Simultaneous Water Sorption and Crystallization in ASDs 1: Stability Studies Lasting for Two Years.

One way to increase the slow dissolution rate and the associated low bioavailability of newly developed active pharmaceutical ingredients (APIs) is to dissolve the API in a polymer, leading to a so-called amorphous solid dispersion (ASD). However, APIs are often supersaturated in ASDs and thus tend to crystallize during storage. The kinetics of the crystallization process is determined by the amount of water the ASD absorbs during storage at relative humidity (RH), storage temperature, polymer type, and the drug load of the ASD. Here, the crystallization kinetics and shelf life of spray-dried ASDs were investigated for ASDs consisting of nifedipine (NIF) or celecoxib (CCX) as the APIs and of poly(vinylpyrrolidone-co-vinyl acetate) or hydroxypropyl methylcellulose acetate succinate as polymers. Samples were stored over 2 years at different RHs covering conditions above and below the glass transition of the wet ASDs. Crystallization kinetics and onset time of the crystallization were qualitatively studied by using powder X-ray diffraction and microscopic inspection and were quantitatively determined by using differential scanning calorimetry. It was found that the NIF ASDs crystallize much faster than CCX ASDs at the same drug load and at the same storage conditions due to both higher supersaturation and higher molecular mobility in the NIF ASDs. Experimental data on crystallization kinetics were correlated using the Johnson-Mehl-Avrami-Kolmogorov equation. A detailed thermodynamic and kinetic modeling will be performed in Part 2 of this paper series.

Dissolution Mechanisms of Amorphous Solid Dispersions: Application of Ternary Phase Diagrams To Explain Release Behavior.

The use of amorphous solid dispersions (ASDs) in commercial drug products has increased in recent years due to the large number of poorly soluble drugs in the pharmaceutical pipeline. However, the release behavior of ASDs is complex and remains not well understood. Often, the drug release from ASDs is rapid and complete at lower drug loadings (DLs) but becomes slow and incomplete at higher DLs. The DL where release becomes hindered is termed the limit of congruency (LoC). Currently, there are no approaches to predict the LoC. However, recent findings show that one potential cause leading to the LoC is a change in phase morphology after water-induced phase separation at the ASD/solution interface. In this study, the phase behavior of ASDs in contact with aqueous solutions was described thermodynamically by constructing experimental and computational ternary phase diagrams, and these were used to predict morphology changes and ultimately the LoC. Experimental ternary phase diagrams were obtained by equilibrating ASD/water mixtures over time. Computational ternary phase diagrams were obtained by Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT). The morphology of the hydrophobic phase was studied with fluorescence confocal microscopy. It was demonstrated that critical point (plait point) composition approximately corresponded to the ASD DL, where the hydrophobic phase, formed during phase separation, became interconnected and hindered ASD release. This work provides mechanistic insights into the ASD release behavior and highlights the potential of in silico ASD design using phase diagrams.

Can Pure Predictions of Activity Coefficients from PC-SAFT Assist Drug-Polymer Compatibility Screening?

The bioavailability of poorly water-soluble active pharmaceutical ingredients (APIs) can be improved via the formulation of an amorphous solid dispersion (ASD), where the API is incorporated into a suitable polymeric carrier. Optimal carriers that exhibit good compatibility (i.e., solubility and miscibility) with given APIs are typically identified through experimental means, which are routinely labor- and cost-inefficient. Therefore, the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state, a popular thermodynamic model in pharmaceutical applications, is examined in terms of its performance regarding the computational pure prediction of API-polymer compatibility based on activity coefficients (API fusion properties were taken from experiments) without any binary interaction parameters fitted to API-polymer experimental data (that is, kij = 0 in all cases). This kind of prediction does not need any experimental binary information and has been underreported in the literature so far, as the routine modeling strategy used in the majority of the existing PC-SAFT applications to ASDs comprised the use of nonzero kij values. The predictive performance of PC-SAFT was systematically and thoroughly evaluated against reliable experimental data for almost 40 API-polymer combinations. We also examined the effect of different sets of PC-SAFT parameters for APIs on compatibility predictions. Quantitatively, the total average error calculated over all systems was approximately 50% in the weight fraction solubility of APIs in polymers, regardless of the specific API parametrization. The magnitude of the error for individual systems was found to vary significantly from one system to another. Interestingly, the poorest results were obtained for systems with self-associating polymers such as poly(vinyl alcohol). Such polymers can form intramolecular hydrogen bonds, which are not accounted for in the PC-SAFT variant routinely applied to ASDs (i.e., that used in this work). However, the qualitative ranking of polymers with respect to their compatibility with a given API was reasonably predicted in many cases. It was also predicted correctly that some polymers always have better compatibility with the APIs than others. Finally, possible future routes to improve the cost-performance ratio of PC-SAFT in terms of parametrization are discussed.

Water Sorption in Rubbery and Glassy Polymers, Nifedipine, and Their ASDs.

Polymers like poly(vinylpyrrolidone-co-vinyl acetate) (PVPVA) or hydroxypropyl methylcellulose acetate succinate (HPMCAS) are commonly used as a matrix for amorphous solid dispersions (ASDs) to enhance the bioavailability of the active pharmaceutical ingredients (APIs). The stability of ASDs is strongly influenced by the water sorption in the ASD from the surrounding air. In this work, the water sorption in the neat polymers PVPVA and HPMCAS, in the neat API nifedipine (NIF), and in their ASDs of different drug loads was measured above and below the glass-transition temperature. The equilibrium water sorption was predicted using the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) combined with the Non-Equilibrium Thermodynamics of Glassy Polymers (NET-GP).The water-sorption kinetics were modeled using the Maxwell-Stefan approach whereas the thermodynamic driving force was calculated using PC-SAFT and NET-GP. The water diffusion coefficients in the polymers, NIF, or ASDs were determined using the Free-Volume Theory. Using the water-sorption kinetics of the pure polymers and of NIF, the water-sorption kinetics of the ASDs were successfully predicted, thus providing the water diffusion coefficients in the ASD as a function of relative humidity and of the water concentration in polymers or ASDs.

Solid-Liquid Equilibrium in Co-Amorphous Systems: Experiment and Prediction.

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 (Tg) 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 Tg values of binary mixtures in which amorphous NAP was stabilized. Based on this analysis, erroneous literature values were identified.

Analysis of the Maximum Efficiency and the Maximum Net Power as Objective Functions for Organic Rankine Cycles Optimization.

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, ß, and the maximum net power output function, ω. 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.

Purely Predicting the Pharmaceutical Solubility: What to Expect from PC-SAFT and COSMO-RS?

A pair of popular thermodynamic models for pharmaceutical applications, namely, the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state and the conductor-like screening model for real solvents (COSMO-RS) are thoroughly benchmarked for their performance in predicting the solubility of active pharmaceutical ingredients (APIs) in pure solvents. The ultimate goal is to provide an illustration of what to expect from these progressive frameworks when applied to the thermodynamic solubility of APIs based on activity coefficients in a purely predictive regime without specific experimental solubility data (the fusion properties of pure APIs were taken from experiments). While this kind of prediction represents the typical modus operandi of the first-principles-aided COSMO-RS, PC-SAFT is a relatively highly parametrized model that relies on experimental data, against which its pure-substance and binary interaction parameters (kij) are fitted. Therefore, to make this benchmark as fair as possible, we omitted any binary parameters of PC-SAFT (i.e., kij = 0 in all cases) and preferred pure-substance parameter sets for APIs not trained to experimental solubility data. This computational approach, together with a detailed assessment of the obtained solubility predictions against a large experimental data set, revealed that COSMO-RS convincingly outperformed PC-SAFT both qualitatively (i.e., COSMO-RS was better in solvent ranking) and quantitatively, even though the former is independent of both substance- and mixture-specific experimental data. Regarding quantitative comparison, COSMO-RS outperformed PC-SAFT for 9 of the 10 APIs and for 63% of the API-solvent systems, with root-mean-square deviations of the predicted data from the entire experimental data set being 0.82 and 1.44 log units, respectively. The results were further analyzed to expand the picture of the performance of both models with respect to the individual APIs and solvents. Interestingly, in many cases, both models were found to qualitatively incorrectly predict the direction of deviations from ideality. Furthermore, we examined how the solubility predictions from both models are sensitive to different API parametrizations.

Measuring and Modeling Water Sorption in Amorphous Indomethacin and Ritonavir.

The amorphous state of an active pharmaceutical ingredient (API) enhances its water solubility compared to its crystalline state. However, it is well known that amorphous substances can absorb significant amounts of water therewith inducing API recrystallization. This work explores methods to obtain reliable information about water sorption in amorphous APIs and its modeling. Experimental water-sorption curves over a broad humidity range were obtained by measuring the mass increase of well-defined films of amorphous APIs. Water-sorption isotherms modeled using perturbed-chain statistical associating fluid theory (PC-SAFT) showed better accordance with the experimental data than those obtained using the Flory-Huggins model. Crank's diffusion equation was used to describe the water-sorption kinetics providing Fickian diffusion coefficients of water in indomethacin and in ritonavir. Stefan-Maxwell diffusion coefficients were obtained by converting Fickian diffusion coefficients using water activity coefficients obtained from PC-SAFT. Finally, the free-volume theory was applied to explain the persistent water concentration dependency of the Stefan-Maxwell diffusion coefficients.

The Shelf Life of ASDs: 1. Measuring the Crystallization Kinetics at Humid Conditions.

Amorphous solid dispersions (ASDs), where an active pharmaceutical ingredient (API) is dissolved in a polymer, are a favored formulation technique to achieve sufficient bioavailability of poorly water-soluble APIs. The shelf life of such ASDs is often limited by API crystallization. Crystallization depends strongly on the storage conditions (relative humidity and temperature) and the polymer selected for generating the ASD. Determining the crystallization kinetics of ASDs under various conditions requires suitable analytical methods. In this work, two different analytical methods were compared and cross-validated: The first builds on water-sorption measurements combined with thermodynamic predictions ( Eur. J. Pharm. Biopharm. 2018, 127, 183-193, DOI: 10.1016/j.toxrep.2018.11.002), whereas the second applies Raman spectroscopy. Using the two independent methods, factors influencing the crystallization kinetics of ASDs containing the API griseofulvin were investigated quantitatively. It was found that crystallization kinetics increases with increasing temperature and relative humidity. Additionally, the influence of different polymers (poly(vinylpyrrolidone-co-vinyl acetate) and Soluplus) on crystallization kinetics were investigated. The experimentally obtained crystallization kinetics were described using the Johnson-Mehl-Avrami-Kolmogorov model and are the basis for future shelf life predictions at desired storage conditions.

Comparative Study of DSC-Based Protocols for API-Polymer Solubility Determination.

Knowledge of the active pharmaceutical ingredient (API) solubility in a polymer is imperative for successful amorphous solid dispersion design and formulation but acquiring this information at storage temperature is challenging. Various solubility determination methods have been established, which utilize differential scanning calorimetry (DSC). In this work, three commonly used DSC-based protocols [i.e., melting point depression (MPD), recrystallization, and zero-enthalpy extrapolation (Z-EE)] and a method that we have developed called "step-wise dissolution" (S-WD) were analyzed. For temperature-composition phase diagram construction, two glass-transition temperature equations (i.e., those of Gordon-Taylor and Kwei) and three solid-liquid equilibrium curve modeling approaches [i.e., the Flory-Huggins model, an empirical equation, and the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EOS)] were considered. Indomethacin (IND) and Kollidon 12 PF (PVP K12) were selected as the API and polymer, respectively. An annealing time investigation revealed that the IND-PVP K12 dissolution process was remarkably faster than demixing, which contradicted previously published statements. Thus, the recrystallization method overestimated the solubility of IND in PVP K12 when a 2-h time of annealing was set as the benchmark. Likewise, the MPD and Z-EE methods overestimated the API solubility because of unreliable IND melting endotherm evaluation at lower API loadings and a relatively slow heating rate, respectively. When the experimental results obtained using the S-WD method (in conjunction with the Kwei equation) were applied to the PC-SAFT EOS, which was regarded as the most reliable combination, the predicted IND solubility in PVP K12 at T = 25 °C was approximately 40 wt %. When applicable, the S-WD method offers the advantage of using a limited number of DSC sample pans and API-polymer physical mixture compositions, which is both cost- and time-effective.

Predicting Deliquescence Relative Humidities of Crystals and Crystal Mixtures.

The presence of water in the form of relative humidity (RH) may lead to deliquescence of crystalline components above a certain RH, the deliquescence RH (DRH). Knowing the DRH values is essential, e.g., for the agrochemical industry, food industry, and pharmaceutical industry to identify stability windows for their crystalline products. This work applies the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) to purely predict the DRH of single components (organic acids, sugars, artificial sweeteners, and amides) and multicomponent crystal mixtures thereof only based on aqueous solubility data of the pure components. The predicted DRH values very well agree with the experimental ones. In addition, the temperature influence on the DRH value could be successfully predicted with PC-SAFT. The DRH prediction also differentiates between formation of hydrates and anhydrates. PC-SAFT-predicted phase diagrams of hydrate-forming components illustrate the influence of additional components on the hydrate formation as a function of RH. The DRH prediction via PC-SAFT allows for the determining of the stability of crystals and crystal mixtures without the need for time-consuming experiments.

Solubility Study of Acetylsalicylic Acid in Ethanol + Water Mixtures: Measurement, Mathematical Modeling, and Stability Discussion.

Solubility determination of poorly water-soluble drugs is pivotal for formulation scientists when they want to develop a liquid formulation. Performing such a test with different ratios of cosolvents with water is time-consuming and costly. The scarcity of solubility data for poorly water-soluble drugs increases the importance of developing correlation and prediction equations for these mixtures. Therefore, the aim of the current research is to determine the solubility of acetylsalicylic acid in binary mixtures of ethanol+water at 25 and 37°C. Acetylsalicylic acid is non-stable in aqueous solutions and readily hydrolyze to salicylic acid. So, the solubility of acetylsalicylic acid is measured in ethanolic mixtures by HPLC to follow the concentration of produced salicylic acid as well. Moreover, the solubility of acetylsalicylic acid is modeled using different cosolvency equations. The measured solubility data were also predicted using PC-SAFT EOS model. DSC results ruled out any changes in the polymorphic form of acetylsalicylic acid after the solubility test, whereas XRPD results showed some changes in crystallinity of the precipitated acetylsalicylic acid after the solubility test. Fitting the solubility data to the different cosolvency models showed that the mean relative deviation percentage for the Jouyban-Acree model was less than 10.0% showing that this equation is able to obtain accurate solubility data for acetylsalicylic acid in mixtures of ethanol and water. Also, the predicted data with an average mean relative deviation percentage (MRD%) of less than 29.65% show the capability of the PC-SAFT model for predicting solubility data. A brief comparison of the solubilities of structurally related solutes to acetylsalicylic acid was also provided.

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.

Thermodynamic Modeling of Solvent-Impact on Phase Separation in Amorphous Solid Dispersions during Drying.

Understanding and prevention of unwanted changes of a pharmaceutical formulation during the production process is part of the critical requirements for the successful approval of a new drug product. Polymer-based formulations, so-called amorphous solid dispersions (ASDs), are often produced via solvent-based processes. In such processes, active pharmaceutical ingredients (APIs) and polymers are first dissolved in a solvent or solvent mixture, then the solvent is evaporated, for example, via spray drying or rotary evaporation. During the drying step, unwanted liquid-liquid phase separation may occur, leading to polymer-rich and API-rich regions with crystallization potential, and thus, heterogeneities and a two-phasic system in the final ASD. Phase separation in ASDs may impact their bioperformance because of the locally higher degree of API supersaturation. Although it is known that the choice of the solvent plays an important role in the formation of heterogeneities, solvent-impact on ASD drying and eventual product quality is often neglected in the process design. This study aims to investigate for the first time the phase behavior and drying process of API/polymer/solvents systems from a thermodynamic perspective. Unwanted phase changes during the drying process of the ASD containing hydroxypropyl methylcellulose acetate succinate and naproxen prepared from acetone/water or ethanol/water solvent mixtures were predicted using the thermodynamic model PC-SAFT. The predicted phase behavior and drying curves were successfully validated by confocal Raman spectroscopy.

In-Silico Screening of Lipid-Based Drug Delivery Systems.

PURPOSE: This work proposes an in-silico screening method for identifying promising formulation candidates in complex lipid-based drug delivery systems (LBDDS). METHOD: The approach is based on a minimum amount of experimental data for API solubilites in single excipients. Intermolecular interactions between APIs and excipients as well as between different excipients were accounted for by the Perturbed-Chain Statistical Associating Fluid Theory. The approach was applied to the in-silico screening of lipid-based formulations for ten model APIs (fenofibrate, ibuprofen, praziquantel, carbamazepine, cinnarizine, felodipine, naproxen, indomethacin, griseofulvin and glibenclamide) in mixtures of up to three out of nine excipients (tricaprylin, Capmul MCM, caprylic acid, Capryol™ 90, Lauroglycol™ FCC, Kolliphor TPGS, polyethylene glycol, carbitol and ethanol). RESULTS: For eight out of the ten investigated model APIs, the solubilities in the final formulations could be enhanced by up to 100 times compared to the solubility in pure tricaprylin. Fenofibrate, ibuprofen, praziquantel, carbamazepine are recommended as type I formulations, whereas cinnarizine and felodipine showed a distinctive solubility gain in type II formulations. Increased solubility was found for naproxen and indomethacin in type IIIb and type IV formulations. The solubility of griseofulvin and glibenclamide could be slightly enhanced in type IIIb formulations. The experimental validation agreed very well with the screening results. CONCLUSION: The API solubility individually depends on the choice of excipients. The proposed in-silico-screening approach allows formulators to quickly determine most-appropriate types of lipid-based formulations for a given API with low experimental effort. Graphical abstract.

Choosing Appropriate Solvents for ASD Preparation.

Amorphous solid dispersions (ASDs) are often used for formulating poorly water-soluble active pharmaceutical ingredients (APIs). In an ASD, the amorphous API is embedded in a suitable matrix excipient in order to stabilize the amorphous state and control the dissolution performance. ASDs can be prepared by commonly dissolving the API and the polymer in a suitable organic solvent which is evaporated afterward (e.g., via spray drying) aiming at a homogeneous API distribution in the polymer matrix. Sometimes, unexpected solvent influences on the heterogeneity of the dry ASD are observed. Thermodynamic predictions using the Perturbed-Chain Statistical Associating Fluid Theory combined with experimental investigations via Raman spectroscopy, differential scanning calorimetry, and microscopy performed in this work revealed the amorphous phase separation (APS) between the solvent and the polymer as causing the ASD heterogeneities. It will be shown that thermodynamic modeling allows for identifying appropriate solvents that will neither show APS with the polymeric excipient nor at any time of the drying process of ASD formulations.

Mutual Impact of Phase Separation/Crystallization and Water Sorption in Amorphous Solid Dispersions.

The molecular integration of poorly water soluble active pharmaceutical ingredients (APIs) in a suitable polymeric matrix is a possible approach to enhance the dissolution behavior and solubility of these APIs. Like all newly developed pharmaceutical formulations, these formulations (often denoted as amorphous solid dispersions (ASDs)) need to undergo storage stability tests at defined relative humidity (RH) and temperature conditions. In a previous work ( Int. J. Pharm. 2017 ; 532 , 635 - 646 ), it was shown that thermodynamic modeling can be successfully used to predict the long-term stability of ASDs against API crystallization and moisture-induced amorphous-amorphous phase separation (MIAPS). This work in turn demonstrates the prediction of water sorption in ASDs accounting for the potential occurrence of API crystallization and MIAPS. The water sorption and phase behavior of ASDs containing the APIs felodipine and ibuprofen incorporated in three different hydrophilic polymers poly(vinylpyrrolidone), poly(vinyl acetate), and poly(vinylpyrrolidone-co-vinyl acetate) at the conditions 25 °C/60% RH and 40 °C/75% RH were predicted using the perturbed-chain statistical-associating fluid theory (PC-SAFT). The predictions were successfully validated via two-year-lasting water sorption experiments. It was shown that crystallization of the API and MIAPS on the one hand and water sorption in the ASDs on the other hand dramatically influence each other and that this behavior can even be quantitatively predicted by PC-SAFT, which already provides valuable insights at early stages of formulation development.

Influence of Low-Molecular-Weight Excipients on the Phase Behavior of PVPVA64 Amorphous Solid Dispersions.

PURPOSE: The oral bioavailability of poorly water-soluble active pharmaceutical ingredients (APIs) can be improved by the preparation of amorphous solid dispersions (ASDs) where the API is dissolved in polymeric excipients. Desired properties of such ASDs like storage stability, dissolution behavior, and processability can be optimized by additional excipients. In this work, the influence of so-called low-molecular-weight excipients (LMWEs) on the phase behavior of ASDs was investigated. METHOD: Binary ASDs of an amorphous API, naproxen (NAP) or acetaminophen (APAP), embedded in poly-(vinylpyrrolidone-co-vinyl acetate) (PVPVA64) were chosen as reference systems. Polyethylene glycol 1500 (PEG1500), D-α-tocopherol polyethylene glycol 1000 succinate (TPGS1000), propylene glycol monocaprylate type II (Capryol™ 90), and propylene glycol monolaurate type I (Lauroglycol™ FCC) were used as LMWEs. The API solubility in the excipients and the glass-transition temperature of the ASDs were modeled using the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) and the Kwei equation, respectively, and compared to corresponding experimental data. RESULTS: The API solubility curves in ternary systems with 90/10 wt%/wt% PVPVA64/LMWE ratios were very close to those in pure PVPVA64. However, the glass-transition temperatures of API/PVPVA64/LMWE ASDs were much lower than those of API/PVPVA64 ASDs. These effects were determined experimentally and agreed with the predictions using the PC-SAFT and Kwei models. CONCLUSION: The impact of the LMWEs on the thermodynamic stability of the ASDs is quite small while the kinetic stability is significantly decreased even by small LMWE amounts. PC-SAFT and the Kwei equation are suitable tools for predicting the influence of LMWEs on the ASD phase behavior.

Long-Term Physical Stability of PVP- and PVPVA-Amorphous Solid Dispersions.

The preparation of amorphous solid dispersion (ASD) formulations is a promising strategy to improve the bioavailability of an active pharmaceutical ingredient (API). By dissolving the API in a polymer it is stabilized in its amorphous form, which usually shows higher water solubility than its crystalline counterpart. To prevent recrystallization, the long-term physical stability of ASD formulations is of big interest. In this work, the solubility of the APIs acetaminophen and naproxen in the excipient polymers poly(vinylpyrrolidone) (PVP K25) and poly(vinylpyrrolidone-co-vinyl acetate) (PVPVA64) was calculated with three models: the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT), the Flory-Huggins model (FH), and an empirical model (Kyeremateng et al., J. Pharm. Sci, 2014, 103, 2847-2858). PC-SAFT and FH were further used to predict the influence of relative humidity (RH) on the API solubility in the polymers. The Gordon-Taylor equation was applied to model the glass-transition temperature of dry ASD and at humid conditions. The calculations were validated by 18 months-long stability studies at standardized storage conditions, 25 °C/0% RH, 25 °C/60% RH, and 40 °C/75% RH. The results of the three modeling approaches for the API solubility in polymers agreed with the experimental solubility data, which are only accessible at high temperatures in dry polymers. However, at room temperature FH resulted in a lower solubility of the APIs in the dry polymers than PC-SAFT and the empirical model. The impact of RH on the solubility of acetaminophen was predicted to be small, but naproxen solubility in the polymers was predicted to decrease with increasing RH with both, PC-SAFT and FH. At 25 °C/60% RH and 40 °C/75% RH, PC-SAFT is in agreement with all results of the long-term stability studies, while FH underestimates the acetaminophen solubility in PVP K25 and PVPVA64.

Thermodynamics of enzyme-catalyzed esterifications: I. Succinic acid esterification with ethanol.

Succinic acid (SA) was esterified with ethanol using Candida antarctica lipase B immobilized on acrylic resin at 40 and 50 °C. Enzyme activity in the reaction medium was assured prior to reaction experiments. Reaction-equilibrium experiments were performed for varying initial molalities of SA and water in the reaction mixtures. This allowed calculating the molality-based apparent equilibrium constant K m as function of concentration and temperature. K m was shown to depend strongly on the molality of water and SA as well as on temperature. It could be concluded that increasing the molality of SA shifted the reaction equilibrium towards the products. Water had a strong effect on the activity of the enzyme and on K m . The concentration dependence of K m values was explained by the activity coefficients of the reacting agents. These were predicted with the thermodynamic models Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT), NRTL, and Universal Quasichemical Functional Group Activity Coefficients (UNIFAC), yielding the ratio of activity coefficients of products and reactants K γ . All model parameters were taken from literature. The models yielded K γ values between 25 and 115. Thus, activity coefficients have a huge impact on the consistent determination of the thermodynamic equilibrium constants K th. Combining K m and PC-SAFT-predicted K γ allowed determining K th and the standard Gibbs energy of reaction as function of temperature. This value was shown to be in very good agreement with results obtained from group contribution methods for Gibbs energy of formation. In contrast, inconsistencies were observed for K th using K γ values from the classical gE-models UNIFAC and NRTL. The importance of activity coefficients opens the door for an optimized reaction setup for enzymatic esterifications.