Developing optimal Wertheim-like models of water for use in Statistical Associating Fluid Theory (SAFT) and related approaches

Local, Sustained, and Targeted Co-Delivery of MEK Inhibitor and Doxorubicin Inhibits Tumor Progression in E-Cadherin-Positive Breast Cancer

Effectively utilizing MEK inhibitors in the clinic remains challenging due to off-target toxicity and lack of predictive biomarkers. Recent findings propose E-cadherin, a breast cancer diagnostic indicator, as a predictor of MEK inhibitor success. To address MEK inhibitor toxicity, traditional methodologies have systemically delivered nanoparticles, which require frequent, high-dose injections. Here, we present a different approach, employing a thermosensitive, biodegradable hydrogel with functionalized liposomes for local, sustained release of MEK inhibitor PD0325901 and doxorubicin. The poly(δ-valerolactone-co-lactide)-b-poly(ethylene-glycol)-b-poly(δ-valerolactone-co-lactide) triblock co-polymer gels at physiological temperature and has an optimal degradation time in vivo. Liposomes were functionalized with PR_b, a biomimetic peptide targeting the α5β1 integrin receptor, which is overexpressed in E-cadherin-positive triple negative breast cancer (TNBC). In various TNBC models, the hydrogel-liposome system delivered via local injection reduced tumor progression and improved animal survival without toxic side effects. Our work presents the first demonstration of local, sustained delivery of MEK inhibitors to E-cadherin-positive tumors alongside traditional chemotherapeutics, offering a safe and promising therapeutic strategy.

Role of site-site interaction on the phase equilibria of multiple-site associating fluids in a functionalized slit pore

Vapor-liquid phase equilibria for multiple sites associating fluids with different associating strengths are investigated in a slit pore using grand-canonical transition matrix Monte Carlo method. The increase of critical temperature from two-site to four-site associating fluids at constant site strength is quite significant as compared to that of the one-site to two-site associating fluids, which is more pronounced at higher associating strength (ϵ* = 6). Monomer fraction and cluster size distribution are used to investigate the association of fluid particles in coexistence phases. The monomer fraction for both phases decreases with increased associating sites on the fluid particles due to more site-site interaction with neighboring fluid particles and forming a larger cluster. Therefore, the number of associating sites and their distribution play a vital role in the association of fluid particles. Moreover, the saturation chemical potential changes with the arrangement of the sites. For two-site associating fluids, we observe early vapor-liquid transition when the sites are oppositely placed, and when the sites are placed at 90°, the vapor-liquid transition is observed at the higher chemical potential. Moreover, four-site associating fluids with a square arrangement show early vapor-liquid phase transition, mainly because these arrangements of sites effectively interact with surface sites and the molecules in the next layer.

Soft fundamental measure theory functional for the Weeks-Chandler-Andersen repulsive potential

We introduce a soft fundamental measure theory functional for the purely repulsive Weeks-Chandler-Andersen (WCA) fluid. This classical density functional could serve as a reference fluid for functionals created using thermodynamic perturbation theory instead of the hard-sphere fluid. Our functional incorporates temperature-dependent parameters describing the length scale and effective softness of the particle interaction, and which reproduce the second virial coefficient of the WCA fluid. We find that this approach is comparable in accuracy to the Barker-Henderson approach combined with the White Bear density functional for the hard-sphere fluid.

The physics of empty liquids: from patchy particles to water

Empty liquids represent a wide class of materials whose constituents arrange in a random network through reversible bonds. Many key insights on the physical properties of empty liquids have originated almost independently from the study of colloidal patchy particles on one side, and a large body of theoretical and experimental research on water on the other side. Patchy particles represent a family of coarse-grained potentials that allows for a precise control of both the geometric and the energetic aspects of bonding, while water has arguably the most complex phase diagram of any pure substance, and a puzzling amorphous phase behavior. It was only recently that the exchange of ideas from both fields has made it possible to solve long-standing problems and shed new light on the behavior of empty liquids. Here we highlight the connections between patchy particles and water, focusing on the modelling principles that make an empty liquid behave like water, including the factors that control the appearance of thermodynamic and dynamic anomalies, the possibility of liquid-liquid phase transitions, and the crystallization of open crystalline structures.

Extension of van der Waals theory for supersaturated thin films

The vapor/liquid interface properties play an essential role in both fundamental models and practical applications. Here, we describe a thin planar film surrounded by supersaturated vapor using the extension of van der Waals theory. We derive the analytical equilibrium conditions, which allow us to define the stress tensor and surface tension. Our model provides the surface tension dependence on the film thickness, correctly reflecting the vapor/liquid interface until full disappearance. The numerical estimations show that the surface tension crucially depends on the film thickness-a decrease in the thickness of 50% results in an 85% reduction in the surface tension.

SAFT-γ-Mie Cross-Interaction Parameters from Density Functional Theory-Predicted Multipoles of Molecular Fragments for Carbon Dioxide, Benzene, Alkanes, and Water

Determining unlike-pair interaction parameters, whether for group contribution equation of state or molecular simulations, is a challenge for the prediction of thermodynamic properties. As the number of components and their respective complexity increase, it becomes impractical to fit all the unlike interactions. Lorentz-Berthelot combining rules work well for systems, where the main interactions are dispersion forces, but they do not account for electrostatics. In this work, we derive predictive combining rules within the SAFT-γ-Mie framework. In the resulting model, the unlike-pair interactions account for the effect of ionization energies, partial charges, dipole moments, and quadrupole moments. We then estimate these properties for molecular fragments using density functional theory calculations and demonstrate their use to obtain realistic cross-interaction energies without the need for experimental data. An open-source python package, Multipole Approach to Predictively Scale Cross-Interactions, is included to facilitate use of the methods presented in this work. A good qualitative agreement was obtained for all phase equilibria calculations of binary mixtures containing carbon dioxide with propane, hexane, benzene, and water, as well as mixtures of hexane and benzene. Finally, we discuss future improvements to our methodology, including the use of physical insights when fitting self-interaction parameters.

Generalized equation of state for fluids: From molecular liquids to colloidal dispersions

In this work, a new parameterization for the Statistical Association Fluid Theory for potentials of Variable Range (SAFT-VR) is coupled to the discrete potential theory to represent the thermodynamic properties of several fluids, ranging from molecular liquids to colloidal-like dispersions. In this way, this version of the SAFT-VR approach can be straightforwardly applied to any kind of either simple or complex fluid. In particular, two interaction potentials, namely, the Lennard-Jones and the hard-core attractive Yukawa potentials, are discretized to study the vapor-liquid equilibrium properties of both molecular and complex liquids, respectively. Our results are assessed with Monte Carlo computer simulations and available and accurate theoretical results based on the self-consistent Ornstein-Zernike approximation.

Volume Phase Transition in Gels: Its Discovery and Development

 The history of volume phase transition of responsive gels from its theoretical prediction to experimental discovery was described and the major role of mixing Gibbs energy function in theoretical models was stressed. For detailed analysis and fine tuning of the volume phase transition, the generalized Flory-Huggins model with concentration and temperature dependent interaction function coupled with Maxwell construction as a tool is very suitable. Application of expansive stresses can uncover the potential of various swelling gels for volume phase transition. Experimentally, the abrupt, equilibrium-controlled phase transition is often hard to achieve due to passage of gel through states of mechanical instability and slow relaxation processes in macroscopic objects.

Breakdown of the law of rectilinear diameter and related surprises in the liquid-vapor coexistence in systems of patchy particles

The phase diagram of molecular or colloidal systems depends strongly on the range and angular dependence of the interactions between the constituent particles. For instance, it is well known that the critical density of particles with "patchy" interactions shifts to lower values as the number of patches is decreased [see Bianchi et al. Phys. Rev. Lett. 97, 168301 (2006)]. Here, we present simulations that show that the phase behavior of patchy particles is even more interesting than had been appreciated. In particular, we find that, upon cooling below the critical point, the width of the liquid-vapor coexistence region of a system of particles with tetrahedrally arranged patches first increases, then decreases, and finally increases again. In other words, this system exhibits a doubly re-entrant liquid-vapor transition. As a consequence, the system exhibits a very large deviation from the law of rectilinear diameter, which assumes that the critical density can be obtained by linear extrapolation of the averages of the densities of the coexisting liquid and vapor phases. We argue that the unusual behavior of this system has the same origin as the density maximum in liquid water and is not captured by the Wertheim theory. The Wertheim theory also cannot account for our observation that the phase diagram of particles with three patches depends strongly on the geometrical distribution of the patches and on the degree to which their position on the particle surface is rigidly constrained. However, the phase diagram is less sensitive to small angular spreads in the patch locations. We argue that the phase behavior reported in this paper should be observable in experiments on patchy colloids and may be relevant for the liquid-liquid equilibrium in solutions of properly functionalized dendrimers.

Towards the description of adsorption of water in slit-like pores with walls covered by molecular brushes

The density profiles, adsorption isotherms, and phase behavior of a water model in a slit-like pore with walls modified by pre-adsorbed tethered chain molecules have been studied in the framework of a density functional theory. Each chain is bonded to the surface by its terminal segment, and the surface density of grafted chains is the same for each wall. The model for water taken from the work of Clark et al. [Mol. Phys. 104, 3561 (2006)] reproduces successfully a bulk equation of state. The mean field approach has been used to describe the effects of attractive interactions. The chemical association effects are taken into account by using the first-order thermodynamic perturbation theory of Wertheim. We have found that the presence of molecular brushes on the pore walls has important consequences for the adsorption and phase behavior of confined water. If the brush segments do not attract water molecules strongly, the vapor-liquid coexistence envelope shrinks upon increasing brush density, but the critical temperature is weakly affected. Alteration from capillary condensation to evaporation is observed with changes in the brush density, number of segments of tethered chains, and/or chemical identity of segments. The crossover temperature is affected by all these factors. Moreover, we have shown that affinity of water to segments of tethers is an important factor determining adsorption of water vapor and the entire phase diagram.

Adsorption and phase behavior of water-like fluid models with square-well attraction and site-site association in slit-like pores: Density functional approach

The adsorption and phase behavior of two model fluids, both with square well inter-particle attraction and site-site associative interaction, in slit-like pores have been studied in the framework of a density functional theory. The mean field approach and the first-order mean spherical approximation have been applied to account for the attractive interactions. The chemical association effects are taken into account by using the first-order thermodynamic perturbation theory of Wertheim. A set of parameters for each fluid model has been chosen according to the work of [Clark et al., Mol. Phys. 104, 3561 (2006)], to describe successfully the vapor-liquid coexistence of water in the bulk phase. The influence of the slit-like pore width and of the strength of gas-solid interaction energy on the vapor-liquid coexistence envelope under confinement has been explored in detail. The theory and the results of the present work are valuable for further exploration of a wide set of models of associating fluids and of fluids with complex molecular architecture in different adsorbents, and to deal with activated carbon surfaces.

Thermodynamic properties of confined square-well fluids with multiple associating sites

In this work, a molecular simulation study of confined hard-spheres particles with square-well (SW) attractive interactions with two and four associating SW sites based on the first-order perturbation form of Wertheim's theory is presented. An extended version of the Gibbs ensemble technique for inhomogeneous fluids [A. Z. Panagiotopoulos, Mol. Phys. 62, 701 (1987)] is used to predict the adsorption density profiles for associating fluids confined between opposite parallel walls. The fluid is confined in four kinds of walls: hard-wall, SW wall, Lennard-Jones (LJ) 12-6 wall potential, and LJ 10-4 wall potential. We analyze the behavior of the confined system for several supercritical temperatures as a function of variation of molecular parameters: potential range λ, bulk densities ρ_b^*, pore width H, cutoff range interaction r_c^*, and range of the potential and depth of the particle-wall (λ_w, ε_w^*). Additionally, we include predictions for liquid-vapor coexistence of bulk associative particles and how their critical properties are modified by the presence of associative sites in the molecule. The molecular simulation data presented in this work are of prime importance to the development of theoretical approaches for inhomogeneous fluids as classical density functional theory. The simulation results presented here are resourceful for predicting adsorption isotherms of real associating fluids such as water.

Predicting the Fluid-Phase Behavior of Aqueous Solutions of ELP (VPGVG) Sequences Using SAFT-VR

The statistical associating fluid theory for potentials of variable range (SAFT-VR) is used to predict the fluid phase behavior of elastin-like polypeptide (ELP) sequences in aqueous solution with special focus on the loci of lower critical solution temperatures (LCSTs). A SAFT-VR model for these solutions is developed following a coarse-graining approach combining information from atomistic simulations and from previous SAFT models for previously reported relevant systems. Constant-pressure temperature-composition phase diagrams are determined for solutions of (VPGVG)_n sequences + water with n = 1 to 300. The SAFT-VR equation of state lends itself to the straightforward calculation of phase boundaries so that complete fluid-phase equilibria can be calculated efficiently. A broad range of thermodynamic conditions of temperature and pressure are considered, and regions of vapor-liquid and liquid-liquid coexistence, including LCSTs, are found. The calculated phase boundaries at low concentrations match those measured experimentally. The temperature-composition phase diagrams of the aqueous ELP solutions at low pressure (0.1 MPa) are similar to those of types V and VI phase behavior in the classification of Scott and van Konynenburg. An analysis of the high-pressure phase behavior confirms, however, that a closed-loop liquid-liquid immiscibility region, separate from the gas-liquid envelope, is present for aqueous solutions of (VPGVG)₃₀; such a phase diagram is typical of type VI phase behavior. ELPs with shorter lengths exhibit both liquid-liquid and gas-liquid regions, both of which become less extensive as the chain length of the ELP is decreased. The strength of the hydrogen-bonding interaction is also found to affect the phase diagram of the (VPGVG)₃₀ system in that the liquid-liquid and gas-liquid regions expand as the hydrogen-bonding strength is decreased and shrink as it is increased. The LCSTs of the mixtures are seen to decrease as the ELP chain length is increased.

Explicit-water theory for the salt-specific effects and Hofmeister series in protein solutions

Effects of addition of salts on stability of aqueous protein solutions are studied theoretically and the results are compared with experimental data. In our approach, all the interacting species, proteins, ions, and water molecules, are accounted for explicitly. Water molecules are modeled as hard spheres with four off-center attractive square-well sites. These sites serve to bind either another water or to solvate the ions or protein charges. The ions are represented as charged hard spheres, and decorated by attractive sites to allow solvation. Spherical proteins simultaneously possess positive and negative groups, represented by charged hard spheres, attached to the surface of the protein. The attractive square-well sites, mimicking the protein-protein van der Waals interaction, are located on the surface of the protein. To obtain numerical results, we utilized the energy route of Wertheim's associative mean spherical approximation. From measurable properties, we choose to calculate the second virial coefficient B2, which is closely related to the tendency of proteins to aggregate and eventually crystalize. Calculations are in agreement with experimental trends: (i) For low concentration of added salt, the alkali halide salts follow the inverse Hofmeister series. (ii) At higher concentration of added salt, the trend is reversed. (iii) When cations are varied, the salts follow the direct Hofmeister series. (iv) In contrast to the colloidal theories, our approach correctly predicts the non-monotonic behavior of B2 upon addition of salts. (v) With respect to anions, the theory predicts for the B2 values to follow different sequences below and above the iso-ionic point, as also confirmed experimentally. (vi) A semi-quantitative agreement between measured and calculated values for the second virial coefficient, as functions of pH of solution and added salt type and concentration, is obtained.

On the use of molecular-based thermodynamic models to assess the performance of solvents for CO2 capture processes: monoethanolamine solutions

Predictive models play an important role in the design of post-combustion processes for the capture of carbon dioxide (CO₂) emitted from power plants. A rate-based absorber model is presented to investigate the reactive capture of CO₂ using aqueous monoethanolamine (MEA) as a solvent, integrating a predictive molecular-based equation of state: SAFT-VR SW (Statistical Associating Fluid Theory-Variable Range, Square Well). A distinctive physical approach is adopted to model the chemical equilibria inherent in the process. This eliminates the need to consider reaction products explicitly and greatly reduces the amount of experimental data required to model the absorber compared to the more commonly employed chemical approaches. The predictive capabilities of the absorber model are analyzed for profiles from 10 pilot plant runs by considering two scenarios: (i) no pilot-plant data are used in the model development; (ii) only a limited set of pilot-plant data are used. Within the first scenario, the mass fraction of CO₂ in the clean gas is underestimated in all but one of the cases, indicating that a best-case performance of the solvent can be obtained with this predictive approach. Within the second scenario a single parameter is estimated based on data from a single pilot plant run to correct for the dramatic changes in the diffusivity of CO₂ in the reactive solvent. This parameter is found to be transferable for a broad range of operating conditions. A sensitivity analysis is then conducted, and the liquid viscosity and diffusivity are found to be key properties for the prediction of the composition profiles. The temperature and composition profiles are sensitive to thermodynamic properties that correspond to major sources of heat generation or dissipation. The proposed modelling framework can be used as an early assessment of solvents to aid in narrowing the search space, and can help in determining target solvents for experiments and more detailed modelling.

Understanding the Phase Behavior of Tetrahydrofuran + Carbon Dioxide, + Methane, and + Water Binary Mixtures from the SAFT-VR Approach

The high-pressure phase diagrams of the tetrahydrofuran(1) + carbon dioxide(2), + methane(2), and + water(2) mixtures are examined using the SAFT-VR approach. Carbon dioxide molecule is modeled as two spherical segments tangentially bonded, water is modeled as a spherical segment with four associating sites to represent the hydrogen bonding, methane is represented as an isolated sphere, and tetrahydrofuran is represented as a chain of m tangentially bonded spherical segments. Dispersive interactions are modeled using the square-well intermolecular potential. In addition, two different molecular model mixtures are developed to take into account the subtle balance between water-tetrahydrofuran hydrogen-bonding interactions. The polar and quadrupolar interactions present in water, tetrahydrofuran, and carbon dioxide are treated in an effective way via square-well potentials of variable range. The optimized intermolecular parameters are taken from the works of Giner et al. (Fluid Phase Equil. 2007, 255, 200), Galindo and Blas (J. Phys. Chem. B 2002, 106, 4503), Patel et al. (Ind. Eng. Chem. Res. 2003, 42, 3809), and Clark et al. (Mol. Phys. 2006, 104, 3561) for tetrahydrofuran, carbon dioxide, methane, and water, respectively. The phase diagrams of the binary mixtures exhibit different types of phase behavior according to the classification of van Konynenburg and Scott, ranging from types I, III, and VI phase behavior for the tetrahydrofuran(1) + carbon dioxide(2), + methane(2), and + water(2) binary mixtures, respectively. This last type is characterized by the presence of a Bancroft point, positive azeotropy, and the so-called closed-loop curves that represent regions of liquid-liquid immiscibility in the phase diagram. The system exhibits lower critical solution temperatures (LCSTs), which denote the lower limit of immiscibility together with upper critical solution temperatures (UCSTs). This behavior is explained in terms of competition between the incompatibility with the alkyl parts of the tetrahydrofuran ring chain and the hydrogen bonding between water and the ether group. A minimum number of unlike interaction parameters are fitted to give the optimal representation of the most representative features of the binary phase diagrams. In the particular case of tetrahydrofuran(1) + water(2), two sets of intermolecular potential model parameters are proposed to describe accurately either the hypercritical point associated with the closed-loop liquid-liquid immiscibility region or the location of the mixture lower- and upper-critical end-points. The theory is not only able to predict the type of phase behavior of each mixture, but also provides a reasonably good description of the global phase behavior whenever experimental data are available.

Approach to approximating the pair distribution function of inhomogeneous hard-sphere fluids

We introduce an approximation for the pair distribution function of the inhomogeneous hard sphere fluid. Our approximation makes use of our recently published averaged pair distribution function at contact, which has been shown to accurately reproduce the averaged pair distribution function at contact for inhomogeneous density distributions. This approach achieves greater computational efficiency than previous approaches by enabling the use of exclusively fixed-kernel convolutions and thus allowing an implementation using fast Fourier transforms. We compare results for our pair distribution approximation with two previously published works and Monte Carlo simulation, showing favorable results.