Surfactant Modeling Using Classical Density Functional Theory and a Group Contribution PC-SAFT Approach

Choline chloride and amino acid solutions taste and hydration behavior with experimental thermodynamic properties and COSMO-PC-SAFT calculation

Aqueous amino acid solutions have been introduced as dietary supplements for both animals and humans. This study investigates the physicochemical properties of the solutions containing amino acids (L-glycine, D,L-alanine, L-proline), choline chloride, and water at temperature range of 288.15 to 318.15 K. The results show that increasing concentrations of amino acids and choline chloride lead to higher solution densities. Analysis of apparent molar volume (Vφ) and apparent molar isentropic compressibility (κφ) reveals that Vφ values increase with choline chloride concentration and temperature, indicating enhanced solute-solvent interactions, while κφ values decrease, suggesting increased solution compression. Thermodynamic analysis using the Redlich-Mayer model and COSMO-based modeling provides insights into molecular interactions. However, COSMO-based parameters show high average relative deviation percentage (ARD %) values, indicating poor predictive performance for the density of these systems. In contrast, the ePC-SAFT equation of state effectively predicts the densities, particularly for L-proline-based solutions, which show very low ARD % values, indicating high accuracy. The ePC-SAFT model also performs reasonably well for L-glycine solutions but shows poorer results for D,L-alanine-based solutions. The study also examines the sweetness and saltiness criteria (ASV and ASIC) of these solutions. The ASV values, which serve as a sweetness criterion, are higher than the ideal range of 0.5 < ASV < 0.7, suggesting an overly sweet taste. The ASIC values follow a similar trend, indicating increased saltiness. To achieve an appropriate grade of sweetness and saltiness, dilution to lower concentrations of the solution is recommended. Furthermore, the use of choline chloride is found to increase salt intake and enhance the taste of salt, which can be beneficial in amino acid supplements used in animal food.

Determining interfacial tension and critical micelle concentrations of surfactants from atomistic molecular simulations

Hypothesis Atomistically-detailed models of surfactants provide quantitative information on the molecular interactions and spatial distributions at fluid interfaces. Hence, it should be possible to extract from this information, macroscopical thermophysical properties such as interfacial tension, critical micelle concentrations and the relationship between these properties and the bulk fluid surfactant concentrations. Simulations and Experiments Molecular-scale interfacial of systems containing n-dodecyl β-glucoside (APG12) are simulated using classical molecular dynamics. The bulk phases and the corresponding interfacial regions are all explicitly detailed using an all-atom force field (PCFF+). During the simulation, the behaviour of the interface is analyzed geometrically to obtain an approximated value of the critical micelle concentration (CMC) in terms of the surfactant area number density and the interfacial tension is assessed through the analysis of the forces amongst molecules. New experimental determinations are reported for the surface tension of APG12 at the water/air and at the water/n-decane interfaces. Findings We showcase the application of a thermodynamic framework that inter-relates interfacial tensions, surface densities, CMCs and bulk surfactant concentrations, which allows the in silico quantitative prediction of interfacial tension isotherms.

Predicting Solvation Free Energies from the Minnesota Solvation Database Using Classical Density Functional Theory Based on the PC-SAFT Equation of State

We critically assess the capabilities of classical density functional theory (DFT) based on the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state to predict the solvation free energies of small molecules in various hydrocarbon solvents. We compare DFT results with experimental data from the Minnesota solvation database and utilize statistical methods to analyze the accuracy of our approach, as well as its weaknesses. The mean absolute error of the solvation free energies is 3.7 kJ mol-1 for n-alkane solvents, ranging from pentane to hexadecane, with 473 solute-solvent systems. For solvents consisting of cyclic hydrocarbons (cyclohexane, benzene, toluene, and ethylbenzene) with 245 solute-solvent systems, we report a slightly larger mean absolute error of 4.2 kJ mol-1. We identify three possible sources of errors: (i) the neglect of solute-solvent and solvent-solvent Coulomb interactions, which limits the applicability of PC-SAFT DFT to nonpolar and weakly polar molecules; (ii) the solute's Lennard-Jones parameters supplied by the general AMBER force field, which are not parametrized toward solvation free energies; and (iii) the application of the Lorentz-Berthelot combining rules to the dispersive interactions between a segment of the PC-SAFT solvent and a Lennard-Jones interaction site of the solute. The approach is more accurate than standard implementations of phenomenological models in common chemistry software packages, which exhibit mean absolute errors larger than 9.12 kJ mol-1, even though newer phenomenological models achieve a mean absolute error of about 2 kJ mol-1. PC-SAFT DFT is more computationally efficient than state of the art explicit molecular simulations in combination with free energy perturbation methods. It is predictive with respect to solvation free energies, i.e., the input for the model is the (element-specific) molecular force field, the solute configuration from molecular dynamics simulations, and the (substance-specific) PC-SAFT parameters. The PC-SAFT parametrization uses pure-component data and does not require experimental solvation free energies. The PC-SAFT equation of state, without applying a DFT formalism, can also be used to calculate solvation free energies, provided that the PC-SAFT parameters for the solute are available. A large number of substances was recently parametrized by members of our group (Esper, T.; Bauer, G.; Rehner, P.; Gross, J. Ind. Eng. Chem. Res. 2023, 62), which enables a comparison to the DFT approach for 103 substances. Accurate results are obtained from the PC-SAFT equation of state with an MAE below 2.51 kJ mol-1. The DFT approach does not require PC-SAFT parameters for the solute and can be applied to all solutes that can be represented by the molecular force field.

Predicting surfactant phase behavior with a molecularly informed field theory

HYPOTHESIS

The computational study of surfactants and self-assembly is challenging because 1) models need to reflect chemistry-specific interactions, and 2) self-assembled structures are difficult to equilibrate with conventional molecular dynamics. We propose to overcome these challenges with a multiscale simulation approach where relative entropy minimization transfers chemically-detailed information from all-atom (AA) simulations to coarse-grained (CG) models that can be simulated using field-theoretic methods. Field-theoretic simulations are not limited by intrinsic physical time scales like diffusion and allow for rigorous equilibration via free energy minimization. This approach should enable the study of properties that are difficult to obtain by particle-based simulations.

SIMULATION WORK

We apply this workflow to sodium dodecylsulfate. To ensure chemical fidelity we present an AA force field calibrated against interfacial tension experiments. We generate CG models from AA simulation trajectories and show that particle-based and field-theoretic simulations of the CG model reproduce AA simulations and experimental measurements.

FINDINGS

The workflow captures the complex balance of interactions in a multicomponent system ultimately described by an atomistic model. The resulting CG models can study complex 3D phases like double or alternating gyroids, and reproduce salt effects on properties like aggregation number and shape transitions.

A simple theory for interfacial properties of dilute solutions

Recent studies suggest that cosolute mixtures may exert significant non-additive effects upon protein stability. The corresponding liquid–vapor interfaces may provide useful insight into these non-additive effects. Accordingly, in this work, we relate the interfacial properties of dilute multicomponent solutions to the interactions between solutes. We first derive a simple model for the surface excess of solutes in terms of thermodynamic observables. We then develop a lattice-based statistical mechanical perturbation theory to derive these observables from microscopic interactions. Rather than adopting a random mixing approximation, this dilute solution theory (DST) exactly treats solute–solute interactions to lowest order in perturbation theory. Although it cannot treat concentrated solutions, Monte Carlo (MC) simulations demonstrate that DST describes the interactions in dilute solutions with much greater accuracy than regular solution theory. Importantly, DST emphasizes a fundamental distinction between the “intrinsic” and “effective” preferences of solutes for interfaces. DST predicts that three classes of solutes can be distinguished by their intrinsic preference for interfaces. While the surface preference of strong depletants is relatively insensitive to interactions, the surface preference of strong surfactants can be modulated by interactions at the interface. Moreover, DST predicts that the surface preference of weak depletants and weak surfactants can be qualitatively inverted by interactions in the bulk. We also demonstrate that DST can be extended to treat surface polarization effects and to model experimental data. MC simulations validate the accuracy of DST predictions for lattice systems that correspond to molar concentrations.

Effect of surface roughness on partition of ionic liquids in nanopores by a perturbed-chain SAFT density functional theory

In this work, the distribution and partition behavior of ionic liquids (ILs) in nanopores with rough surfaces are investigated by a two-dimensional (2D) classical density functional theory (DFT) model. The model is consistent with the equation of state (EoS) that combines the perturbed-chain statistical associating fluid theory (PC-SAFT) and the mean spherical approximation (MSA) theory for bulk fluid. Its performance is verified by comparing the theoretical predictions to the results from molecular simulations. The fast Fourier transform (FFT) and a hybrid iteration method of Picard iteration and Anderson mixing are used to efficiently obtain the solution of density profile for the sizeable 2D system. The molecular parameters for IL-ions are obtained by fitting to experimental densities of bulk ILs. The model is applied to study the structure and partition of the ILs in nanopores. The results show that the peak of the density profile of counterions near a rough surface is much higher than that near a smooth surface. The adsorption of counterion and removal of coions are enhanced by surface roughness. Thus the nanopore with rough surfaces can store more charge. At low absolute surface potential, the partition coefficient for ions on rough surfaces is lower than that on smooth surfaces. At high absolute surface potential, increasing surface roughness leads to an increase in partition coefficient for counterions and a decrease in partition coefficient for coions.

Machine learning hybrid approach for the prediction of surface tension profiles of hydrocarbon surfactants in aqueous solution

HYPOTHESIS

Predicting the surface tension (SFT)-log(c) profiles of hydrocarbon surfactants in aqueous solution is computationally non-trivial, and empirically challenging due to the diverse and complex architecture and interactions of surfactant molecules. Machine learning (ML), combining a data-based and knowledge-based approach, can provide a powerful means to relate molecular descriptors to SFT profiles.

EXPERIMENTS

A dataset of SFT for 154 model hydrocarbon surfactants at 20-30 °C is fitted to the Szyszkowski equation to extract three characteristic parameters (Γ_max,K_L and critical micelle concentration (CMC)) which are correlated to a series of 2D and 3D molecular descriptors. Key (∼10) descriptors were selected by removing co-correlation, and employing a gradient-boosted regressor model to rank feature importance and carry out recursive feature elimination (RFE). The hyperparameters of each target-variable model were fine-tuned using a randomised cross-validated grid search, to improve predictive ability and reduce overfitting.

FINDINGS

The ML models correlate favourably with test experimental data, with R²= 0.69-0.87, and the merits and limitations of the approach are discussed based on 'unseen' hydrocarbon surfactants. The incorporation of a knowledge-based framework provides an appropriate smoothing of the experimental data which simplifies the data-driven approach and enhances its generality. Open-source codes and a brief tutorial are provided.

Equation of state and Helmholtz energy functional for fused heterosegmented hard chains

Modern equations of state for real nonspherical molecules are often based on Wertheim's first-order thermodynamic perturbation theory (TPT1). A major drawback of TPT1 is that it assumes tangentially bonded spheres. In this work, we develop a Helmholtz energy functional for systems comprising hard heterosegmented chains with arbitrary bond lengths. This is achieved by using hard-sphere fragments (i.e., hard spheres with spherical caps removed at the intersection to their neighbors) as monomers as opposed to full hard spheres. The model is written as a Helmholtz energy functional for inhomogeneous systems and the equation of state for a homogeneous system is determined as a special case. We thereby obtain an equation of state that can be used as a reference to develop statistical associating fluid theory models that more accurately describe the thermodynamic properties of nonspherical molecules. The model is validated against molecular simulation results of bulk pressures and density profiles in slit pores. For the bulk pressures, we show that the equation of state is in excellent agreement with results from molecular simulation for dimers, trimers, and chains of up to 20 segments. The density profiles of individual segments of the chains are regarded in slit pores. Some deviations of the theory from results of molecular simulations are observed for strongly fused chains. Overall, however, good agreement is found for inhomogeneous systems.

Hydrodynamic density functional theory for mixtures from a variational principle and its application to droplet coalescence

Dynamic density functional theory (DDFT) allows the description of microscopic dynamical processes on the molecular scale extending classical DFT to non-equilibrium situations. Since DDFT and DFT use the same Helmholtz energy functionals, both predict the same density profiles in thermodynamic equilibrium. We propose a molecular DDFT model, in this work also referred to as hydrodynamic DFT, for mixtures based on a variational principle that accounts for viscous forces as well as diffusive molecular transport via the generalized Maxwell-Stefan diffusion. Our work identifies a suitable expression for driving forces for molecular diffusion of inhomogeneous systems. These driving forces contain a contribution due to the interfacial tension. The hydrodynamic DFT model simplifies to the isothermal multicomponent Navier-Stokes equation in continuum situations when Helmholtz energies can be used instead of Helmholtz energy functionals, closing the gap between micro- and macroscopic scales. We show that the hydrodynamic DFT model, although not formulated in conservative form, globally satisfies the first and second law of thermodynamics. Shear viscosities and Maxwell-Stefan diffusion coefficients are predicted using an entropy scaling approach. As an example, we apply the hydrodynamic DFT model with a Helmholtz energy density functional based on the perturbed-chain statistical associating fluid theory equation of state to droplet and bubble coalescence in one dimension and analyze the influence of additional components on coalescence phenomena.