Search Results (33)

Knowledge of the solubility of metal precursors in supercritical (sc) CO₂ is a key factor for determining the best operation conditions for the synthesis of supported metallic nanoparticles. In this paper, new experimental solubility data of Cu(acac)₂, Pd(acac)₂, and Pt(acac)₂ in scCO₂ for temperatures from 313 to 353 K and pressures from 10 to 40 MPa are presented and compared with the literature data and correlated with semi-empirical density-based models (Chrastil, extended Kumar and Johnston, extended Bartle, and the original and modified Méndez–Santiago–Teja). In addition, literature data for the solubility of Cu(tmhd)₂, Pd(tmhd)₂, and Pt(cod)me₂ in scCO₂ were also correlated with the above-mentioned models. The best result, i.e., the best agreement between the experimental and calculated solubility datasets, was observed for the Chrastil model. Applying the Chrastil and extended Bartle models, the dissolution, sublimation, and solvation enthalpies were estimated. Furthermore, these correlation results were compared with the results from Ushiki et al., who correlated the solubilities of metal acetylacetonates in scCO₂ from the literature using the PC-SAFT equation of state. This comparison showed that the original Méndez–Santiago–Teja model enabled a better description of the experimental data by a factor of three. Full article

The study of solid–liquid equilibria offers critical insights into the molecular interactions between constituents in binary mixtures. Predicting these equilibria often requires comprehensive thermodynamic models, yet simplified approaches can provide valuable perspectives. In this work, we explore the application of the Bragg–Williams model to solid–liquid equilibria in binary mixtures leading to the formation of eutectic solvents. This model relies on a single parameter—the molar energy change upon mixing compounds—and demonstrates noteworthy features: the parameter can be estimated from a few (in principle, from a single) experimental melting points, and it correlates strongly with interaction energy parameters from more complex models, such as the PC-SAFT molecular-based equation of state. By using the Bragg–Williams model, we provide a straightforward and informative framework for characterizing solid–liquid equilibria, enabling insights into molecular interactions while requiring few data points as input. Despite its simplicity, the model effectively captures the essence of binary mixture energetics, positioning it as a practical tool for advancing the understanding of phase behavior in eutectic solvent systems. Full article

Background: During the dissolution of amorphous solid dispersion (ASD) formulations, the drug load (DL) often impacts the release mechanism and the occurrence of loss of release (LoR). The ASD/water interfacial gel layer and its specific phase behavior in connection with DL strongly dictate the release mechanism and LoR of ASDs, as reported in the literature. Thermodynamically driven liquid-liquid phase separation (LLPS) and/or drug crystallization at the interface are the key phase transformations that drive LoR. Methods: In this study, a combination of Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) thermodynamic modeling and in silico molecular simulation was applied to investigate the release mechanism and the occurrence LoR of an ASD formulation consisting of ritonavir as the active pharmaceutical ingredient (API) and the polymer, polyvinylpyrrolidone-co-vinyl acetate (PVPVA64). A thermodynamically modeled ternary phase diagram of ritonavir (PVPVA64) and water was applied to predict DL-dependent LLPS in the ASD/water interfacial gel layer. Microscopic Erosion Time Testing (METT) was used to experimentally validate the phase diagram predictions. Additionally, in silico molecular simulation was applied to provide further insights into the phase separation, the release mechanism, and aggregation behavior on a molecular level. Results: Thermodynamic modeling, molecular simulation, and experimental results were consistent and complementary, providing evidence that ASD/water interactions and phase separation are essential factors driving the dissolution behavior and LoR at 40 wt% DL of the investigated ritonavir/PVPVA64 ASD system, consistent with previous studies. Conclusions: This study provides insights into the potential of blending thermodynamic modeling, molecular simulation, and experimental research to comprehensively understand ASD formulations. Such a combined approach can be leveraged as a computational framework to gain insights into the ASD dissolution mechanism, thereby facilitating in silico screening, designing, and optimization of formulations with the benefit of significantly reducing the number of experimental tests. Full article

Industrial buildings have numerous kinds of energy-losing equipment, such as engines, ovens, boilers and heat exchangers. Energy losses are related to inefficient energy use and lousy work conditions for the people inside the buildings. This work is devoted to the recovery of lost energy from industrial buildings. Firstly, the residual energy of the building is extracted to be used to warm water. Consequently, the work conditions of the people inside industrial buildings can be improved by maintaining the adequate temperature. The recovery of the energy is performed by a multipurpose heat pump system (HP system). The working fluid used in the HP system is R134a, which is a traditional and cheap working fluid. The thermophysical properties of R134a are obtained through the PC-SAFT equation of state. This work presents a performance mapping based on the intercepted areas framework to evaluate which working conditions are the optimal operating variables. The latter depends on several key parameters, such as compressor work, heat delivery, heat absorbed and exergetic efficiency. The results show that the optimal work conditions are found at different condenser and evaporator temperatures, and these may be limited by what the designer considers a sound performance of the heat pump system. Full article

Prospective environmental and technological assessment of emerging chemical processes is necessary to identify, analyze and evaluate the technologies that are highly imperative in the transition towards climate neutrality. The investigation of the environmental impacts and material and energy requirements of the processes at the low technology readiness level (TRL) is important in making early decisions about the feasibility of adapting and upscaling the process to the industrial level. However, the upscaling of new chemical processes has always been a major challenge; and in this context, there is no general methodological guidance available in the literature. Hence, a new comprehensive methodological framework for upscaling of novel chemical processes is designed and presented based on thermodynamic process modeling and simulation. The practical implementation of the proposed methodology is extensively discussed by developing a scaled-up novel carbon capture and utilization (CCU) process comprised of sequestration of carbon dioxide (CO₂) from blast furnace gas with a capacity of 1000 liter per hour (L/h) using methanol and its utilization as a precursor to produce methane (CH₄). It was found that thermodynamic process modeling and simulations based on the perturbed-chain statistical associating (PC-SAFT) equation of state (EOS) can precisely estimate the CO₂ solubility in methanol and conversion to CH₄ at various temperature and pressure conditions. The achieved thermophysical property and kinetics parameters can be employed in process simulations to estimate scaled-up environmental flows and material and energy requirements of the process. Full article

In order to determine the water vapor adsorption performance of a rotary desiccant-based air conditioning system, the behavior of water adsorption on cylindrical pores of different sizes was studied by using classical density functional theory (CDFT) based on perturbated chain statistical associating fluid theory (PC-SAFT). Firstly, the structural parameters of the desiccant material were characterized by scanning electron microscopy (SEM), X-ray Energy Dispersive Spectrum (EDS), and N₂ adsorption/desorption isotherms, as well as adsorption equilibrium measurements of water vapor at temperature range 293–308 K. Secondly, the potential energy equation of water molecules in cylindrical pores was determined, and contribution of various terms of PC-SAFT for simulating fluid in cylindrical pores were established. Finally, the pore size distribution (PSD) of the desiccant materials is determined by the PC-SAFT kernel. Moreover, water vapor condensation was investigated with the PC-SAFT model in micropores. The results indicate that the rotary desiccant materials have a large number of micropores with a volume of 0.3669 cm³/g and the amount of water adsorption is about 0.285 g/g. The condensation pressure and the pore width corresponding to the saturated pressure P0 grow with an increase in the temperature, signifying that adjusting the PSD of the material has a significant effect on improving the dehumidification performance. The research concludes that the PSD range of the oxide cylindrical pore between 1.09 and 1.53 nm is particularly beneficial for dehumidification. This study provides valuable theoretical guidance for optimizing dehumidification materials. Full article

Maximum efficiency and maximum net power output are some of the most important goals to reach the optimal conditions of organic Rankine cycles. This work compares two objective functions, the maximum efficiency function, $\beta$, and the maximum net power output function, $\omega$. The van der Waals and PC-SAFT equations of state are used to calculate the qualitative and quantitative behavior, respectively. The analysis is performed for a set of eight working fluids, considering hydrocarbons and fourth-generation refrigerants. The results show that the two objective functions and the maximum entropy point are excellent references for describing the optimal organic Rankine cycle conditions. These references enable attaining a zone where the optimal operating conditions of an organic Rankine cycle can be found for any working fluid. This zone corresponds to a temperature range determined by the boiler outlet temperature obtained by the maximum efficiency function, maximum net power output function, and maximum entropy point. This zone is named the optimal temperature range of the boiler in this work. Full article

During the dissolution of amorphous solid dispersion (ASD) formulations, the gel layer that forms at the ASD/water interface strongly dictates the release of the active pharmaceutical ingredient (API) and, hence, the dissolution performance. Several studies have demonstrated that the switch of the gel layer from eroding to non-eroding behavior is API-specific and drug-load (DL)-dependent. This study systematically classifies the ASD release mechanisms and relates them to the phenomenon of the loss of release (LoR). The latter is thermodynamically explained and predicted via a modeled ternary phase diagram of API, polymer, and water, and is then used to describe the ASD/water interfacial layers (below and above the glass transition). To this end, the ternary phase behavior of the APIs, naproxen, and venetoclax with the polymer poly(vinylpyrrolidone-co-vinyl acetate) (PVPVA64) and water was modeled using the perturbed-chain statistical associating fluid theory (PC-SAFT). The glass transition was modeled using the Gordon–Taylor equation. The DL-dependent LoR was found to be caused by API crystallization or liquid-liquid phase separation (LLPS) at the ASD/water interface. If crystallization occurs, it was found that API and polymer release was impeded above a threshold DL at which the APIs crystallized directly at the ASD interface. If LLPS occurs, an API-rich phase and a polymer-rich phase are formed. Above a threshold DL, the less mobile and hydrophobic API-rich phase accumulates at the interface which prevents API release. LLPS is further influenced by the composition and glass transition temperature of the evolving phases and was investigated at 37 °C and 50 °C regarding impact of temperature of. The modeling results and LoR predictions were experimentally validated by means of dissolution experiments, microscopy, Raman spectroscopy, and size exclusion chromatography. The experimental results were found to be in very good agreement with the predicted release mechanisms deduced from the phase diagrams. Thus, this thermodynamic modeling approach represents a powerful mechanistic tool that can be applied to classify and quantitatively predict the DL-dependent LoR release mechanism of PVPVA64-based ASDs in water. Full article

The poor bioavailability of an active pharmaceutical ingredient (API) can be enhanced by dissolving it in a polymeric matrix. This formulation strategy is commonly known as amorphous solid dispersion (ASD). API crystallization and/or amorphous phase separation can be detrimental to the bioavailability. Our previous work (Pharmaceutics 2022, 14(9), 1904) provided analysis of the thermodynamics underpinning the collapse of ritonavir (RIT) release from RIT/poly(vinylpyrrolidone-co-vinyl acetate) (PVPVA) ASDs due to water-induced amorphous phase separation. This work aimed for the first time to quantify the kinetics of water-induced amorphous phase separation in ASDs and the compositions of the two evolving amorphous phases. Investigations were performed via confocal Raman spectroscopy, and spectra were evaluated using so-called Indirect Hard Modeling. The kinetics of amorphous phase separation were quantified for 20 wt% and 25 wt% drug load (DL) RIT/PVPVA ASDs at 25 °C and 94% relative humidity (RH). The in situ measured compositions of the evolving phases showed excellent agreement with the ternary phase diagram of the RIT/PVPVA/water system predicted by PC-SAFT in our previous study (Pharmaceutics 2022, 14(9), 1904). Full article

In this work, the solid–liquid equilibrium (SLE) of four binary systems combining two active pharmaceutical ingredients (APIs) capable of forming co-amorphous systems (CAMs) was investigated. The binary systems studied were naproxen-indomethacin, naproxen-ibuprofen, naproxen-probucol, and indomethacin-paracetamol. The SLE was experimentally determined by differential scanning calorimetry. The thermograms obtained revealed that all binary mixtures investigated form eutectic systems. Melting of the initial binary crystalline mixtures and subsequent quenching lead to the formation of CAM for all binary systems and most of the compositions studied. The experimentally obtained liquidus and eutectic temperatures were compared to theoretical predictions using the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state and conductor-like screening model for real solvents (COSMO-RS), as implemented in the Amsterdam Modeling Suite (COSMO-RS-AMS). On the basis of the obtained results, the ability of these models to predict the phase diagrams for the investigated API–API binary systems was evaluated. Furthermore, the glass transition temperature (T_g) of naproxen (NAP), a compound with a high tendency to recrystallize, whose literature values are considerably scattered, was newly determined by measuring and modeling the T_g values of binary mixtures in which amorphous NAP was stabilized. Based on this analysis, erroneous literature values were identified. Full article

This study proposes a simple correlation for approximating hydrogen solubility in biomaterials as a function of pressure and temperature. The pre-exponential term of the proposed model linearly relates to the pressure, whereas the exponential term is merely a function of temperature. The differential evolution (DE) optimization algorithm helps adjust three unknown coefficients of the correlation. The proposed model estimates 134 literature data points for the hydrogen solubility in biomaterials with an excellent absolute average relative deviation (AARD) of 3.02% and a coefficient of determination (R) of 0.99815. Comparing analysis justifies that the developed correlation has higher accuracy than the multilayer perceptron artificial neural network (MLP-ANN) with the same number of adjustable parameters. Comparing analysis justifies that the Arrhenius-type correlation not only needs lower computational effort, it also has higher accuracy than the PR (Peng-Robinson), PC-SAFT (perturbed-chain statistical associating fluid theory), and SRK (Soave-Redlich-Kwong) equations of state. Modeling results show that hydrogen solubility in the studied biomaterials increases with increasing temperature and pressure. Furthermore, furan and furfuryl alcohol show the maximum and minimum hydrogen absorption capacities, respectively. Such a correlation helps in understanding the biochemical–hydrogen phase equilibria which are necessary to design, optimize, and control biofuel production plants. Full article

Prediction of compatibility of the active pharmaceutical ingredient (API) with the polymeric carrier plays an essential role in designing drug delivery systems and estimating their long-term physical stability. A key element in deducing API–polymer compatibility is knowledge of a complete phase diagram, i.e., the solubility of crystalline API in polymer and mutual miscibility of API and polymer. In this work, the phase behavior of ibuprofen (IBU) with different grades of poly(D,L-lactide-co-glycolide) (PLGA) and polylactide (PLA), varying in composition of PLGA and molecular weight of PLGA and PLA, was investigated experimentally using calorimetry and computationally by the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EOS). The phase diagrams constructed based on a PC-SAFT EOS modeling optimized using the solubility data demonstrated low solubility at typical storage temperature (25 °C) and limited miscibility (i.e., presence of the amorphous–amorphous phase separation region) of IBU with all polymers studied. The ability of PC-SAFT EOS to capture the experimentally observed trends in the phase behavior of IBU–PLA/PLGA systems with respect to copolymer composition and molecular weight was thoroughly investigated and evaluated. Full article

The study of chemical reactions in multiple liquid phase systems is becoming more and more relevant in industry and academia. The ability to predict combined chemical and phase equilibria is interesting from a scientific point of view but is also crucial to design innovative separation processes. In this work, an algorithm to perform the combined chemical and liquid–liquid phase equilibrium calculation was implemented in the PC-SAFT framework in order to predict the thermodynamic equilibrium behavior of two multicomponent esterification systems. Esterification reactions involve hydrophobic reacting agents and water, which might cause liquid–liquid phase separation along the reaction coordinate, especially if long-chain alcoholic reactants are used. As test systems, the two quaternary esterification systems starting from the reactants acetic acid + 1-pentanol and from the reactants acetic acid + 1-hexanol were chosen. It is known that both quaternary systems exhibit composition regions of overlapped chemical and liquid–liquid equilibrium. To the best of our knowledge, this is the first time that PC-SAFT was used to calculate simultaneous chemical and liquid–liquid equilibria. All the binary subsystems were studied prior to evaluating the predictive capability of PC-SAFT toward the simultaneous chemical equilibria and phase equilibria. Overall, PC-SAFT proved its excellent capabilities toward predicting chemical equilibrium composition in the homogeneous composition range of the investigated systems as well as liquid–liquid phase behavior. This study highlights the potential of a physical sound model to perform thermodynamic-based modeling of chemical reacting systems undergoing liquid–liquid phase separation. Full article

There is an increasing focus on two-phase flow in micro- or mini-structured apparatuses for various manufacturing and measurement instrumentation applications, including the field of crystallization as a separation technique. The slug flow pattern offers salient features for producing high-quality products, since narrow residence time distribution of liquid and solid phases, intensified mixing and heat exchange, and an enhanced particle suspension are achieved despite laminar flow conditions. Due to its unique features, the slug flow crystallizer (SFC) represents a promising concept for small-scale continuous crystallization achieving high-quality active pharmaceutical ingredients (API). Therefore, a time-efficient strategy is presented in this study to enable crystallization of a desired solid product in the SFC as quickly as possible and without much experimental effort. This strategy includes pre-selection of the solvent/solvent mixture using heuristics, verifying the slug flow stability in the apparatus by considering the static contact angle and dynamic flow behavior, and modeling the temperature-dependent solubility in the supposed material system using perturbed-chain statistical associating fluid theory (PC-SAFT). This strategy was successfully verified for the amino acids l-alanine and l-arginine and the API paracetamol for binary and ternary systems and, thus, represents a general approach for using different material systems in the SFC. Full article

The thermodynamic phase behavior of charged polymers is a crucial property underlying their role in biology and various industrial applications. A complete understanding of the phase behaviors of such polymer solutions remains challenging due to the multi-component nature of the system and the delicate interplay among various factors, including the translational entropy of each component, excluded volume interactions, chain connectivity, electrostatic interactions, and other specific interactions. In this work, the phase behavior of partially charged ion-containing polymers in polar solvents is studied by further developing a liquid-state (LS) theory with local shortrange interactions. This work is based on the LS theory developed for fully-charged polyelectrolyte solutions. Specific interactions between charged groups of the polymer and counterions, between neutral segments of the polymer, and between charged segments of the polymer are incorporated into the LS theory by an extra Helmholtz free energy from the perturbed-chain statistical associating fluid theory (PC-SAFT). The influence of the sequence structure of the partially charged polymer is modeled by the number of connections between bonded segments. The effects of chain length, charge fraction, counterion valency, and specific short-range interactions are explored. A computational App for salt-free polymer solutions is developed and presented, which allows easy computation of the binodal curve and critical point by specifying values for the relevant model parameters. Full article