An equation-of-state contribution for polar components: Quadrupolar molecules

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.

Development of thermodynamically consistent machine-learning equations of state: Application to the Mie fluid

A procedure for deriving thermodynamically consistent data-driven equations of state (EoS) for fluids is presented. The method is based on fitting the Helmholtz free energy using artificial neural networks to obtain a closed-form relationship between the thermophysical properties of fluids (FE-ANN EoS). As a proof-of-concept, an FE-ANN EoS is developed for the Mie fluids, starting from a database obtained by classical molecular dynamics simulations. The FE-ANN EoS is trained using first- (pressure and internal energy) and second-order (e.g., heat capacities, Joule-Thomson coefficients) derivative data. Additional constraints ensure that the data-driven model fulfills thermodynamically consistent limits and behavior. The results for the FE-ANN EoS are shown to be as accurate as the best available analytical model while being developed in a fraction of the time. The robustness of the "digital" equation of state is exemplified by computing physical behavior it has not been trained on, for example, fluid phase equilibria. Furthermore, the model's internal consistency is successfully assessed using Brown's characteristic curves.

Multipolar SAFT-VR Mie Equation of State: Predictions of Phase Equilibria in Refrigerant Systems with No Binary Interaction Parameter

An extension of the SAFT-VR Mie equation of state is proposed to predict the properties of multipolar fluids. The new model, referred to as multipolar M-SAFT-VR Mie, incorporates the general multipolar term developed by Gubbins and co-workers, which accounts for dipole-dipole, quadrupole-quadrupole, and dipole-quadrupole interactions. A modification of the third order terms in the perturbation theory results in an accurate description of the simulation data for multipolar Lennard-Jones fluids. Both the M-SAFT-VR Mie and polar soft-SAFT models are extended to account for polarizability, and a good agreement is obtained with molecular simulation data. The M-SAFT-VR Mie model is applied to refrigerant systems, and it is found that including both dipole and quadrupole moments in molecular models leads to more accurate results than using only a dipole moment. The new model provides excellent predictions of the vapor-liquid equilibria of zeotropic and azeotropic refrigerant mixtures without the need for binary interaction parameters, making it a valuable tool for formulating low-GWP working fluids.

Interfacial properties of the hexane + carbon dioxide + water system in the presence of hydrophilic silica

Molecular dynamics simulations were conducted to study the interfacial behavior of the CO₂ + H₂O and hexane + CO₂ + H₂O systems in the presence of hydrophilic silica at geological conditions. Simulation results for the CO₂ + H₂O and hexane + CO₂ + H₂O systems are in reasonable agreement with the theoretical predictions based on the density functional theory. In general, the interfacial tension (IFT) of the CO₂ + H₂O system exponentially (linearly) decreased with increasing pressure (temperature). The IFTs of the hexane + CO₂ + H₂O (two-phase) system decreased with the increasing mole fraction of CO₂ in the hexane/CO₂-rich phase x_CO2 . Here, the negative surface excesses of hexane lead to a general increase in the IFTs with increasing pressure. The effect of pressure on these IFTs decreased with increasing x_CO2 due to the positive surface excesses of carbon dioxide. The simulated water contact angles of the CO₂ + H₂O + silica system fall in the range from 43.8° to 76.0°, which is in reasonable agreement with the experimental results. These contact angles increased with pressure and decreased with temperature. Here, the adhesion tensions are influenced by the variations in fluid-fluid IFT and contact angle. The simulated water contact angles of the hexane + H₂O + silica system fall in the range from 58.0° to 77.0° and are not much affected by the addition of CO₂. These contact angles increased with pressure, and the pressure effect was less pronounced at lower temperatures. Here, the adhesion tensions are mostly influenced by variations in the fluid-fluid IFTs. In all studied cases, CO₂ molecules could penetrate into the interfacial region between the water droplet and the silica surface.

Predicting the Thermodynamics of Ionic Liquids: What to Expect from PC-SAFT and COSMO-RS?

Two popular thermodynamic modeling frameworks, namely, the PC-SAFT equation of state and the COSMO-RS model, are benchmarked for their performance in predicting the thermodynamic properties of pure ionic liquids (ILs) and the solubility of CO₂ in ILs. The ultimate goal is to provide an illustration of what to expect from these frameworks when applied to ILs in a purely predictive way with established parametrization approaches, since the literature generally lacks their mutual comparisons. Two different modeling approaches with respect to the description of the molecular structure of ILs are tested within both models: a cation-anion pair as (i) a single electroneutral supermolecule and (ii) a pair of separately modeled counterions (ion-based approach). In general, we illustrate that special attention should be paid when estimating unknown thermodynamic data of ILs even with these two progressive thermodynamic frameworks. For both PC-SAFT and COSMO-RS, the supermolecule approach generally yields better results for the vapor pressure and the vaporization enthalpy of pure ILs, while the ion-based approach is found to be more suitable for the solubility of CO₂. In spite of some shortcomings, COSMO-RS with the supermolecule approach shows the best overall predictive capabilities for the studied properties. The ion-based strategy within both models has significant limitations in the case of the vaporization properties of ILs. In COSMO-RS, these limitations can, to a certain extent, be surpassed by additional quantum mechanical calculations of the ion pairing in the gas phase, while the ion-based PC-SAFT approach still needs a sophisticated improvement to be developed. As an initiating point, we explore one possible and simple route considering a high degree of cross associations between the counterions in the gas phase.

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.

Hydrodynamic density functional theory for mixtures from a variational principle and its application to droplet coalescence

Dynamic density functional theory (DDFT) allows the description of microscopic dynamical processes on the molecular scale extending classical DFT to non-equilibrium situations. Since DDFT and DFT use the same Helmholtz energy functionals, both predict the same density profiles in thermodynamic equilibrium. We propose a molecular DDFT model, in this work also referred to as hydrodynamic DFT, for mixtures based on a variational principle that accounts for viscous forces as well as diffusive molecular transport via the generalized Maxwell-Stefan diffusion. Our work identifies a suitable expression for driving forces for molecular diffusion of inhomogeneous systems. These driving forces contain a contribution due to the interfacial tension. The hydrodynamic DFT model simplifies to the isothermal multicomponent Navier-Stokes equation in continuum situations when Helmholtz energies can be used instead of Helmholtz energy functionals, closing the gap between micro- and macroscopic scales. We show that the hydrodynamic DFT model, although not formulated in conservative form, globally satisfies the first and second law of thermodynamics. Shear viscosities and Maxwell-Stefan diffusion coefficients are predicted using an entropy scaling approach. As an example, we apply the hydrodynamic DFT model with a Helmholtz energy density functional based on the perturbed-chain statistical associating fluid theory equation of state to droplet and bubble coalescence in one dimension and analyze the influence of additional components on coalescence phenomena.

Quantifying the effect of polar interactions on the behavior of binary mixtures: Phase, interfacial, and excess properties

In this work, polar soft-Statistical Associating Fluid Theory (SAFT) was used in a systematic manner to quantify the influence of polar interactions on the phase equilibria, interfacial, and excess properties of binary mixtures. The theory was first validated with available molecular simulation data and then used to isolate the effect of polar interactions on the thermodynamic behavior of the mixtures by fixing the polar moment of one component while changing the polar moment of the second component from non-polar to either highly dipolar or quadrupolar, examining 15 different binary mixtures. It was determined that the type and magnitude of polar interactions have direct implications on the vapor-liquid equilibria (VLE), resulting in azeotropy for systems of either dipolar or quadrupolar fluids when mixed with non-polar or low polar strength fluids, while increasing the polar strength of one component shifts the VLE to be more ideal. Additionally, excess properties and interfacial properties such as interfacial tension, density profiles, and relative adsorption at the interface were also examined, establishing distinct enrichment in the case of mixtures with highly quadrupolar fluids. Finally, polar soft-SAFT was applied to describe the thermodynamic behavior of binary mixtures of experimental systems exhibiting various intermolecular interactions (non-polar and polar), not only demonstrating high accuracy and robustness through agreement with experimental data but also providing insights into the effect of polarity on the interfacial properties of the studied mixtures. This work proves the value of having an accurate theory for isolating the effect of polarity, especially for the design of ad hoc polar solvents.

Polar soft-SAFT: theory and comparison with molecular simulations and experimental data of pure polar fluids

The consideration of polar interactions is of vital importance for the development of predictive and accurate thermodynamic models for polar fluids, as they govern most of their thermodynamic properties, making them highly non-ideal fluids.

Molecular simulation data for the vapor-liquid phase equilibria of binary mixtures of HFO-1123 with R-32, R-1234yf, R-1234ze(E), R-134a and CO2 and their modelling by the PCP-SAFT equation of state

In this Data in Brief article, we present predictive data for the vapor-liquid equilibria of the binary mixtures of HFO-1123 with R-32, HFO-1234yf, HFO-1234ze(E), R-134a and CO₂ from molecular simulation. The VLE in the binary mixtures are then modeled by the PCP-SAFT equation of state. Therefore we determined PCP-SAFT parameters for the pure HFO compounds as well as binary interaction parameters for all mixtures. The simulation data and the PCP-SAFT modelling are discussed in a related research article (Raabe, 2019).