COSMOPharm: Drug-Polymer Compatibility of Pharmaceutical Amorphous Solid Dispersions from COSMO-SAC.

The quantum mechanics-aided COSMO-SAC activity coefficient model is applied and systematically examined for predicting the thermodynamic compatibility of drugs and polymers. The drug-polymer compatibility is a key aspect in the rational selection of optimal polymeric carriers for pharmaceutical amorphous solid dispersions (ASD) that enhance drug bioavailability. The drug-polymer compatibility is evaluated in terms of both solubility and miscibility, calculated using standard thermodynamic equilibrium relations based on the activity coefficients predicted by COSMO-SAC. As inherent to COSMO-SAC, our approach relies only on quantum-mechanically derived σ-profiles of the considered molecular species and involves no parameter fitting to experimental data. All σ-profiles used were determined in this work, with those of the polymers being derived from their shorter oligomers by replicating the properties of their central monomer unit(s). Quantitatively, COSMO-SAC achieved an overall average absolute deviation of 13% in weight fraction drug solubility predictions compared to experimental data. Qualitatively, COSMO-SAC correctly categorized different polymer types in terms of their compatibility with drugs and provided meaningful estimations of the amorphous-amorphous phase separation. Furthermore, we analyzed the sensitivity of the COSMO-SAC results for ASD to different model configurations and σ-profiles of polymers. In general, while the free volume and dispersion terms exerted a limited effect on predictions, the structures of oligomers used to produce σ-profiles of polymers appeared to be more important, especially in the case of strongly interacting polymers. Explanations for these observations are provided. COSMO-SAC proved to be an efficient method for compatibility prediction and polymer screening in ASD, particularly in terms of its performance-cost ratio, as it relies only on first-principles calculations for the considered molecular species. The open-source nature of both COSMO-SAC and the Python-based tool COSMOPharm, developed in this work for predicting the API-polymer thermodynamic compatibility, invites interested readers to explore and utilize this method for further research or assistance in the design of pharmaceutical formulations.

Topology of thermodynamic potentials using physical models: Helmholtz, Gibbs, Grand, and Null.

Thermodynamic potentials play a substantial role in numerous scientific disciplines and serve as basic constructs for describing the behavior of matter. Despite their significance, comprehensive investigations of their topological characteristics and their connections to molecular interactions have eluded exploration due to experimental inaccessibility issues. This study addresses this gap by analyzing the topology of the Helmholtz energy, Gibbs energy, Grand potential, and Null potential that are associated with different isothermal boundary conditions. By employing Monte Carlo simulations in the NVT, NpT, and µVT ensembles and a molecular-based equation of state, methane, ethane, nitrogen, and methanol are investigated over a broad range of thermodynamic conditions. The predictions from the two independent methods are overall in very good agreement. Although distinct quantitative differences among the fluids are observed, the overall topology of the individual thermodynamic potentials remains unaffected by the molecular architecture, which is in line with the corresponding states principle-as expected. Furthermore, a comparative analysis reveals significant differences between the total potentials and their residual contributions.

Fundamental equation of state for mixtures of nitrogen, oxygen, and argon based on molecular simulation data.

A fundamental equation of state in terms of the Helmholtz energy is presented for mixtures of nitrogen, oxygen, and argon at any composition. It is expressed in terms of the residual Helmholtz energy and can be used to calculate all thermodynamic equilibrium properties including vapor-liquid equilibria. The parameters of the equations for the pure-fluid and mixture contributions are fitted exclusively to molecular simulation data so that the model has a predictive character. The description of the mixture-specific reducing parameters is realized via generalized correlations of the critical parameters of the pure fluids so that an extension of the model to additional components can be implemented straightforwardly. Extensive comparisons to experimental data and the GERG-2008 reference equation of state show that the prediction of thermodynamic properties is satisfactory.

Influence of repulsion on entropy scaling and density scaling of monatomic fluids.

Entropy scaling is applied to the shear viscosity, self-diffusion coefficient, and thermal conductivity of simple monatomic fluids. An extensive molecular dynamics simulation series is performed to obtain these transport properties and the residual entropy of three potential model classes with variable repulsive exponents: n, 6 Mie (n = 9, 12, 15, and 18), Buckingham's exponential-six (α = 12, 14, 18, and 30), and Tang-Toennies (αT = 4.051, 4.275, and 4.600). A wide range of liquid and supercritical gas- and liquid-like states is covered with a total of 1120 state points. Comparisons to equations of state, literature data, and transport property correlations are made. Although the absolute transport property values within a given potential model class may strongly depend on the repulsive exponent, it is found that the repulsive steepness plays a negligible role when entropy scaling is applied. Hence, the plus-scaled transport properties of n, 6 Mie, exponential-six, and Tang-Toennies fluids lie basically on one master curve, which closely corresponds with entropy scaling correlations for the Lennard-Jones fluid. This trend is confirmed by literature data of n, 6 Mie, and exponential-six fluids. Furthermore, entropy scaling holds for state points where the Pearson correlation coefficient R is well below 0.9. The condition R > 0.9 for strongly correlating liquids is thus not necessary for the successful application of entropy scaling, pointing out that isomorph theory may be a part of a more general framework that is behind the success of entropy scaling. Density scaling reveals a strong influence of the repulsive exponent on this particular approach.

Phase equilibria of symmetric Lennard-Jones mixtures and a look at the transport properties near the upper critical solution temperature.

This study investigates phase equilibria and transport properties of five symmetric binary Lennard-Jones mixtures using molecular simulation and equation of state models. The mixtures are selected for their representation of different types of phase behavior and the research contributes to the development of simulation techniques, mixture theories and understanding of thermophysical mixture properties. A novel method is introduced for determining the critical end point (CEP) and critical azeotropic end point (CAEP) by molecular simulation. The van der Waals one-fluid theory is assessed for its performance in conjunction with Lennard-Jones equation of state models, while addressing different phase equilibrium types simultaneously. An empirical correlation is introduced to account for deviations between the equation of state and simulation that arise when using the same binary interaction parameter. This study also investigates the influence of the liquid-liquid critical point on thermophysical properties, which are found to exhibit no significant anomalies or singularities. System-size effects of diffusion coefficients are addressed by extrapolating simulation data to the thermodynamic limit and applying analytical finite-size corrections.

Equation of state for the Mie (λr,6) fluid with a repulsive exponent from 11 to 13.

An empirical multi-parameter equation of state in terms of the reduced Helmholtz energy is presented for the Mie (λr-6) fluid with a repulsive exponent λr from 11 to 13. The equation is fitted to an extensive dataset from molecular dynamics simulation as well as the second and third thermal virial coefficients. It is comprehensively compared with the SAFT-VR model and is a more accurate description of the considered fluid class. The equation is valid for reduced temperatures T/Tc from 0.55 to 4.5 and for reduced pressures of up to p/pc = 265. A good extrapolation behavior and the occurrence of a single Maxwell loop down to the vicinity of the triple point temperature are realized.

Thermodynamics of supercritical carbon dioxide mixtures across the Widom line.

Supercritical carbon dioxide (scCO2) mixtures are essential for many industrial applications. However, the knowledge of their thermophysical properties in the extended critical region is insufficient. Here, supercritical liquid- and gas-like regions dominated by distinct dynamics and thermodynamics exist and are demarcated by the so-called Widom line. The nature of the anomalies observed for several thermophysical properties at the crossover between these two regions is the subject of a lively debate. Hence, the extended critical region of scCO2 and seven of its binary mixtures with hydrogen, methane, ethane, isobutane, benzene, toluene or naphthalene is studied with respect to thermodynamic, transport and structural properties on the basis of molecular dynamics simulations and equation of state calculations. The Widom line is evaluated employing five criteria and a new empirical equation is proposed for its prediction. Further, the crossover anomalies are investigated in the light of pseudo-boiling theory, diffusion and viscosity as well as structural characteristics given by the radial distribution function.

Connecting entropy scaling and density scaling.

It is shown that the residual entropy (entropy minus that of the ideal gas at the same temperature and density) is mostly synonymous with the independent variable of density scaling, identifying a direct link between these two approaches. The residual entropy and the effective hardness of interaction (itself a derivative at constant residual entropy) are studied for the Lennard-Jones monomer and dimer as well as a range of rigid molecular models for carbon dioxide. It is observed that the density scaling exponent appears to be related to the two-body interactions in the dilute-gas limit.

Diffusion of the carbon dioxide-ethanol mixture in the extended critical region.

The effect of traces of ethanol in supercritical carbon dioxide on the mixture's thermodynamic properties is studied by molecular simulations and Taylor dispersion measurements. This mixture is investigated along the isobar p = 10 MPa in the temperature range between T = 304 and 343 K. Along this path, the mixture undergoes two transitions: First, the Widom line is crossed, marking the transition from liquid-like to gas-like conditions. A second transition occurs from the supercritical gas-like domain to a subcritical gas. The Widom line crossover entails inflection points for most of the studied properties, i.e. density, enthalpy, shear viscosity, Maxwell-Stefan and intradiffusion coefficients. On the other hand, the transition between the super- and subcritical regions is found to be generally smooth, an observation that is qualitatively confirmed by experimental Taylor dispersion measurements. Dedicated atomistic simulations show the presence of microheterogeneities due to ethanol self-association along the investigated path, which lead to the mixture's anomalous behavior in its extended critical region.

Bulk viscosity of liquid noble gases.

An equation of state for the bulk viscosity of liquid noble gases is proposed. On the basis of dedicated equilibrium molecular dynamics simulations, a multi-mode relaxation ansatz is used to obtain precise bulk viscosity data over a wide range of liquid states. From this dataset, the equation of state emerges as a two-parametric power function with both parameters showing a conspicuous saturation behavior over temperature. After passing a temperature threshold, the bulk viscosity is found to vary significantly over density, a behavior that resembles the frequency response of a one pole low-pass filter. The proposed equation of state is in good agreement with available experimental sound attenuation data.

Dielectric constant and density of aqueous alkali halide solutions by molecular dynamics: A force field assessment.

The concentration dependence of the dielectric constant and the density of 11 aqueous alkali halide solutions (LiCl, NaCl, KCl, RbCl, CsCl, LiI, NaI, KI, CsI, KF, and CsF) is investigated by molecular simulation. Predictions using eight non-polarizable ion force fields combined with the TIP4P/ε water model are compared to experimental data. The influence of the water model and the temperature on the results for the NaCl brine are also addressed. The TIP4P/ε water model improves the accuracy of dielectric constant predictions compared to the SPC/E water model. The solution density is predicted well by most ion models. Almost all ion force fields qualitatively capture the decline of the dielectric constant with the increase of concentration for all solutions and with the increase of temperature for NaCl brine. However, the sampled dielectric constant is mostly in poor quantitative agreement with experimental data. These results are related to the microscopic solution structure, ion pairing, and ultimately the force field parameters. Ion force fields with excessive contact ion pairing and precipitation below the experimental solubility limit generally yield higher dielectric constant values. An adequate reproduction of the experimental solubility limit should therefore be a prerequisite for further investigations of the dielectric constant of aqueous electrolyte solutions by molecular simulation.

Structure and dynamics of the Lennard-Jones fcc-solid focusing on melting precursors.

The Lennard-Jones potential is taken as a basis to study the structure and dynamics of the face centered cubic (fcc) solid along an isochore from low temperatures up to the solid/fluid transition. The Z method is applied to estimate the melting point. Molecular dynamics simulations are used to calculate the pair distribution function, numbers of nearest neighbors, and the translational order parameter, analyzing the weakening of the fcc-symmetry due to emerging premelting effects. A range of dynamic properties, such as the mean-squared displacement, non-Gaussian parameter, Debye-Waller factor, and vibrational density of states, is considered for the analysis of the solid state. All of these parameters clearly show that bulk mobility is activated at about 2/3 of the melting temperature, known as the Tammann temperature. This indicates that vibrational motion of atoms is not maintained exclusively in the entire stable solid state and that collective atomic motion constitutes a precursor of the melting process.

Thermophysical Properties of the Lennard-Jones Fluid: Database and Data Assessment.

Literature data on the thermophysical properties of the Lennard-Jones fluid, which were sampled with molecular dynamics and Monte Carlo simulations, were reviewed and assessed. The literature data were complemented by simulation data from the present work that were taken in regions in which previously only sparse data were available. Data on homogeneous state points (for given temperature T and density ρ: pressure p, thermal expansion coefficient α, isothermal compressibility ß, thermal pressure coefficient γ, internal energy u, isochoric heat capacity cv, isobaric heat capacity cp, Grüneisen parameter Γ, Joule-Thomson coefficient µJT, speed of sound w, Helmholtz energy a, and chemical potential) were considered, as well as data on the vapor-liquid equilibrium (for given T: vapor pressure ps, saturated liquid and vapor densities ρ' and ρ″, respectively, enthalpy of vaporization Δhv, and as well as surface tension γ). The entire set of available data, which contains about 35 000 data points, was digitalized and included in a database, which is made available in the Supporting Information of this paper. Different consistency tests were applied to assess the accuracy and precision of the data. The data on homogeneous states were evaluated pointwise using data from their respective vicinity and equations of state. Approximately 10% of all homogeneous bulk data were discarded as outliers. The vapor-liquid equilibrium data were assessed by tests based on the compressibility factor, the Clausius-Clapeyron equation, and by an outlier test. Seven particularly reliable vapor-liquid equilibrium data sets were identified. The mutual agreement of these data sets is approximately ±1% for the vapor pressure, ±0.2% for the saturated liquid density, ±1% for the saturated vapor density, and ±0.75% for the enthalpy of vaporization-excluding the region close to the critical point.

Evaporation sampled by stationary molecular dynamics simulation.

A nonequilibrium method is developed to sample evaporation of a liquid across a planar interface in a stationary scenario by molecular dynamics. The method does not rely on particle insertions which are challenging when they are used to maintain mass conservation. Its algorithm has a low complexity and is well suited for massively parallel simulations that may yield results with an excellent statistical accuracy. Spatially resolved classical profiles, e.g., for temperature, density, and force, are sampled with a high resolution for a varying hydrodynamic velocity of the evaporation flow. Relatively large systems are simulated, allowing for a detailed study of velocity distribution functions. Varying the hydrodynamic velocity from zero to the speed of sound, it is found that the evaporation flux increases asymptotically, reaching about 90% of its maximum value when the hydrodynamic velocity is about half of its maximum value. A deviation from the Maxwell distribution is identified for the transversal particle velocity near the interface which selectively hinders the migration of individual particles from liquid to vapor with its potential well, allowing only the faster ones to escape. The vapor region in the vicinity of the interface exhibits a spread between the transversal and longitudinal temperature, but equipartition is reattained through particle interactions such that Maxwell distributions are found at a certain distance from the interface. A detailed discussion of the atomistic mechanisms during evaporation is provided, facilitating understanding of this ubiquitous process.

Composition dependent transport diffusion in non-ideal mixtures from spatially resolved nuclear magnetic resonance spectroscopy.

Nuclear magnetic resonance (NMR) spectroscopy is a well-established technique for the measurement of intra-diffusion coefficients. Recently, such information has been used as a basis of predictive models to extrapolate to the Fick diffusion coefficient of liquid mixtures. The present work presents a new approach to directly access the Fick diffusion coefficient by spatially resolved NMR experiments. The Fick diffusion coefficient of the binary mixture TEA/H2O was determined at two temperatures, 283.2 K and 275.2 K. The results are consistent with values previously reported either from optical experiments or predictive Darken-type models developed for this system. The proposed methodology adds high-resolution NMR to the toolbox for the study of the transport diffusion of multicomponent mixtures. It is, however, still limited to mixtures with liquid-liquid equilibrium phase separation.

Interplay of structure and diffusion in ternary liquid mixtures of benzene + acetone + varying alcohols.

The Fick diffusion coefficient matrix of ternary mixtures containing benzene + acetone + three different alcohols, i.e., methanol, ethanol, and 2-propanol, is studied by molecular dynamics simulation and Taylor dispersion experiments. Aiming to identify common features of these mixtures, it is found that one of the main diffusion coefficients and the smaller eigenvalue do not depend on the type of alcohol along the studied composition path. Two mechanisms that are responsible for this invariant behavior are discussed in detail, i.e., the interplay between kinetic and thermodynamic contributions to Fick diffusion coefficients and the presence of microscopic heterogeneities caused by hydrogen bonding. Experimental work alone cannot explain these mechanisms, while present simulations on the molecular level indicate structural changes and uniform intermolecular interactions between benzene and acetone molecules in the three ternary mixtures. The main diffusion coefficients of these ternary mixtures exhibit similarities with their binary subsystems. Analyses of radial distribution functions and hydrogen bonding statistics quantitatively evidence alcohol self-association and cluster formation, as well as component segregation. Furthermore, the excess volume of the mixtures is analyzed in the light of intermolecular interactions, further demonstrating the benefits of the simultaneous use of experiment and simulation. The proposed framework for studying diffusion coefficients of a set of ternary mixtures, where only one component varies, opens the way for further investigations and a better understanding of multicomponent diffusion. The presented numerical results may also give an impulse to the development of predictive approaches for multicomponent diffusion.

Mutual diffusion governed by kinetics and thermodynamics in the partially miscible mixture methanol + cyclohexane.

To gain an understanding of the transport and thermodynamic behavior of the highly non-ideal mixture methanol + cyclohexane, three complementary approaches, i.e. experiment, molecular simulation and predictive equations, are employed. The temperature and composition dependence of different diffusion coefficients is studied around the miscibility gap at ambient pressure. On the one hand Fick diffusion coefficients are measured experimentally by interferometric probing and on the other hand Maxwell-Stefan diffusion coefficients and intradiffusion coefficients are sampled by equilibrium molecular dynamics simulation at five temperatures below the upper critical temperature of ∼319 K. The spinodal curve is determined from extrapolation of the experimental Fick diffusion coefficient data and compared to predictions from excess Gibbs energy models. It is found that these models are not capable to correctly describe the activity coefficients over the whole composition range of the studied mixture. Thus, different parameter sets for a modified Wilson model are used for calculations of the thermodynamic factor, which is needed to transform Maxwell-Stefan into Fick diffusion coefficients and vice versa. Further, predictive equations for the Maxwell-Stefan diffusion coefficient, which are based on intradiffusion coefficients, are compared to simulation results. Using different approaches provides a clearer understanding of the relations between kinetic and thermodynamic properties contributing to the diffusion behavior of partially miscible mixtures.

Premelting, solid-fluid equilibria, and thermodynamic properties in the high density region based on the Lennard-Jones potential.

The Lennard-Jones potential is used to study the high density fluid and face centered cubic solid state region, including solid-fluid equilibria. Numerous thermodynamic properties are considered, elucidating the behavior of matter in this poorly studied region. The present molecular simulation results are extensively compared to the latest and most accurate equation of state models for fluid and solid phases. It is shown that current models do not cover the thermodynamics of the system adequately near the solid-fluid phase transition. Furthermore, thermodynamic stability is analyzed, indicating that published solid-fluid coexistence data may not be correct at high temperatures. Particular attention is paid to the premelting zone, a range of states close to the melting line, which is characterized by strong variations of several thermodynamic properties. Because the underlying microscopic mechanisms are not yet fully understood, it is hoped that these data may contribute to the development of a theoretical framework for describing premelting effects.

Assessing the accuracy of improved force-matched water models derived from Ab initio molecular dynamics simulations.

The accuracy of water models derived from ab initio molecular dynamics simulations by means on an improved force-matching scheme is assessed for various thermodynamic, transport, and structural properties. It is found that although the resulting force-matched water models are typically less accurate than fully empirical force fields in predicting thermodynamic properties, they are nevertheless much more accurate than generally appreciated in reproducing the structure of liquid water and in fact superseding most of the commonly used empirical water models. This development demonstrates the feasibility to routinely parametrize computationally efficient yet predictive potential energy functions based on accurate ab initio molecular dynamics simulations for a large variety of different systems. © 2016 Wiley Periodicals, Inc.

Communication: Evaporation: Influence of heat transport in the liquid on the interface temperature and the particle flux.

Molecular dynamics simulations are reported for the evaporation of a liquid into vacuum, where a Lennard-Jones type fluid with truncated and shifted potential at 2.5σ is considered. Vacuum is enforced locally by particle deletion and the liquid is thermostated in its bulk so that heat flows to the planar interface driving stationary evaporation. The length of the non-thermostated transition region between the bulk liquid and the interface Ln is under study. First, it is found for the reduced bulk liquid temperature Tl/Tc = 0.74 (Tc is the critical temperature) that by increasing Ln from 5.2σ to 208σ the interface temperature Ti drops by 17% and the evaporation flux decreases by a factor of 4.4. From a series of simulations for increasing values of Ln, an asymptotic value Ti (∞) of the interface temperature for Ln → ∞ can be estimated which is 21% lower than the bulk liquid temperature Tl. Second, it is found that the evaporation flux is solely determined by the interface temperature Ti, independent on Tl or Ln. Combining these two findings, the evaporation coefficient α of a liquid thermostated on a macroscopic scale is estimated to be α ≈ 0.14 for Tl/Tc = 0.74.