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.

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.

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 (k_ij) are fitted. Therefore, to make this benchmark as fair as possible, we omitted any binary parameters of PC-SAFT (i.e., k_ij = 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.

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

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

Does Explicit Polarizability Improve Molecular Dynamics Predictions of Glass Transition Temperatures of Ionic Liquids?

Molecular dynamics simulations are used for predictions of the glass transition temperatures for a test set of five aprotic ionic liquids. Glass transitions are localized with the trend-shift method, analyzing volumetric and transport properties of bulk amorphous phases. A classical nonpolarizable all-atom OPLS force-field model developed by Canongia Lopes and Pádua (CL&P) is employed as a starting level of theory for all calculations. Alternative approaches of charge scaling and the Drude oscillator model, accounting for atomic polarizability either implicitly or explicitly, respectively, are used to investigate the sensitivity of the glass transition temperatures to induction effects. The former nonpolarizable model overestimates the glass transition temperature by tens of Kelvins (37 K on average). The charge-scaling technique yields a significant improvement, and the best estimations were achieved using polarizable simulations with the Drude model, which yielded an average deviation of 11 K. Although the volumetric data usually exhibit a lesser trend shift upon vitrification, their lower statistical uncertainty enables to predict the glass transition temperature with lower uncertainty than the ionic self-diffusivities, the temperature dependence of which is usually more scattered. Additional analyses of the simulated data were also performed, revealing that the Drude model predicts lower densities for most subcooled liquids but higher densities for the glasses than the original CL&P, and that the Drude model also invokes some longer-range organization of the subcooled liquid, greatly impacting the temperature trend of ionic self-diffusivities in the low-temperature region.

Does Explicit Polarizability Improve Simulations of Phase Behavior of Ionic Liquids?

Molecular dynamics simulations are performed for a test set of 20 aprotic ionic liquids to investigate whether including an explicit polarizability model in the force field leads to higher accuracy and reliability of the calculated phase behavior properties, especially the enthalpy of fusion. A classical nonpolarizable all-atom optimized potentials for liquid simulations (OPLS) force-field model developed by Canongia Lopes and Pádua (CL&P) serves as a reference level of theory. Polarizability is included either in the form of Drude oscillators, resulting in the CL&P-D models, or in the framework of the atomic multipole optimized energetics for biomolecular application (AMOEBA) force field with polarizable atomic sites. Benchmarking of the calculated fusion enthalpy values against the experimental data reveals that overall the nonpolarizable CL&P model and polarizable CL&P-D models perform similarly with average deviations of about 30%. However, fusion enthalpies from the CL&P-D models exhibit a stronger correlation with their experimental counterparts. The least successful predictions are interestingly obtained from AMOEBA (deviation ca. 60%), which may indicate that a reparametrization of this force-field model is needed to achieve improved predictions of the fusion enthalpy. In general, all FF models tend to underestimate the fusion enthalpies. In addition, quantum chemical calculations are used to compute the electronic cohesive energies of the crystalline phases of the ionic liquids and of the interaction energies within the ion pair. Significant positive correlations are found between the fusion enthalpy and the cohesive energies. The character of the present anions predetermines the magnitude of individual mechanistic components of the interaction energy and related enthalpic and cohesive properties.

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.