The re-entrant transition from the molecular to atomic phases of dense fluids: The case of hydrogen.

A simple phenomenological thermodynamic model is developed to describe the chemical bonding and unbonding in homonuclear diatomic systems. This model describes the entire phase diagram of dimer-forming systems and shows a transition from monomers to dimers, with monomers favored at both very low and very high pressures, as well as at high temperatures. In the context of hydrogen, the former region corresponds to hydrogen present in most interstellar gas clouds, while the latter is associated with the long sought-after fluid metallic phase. The model predicts a molecular to atomic fluid transition in dense deuterium, which is in agreement with recently reported experimental measurements.

Using the Zeno line to assess and refine molecular models.

The Zeno line is the locus of points on the temperature-density plane where the compressibility factor of the fluid is equal to one. It has been observed to be straight for a broad variety of real fluids, although the underlying reasons for this are still unclear. In this work, a detailed study of the Zeno line and its relation to the vapor-liquid coexistence curve is performed for two simple model pair-potential fluids: attractive square-well fluids with varying well-widths λ and Mie n-6 fluids with different repulsive exponents n. Interestingly, the Zeno lines of these fluids are curved, regardless of the value of λ or n. We find that for square-well fluids, λ ≈ 1.8 presents a Zeno line, which is the most linear over the largest temperature range. For Mie n-6 fluids, we find that the straightest Zeno line occurs for n between 8 and 10. Additionally, the square-well and Mie fluids with the straightest Zeno line showed the closest quantitative agreement with the vapor-liquid coexistence curve for experimental fluids that follow the principle of corresponding states (e.g., argon, xenon, krypton, methane, nitrogen, and oxygen). These results suggest that the Zeno line can provide a useful additional feature, in complement to other properties, such as the phase envelope, to evaluate molecular models.

From Atoms to Colloids: Does the Frenkel Line Exist in Discontinuous Potentials?

The Frenkel line has been proposed as a crossover in the fluid region of phase diagrams between a "nonrigid" and a "rigid" fluid. It is generally described as a crossover in the dynamical properties of a material and as such has been described theoretically using a very different set of markers from those with which is it investigated experimentally. In this study, we have performed extensive calculations using two simple yet fundamentally different model systems: hard spheres and square-well potentials. The former has only hardcore repulsion, while the latter also includes a simple model of attraction. We computed and analyzed a series of physical properties used previously in simulations and experimental measurements and discuss critically their correlations and validity as to being able to uniquely and coherently locate the Frenkel line in discontinuous potentials.

Tethered hard spheres: A bridge between the fluid and solid phases.

The thermodynamics of hard spheres tethered to a Face-Centered Cubic (FCC) lattice is investigated using event-driven molecular-dynamics. The particle-particle and the particle-tether collision rates are related to the phase space geometry and are used to study the FCC and fluid states. In tethered systems, the entropy can be determined by at least two routes: (i) through integration of the tether collision rates with the tether length rT or (ii) through integration of the particle-particle collision rates with the hard-sphere diameter σ (or, equivalently, the density). If the entropy were an entirely analytic function of rT and σ, these two methods for calculating the entropy should lead to the same results; however, a non-analytic region exists as an extension of the solid-fluid phase transition of the untethered hard-sphere system, and integration paths that cross this region will lead to values for the entropy that depend on the particular path chosen. The difference between the calculated entropies appears to be related to the communal entropy, and the location of the non-analytic region appears to be related to conditions where the regions of phase space associated with the FCC configuration become separated from those associated with the disordered fluid. The non-analytic region is finite in extent, vanishing below rT/a ≈ 0.55, where a is the lattice spacing, and there are many continuous paths that connect the fluid and solid phases that can be used to determine the crystal free energy with respect to the fluid.

Temperature Dependence of Solubility Predicted from Thermodynamic Data Measured at a Single Temperature: Application to α, ß, and γ-Glycine.

Understanding of solid-liquid equilibria for polymorphic systems is crucial for rational design and efficient operation of crystallization processes. In this work, we present a framework to determine the temperature dependent solubility based on experimentally accessible thermodynamic data measured at a single temperature. Using this approach, we investigate aqueous solubility of α, ß, and γ-glycine, which, despite numerous studies, have considerable quantitative uncertainty, in particular for the most stable (γ) and the least stable (ß) solid forms. We benchmark our framework on α-glycine giving predictions in excellent agreement with direct solubility measurements between 273-340 K, using only thermodynamic data measured at the reference temperature (298.15 K). We analyze the sensitivity of solubility predictions with respect to underlying measurement uncertainty, as well as the excess Gibbs free energy models used to derive required thermodynamic quantities before providing solubility predictions for ß and γ-glycine between 273-310 and 273-330 K, respectively. Crucially, this approach to predict solubility as a function of temperature does not rely on measurement of solute melting properties which will be particularly useful for compounds that undergo thermal decomposition or polymorph transition prior to melting.

Modeling Diffusive Mixing in Antisolvent Crystallization.

Diffusion controls local concentration profiles at interfaces between segregated fluid elements during mixing processes. This is important for antisolvent crystallization, where it is intuitively argued that local concentration profiles at interfaces between solution and antisolvent fluid elements can result in significant supersaturation overshoots over and above that at the final mixture composition, leading to poorly controlled nucleation. Previous work on modeling diffusive mixing in antisolvent crystallization has relied on Fickian diffusion, where concentration gradients are the driving force for diffusion. This predicts large overshoots in the supersaturation at interfaces between solution and antisolvent, as is often intuitively expected. However, chemical potential gradients provide a more physically realistic driving force for diffusion, and in highly nonideal solutions, such as those in antisolvent crystallization, this leads to nonintuitive behavior. In particular, as solute diffusion toward antisolvent is severely hindered, it can diffuse against its concentration gradient away from antisolvent. We apply thermodynamically consistent diffusion model based on the multicomponent Maxwell-Stefan formulation to examine diffusive mixing in a nonideal antisolvent crystallization system. Large supersaturation overshoots above that at the final mixture composition are not found when a thermodynamically consistent approach is used, demonstrating that these overshoots are modeling artifacts and are not expected to be present in physical systems. In addition, for certain conditions, localized liquid-liquid spinodal demixing is predicted to occur during the diffusive mixing process, even when the final mixture composition is outside the liquid-liquid phase separation region. Intermittent spinodal demixing driven by diffusive mixing may provide a novel explanation for differences of nucleation behaviors among various antisolvents.

Employing Constant Rate Filtration To Assess Active Pharmaceutical Ingredient Washing Efficiency.

Washing is a key step in pharmaceutical isolation to remove unwanted crystallization solvents and dissolved impurities (mother liquor) from the active pharmaceutical ingredient (API) filter cake to ensure the purity of the product whilst maximizing yield. It is therefore essential to avoid both product dissolution and impurity precipitation during washing, especially precipitation of impurities caused by the wash solvent acting as an antisolvent, affecting purity and causing agglomerate formation. This work investigates the wash solvent flow through a saturated filter cake to optimize washing by displacement, taking account of diffusional mechanisms and manipulating the wash contact time. Constant rate filtration/washing is employed in this study using readily available laboratory equipment. One advantage of using constant rate filtration in this work is that it allows for the collection of separate aliquots during all stages of filtration, washing, and deliquoring of the API cake. This enables a wash profile to be obtained, as well as providing an overall picture on the mass of API lost during isolation and so can assist in optimizing the washing strategy. Particle size analysis of damp cake obtained straight after washing is also performed using laser diffraction. This allowed for agglomerate formation caused during washing to be distinguished from agglomeration that would be caused by subsequent drying of the wet filter cake. This work aims at improving pharmaceutical product quality, increasing sustainability, and reducing manufacturing cost.

Molecular dynamics study of six-dimensional hard hypersphere crystals.

Six-dimensional hard hypersphere systems in the A6, D6, and E6 crystalline phases have been studied using event-driven molecular dynamics simulations in periodic, skew cells that reflect the underlying lattices. In all the simulations, the systems had sufficient numbers of hyperspheres to capture the first coordination shells, and the larger simulations also included the complete second coordination shell. The equations of state, for densities spanning the fluid, metastable fluid, and solid regimes, were determined. Using molecular dynamics simulations with the hyperspheres tethered to lattice sites allowed the computation of the free energy for each of the crystal lattices relative to the fluid phase. From these free energies, the fluid-crystal coexistence region was determined for the E6, D6, and A6 lattices. Pair correlation functions for all the examined states were computed. Interestingly, for all the states examined, the pair correlation functions displayed neither a split second peak nor a shoulder in the second peak. These behaviors have been previously used as a signature of the freezing of the fluid phase for hard hyperspheres in two to five dimensions.

Tethered-particle model: The calculation of free energies for hard-sphere systems.

Two methods for computing the entropy of hard-sphere systems using a spherical tether model are explored, which allow the efficient use of event-driven molecular-dynamics simulations. An intuitive derivation is given, which relates the rate of particle collisions, either between two particles or between a particle and its respective tether, to an associated hypersurface area, which bounds the system's accessible configurational phase space. Integrating the particle-particle collision rates with respect to the sphere diameter (or, equivalently, density) or the particle-tether collision rates with respect to the tether length then directly determines the volume of accessible phase space and, therefore, the system entropy. The approach is general and can be used for any system composed of particles interacting with discrete potentials in fluid, solid, or glassy states. The entropies calculated for the liquid and crystalline hard-sphere states using these methods are found to agree closely with the current best estimates in the literature, demonstrating the accuracy of the approach.

Exploring the Role of Anti-solvent Effects during Washing on Active Pharmaceutical Ingredient Purity.

Washing is a key step in pharmaceutical isolation to remove the unwanted crystallization solvent (mother liquor) from the active pharmaceutical ingredient (API) filter cake. This study looks at strategies for optimal wash solvent selection, which minimizes the dissolution of API product crystals while preventing the precipitation of product or impurities. Selection of wash solvents to avoid both these phenomena can be challenging but is essential to maintain the yield, purity, and particle characteristics throughout the isolation process. An anti-solvent screening methodology has been developed to quantitatively evaluate the propensity for precipitation of APIs and their impurities of synthesis during washing. This is illustrated using paracetamol (PCM) and two typical impurities of synthesis during the washing process. The solubility of PCM in different binary wash solutions was measured to provide a basis for wash solvent selection. A map of wash solution composition boundaries for precipitation for the systems investigated was developed to depict where anti-solvent phenomena will take place. For some crystallization and wash solvent combinations investigated, as much as 90% of the dissolved PCM and over 10% of impurities present in the PCM saturated mother liquor were found to precipitate out. Such levels of uncontrolled crystallization during washing in a pharmaceutical isolation process can have a drastic effect on the final product purity. Precipitation of both the product and impurities from the mother liquor can be avoided by using a solvent in which the API has a solubility similar to that in the mother liquor; for example, the use of acetonitrile as a wash solvent does not result in precipitation of either the PCM API or its impurities. However, the high solubility of PCM in acetonitrile would result in noticeable dissolution of API during washing and would lead to agglomeration during the subsequent drying step. Contrarily, the use of n-heptane as a wash solvent for a PCM crystal slurry resulted in the highest amount of precipitation among the solvent pairs evaluated. This can be mitigated by designing a multi-stage washing strategy where wash solutions of differing wash solvent concentrations are used to minimize step changes in solubility when the mother liquor and the wash solvent come into contact.

Simple corrections for the static dielectric constant of liquid mixtures from model force fields.

Pair-wise additive force fields provide fairly accurate predictions, through classical molecular simulations, for a wide range of structural, thermodynamic, and dynamical properties of many materials. However, one key property that has not been well captured is the static dielectric constant, which characterizes the response of a system to an applied electric field and is important in determining the screening of electrostatic interactions through a system. A simple correction has been found to provide a relatively robust method to improve the estimate of the static dielectric constant from molecular simulations for a broad range of compounds. This approach accounts for the electronic contribution to molecular polarizability and assumes that the charges that couple a molecule to an applied electric field are proportional to the effective force field charges. In this work, we examine how this correction performs for systems at different temperatures and for binary mixtures. Using a value for the electronic polarizability, based on the experimental index of refraction, and a charge scaling factor, determined at a single temperature, we find that the static dielectric constant can be predicted remarkably well, in comparison to the experimentally measured values. This provides good evidence that the effective charges that appear in pair-wise additive force fields developed to reproduce the potential energy surface of a system are not the same as those that determine the static dielectric constant; however, they can be captured in a relatively simple manner, which is dependent on the particular force field.

Anomalous heat transport in binary hard-sphere gases.

Equilibrium and nonequilibrium molecular dynamics (MD) are used to investigate the thermal conductivity of binary hard-sphere fluids. It is found that the thermal conductivity of a mixture can not only lie outside the series and parallel bounds set by their pure component values, but can lie beyond even the pure component fluid values. The MD simulations verify that revised Enskog theory can accurately predict nonequilibrium thermal conductivities at low densities and this theory is applied to explore the model parameter space. Only certain mass and size ratios are found to exhibit conductivity enhancements above the parallel bounds and dehancement below the series bounds. The anomalous dehancement is experimentally accessible in helium-hydrogen gas mixtures and a review of the literature confirms the existence of mixture thermal conductivity below the series bound and even below the pure fluid values, in accordance with the predictions of revised Enskog theory. The results reported here may reignite the debate in the nanofluid literature on the possible existence of anomalous thermal conductivities outside the series and parallel bounds as this Rapid Communication demonstrates they are a fundamental feature of even simple fluids.

Interaction between charged lipid vesicles and point- or rod-like trivalent ions.

This work examines the influence of the charge distribution of trivalent cations on their interaction with soft anionic particles, using a combination of experimental measurements and theoretical modelling. In particular, we perform electrophoresis measurements to determine the zeta-potential of anionic liposomes in the presence of spermidine and lanthanum cations. We work in a range of electrolyte concentration where a reversal in the electrophoretic mobility of the liposomes is expected; however, unlike the case of lanthanum cations, spermidine does not induce mobility reversal of liposomes. As a result, the charge distribution within the counterion appears to be a key factor. This conclusion is supported by a theory that accounts for intra-ionic correlations, which has previously been successfully used to describe the colloidal electric double layer. It allows us to model spermidine as rod-like ions and lanthanum cations as point-like ions in order to test the importance of the ionic geometry in the interactions with soft particles such as lipid vesicles.

The dielectric constant: Reconciling simulation and experiment.

In this paper, we present a simple correction scheme to improve predictions of dielectric constants by classical non-polarisable models. This scheme takes into account electronic polarisation effects, through the experimental refractive index of the liquid, and a possible mismatch between the potential energy surface and the dipole moment surface. We have described the latter effect by an empirical scaling factor on the point charges, the value of which was determined by fitting the dielectric constant of methanol. Application of the same scaling factor to existing benchmark datasets, comprising four different models and a wide range of compounds, led to remarkable improvements in the quality of the predictions. In particular, the observed systematic underestimation of the dielectric constant was eliminated by accounting for the two missing terms in standard models. We propose that this correction term be included in future development and validation efforts of classical non-polarisable models.

Why different water models predict different structures under 2D confinement.

Experiments of nanoconfined water between graphene sheets at high pressure suggest that it forms a square ice structure (Algara-Siller et al., Nature, 2015, 519, 443). Molecular dynamics (MD) simulations have been used to attempt to recreate this structure, but there have been discrepancies in the structure formed by the confined water depending on the simulation set-up that was employed and particularly on the choice of water model. Here, using classical molecular dynamics simulations, we have systematically investigated the effect that three different water models (SPC/E, TIP4P/2005 and TIP5P) have on the structure of water confined between two rigid graphene sheets with a 0.9 nm separation. We show that the TIP4P/2005 and the TIP5P water models form a hexagonal AA-stacked structure, whereas the SPC/E model forms a rhombic AB-stacked structure. Our work demonstrates that the formation of these structures is driven by differences in the strength of hydrogen bonds predicted by the three water models, and that the nature of the graphene/water interaction only mildly affects the phase diagram. Considering the available experimental data and first-principle simulations we conclude that, among the models tested, the TIP4P/2005 and TIP5P force fields are for now the most reliable when simulating water under confinement. © 2018 Wiley Periodicals, Inc.

A diagrammatic analysis of the variational perturbation method for classical fluids.

The statistical mechanics of classical fluids can be approached from the particle perspective, where the focus is on the various positions and interactions of the particles, and from the field perspective, where the focus is on the form of the interaction fields generated by the particles. In this work, we combine these two perspectives by examining the variational perturbation method for classical fluids, which has been widely used to describe nonuniform electrolyte systems. Most of this work has been for low orders of the approximation, it has been limited to cases where the electrostatic interactions are weak. We present an exact diagrammatic representation of the method, which greatly facilitates the enumeration and evaluation of higher order corrections to the free energy functional. This framework is able to encapsulate several different approximate theories. Performing a cumulant expansion, leads to the Debye-Hückel and higher order corrections. Including the contribution of chain diagrams leads to a theory closely related to the splitting theory [Hatlo and Lue, Europhys. Lett., 2010, 89, 25002], which has been shown to be accurate from the weak through to the strong coupling limits. Including all chain and ring diagrams leads to the hypernetted chain approximation; this is a more direct route to the conventional derivation, which also requires a renormalization of the Mayer f-bonds to the total correlation functions. These approximations to the variational perturbation method are applied to the classical one-component plasma in order to assess their relative accuracy and understand their relationship to each other. Strategies for developing improved approximations are discussed.

Molecular Dynamics Investigation of the Influence of the Hydrogen Bond Networks in Ethanol/Water Mixtures on Dielectric Spectra.

The dielectric response of fluids to electromagnetic radiation in the microwave region originates from processes occurring at the molecular level. Understanding these processes in more detail is relevant to many fields, such as microwave heating, fluid mixing, and separation technologies. In this work, we use molecular dynamics (MD) simulations to study the dielectric spectra of ethanol/water mixtures. We compare our predictions with experimental results at different compositions. We show how the dielectric response can be estimated to a high level of accuracy using three dielectric relaxations: a dominant and slower process at microwave frequencies and two faster processes. A deeper study of the dynamics of the hydrogen bond network formed in these systems reveals how collective processes between the individual species are the origin of the final dielectric response. Our results agree with the "wait-and-switch" mechanism, which describes the dynamics of the hydrogen bond network as the combination of two processes: the fast breakage and formation of individual hydrogen bonds and the subsequent reorganization of the entire network once this process becomes energetically favorable. Since the dielectric response is related to dipole reorientations in the system, it is directly linked to these mechanisms.

Communication: The cluster vapor to cluster solid transition.

Until now, depletion induced transitions have been the hallmark of multicomponent systems only. Monte Carlo simulations reveal a depletion-induced phase transition from cluster vapor to cluster solid in a one-component fluid with competing short range and long range interactions. This confirms a prediction made by earlier theoretical work. Analysis of renormalized cluster-cluster and cluster-vapor interactions suggests that a cluster liquid is also expected within a very narrow range of model parameters. These insights could help identify the mechanisms of clustering in experiments and assist the design of colloidal structures through engineered self-assembly.

Interactions between charged surfaces mediated by stiff, multivalent zwitterionic polymers.

The interaction between like-charged objects in electrolyte solutions can be heavily altered by the presence of multivalent ions which possess a spatially distributed charge. In this work, we examine the influence of stiff, multivalent zwitterionic polymers on the interaction between charged surfaces using a splitting field theory previously shown to be accurate for the weak to the intermediate to the strong electrostatic coupling regimes. The theory is compared to Monte Carlo simulations and good agreement is found between both approaches. For surface separations shorter than the polymer length, the polymers are mainly oriented parallel to the surfaces, and the surface-surface interaction is repulsive. When the surface separation is comparable to the length of polymers, the polymers have two main orientations. The first corresponds to the polymers adsorbed onto the surface with their centers located near to or in contact with the surface; the second corresponds to polymers which are perpendicular to the charged surfaces, bridging both surfaces and leading to an attractive force between them. Increasing the surface charge density leads to more pronounced attraction via bridging. At surface separations greater than the polymer length, the polymers in the center of the system are still mainly perpendicular to the surfaces, due to "chaining" between zwitterions that enable them to bridge the surfaces at larger separations. This leads to an attractive interaction between the surfaces with a range significantly longer than the length of the polymers.

Ions confined in spherical dielectric cavities modeled by a splitting field-theory.

The properties of ions confined within spherical dielectric cavities are examined by a splitting field-theory and Monte Carlo simulations. Three types of cavities are considered: one possessing a uniform surface charge density, one with a uniform volume charge density, and one containing mobile ions. In all cases, mobile counterions are present within the dielectric sphere. The splitting theory is based on dividing the electrostatic interaction into long- and short-wavelength contributions and applying different approximations on the two contributions. The splitting theory works well for the case where the dielectric constant of the confining sphere is equal to or less than that of the medium external to the sphere. Nevertheless, by extending the theory with a virial expansion, the predictions are improved. However, when the dielectric constant of the confining sphere is greater than that of the medium outside the sphere, the splitting theory performs poorly, only qualitatively agreeing with the simulation data. In this case, the strong-coupling expansion does not seem to work well, and a modified mean-field theory where the counterions interact directly with only their own image charge gives improved predictions. The splitting theory works best for the system with a uniform surface charge density and worst for the system with a uniform volume charge density. Increasing the number of ions within the sphere, at a fixed radius, tends to increase the ion density near the surface of the sphere and leads to a depletion region in the sphere interior; however, varying the ion number does not lead to any qualitative changes in the performance of the splitting theory.