Perturbed-chain Statistical Associating Fluid Theory Research Articles

Solubility of Pharmaceutical Ingredients in Natural Edible Oils.

Natural edible oils (NEOs) are common excipients for lipid-based formulations. Many of them are complex mixtures comprising hundreds of different triglycerides (TGs). One major challenge in developing lipid-based formulations is the variety in NEO compositions affecting the solubility of active pharmaceutical ingredients. In this work, solubilities of indomethacin (IND), ibuprofen (IBU), and fenofibrate (FFB) in soybean oil and in coconut oil were measured via differential scanning calorimetry, high-performance liquid chromatography, and Raman spectroscopy. Furthermore, this work proposes an approach that mimics NEOs using one key TG and models the API solubilities in these NEOs based on perturbed-chain statistical associating fluid theory (PC-SAFT). Key TGs were determined using the 1,2,3-random hypothesis, and PC-SAFT parameters were estimated via a group-contribution method. Using the proposed approach, the solubility of IBU and FFB was modeled in soybean oil and coconut oil. Furthermore, the solubilities of five more APIs (IND, cinnarizine, naproxen, griseofulvin, and felodipine) were modeled in soybean oil. All modeling results were found in very good agreement with the experimental data. The influence of different NEO kinds on API solubility was examined by comparing FFB and IBU solubilities in soybean oil and refined coconut oil. PC-SAFT was thus found to allow assessing the batch-to-batch consistency of NEO batches in silico.

Interfacial structure and differential capacitance of ionic liquid/graphite interface: A perturbed-chain SAFT density functional theory study

The perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) was combined with the electrostatic free energy from the mean spherical approximation (MSA) theory, and applied to represent densities of pure imidazolium ionic liquids (ILs) with anion [BF4]−. The PC-SAFT parameters of cations were linearized with their molar mass and obtained by simultaneously fitting the model predictions to experimental densities of some ILs. The PC-SAFT-MSA model provides accurate correlations and predictions of densities comparing with experimental data. Then a classical density functional theory (DFT) was developed based on PC-SAFT-MSA. The DFT model was applied to explore the structure and differential capacitance of the electrical double layer (EDL) in ILs on graphite. The model predicts similar density profiles for both cation and anion on a neutral surface, and layered structure with alternating layers of cations and anions on a charged surface. The charge inversion phenomena were also studied based on ion distributions. We further studied the effects of the alkyl chain length, temperature and non-electrostatic solid-fluid interactions on the differential capacitance of the EDL. The model provides bell-shaped differential capacitance curves. The peak positions of differential capacitance curves shift toward positive potentials as ions size asymmetry increases in agreement with previous experiments and simulations studies. The maximum capacitance decreases with increasing alkyl chain length as well as increasing temperature.

Wide-ranging prediction of phase behavior in complex systems by CP-PC-SAFT with universal kij values. I. Mixtures of non-associating compounds with [C2mim][EtSO4], [C4mim][MeSO4], and [C2mim][MeSO3] ionic liquids

This study shows that the inter-relations between critical constants can explain various phenomena occurring in the ionic liquids (IL) systems, such as the higher solubility of aromatic compounds and the differences between solubilities in the specific ILs. Indeed, as the critical constants get more remote, the systems become more asymmetric, increasing thus the immiscibility gaps. The Critical Point-based Perturbed-Chain Statistical Association Fluid Theory (CP-PC-SAFT) EoS rigorously obeys the Tc and Pc of ordinary substances. Moreover, its high precision in modelling the liquid phase properties yields realistic estimations of the imaginary critical constants of ILs. Such features attach an enhanced predictive capacity to this model, even while neglecting the complex chemical background of ILs. Although the substantial disagreements between different sources allow examining the general truthfulness of predictions rather their quantitative precision, it is demonstrated that using the universal value of k12 = 0.027 obtained for just one of the VLE datasets, CP-PC-SAFT realistically predicts various phase equilibria in mixtures of non-reacting gases, n-alkanes, aromatic hydrocarbons, ethers, ketones and haloalkanes with the considered ILs. The accuracies of these predictions are comparable with the widely implemented COSMO-RS approach. However, unlike it, CP-PC-SAFT can be applied for estimating high-pressure phase equilibria and it provides accurate predictions of volumetric data of mixtures in the particularly wide range of conditions.

Standard Gibbs energy of metabolic reactions: VI. Glyceraldehyde 3-phosphate dehydrogenase reaction

Glycolysis is a very central metabolic pathway for many organisms because it represents a key component in their energy production. For this reason, it has always been an extensively studied pathway. The glyceraldehyde 3-phosphate dehydrogenase (GDH) reaction is an important reaction of glycolysis yielding nicotinamide adenine dinucleotide (NADH). The aim of this work is to investigate the thermodynamics of the GDH reaction and determine the standard Gibbs energy of reaction ΔRg'0 and standard enthalpy of reaction ΔRh'0. Currently, so-called ‘standard’ data exist in the literature that depend on the conditions they were measured at. In this work, ΔRg'0 and ΔRh'0 values were determined that are independent from reaction conditions by accounting for the activity coefficients of the reacting substances. Therefore, the equation of state electrolyte Perturbed-Chain Statistical Associating Fluid Theory (ePC-SAFT) was used. The required ePC-SAFT parameters were taken from literature or fitted to new experimental osmotic coefficients. A value of ΔRg'0 = 51.5 ± 0.4 kJ mol−1 was determined at 298.15 K. This value deviates by up to 10 kJ mol−1 from existing literature values, caused by activity coefficients in the reaction medium. It can be used to determine the Gibbs energy of reaction ΔRg', which will allow statements concerning the feasibility of the GDH reaction. Further, a method is presented to predict influences of pH, initial substrate concentration and Mg2+ concentration on the reaction equilibrium. Finally, we measured the standard reaction enthalpy for the GDH reaction ΔRh'0 by titration calorimetric measurements (ΔRh'0 = 4.6 ± 0.1 kJ mol−1). This value was within van ’t Hoff evaluated ΔRh'0 (9 ± 16 kJ mol−1) using temperature-dependent equilibrium constants from equilibrium measurements corrected by ePC-SAFT predicted activity coefficients.

The role of molecular interactions on Michaelis constants of α-chymotrypsin catalyzed peptide hydrolyses

In this work, the effects of co-solvent and pressure on Michaelis constants at ambient temperature were analyzed for the enzymatic peptide hydrolyses of L-phenylalanine-p-nitroanilide (HPNA) and of N-succinyl-L-phenylalanine-p-nitroanilide (SPNA). These two substrates resemble each other in their molecular structure. That is, at the position of SPNA’s succinyl-group (S), HPNA possesses a hydrogen atom (H). Two co-solvents were considered: trimethylamine N-oxide and dimethyl sulfoxide. The thermodynamic model Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) was used to predict the activity of HPNA and SPNA under different reaction conditions regarding solvent composition and pressure. The PC-SAFT parameters (pure-component parameters and one binary parameter between substrate and solvent) were fitted to solubility data of HPNA in different solvents (water, ethanol, ethyl acetate, dimethyl sulfoxide), which were measured in this work at 30 °C and 1 bar. The resulting PC-SAFT predicted Michaelis constants were validated by experimental literature data. Results show that pressure decreased the Michaelis constants of both reactions, HPNA hydrolysis and SPNA hydrolysis. In spite of that, co-solvent effects on the Michaelis constants were predicted to be contrary for the two hydrolysis reactions. For the hydrolysis of HPNA, the co-solvents under investigation decreased the Michaelis constant while the co-solvents increased the Michaelis constant for the hydrolysis of SPNA. These PC-SAFT predictions were in qualitative agreement with the experimental literature data. This shows that molecular interactions are the key to understand the effects of co-solvents on Michaelis constants for the considered reactions. Applying the thermodynamic model PC-SAFT allowed predicting the observed combined effects of co-solvent and pressure on enzymatic reaction kinetics, which opens the door for solvent design of enzymatic reactions in the future.

Hydrocarbon Dew Point Measurement and Model Evaluation of Synthetic and Real Natural Gases.

Hydrocarbon dew point (HCDP) is one of the most important quality specifications of natural gas. Measuring and predicting the HCDP accurately are essential for the natural gas industry. However, the comprehensive experimental HCDP curve data are still rare, and knowledge about adopting proper prediction models remains unclear. In view of this, HCDP determination work by use of an improved test system and model evaluation based on more than 1000 dew points data have been done to improve the aforementioned dilemma. HCDP curve data of three gravimetrically prepared synthetic natural gases (SNGs) and one real gas (RG) are determined first. Then, one set of data containing 712 dew points from 28 SNGs and 334 dew points from 14 RGs is used to evaluate the performance of eight different HCDP prediction models including Soave–Redlich–Kwong (SRK), SRK–Twu, Peng–Robinson (PR), Twu–Sim–Tassone (TST), predictive SRK (PSRK), GERG-2008, PSRK, and perturbed-chain statistical associating fluid theory (PC-SAFT) models. Considerable prediction deviation of these models in the high-pressure region (pressure above 6.0 MPa) is observed compared to that in the low-pressure region (under 6.0 MPa), and the reasons for that difference are discussed. Evaluation results reveal that among the eight prediction models, GERG-2008 has the best performance (overall average absolute deviation (AAD): 1.44 °C) for SNGs, and PSRK and SRK–Twu fits the experimental data best for RGs (overall AAD: 2.50 °C). Therefore, GERG-2008 is recommended for HCDP prediction of relatively lean gas, whereas PSRK and SRK–Twu are recommended for calculating the HCDP of relatively heavy natural gases in low-pressure and high-pressure regions, respectively.

Evaluation of different thermodynamic models in predicting asphaltene precipitation: A comparative study

One of the major issues in the oil industry is asphaltene precipitation. Modeling asphaltene precipitation is still considered as a complex problem due to various characteristics of different heavy components existing in the crude oil. Thermodynamic models have been found as accurate models for studying asphaltene precipitation in the past few years and a great deal of effort has been devoted to model this process by using different empirical models and equations of state. In this study, the obtained results of asphaltene precipitation from different models based on perturbed-chain statistical associating fluid theory (PC-SAFT), cubic-plus-association (CPA), solid model, Flory-Huggins (FH), and the modified Flory-Huggins (MFH) are compared and their accuracy and reliability are analyzed in detail. For this purpose, twelve crude oil types with different characteristics and asphaltene precipitation behavior are used. Additionally, the performance of the introduced models in predicting asphaltene precipitation during gas injection into the studied oil is investigated. Results demonstrated that PC-SAFT and CPA models have the highest accuracy for both precipitation estimation and behavior trend prediction. Afterward, sensitivity analysis is performed by using Monte-Carlo algorithm for better understanding of the effect of different adjusting parameters, which were used during the tuning process, on each model outputs. Results indicated that cross-association energy between asphaltene and heavy component (HC), self-association energy of asphaltene, and binary interaction coefficient between asphaltene and CO2 are the most sensitive tuning variables for PC-SAFT, CPA, and solid models, respectively. Finally, the CPU times of various models for simulating this process were compared. This comparison showed that the PC-SAFT model has more computational time due to the involved iterative processes for phase equilibrium calculations.

Density and Viscosity for Binary Mixtures of the Ionic Liquid 1-Butyl-3-methylimidazolium Tetrafluoroborate with 2-Propanol, N,N-Dimethylacetamide and N,N-Dimethylformamide at 293.15–323.15 K: Experimental and PC-SAFT Modeling

For three binary mixtures composed of ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate ([Bmim][BF4]) with 2-propanol, N,N‑dimethylacetamide (DMA) and N,N‑dimethylformamide (DMF), the values of the experimental density and viscosity over the whole composition range for T = (293.15 to 323.15 K) are reported. Excess molar volume $$\mathop V\nolimits_{{\text{m}}}^{{\text{E}}}$$, partial molar volume $$\overline{{V_{i} }}$$, and the deviation in viscosity $$\Delta \eta$$ are calculated and explained in order to clarify the intermolecular interactions among the species in the mixtures. For all of the binary mixtures, the negative values of $$\mathop V\nolimits_{{\text{m}}}^{{\text{E}}}$$ and $$\Delta \eta$$ were fitted with the Redlich–Kister polynomial function. An increase in temperature decreases the values of $$\mathop V\nolimits_{{\text{m}}}^{{\text{E}}}$$ and increases the values of $$\Delta \eta$$. The results have been discussed regarding binary interaction forces and the formation of a complex between dissimilar molecules. For the correlation and prediction of the binary system densities, perturbed chain statistical associating fluid theory (PC-SAFT) was used. The results obtained from this theory are consistent with the experimental data.

Modeling Highly Cross-Linked Epoxy Resins in Solvents of Different Polarities with PC-SAFT

The solvent uptake in equilibrium of a highly cross-linked epoxy o-cresol novolac resin in water, isopropanol, and heptane was experimentally measured and modeled with the perturbed-chain statistical association fluid theory (PC-SAFT) equation of state. As suggested in the literature, PC-SAFT was combined with a network term, which takes additional elastic forces into account. The model parameters of the epoxy resin were generated by fitting them to the measured solvent uptake in pure substances and to the density of the epoxy resin, which provided a very good agreement with the experimental data. Furthermore, the solvent uptake in the mixtures isopropanol/water and isopropanol/heptane was predicted in very good agreement to the experimental data. For the first time, a thermodynamic model was developed to calculate the solvent uptake in an epoxy resin.

On the Selection of Boundary Conditions for Droplet Evaporation and Condensation at high Pressure and Temperature Conditions from interfacial Transport Resistivities

Understanding suitable boundary conditions for vapor-liquid interfaces is important for the development of physically realistic simulations of evaporation and condensation processes. This work addresses the question whether the inclusion of interfacial temperature jumps is necessary in the modeling of droplet evaporation or condensation. The analysis is divided into two parts. First, a model for coupled heat and mass transfer resistivities for sharp vapor-liquid interfaces is derived from a diffuse interface model. Local resistivities within the interface of n-alkane/nitrogen mixtures are predicted for diffuse interfaces by means of classical density functional theory (DFT) in combination with the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state. Integration over different domains of the local resistivities yields integral resistivities for sharp, or diffuse, interfaces. This allows computation of temperature jumps projected onto sharp interfaces under non-equilibrium conditions. Using this projection we found that interfacial jumps across the vapor-liquid interface are typically small, even for large temperature differences between droplet and ambient vapor. Second, an evaporation model is considered that includes a diffuse transition layer (Knudsen layer) in the order of a few mean free paths around the droplet, where transport processes are described by kinetic molecular theory. The analysis shows that discontinuities in temperature and chemical potential across the interface are important when heat and mass transfer are dominated by molecular collisions. This may occur not only at low pressures, but also at high pressures and temperatures for conditions sufficiently far from global thermodynamic equilibrium, resulting in large heat and mass fluxes and/or for sufficiently small droplets. On a macroscopic scale, the resulting correction to the boundary conditions for classical diffusion-controlled models may be significant at high evaporation or condensation rates.

Density, compressibility and phase equilibrium of high pressure-high temperature reservoir fluids up to 473 K and 140 MPa

Experimental measurement of volumetric and phase equilibrium properties of two high pressure - high temperature reservoir fluids was performed in this work. One fluid is volatile oil and the other is gas condensate. The density, isothermal compressibility, saturation pressure, and liquid fraction below the saturation pressure were determined in the temperature range up to 473.15 K by using a high pressure vibrating tube densitometer and a PVT cell. The obtained data were modelled by using equations of state including Soave-Redlich-Kwong (SRK), Peng-Robinson (PR), volume translated SRK (SRK-VT), volume translated PR (PR-VT) and Perturbed-Chain Statistical Association Fluid Theory (PC-SAFT). Among these models, the performance in saturation pressure prediction is system-dependent and it is hard to generalize the observation. PC-SAFT models volumetric properties satisfactorily. Regarding density calculation, it performs similarly to SRK-VT and PR-VT for the two fluids investigated here. Concerning isothermal compressibility, PC-SAFT is slightly better.

Phase behavior of pharmaceutically relevant polymer/solvent mixtures.

In the pharmaceutical industry, polymers are used as excipients for formulating poorly water-soluble active pharmaceutical ingredients (APIs) in so-called "amorphous solid dispersions" (ASDs). ASDs can be produced via solvent-based processes, where API and polymer are both dissolved in a solvent, followed by a solvent evaporation step (e.g. spray drying). Aiming at a homogeneous API/polymer formulation, phase separation of the components (API, polymer, solvent) during solvent evaporation must be avoided. The latter is often determined by the phase behavior of polymer/solvent mixtures used for ASD processing. Therefore, this work investigates the polymer-solvent interactions in these mixtures. Suitable polymer/solvent combinations investigated in this work comprise the pharmaceutically relevant polymers poly(vinylpyrrolidone) (PVP), poly(vinylpyrrolidone-co-vinyl acetate) (PVPVA64), and hydroxyppropyl methylcellulose acetate succinate 126G (HPMCAS) as well as the solvents acetone, dichloromethane (DCM), ethanol, ethyl acetate, methanol, and water. Based on vapor-sorption experiments demixing of solvents and polymers were predicted using the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT). These were found to be correct for all investigated solvent/polymer mixtures. Acetone, DCM, ethanol, methanol, and water were found to be completely miscible with PVPVA64. DCM, ethanol, methanol, and water were found to be completely miscible with PVP K90, while none of the investigated solvents was appropriate for avoiding immiscibility with HPMCAS. In addition, the impact of temperature, polymer molecular weight, and solvent-mixture composition on miscibility was successfully predicted using PC-SAFT. Thus, the proposed methodology allows identifying suitable solvents or solvent mixtures relevant for solvent-based preparations of pharmaceutical ASD formulations with low experimental effort.

Estimation of PC-SAFT binary interaction coefficient by artificial neural network for multicomponent phase equilibrium calculations

Perturbed-Chain Statistical Associating Fluid Theory Equation of State (PC-SAFT EoS) requires cross interaction parameter for each binary pair in the mixture. For real mixtures, these parameters should be corrected by binary interaction coefficients (kij's). The values of kij's are tuned by an optimization method in order to minimize the deviation from equilibrium data. The Particle Swarm Optimization (PSO) algorithm is employed for optimization of kij's due to the continuous nature of kij and highly nonlinear nature of PC-SAFT EoS. Although kij can be adjusted using the mentioned algorithm, it is cumbersome and highly time-consuming because the optimization should be performed for each pair that exists in the multicomponent mixture. It has been shown that these optimal values can be obtained based on the basic characteristic properties of the participating molecules in each pair, this is particularly useful to avoid solving any optimization problem. Furthermore, Artificial Neural Networks (ANNs) as powerful function approximators have been used to predict binary interaction coefficients based on basic characteristic properties of molecules that exist in each pair. Two types of characteristic properties have been examined as inputs of the ANN's utilized to predict the optimum kij's. The first one contains PC-SAFT parameters (m, ε/k, σ) and molecular weight of each component; while the second category contains specific gravity, normal boiling point and molecular weight of each component.The best structure of ANN has been obtained by two approaches: 1) Genetic Algorithm (GA) and 2) a constructive approach. GA can find the structure with any possible connections between neurons whereas the constructive approach can only find the best structure for fully connected networks. The results show that the genetically designed ANN that uses the second set of inputs outperforms the others. This ANN is used to estimate kij's of PC−SAFT for a wide range of non-associating materials where the predicted kij's are in close agreement with those obtained by PSO with coefficient of determination R2 = (0.9921, 0.9631) for training and validation data, respectively. In addition to the evaluation of the ANN by validation data, its performance has been examined by using its estimated kij's in flash calculation of a synthesized multi-component mixture and bubble point calculation of a reservoir fluid. Comparing the results of equilibrium calculations with their experimental counterparts shows that they closely follow the measured data. Furthermore, its performance has been compared with other approaches of estimation of kij such as London theory and QSPR method and the results show that the proposed ANN outperforms the others.

Standard Gibbs energy of metabolic reactions: V. Enolase reaction

The glycolytic pathway is one of the most important pathways for living organisms, due to its role in energy production and as supplier of precursors for biosynthesis in living cells. This work focuses on determination of the standard Gibbs energy of reaction ΔRg′0 of the enolase reaction, the ninth reaction in the glycolysis pathway. Exact ΔRg′0 values are required to predict the thermodynamic feasibility of single metabolic reactions or even of metabolic reaction sequences under cytosolic conditions. So-called “apparent” standard data from literature are only valid at specific conditions. Nevertheless, such data are often used in pathway analyses, which might lead to misinterpretation of the results. In this work, equilibrium measurements were combined with activity coefficients in order to obtain new standard values ΔRg′0 for the enolase reaction that are independent of the cytosolic conditions. Reaction equilibria were measured at different initial substrate concentrations and temperatures of 298.15 K, 305.15 K and 310.15 K at pH 7. The activity coefficients were predicted using the equation of state electrolyte Perturbed-Chain Statistical Associating Fluid Theory (ePC-SAFT). The ePC-SAFT parameters were taken from literature or fitted to new experimentally determined osmotic coefficients and densities. At 298.15 K and pH 7, a ΔRg′0(298.15 K, pH 7) value of −2.8 ± 0.2 kJ mol−1 was obtained. This value differs by up to 5 kJ mol−1 from literature data. Reasons are the poorly defined “standard” conditions and partly undefined reaction conditions of literature works. Finally, using temperature-dependent equilibrium constants and the van ‘t Hoff equation, the standard enthalpy of reaction of ΔRh′0(298.15 K, pH 7) = 27 ± 10 kJ mol−1 was determined, and a similar value was found by quantum-chemistry calculations.

Correctly Measuring and Predicting Solubilities of Solvates, Hydrates, and Polymorphs

The formation of solvates, hydrates, or different polymorphs significantly alters the physicochemical properties of a target component (TC) (e.g., active pharmaceutical or agrochemical active ingredient), such as solubility and dissolution behavior. Thus, it is very important to know under which conditions a certain solvate, hydrate, or polymorph is formed. This information can be obtained from phase diagrams, which are usually based on solubility measurements. Possible pitfalls in measuring the solubility of TC hydrates or solvates in pure solvents and solvent mixtures are discussed, and strategies for obtaining reliable solubility data are proposed. To substantiate the proposed solubility-measurement strategies, a thermodynamic approach based on the Perturbed-Chain Statistical Associating Fluid Theory for modeling solvate/hydrate solubilities was developed. This approach allows identifying stability regions of solvates/hydrates and predicting solubilities of solvates/hydrates or of polymorphs in pure solvents and solvent mixtures. It was successfully verified for modeling the solubility of the indomethacin-methanol solvate in methanol and of the carbamazepine dihydrate in water. Furthermore, the solubility of carbamazepine dihydrate and theophylline monohydrate in water/ethanol mixtures was predicted in excellent agreement with experimental data.

A Hybrid Framework for Simultaneous Process and Solvent Optimization of Continuous Anti-Solvent Crystallization with Distillation for Solvent Recycling

Anti-solvent crystallization is frequently applied in pharmaceutical processes for the separation and purification of intermediate compounds and active ingredients. The selection of optimal solvent types is important to improve the economic performance and sustainability of the process, but is challenged by the discrete nature and large number of possible solvent combinations and the inherent relations between solvent selection and optimal process design. A computational framework is presented for the simultaneous solvent selection and optimization for a continuous process involving crystallization and distillation for recycling of the anti-solvent. The method is based on the perturbed-chain statistical associated fluid theory (PC-SAFT) equation of state to predict relevant thermodynamic properties of mixtures within the process. Alternative process configurations were represented by a superstructure. Due to the high nonlinearity of the thermodynamic models and rigorous models for distillation, the resulting mixed-integer nonlinear programming (MINLP) problem is difficult to solve by state-of-the-art solvers. Therefore, a continuous mapping method was adopted to relax the integer variables related to solvent selection, which makes the scale of the problem formulation independent of the number of solvents under consideration. Furthermore, a genetic algorithm was used to optimize the integer variables related to the superstructure. The hybrid stochastic and deterministic optimization framework converts the original MINLP problem into a nonlinear programming (NLP) problem, which is computationally more tractable. The successful application of the proposed method was demonstrated by a case study on the continuous anti-solvent crystallization of paracetamol.

Experimental and modeling study of diisopropyl ether and 2-alkanol; PC-SAFT model and free volume theory

In the present study, with the aim to discover the governing interactions in binary mixtures containing diisopropyl ether and short-range 2-alkanol (from 2-propanol to 2-hexanol), experimental values of density and viscosity at temperature range 293.15 K–323.15 K were reported. From these data, values of excess molar volume, partial molar volume, and viscosity deviation for mentioned systems were calculated. Findings show that strong interactions occur among unlike molecules while increasing in the carbon chain length of 2-alkanol, reinforces the interactions. Also, the perturbed-chain SAFT (PC-SAFT) equation of state was implemented to study the density and partial molar volume of binary mixtures. Combination of this model with Free Volume Theory was applied for prediction of binary viscosities. Maximum deviation in AAD for density correlation regarding PC-SAFT model was 1.21%, and for viscosity calculation was 2.19%.

Recent advances of pharmaceutical crystallization theories

Abstract As a technology of separation and purification, crystallization plays a vital role in diverse industries such as inorganic salt, pharmaceutical, and food industries, which has a huge impact on purity, crystal polymorph, crystal morphology, and particle size distribution of final products. In the past few decades, with the rapid advancement of experimental approaches and molecular simulation methods, considerable advances in the interpretation of crystallization mechanisms have been obtained, promoting the investigation and understanding of crystallization theories greatly. In this review, the advances of pharmaceutical crystallization theories in recent years from the perspectives of nucleation and crystal growth are summarized and discussed. Two thermodynamic models that are helpful in the study of the crystallization mechanisms will be introduced. In this section, the perturbed-chain statistical associating fluid theory (PC-SAFT) and a chemical-potential-gradient model will be introduced, which have been successfully applied in pharmaceutical solubility prediction, the research of dissolution mechanism as well as dissolution kinetics analysis. These two models are expected to be applied to the study of pharmaceutical crystallization process and mechanism. Furthermore, molecular simulation based on the interaction between particles can provide structural information, thermodynamics, and dynamics properties of complex systems at the molecular level, like intermolecular interaction and surface adsorption energies. Application and some shortcomings of molecular simulation, especially molecular dynamics simulation, in the field of pharmaceutical crystallization will be expounded.

Modeling of precipitation considering multi-component form of Asphaltene using a solid solution framework

Many investigations have focused on determining the precipitation conditions for Asphaltene content in reservoir fluids. In addition, there are experimental observations in reservoir fluids titration, using different normal alkanes, proving multi-component form for Asphaltene in crude oil. In this work, the thermodynamic modeling approach of Hosseinzadeh Dehaghani et al. (2018) is extended through replacing the multi-solid approach with a solid-solution approach, which is closer to the real nature of Asphaltene solid phase in estimation of phase behavior and precipitation conditions. Therefore, after characterization of Asphaltene content into a few sub-components, solid-solution framework was considered to model the solid phase. To do this, the UNIQUAC activity coefficient model was used to describe solid phase non-idealities. The liquid and high-pressure vapor phase non-idealities were modeled using both Peng-Robinson (PR) and perturbed chain statistical associating fluid theory (PC-SAFT) equations of state (EOSs). The results obtained from modeling of bubble point pressure, onset pressure and crude oil titration with n-pentane were compared with experimental data of two oil samples from literature. The analysis of the results shows that the multi-component modeling of Asphaltene content provides a higher accuracy in comparison to single component modeling. For multi-component analysis, the highest and lowest “mean absolute percentage errors” in calculation of precipitation amount for the first oil sample were 10.26 and 1.59, for PR + UNIQUAC and PC-SAFT + UNIQUAC, respectively; while values for the second oil sample were 4.15 and 1.02, for PR + UNIQUAC and PC-SAFT + UNIQUAC, respectively.

Solubility of pharmaceutical ingredients in triglycerides

Lipid-based drug delivery systems (LBDDS) are highly relevant as pharmaceutical formulations significantly enhancing the bioavailability of active pharmaceutical ingredients (APIs). These formulations often are complex mixtures of APIs, various lipids, and other excipients (e.g. surfactants). In their simplest form, LBDDS contain one API being dissolved in a pure lipid, which often is a triglyceride (TG). In this work, solubilities of the APIs indomethacin, ibuprofen, and fenofibrate in pure TGs of different chain lengths (C chain 8–18) and degree of saturation were investigated. Solubilities of APIs in TGs were measured via differential scanning calorimetry, hot-stage microscopy, high-performance liquid chromatography, and Raman spectroscopy. The influence of fatty-acid chain length and degree of saturation on the API solubility in the TGs was investigated. APIs showed a higher solubility in saturated (wIBU = 10.5 wt% at 25 °C in tricaprylin) TGs compared to unsaturated ones (wIBU = 4.0 wt% at 25 °C in triolein). The fatty-acid chain length of TGs only slightly affects the solubility of ibuprofen and fenofibrate, but strongly influences the eutectic temperature of the API/TG mixtures.API solubilities in TGs and TG mixtures (mixtures of tricaprylin and tricaprin) were successfully modeled using the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) accounting for the intermolecular API/TG interactions providing a deep understanding of the energetic and structural impact of the TGs on API solubility.