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.

Interplay of self-association and solvation in polar liquids.

The association constants for formation a 1:1 complex between 4-phenyl azophenol and tri-n-butylphosphine oxide were measured in mixtures of n-octane and n-decanol, n-octane and n-hexanoic acid, and n-octane and 2-ethylhexyl acetamide. The experiments provide insight into the competition between solvent self-association and solvent-solute interactions in these systems. The solvation properties of the three polar solvents are quite different from one another and from polar solvents that do not self-associate. Carboxylic acids form dimers in concentrated solution (>1 mM in alkanes). Carboxylic acid dimers have exposed H-bond acceptor sites that solvate H-bond donor solutes with a similar binding affinity to carboxylic acid monomers. The carboxylic acid H-bond donor site is inaccessible in the dimer and is not available to solvate H-bond acceptor solutes. The result is that solvation of H-bond acceptor solutes is in competition with solvent dimerization, whereas solvation of H-bond donor solutes is not. Secondary amides form linear polymers in concentrated solution (>10 mM in alkanes). The solvation properties of the secondary amide aggregates are similar to those of carboxylic acid dimers. Solvation of H-bond acceptor solutes must compete with solvent self-association, because the amide H-bond donor site is not accessible in the middle of a polymeric aggregate. However, the amide aggregates have exposed H-bond acceptor sites, which solvate H-bond donor solutes with similar binding affinity to amide monomers. Alcohols form cyclic tetramers at concentrations of 100 mM in alkanes, and these cyclic aggregates are in equilibrium with linear polymeric aggregates at concentrations above 1 M. The alcohol aggregates have exposed H-bond acceptor sites that solvate H-bond donor solutes with similar binding affinity to alcohol monomers. Although the alcohol H-bond donor sites are involved in H-bond interactions with other alcohols in the aggregates, these sites are sufficiently exposed to form a second bifurcated H-bond with H-bond acceptor solutes, and these interactions have a similar binding affinity to alcohol monomers. The result is that self-association of alcohols does not compete with solvation of solutes, and alcohols are significantly more polar solvents than expected based on the properties of alcohol monomers.

Systematic Parameterization of Ion-Surfactant Interactions in Dissipative Particle Dynamics Using Setschenow Coefficients.

Dissipative particle dynamics (DPD) simulations of nonionic surfactants with an added salt show that the Setschenow relationship is reproduced; that is, the critical micelle concentration is log-linearly dependent on the added salt concentration. The simulated Setschenow coefficients depend on the DPD bead-bead repulsion amplitudes, and matching to the experimentally determined values provides a systematic method to parameterize the interactions between salt ion beads and surfactant beads. The optimized ion-specific interaction parameters appear to be transferrable and follow the same trends as the empirical Hofmeister series.

Molecular recognition probes of solvation thermodynamics in solvent mixtures.

High-throughput UV-Vis experiments using four molecular recognition-based probes, made by the combination of two hydrogen bond acceptors, tri-n-butylphosphine oxide and N,N'-bis(2-ethylhexyl)acetamide, and two hydrogen bond donors, 4-phenylazophenol and 4-nitrophenol, were performed. The association constants for the 1 : 1 H-bond interaction involved in each probe system were measured in mixtures of a polar and non-polar solvent, di-n-hexyl ether and n-octane, respectively. Similar behaviour was observed for all four systems. When the concentration of the polar solvent was low, the association constant was identical to that observed in pure n-octane. However, once the concentration of the polar solvent exceeded a threshold, the association constant decreased linearly with the concentration of di-n-hexyl ether. Selective solvation in mixtures can be understood based on the competition between the multiple competing equilibria in the system. In this case, solvation thermodynamics are dominated by competition of the ether for solvation of H-bond donors. For the more polar solute, 4-nitrophenol, the selective solvation starts at lower concentrations of the polar solvent compared with the less polar solute, 4-phenylazophenol. Thus the speciation and hence the properties of systems containing multiple solutes and multiple solvents can be estimated from the H-bond properties and the concentrations of the individual functional groups.

Translation of Chemical Structure into Dissipative Particle Dynamics Parameters for Simulation of Surfactant Self-Assembly.

Dissipative particle dynamics (DPD) can be used to simulate the self-assembly properties of surfactants in aqueous solutions, but in order to simulate a new compound, a large number of new parameters are required. New methods for the calculation of reliable DPD parameters directly from chemical structure are described, allowing the DPD approach to be applied to a much wider range of organic compounds. The parameters required to describe the bonded interactions between DPD beads were calculated from molecular mechanics structures. The parameters required to describe the nonbonded interactions were calculated from surface site interaction point (SSIP) descriptions of molecular fragments that represent individual beads. The SSIPs were obtained from molecular electrostatic potential surfaces calculated using density functional theory and used in the SSIMPLE algorithm to calculate transfer free energies between different bead liquids. This approach was used to calculate DPD parameters for a range of different types of surfactants, which include ester, amide, and sugar moieties. The parameters were used to simulate the self-assembly properties in aqueous solutions, and comparison of the results for 27 surfactants with the available experimental data shows that these DPD simulations accurately predict critical micelle concentrations, aggregation numbers, and the shapes of the supramolecular assemblies formed. The methods described here provide a general approach to determining DPD parameters for neutral organic compounds of arbitrary structure.

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.

Functional group interaction profiles: a general treatment of solvent effects on non-covalent interactions.

Solvation has profound effects on the behaviour of supramolecular systems, but the effects can be difficult to predict even at a qualitative level. Functional group interaction profiles (FGIPs) provide a simple visual method for understanding how solvent affects the free energy contribution due to a single point interaction, such as a hydrogen bond, between two solute functional groups. A generalised theoretical approach has been developed, which allows calculation of FGIPs for any solvent or solvent mixture, and FGIPs for 300 different solvents have been produced, providing a comprehensive description of solvent effects on non-covalent chemistry. The free energy calculations have been validated using experimental measurements of association constants for hydrogen bonded complexes in multiple solvent mixtures. The calculated FGIPs provide good descriptions of the solvation of polar solutes, solvophobic interactions between non-polar solutes in polar solvents like water, and preferential solvation in solvent mixtures. Applications are explored of the use of FGIPs in drug design, for optimising receptor-ligand interactions, and in enantioselective catalysis for solvent selection to optimise selectivity.

A Surface Site Interaction Point Method for Dissipative Particle Dynamics Parametrization: Application to Alkyl Ethoxylate Surfactant Self-Assembly.

Dissipative particle dynamics (DPD) is a coarse-grained approach to the simulation of large supramolecular systems, but one limitation has been that the parameters required to describe the noncovalent interactions between beads are not readily accessible. A first-principles computational method has been developed so that bead interaction parameters can be calculated directly from ab initio gas-phase molecular electrostatic potential surfaces of the molecular fragments that represent the beads. A footprinting algorithm converts the molecular electrostatic potential surfaces into a discrete set of surface site interaction points (SSIPs), and these SSIPs are used in the SSIMPLE (surface site interaction model for the properties of liquids at equilibrium) algorithm to calculate the free energies of transfer of one bead into a solution of any other bead. The bead transfer free energies are then converted into the required DPD interaction parameters for all pairwise combinations of different beads. The reliability of the parameters was demonstrated using DPD simulations of a range of alkyl ethoxylate surfactants. The simulations reproduce the experimentally determined values of the critical micelle concentration and mean aggregation number well for all 22 surfactants studied.

H-Bond donor parameters for cations.

UV/Vis absorption and NMR spectroscopy titrations have been used to investigate the formation of complexes between cations and neutral H-bond acceptors in organic solvents. Complexes formed by two different H-bond acceptors with fifteen different cations were studied in acetone and in acetonitrile. The effects of water and ion pairing with the counter-anion were found to be negligible in the two polar solvents employed for this study. The data were used to determine self-consistent H-bond donor parameters (α) for a series of organic and inorganic cations; guanidinium, primary, tertiary and quaternary ammonium, imidazolium, methylpyridinium, lithium, sodium, potassium, rubidium and caesium. The results demonstrate the transferability of α parameters for cations between different solvents and different H-bond acceptor partners, allowing reliable prediction of cation recognition properties in different environments. Lithium and protonated nitrogen cations form the most stable complexes, but the α parameter is only 5.0, which is similar to the neutral H-bond donor 3-trifluoromethyl,4-nitrophenol (α = 5.1). Quaternary ammonium is the weakest H-bond donor investigated with an α value of 2.7, which is comparable to an alcohol. The α parameters for alkali metal cations decrease down the group from 5.0 (Li+) to 3.5 (Cs+).

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.

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.

Influence of solvent polarity on preferential solvation of molecular recognition probes in solvent mixtures.

The association constants for formation of 1:1 complexes between a H-bond acceptor, tri-n-butylphosphine oxide, and a H-bond donor, 4-phenylazophenol, have been measured in a range of different solvent mixtures. Binary mixtures of n-octane and a more polar solvent (ether, ester, ketone, nitrile, sulfoxide, tertiary amide, and halogenated and aromatic solvents) have been investigated. Similar behavior was observed in all cases. When the concentration of the more polar solvent is low, the association constant is identical to that observed in pure n-octane. Once a threshold concentration of the more polar solvent in reached, the logarithm of the association constant decreases in direct proportion to the logarithm of the concentration of the more polar solvent. This indicates that one of the two solutes is preferentially solvated by the more polar solvent, and it is competition with this solvation equilibrium that determines the observed association constant. The concentration of the more polar solvent at which the onset of preferential solvation takes place depends on solvent polarity: 700 mM for toluene, 60 mM for 1,1,2,2-tetrachloroethane, 20 mM for the ether, ester, ketone, and nitrile, 0.2 mM for the tertiary amide, and 0.1 mM for the sulfoxide solvents. The results can be explained by a simple model that considers only pairwise interactions between specific sites on the surfaces of the solutes and solvents, which implies that the bulk properties of the solvent have little impact on solvation thermodynamics.