Local density dependent potentials for an underlying van der Waals equation of state: A simulation and density functional theory analysis.

There is an ever increasing use of local density dependent potentials in the mesoscale modeling of complex fluids. Questions remain, though, about the dependence of the thermodynamic and structural properties of such systems on the cutoff distance used to calculate these local densities. These questions are particularly acute when it comes to the stability and structure of the vapor/liquid interface. In this article, we consider local density dependent potentials derived from an underlying van der Waals equation of state. We use simulation and density functional theory to examine how the bulk thermodynamic and interfacial properties vary with the cutoff distance, rc, used to calculate the local densities. We show quantitatively how the simulation results for bulk thermodynamic properties and vapor-liquid equilibrium approach the van der Waals limit as rc increases and demonstrate a scaling law for the radial distribution function in the large rc limit. We show that the vapor-liquid interface is stable with a well-defined surface tension and that the interfacial density profile is oscillatory, except for temperatures close to critical. Finally, we show that in the large rc limit, the interfacial tension is proportional to rc and, therefore, unlike the bulk thermodynamic properties, does not approach a constant value as rc increases. We believe that these results give new insights into the properties of local density dependent potentials, in particular their unusual interfacial behavior, which is relevant for modeling complex fluids in soft matter.

Microstructural and thermodynamic characterization of wormlike micelles formed by polydisperse ionic surfactant solutions.

For industrial applications of self-assembled wormlike micelles, measurement and characterization of a micellar material's microstructure and rheology are paramount for the development and deployment of new high-performing and cost-effective formulations. Within this workflow, there are significant bottlenecks associated with experimental delays and a lack of transferability of results from one chemistry to another. In this work, we outline a process to predict microscopic and thermodynamic characteristics of wormlike micelles directly from rheological data by combining a more robust and efficient fitting algorithm with a recently published constitutive model called the Toy Shuffling model [J. D. Peterson and M. E. Cates, J. Rheol. 64, 1465-1496 (2020) and J. D. Peterson and M. E. Cates, J. Rheol. 65, 633-662 (2021)]. To support this work, linear rheology measurements were taken for 143 samples comprising a common base formulation of commercial sodium lauryl ether sulfate, cocamidopropyl betaine, and salt (NaCl). The steady state zero shear viscosity evident in linear rheology was measured in duplicate via direct steady and oscillatory shear experiments. Fitting the collected data to the model, we found trends in the microstructural and thermodynamic characteristics that agree with molecular dynamics simulations. These trends validate our new perspective on the parameters that inform the study of the relationship between chemical formulation and rheology. This work, when implemented at scale, can potentially be used to inform and test strategies for predicting self-assembled micellar structures based on chemical formulation.

Coarse-Grained Model Incorporating Short- and Long-Range Effective Potentials for the Fast Simulation of Micelle Formation in Solutions of Ionic Surfactants.

A coarse-grained model comprising short- and long-range effective potentials, parametrized with the iterative Boltzmann inversion (IBI) method, is presented for capturing micelle formation in aqueous solutions of ionic surfactants using as a model system sodium dodecyl sulfate (SDS). In the coarse-grained (CG) model, each SDS molecule is represented as a sequence of four beads while each water molecule is modeled as a single bead. The proposed CG scheme involves ten potential energy functions: four of them describe bonded interactions and control the distribution functions of intramolecular degrees of freedom (bond lengths, valence angles, and dihedrals) along an SDS molecule while the other six account for intermolecular interactions between pairs of SDS and water beads and control the radial distribution functions. The nonbonded effective potentials between coarse-grained SDS molecules extend up to about 12 nm and capture structural and morphological features of the micellar solution both at short and long distances. The long-range component of these potentials, in particular, captures correlations between surfactant molecules belonging to different micelles and is essential to describe ordering associated with micelle formation. A new strategy is introduced for determining the effective potentials through IBI by using information (target distribution functions) extracted from independent atomistic simulations of a micellar reference system (a salt-free SDS solution at total surfactant concentration cT equal to 103 mM, temperature T equal to 300 K, and pressure P equal to 1 atm) obtained through a multiscale approach described in an earlier study. It employs several optimization steps for bonded and nonbonded interactions and a gradual parametrization of the short- and long-range components of the latter, followed by reparametrization of the bonded ones. The proposed CG model can reproduce remarkably accurately the microstructure and morphology of the reference system within only a few hours of computational time. It is therefore very promising for future studies of structural and morphological behavior of various liquid surfactant formulations.

Analytical modeling of micelle growth. 3. Electrostatic free energy of ionic wormlike micelles - Effects of activity coefficients and spatially confined electric double layers.

HYPOTHESES: To correctly predict the aggregation number and size of wormlike micelles from ionic surfactants, the molecular-thermodynamic theory has to calculate the free energy per molecule in the micelle with accuracy better than 0.01 kT, which is a serious challenge. The problem could be solved if the effects of mutual confinement of micelle counterion atmospheres, as well as the effects of counterion binding, surface curvature and ionic interactions in the electric double layer (EDL), are accurately described. THEORY: The electric field is calculated using an appropriate cell model, which takes into account the aforementioned effects. Expressions for the activity coefficients have been used, which vary across the EDL and describe the electrostatic, hard sphere, and specific interactions between the ions. New approach for fast numerical calculation of the electrostatic free energy is developed. FINDINGS: The numerical results demonstrate the variation of quantities characterizing the EDL of cylindrical and spherical micelles with the rise of electrolyte concentration. The effect of activity coefficients leads to higher values of the free energy per surfactant molecule in the micelle as compared with the case of neglected ionic interactions. The results are essential for the correct prediction of the size of wormlike micelles from ionic surfactants. This study can be extended to mixed micelles of ionic and nonionic surfactants for interpretation of the observed synergistic effects.

Analytical modeling of micelle growth. 4. Molecular thermodynamics of wormlike micelles from ionic surfactants: Theory vs. experiment.

HYPOTHESES: The aggregation number and length of spherocylindrical (rodlike, wormlike) micelles in solutions of an ionic surfactant and salt can be predicted knowing the molecular parameters and the input concentrations of the species. This can be achieved by upgrading the quantitative molecular thermodynamic model from the previous parts of this series with an expression for the electrostatic component of micelle scission energy that is the excess free energy of the spherical endcaps with respect to the cylindrical part of the micelle. THEORY: The thermodynamics of micellization is extended to the case of multicomponent system, which may contain several surfactants (both ionic and nonionic) and salts, taking into account the effect of counterion binding in the Stern layer on the micellar surface. Furthermore, the considerations are focused on a system that consists of single ionic surfactant plus salt. FINDINGS: Excellent agreement was achieved between the theoretical model and experimental data for wormlike micelles from anionic and cationic surfactants at various concentrations of salt and temperatures. In accord with the experimental observations, at high salt concentrations, the model predicts loss of chemical equilibrium between the endcaps and cylindrical part of the wormlike micelles, which implies transition to self-assemblies of other, e.g. branched, morphology or the onset of crystallization and phase separation.

Quantitative Prediction of the Structure and Viscosity of Aqueous Micellar Solutions of Ionic Surfactants: A Combined Approach Based on Coarse-Grained MARTINI Simulations Followed by Reverse-Mapped All-Atom Molecular Dynamics Simulations.

We address the problem of the quantitative prediction of micelle formation in dilute aqueous solutions of ionic surfactants using sodium dodecyl sulfate (SDS) as a model system through a computational approach that involves three steps: (a) execution of coarse-grained simulations based on the MARTINI force field (with slightly modified parameters to afford the formation of large micelles); (b) reverse mapping of the final self-assembled coarse-grained configuration into an all-atom configuration; and (c) final relaxation of this all-atom configuration through short-time (on the order of a few tens of nanoseconds), detailed isothermal-isobaric molecular dynamics simulations using the CHARMM36 force field. For a given concentration of the solution in SDS molecules, the modified MARTINI-based coarse-grained simulations lead to the formation of large micelles characterized by mean aggregation numbers above the experimentally observed ones. However, by reintroducing the detailed chemical structure through a strategy that solves a well-defined geometric problem and re-equilibrating, these large micellar aggregates quickly dissolve to smaller ones and equilibrate to sizes that perfectly match the average micelle size measured experimentally at the given surfactant concentration. From the all-atom molecular dynamics simulations, we also deduce the surfactant diffusivity DSDS and the zero-shear rate viscosity, η0, of the solution, which are observed to compare very favorably with the few experimental values that we were able to find in the literature.

Analytical modeling of micelle growth. 2. Molecular thermodynamics of mixed aggregates and scission energy in wormlike micelles.

HYPOTHESES: Quantitative molecular-thermodynamic theory of the growth of giant wormlike micelles in mixed nonionic surfactant solutions can be developed on the basis of a generalized model, which includes the classical "phase separation" and "mass action" models as special cases. The generalized model describes spherocylindrical micelles, which are simultaneously multicomponent and polydisperse in size. THEORY: The model is based on explicit analytical expressions for the four components of the free energy of mixed nonionic micelles: interfacial-tension, headgroup-steric, chain-conformation components and free energy of mixing. The radii of the cylindrical part and the spherical endcaps, as well as the chemical composition of the endcaps, are determined by minimization of the free energy. FINDINGS: In the case of multicomponent micelles, an additional term appears in the expression for the micelle growth parameter (scission free energy), which takes into account the fact that the micelle endcaps and cylindrical part have different compositions. The model accurately predicts the mean mass aggregation number of wormlike micelles in mixed nonionic surfactant solutions without using any adjustable parameters. The endcaps are enriched in the surfactant with smaller packing parameter that is better accommodated in regions of higher mean surface curvature. The model can be further extended to mixed solutions of nonionic, ionic and zwitterionic surfactants used in personal-care and house-hold detergency.

Analytical modeling of micelle growth. 1. Chain-conformation free energy of binary mixed spherical, wormlike and lamellar micelles.

HYPOTHESES: A quantitative molecular-thermodynamic theory of the growth of giant wormlike micelles of nonionic surfactants can be developed on the basis of a generalized model, which includes the classical "phase separation" and "mass action" models as special cases. The generalized model describes spherocylindrical micelles, which are simultaneously multicomponent and polydisperse in size. THEORY: By analytical minimization of the free-energy functional we derived explicit expressions for the chain-extension and chain-end distribution functions in the hydrocarbon core of mixed micelles from two surfactants of different chainlengths. FINDINGS: The hydrocarbon core of a two-component micelle is divided in two regions, outer and inner, where the ends of the shorter and longer chains are located. The derived analytical expression for the chain-conformation free energy implies that the mixing of surfactants with different chainlengths is always nonideal and synergistic, i.e. it leads to decrease of the micellar free energy and to enhancement of micellization and micelle growth. The derived expressions are applicable to surfactants with different headgroups (nonionic, ionic, zwitterionic) and to micelles of different shapes (spherical, wormlike, lamellar). The results can be incorporated in a quantitative theory of the growth of giant mixed micelles in formulations with practical applications in detergency.

Using Machine Learning to Predict Synergistic Antimalarial Compound Combinations With Novel Structures.

The parasite Plasmodium falciparum is the most lethal species of Plasmodium to cause serious malaria infection in humans, and with resistance developing rapidly novel treatment modalities are currently being sought, one of which being combinations of existing compounds. The discovery of combinations of antimalarial drugs that act synergistically with one another is hence of great importance; however an exhaustive experimental screen of large drug space in a pairwise manner is not an option. In this study we apply our machine learning approach, Combination Synergy Estimation (CoSynE), which can predict novel synergistic drug interactions using only prior experimental combination screening data and knowledge of compound molecular structures, to a dataset of 1,540 antimalarial drug combinations in which 22.2% were synergistic. Cross validation of our model showed that synergistic CoSynE predictions are enriched 2.74 × compared to random selection when both compounds in a predicted combination are known from other combinations among the training data, 2.36 × when only one compound is known from the training data, and 1.5 × for entirely novel combinations. We prospectively validated our model by making predictions for 185 combinations of 23 entirely novel compounds. CoSynE predicted 20 combinations to be synergistic, which was experimentally validated for nine of them (45%), corresponding to an enrichment of 1.70 × compared to random selection from this prospective data set. Such enrichment corresponds to a 41% reduction in experimental effort. Interestingly, we found that pairwise screening of the compounds CoSynE individually predicted to be synergistic would result in an enrichment of 1.36 × compared to random selection, indicating that synergy among compound combinations is not a random event. The nine novel and correctly predicted synergistic compound combinations mainly (where sufficient bioactivity information is available) consist of efflux or transporter inhibitors (such as hydroxyzine), combined with compounds exhibiting antimalarial activity alone (such as sorafenib, apicidin, or dihydroergotamine). However, not all compound synergies could be rationalized easily in this way. Overall, this study highlights the potential for predictive modeling to expedite the discovery of novel drug combinations in fight against antimalarial resistance, while the underlying approach is also generally applicable.

Growth of wormlike micelles in nonionic surfactant solutions: Quantitative theory vs. experiment.

Despite the considerable advances of molecular-thermodynamic theory of micelle growth, agreement between theory and experiment has been achieved only in isolated cases. A general theory that can provide self-consistent quantitative description of the growth of wormlike micelles in mixed surfactant solutions, including the experimentally observed high peaks in viscosity and aggregation number, is still missing. As a step toward the creation of such theory, here we consider the simplest system - nonionic wormlike surfactant micelles from polyoxyethylene alkyl ethers, CiEj. Our goal is to construct a molecular-thermodynamic model that is in agreement with the available experimental data. For this goal, we systematized data for the micelle mean mass aggregation number, from which the micelle growth parameter was determined at various temperatures. None of the available models can give a quantitative description of these data. We constructed a new model, which is based on theoretical expressions for the interfacial-tension, headgroup-steric and chain-conformation components of micelle free energy, along with appropriate expressions for the parameters of the model, including their temperature and curvature dependencies. Special attention was paid to the surfactant chain-conformation free energy, for which a new more general formula was derived. As a result, relatively simple theoretical expressions are obtained. All parameters that enter these expressions are known, which facilitates the theoretical modeling of micelle growth for various nonionic surfactants in excellent agreement with the experiment. The constructed model can serve as a basis that can be further upgraded to obtain quantitative description of micelle growth in more complicated systems, including binary and ternary mixtures of nonionic, ionic and zwitterionic surfactants, which determines the viscosity and stability of various formulations in personal-care and house-hold detergency.

Dissipative particle dynamics: Systematic parametrization using water-octanol partition coefficients.

We present a systematic, top-down, thermodynamic parametrization scheme for dissipative particle dynamics (DPD) using water-octanol partition coefficients, supplemented by water-octanol phase equilibria and pure liquid phase density data. We demonstrate the feasibility of computing the required partition coefficients in DPD using brute-force simulation, within an adaptive semi-automatic staged optimization scheme. We test the methodology by fitting to experimental partition coefficient data for twenty one small molecules in five classes comprising alcohols and poly-alcohols, amines, ethers and simple aromatics, and alkanes (i.e., hexane). Finally, we illustrate the transferability of a subset of the determined parameters by calculating the critical micelle concentrations and mean aggregation numbers of selected alkyl ethoxylate surfactants, in good agreement with reported experimental values.

Chemically Aware Model Builder (camb): an R package for property and bioactivity modelling of small molecules.

BACKGROUND: In silico predictive models have proved to be valuable for the optimisation of compound potency, selectivity and safety profiles in the drug discovery process. RESULTS: camb is an R package that provides an environment for the rapid generation of quantitative Structure-Property and Structure-Activity models for small molecules (including QSAR, QSPR, QSAM, PCM) and is aimed at both advanced and beginner R users. camb's capabilities include the standardisation of chemical structure representation, computation of 905 one-dimensional and 14 fingerprint type descriptors for small molecules, 8 types of amino acid descriptors, 13 whole protein sequence descriptors, filtering methods for feature selection, generation of predictive models (using an interface to the R package caret), as well as techniques to create model ensembles using techniques from the R package caretEnsemble). Results can be visualised through high-quality, customisable plots (R package ggplot2). CONCLUSIONS: Overall, camb constitutes an open-source framework to perform the following steps: (1) compound standardisation, (2) molecular and protein descriptor calculation, (3) descriptor pre-processing and model training, visualisation and validation, and (4) bioactivity/property prediction for new molecules. camb aims to speed model generation, in order to provide reproducibility and tests of robustness. QSPR and proteochemometric case studies are included which demonstrate camb's application.Graphical abstractFrom compounds and data to models: a complete model building workflow in one package.