Correct Way of Reporting Results when Modelling Supercritical Phase Equilibria using Equations of State

Studies on solubility measurement of codeine phosphate (pain reliever drug) in supercritical carbon dioxide and modeling

In this study, the solubilities of codeine phosphate, a widely used pain reliever, in supercritical carbon dioxide (SC-CO2) were measured under various pressures and temperature conditions. The lowest determined mole fraction of codeine phosphate in SC-CO2 was 1.297 × 10-5 at 308 K and 12 MPa, while the highest was 6.502 × 10-5 at 338 K and 27 MPa. These measured solubilities were then modeled using the equation of state model, specifically the Peng-Robinson model. A selection of density models, including the Chrastil model, Mendez-Santiago and Teja model, Bartle et al. model, Sodeifian et al. model, and Reddy-Garlapati model, were also employed. Additionally, three forms of solid-liquid equilibrium models, commonly called expanded liquid models (ELMs), were used. The average solvation enthalpy associated with the solubility of codeine phosphate in SC-CO2 was calculated to be - 16.97 kJ/mol. The three forms of the ELMs provided a satisfactory correlation to the solubility data, with the corresponding average absolute relative deviation percent (AARD%) under 12.63%. The most accurate ELM model recorded AARD% and AICc values of 8.89% and - 589.79, respectively.

Solubility measurement and modeling of hydroxychloroquine sulfate (antimalarial medication) in supercritical carbon dioxide

A supercritical fluid, such as supercritical carbon dioxide (scCO₂) is increasingly used for the micronization of pharmaceuticals in the recent past. The role of scCO₂ as a green solvent in supercritical fluid (SCF) process is decided by the solubility information of the pharmaceutical compound in scCO₂. The commonly used SCF processes are the rapid expansion of supercritical solution (RESS) and supercritical antisolvent precipitation (SAS). To implement micronization process, solubility of pharmaceuticals in scCO₂ is required. Present study is aimed at both measuring and modeling of solubilities of hydroxychloroquine sulfate (HCQS) in scCO₂. Experiments were conducted at various conditions (P = 12 to 27 MPa and T = 308 to 338 K), for the first time. The measured solubilities were found to be ranging between (0.0304 × 10^-4 and 0.1459 × 10^-4) at 308 K, (0.0627 × 10^-4 and 0.3158 × 10^-4) at 318 K, (0.0982 × 10^-4 and 0.4351 × 10^-4) at 328 K, (0.1398 × 10^-4 and 0.5515 × 10^-4) at 338 K. To expand the usage of the data, various models were tested. For the modelling task existing models (Chrastil, reformulated Chrastil, Méndez-Santiago and Teja (MST), Bartle et al., Reddy-Garlapati, Sodeifian et al., models) and new set of solvate complex models were considered. Among the all models investigated Reddy-Garlapati and new solvate complex models are able to fit the data with the least error. Finally, the total and solvation enthalpies of HCQS in scCO₂ were calculated with the help of model constants obtained from Chrastil, reformulated Chrastil and Bartle et al., models.

Research of a Thermodynamic Function (∂p∂x)T, x→0: Temperature Dependence and Relation to Properties at Infinite Dilution

In this work, we propose the idea of considering (∂p∂x)T, x→0 as an infinite dilution thermodynamic function. Our research shows that (∂p∂x)T,x→0 as a thermodynamic function is closely related to temperature, with the relation being simply expressed as: ln(∂p∂x)T, x→0=AT+B. Then, we use this equation to correlate the isothermal vapor−liquid equilibrium (VLE) data for 40 systems. The result shows that the total average relative deviation is 0.15%, and the total average absolute deviation is 3.12%. It indicates that the model correlates well with the experimental data. Moreover, we start from the total pressure expression, and use the Gibbs−Duhem equation to re-derive the relationship between (∂p∂x)T,x→0 and the infinite dilution activity coefficient (γ∞) at low pressure. Based on the definition of partial molar volume, an equation for (∂p∂x)T,x→0 and gas solubility at high pressure is proposed in our work. Then, we use this equation to correlate the literature data on the solubility of nitrogen, hydrogen, methane, and carbon dioxide in water. These systems are reported at temperatures ranging from 273.15 K to 398.15 K and pressures up to 101.325 MPa. The total average relative deviation of the predicted values with respect to the experimental data is 0.08%, and the total average absolute deviation is 2.68%. Compared with the Krichevsky−Kasarnovsky equation, the developed model provides more reliable results.

Measurement and modeling of clemastine fumarate (antihistamine drug) solubility in supercritical carbon dioxide

The solubilities of clemastine fumarate in supercritical carbon dioxide (ScCO₂) were measured for the first time at temperature (308 to 338 K) and pressure (12 to 27 MPa). The measured solubilities were reported in terms of mole faction (mol/mol total) and it had a range from 1.61 × 10^–6 to 9.41 × 10^–6. Various models were used to correlate the data. The efficacy of the models was quantified with corrected Akaike’s information criterion (AICc). A new cluster salvation model was derived to correlate the solubility data. The new model was able to correlate the data and deviation was 10.3% in terms of average absolute relative deviation (AARD). Furthermore, the measured solubilities were also correlated with existing K.-W. Chen et al., model, equation of state model and a few other density models. Among density models, Reddy and Garlapati model was observed to be the best model and corresponding AARD was 7.57% (corresponding AIC_c was − 678.88). The temperature independent Peng–Robinson equation of state was able to correlate the data and AARD was 8.25% (corresponding AIC_c was − 674.88). Thermodynamic parameters like heats of reaction, sublimation and solvation of clemastine fumarate were calculated and reported.

Penicillins' Solubility in Supercritical Carbon Dioxide: Modeling by Cubic Equations of States Revisited

Development of processes using green solvents as supercritical fluids (SCFs) depends on the accuracy of modeling and predicting phase equilibrium which is of considerable importance to exploit the use of SCF process at the level of pharmaceutical industries. Solid-Fluid equilibrium modeling is associated to many drawbacks when compressed gas-based models as cubic equations of states (cEoSs) are used. The unavailability of experimental values of solute's sublimation pressure presents one of the major obstacles to the solubility modeling with this type of models, and thus, its estimation is essential and inevitable. This work is an attempt to address a question regarding "accurate estimated value" of sublimation pressure of two antibiotics Penicillin G (benzyl penicillin) and Penicillin V (phenoxymethyl penicillin). Toward that, first, cEoSs are provided as the thermodynamics modeling framework and fundamental approach. Second, a discussion and a review of some literature results are given. Third, results are invoked to present a criticism analysis that comes from the use of modified form of Peng-Robinson (PR) equation of states. Finally, considerable improvement of modeling results by using a new sublimation pressure is shown.