategy. The validity of the model was assessed by comparing the experimental solubility data with the results obtained from thermodynamic model based on average absolute relative deviation (AARD). An empirical correlation was proposed for the correlation of the solid solubilities in supercritical CO2. For each compound, the constants of this equation were obtained in such a manner to correlate the solubility at different temperatures and pressures.

A critical review on the particle generation and other applications of rapid expansion of supercritical solution

The novel particle generation processes of Active Pharmaceutical Ingredient (API)/drug have been extensively explored in recent decades due to their wide-range applications in the pharmaceutical industry. The Rapid Expansion of Supercritical Solutions (RESS) is one of the promising techniques to obtain the fine particles (micro to nano-size) of APIs with narrow particle size distribution (PSD). In RESS, supercritical carbon dioxide (SC CO₂) and API are used as solvent and solute respectively. In this literature survey, the application of RESS in the formation of fine particles is critically reviewed. Solubility of API in SC CO₂ and supersaturation are the key factors in tuning the particle size. The different approaches to model and predict the solubility of API in SC CO₂ are discussed. Then, the effect of process parameters on mean particle size and the particle size distribution are interpreted in the context of solubility and supersaturation. Furthermore, the less-explored applications of RESS in preparation of solid-lipid nanoparticles, liposome, polymorphic conversion, cocrystallization and inclusion complexation are compared with traditional processes. The solubility enhancement of API in SC CO₂ using co-solvent and its applications in particle generation are explored in published literature. The development and modifications in the conventional RESS process to overcome the limitations of RESS are presented. Finally, the perspective on RESS with special attention to its commercial operation is highlighted.

Application of Fluids in Supercritical Conditions in the Polymer Industry

This article reviews the use of fluids under supercritical conditions in processes related to the modern and innovative polymer industry. The most important processes using supercritical fluids are: extraction, particle formation, micronization, encapsulation, impregnation, polymerization and foaming. This review article briefly describes and characterizes the individual processes, with a focus on extraction, micronization, particle formation and encapsulation. The methods mentioned focus on modifications in the scope of conducting processes in a more ecological manner and showing higher quality efficiency. Nowadays, due to the growing trend of ecological solutions in the chemical industry, we see more and more advanced technological solutions. Less toxic fluids under supercritical conditions can be used as an ecological alternative to organic solvents widely used in the polymer industry. The use of supercritical conditions to conduct these processes creates new opportunities for obtaining materials and products with specialized applications, in particular in the medical, pharmacological, cosmetic and food industries, based on substances of natural sources. The considerations contained in this article are intended to increase the awareness of the need to change the existing techniques. In particular, the importance of using supercritical fluids in more industrial methods and for the development of already known processes, as well as creating new solutions with their use, should be emphasized.

Solubility of Anthraquinone Derivatives in Supercritical Carbon Dioxide: New Correlations

Solubility of several anthraquinone derivatives in supercritical carbon dioxide was readily available in the literature, but correcting ability of the existing models was poor. Therefore, in this work, two new models have been developed for better correlation based on solid-liquid phase equilibria. The new model has five adjustable parameters correlating the solubility isotherms as a function of temperature. The accuracy of the proposed models was evaluated by correlating 25 binary systems. The proposed models observed provide the best overall correlations. The overall deviation between the experimental and the correlated results was less than 11.46% in averaged absolute relative deviation (AARD). Moreover, exiting solubility models were also evaluated for all the compounds for the comparison purpose.

Solubility of Anthraquinone Derivatives in Supercritical Carbon Dioxide: New Correlations

Solubility of several anthraquinone derivatives in supercritical carbon dioxide was readily available in the literature, but correcting ability of the existing models was poor. Therefore, in this work, two new models have been developed for better correlation based on solid-liquid phase equilibria. The new model has five adjustable parameters correlating the solubility isotherms as a function of temperature. The accuracy of the proposed models was evaluated by correlating 25 binary systems. The proposed models observed provide the best overall correlations. The overall deviation between the experimental and the correlated results was less than 11.46% in averaged absolute relative deviation (AARD). Moreover, exiting solubility models were also evaluated for all the compounds for the comparison purpose.