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

Many-body dissipative particle dynamics simulations of micellization of sodium alkyl sulfates

We present a study of micelle formation in alkyl sulfate surfactants using the simulation method of many-body dissipative particle dynamics (MDPD). We parametrise our model by tuning the intermolecular interactions in order to reproduce experimental values for the chemical potential and density at room temperature. Using this approach, we find that our model shows good agreement with experimental values for the critical micelle concentration (CMC). Furthermore, we show that our model can accurately predict CMC trends, which result from varying properties such as surfactant tail length and the salt concentration. We apply our model to investigate the effect of aggregation number on various micellar properties, such as the shape of individual micelles and the fraction of bound counterions. We show that micelles become aspherical at large aggregation numbers, in line with experimental predictions, and that longer tail surfactants are generally more spherical at all aggregation numbers compared to those which are shorter. We find excellent agreement between our simulations and experimental values for the degree of counterion binding, a factor that is crucial to accurately studying micellar shape, but one that is typically overlooked in the existing literature.

Multiscale modelling of transport in polymer-based reverse-osmosis/nanofiltration membranes: present and future

Nanofiltration (NF) and reverse osmosis (RO) processes are physical separation technologies used to remove contaminants from liquid streams by employing dense polymer-based membranes with nanometric voids that confine fluids at the nanoscale. At this level, physical properties such as solvent and solute permeabilities are intricately linked to molecular interactions. Initially, numerous studies focused on developing macroscopic transport models to gain insights into separation properties at the nanometer scale. However, continuum-based models have limitations in nanoconfined situations that can be overcome by force field molecular simulations. Continuum-based models heavily rely on bulk properties, often neglecting critical factors like liquid structuring, pore geometry, and molecular/chemical specifics. Molecular/mesoscale simulations, while encompassing these details, often face limitations in time and spatial scales. Therefore, achieving a comprehensive understanding of transport requires a synergistic integration of both approaches through a multiscale approach that effectively combines and merges both scales. This review aims to provide a comprehensive overview of the state-of-the-art in multiscale modeling of transport through NF/RO membranes, spanning from the nanoscale to continuum media.

Dioctyl sodium sulfosuccinate surfactant self-assembly dependency of solvent hydrophilicity: a modelling study

The self-assembly of dioctyl sodium sulfosuccinate (AOT) model surfactant in solvent environments of differing polarity is examined by means of dissipative particle dynamics (DPD) bead model parametrized against Hildebrand solubility parameters from atomistic molecular dynamics (MD) simulations. The model predicts that in hydrophobic solvents (e.g. dodecane) the surfactant forms small (Nagg ∼ 8) reverse micellar aggregates, while in a solvent corresponding to water lamellar assembly takes place, in good agreement with literature structural parameters. Interestingly, solvents of intermediate polarity lead to formation of large, internally structured aggregates. In these, the surfactant headgroups cluster within the aggregate, surrounded by a continuous phase formed by the hydrocarbon tails. We show that the partitioning of the headgroups between the aggregate surface layer and the inner clustered phase depends primarily on solvent polarity, and can be controlled by the solvent, but also system composition. Finally, we compare the DPD assembly response to simplified effective interaction potentials derived at dilute concentration limit for the interactions. The comparison reveals that the simplified effective potential descriptions provide good level of insight on the assembly morphologies, despite drastic, isotropic interactions simplification involved.

A many-body dissipative particle dynamics parametrisation scheme to study behaviour at air-water interfaces

In this article, we present a general parametrisation scheme for many-body dissipative particle dynamics (MDPD). The scheme is based on matching model components to experimental surface tensions and chemical potentials. This allows us to obtain the correct surface and mixing behaviours of complex, multicomponent systems. The methodology is tested by modelling the behaviour of nonionic polyoxyethylene alkyl ether surfactants at an air/water interface. In particular, the influence of the number of ethylene oxide units in the surfactant head group is investigated. We find good agreement with many experimentally obtained parameters, such as minimum surface area per molecule; and a decrease in the surface tension with increasing surfactant surface density. Moreover, we observe an orientational transition, from surfactants lying directly on the water surface at low surface coverage, to surfactants lying parallel or tilted with respect to the surface normal at high surface coverage. The parametrisation scheme is also extended to cover the zwitterionic surfactant lauryldimethylamine oxide (LDAO), where we provide good predictions for the surface tension at maximum surface coverage. Here, if we exceed this coverage, we are able to demonstrate the spontaneous production of micelles from the surface surfactant layer.

Phase Behavior of Alkyl Ethoxylate Surfactants in a Dissipative Particle Dynamics Model

We present a dissipative particle dynamics (DPD) model capable of capturing the liquid state phase behavior of nonionic surfactants from the alkyl ethoxylate (C_nE_m) family. The model is based upon our recent work [Anderson et al. J. Chem. Phys. 2017, 147, 094503] but adopts tighter control of the molecular structure by setting the bond angles with guidance from molecular dynamics simulations. Changes to the geometry of the surfactants were shown to have little effect on the predicted micelle properties of sampled surfactants, or the water-octanol partition coefficients of small molecules, when compared to the original work. With these modifications the model is capable of reproducing the binary water-surfactant phase behavior of nine surfactants (C₈E₄, C₈E₅, C₈E₆, C₁₀E₄, C₁₀E₆, C₁₀E₈, C₁₂E₆, C₁₂E₈, and C₁₂E₁₂) with a good degree of accuracy.

Generalized Energy-Conserving Dissipative Particle Dynamics with Mass Transfer. Part 1: Theoretical Foundation and Algorithm

An extension of the generalized energy-conserving dissipative particle dynamics method (GenDPDE) that allows mass transfer between mesoparticles via a diffusion process is presented. By considering the concept of the mesoparticles as property carriers, the complexity and flexibility of the GenDPDE framework were enhanced to allow for interparticle mass transfer under isoenergetic conditions, notated here as GenDPDE-M. In the formulation, diffusion is described via the theory of mesoscale irreversible processes based on linear relationships between the fluxes and thermodynamic forces, where their fluctuations are described by Langevin-like equations. The mass exchange between mesoparticles is such that the mass of the mesoparticle remains unchanged after the transfer process and requires additional considerations regarding the coupling with other system properties such as the particle internal energy. The proof-of-concept work presented in this article is the first part of a two-part article series. In Part 1, the development of the GenDPDE-M theoretical framework and the derivation of the algorithm are presented in detail. Part 2 of this article series is targeted for practitioners, where applications, demonstrations, and practical considerations for implementing the GenDPDE-M method are presented and discussed.

Studying the Structure of Sodium Lauryl Ether Sulfate Solutions Using Dissipative Particle Dynamics

Sodium lauryl ether sulfate (SLES) is a common anionic surfactant used in a large number of personal care products. Commercial products typically contain a distribution in the number of ethoxy groups; despite this, there is limited existing work studying the effect of the ethoxy groups on the phase formation and structure. This is particularly important for the effect the structure has on the viscosity, an important consideration for commercial products. Dissipative particle dynamics is used to simulate the full phase diagram of SLES in water, including both micellar and lyotropic liquid crystal phases. Phase transitions occur at locations which are in good agreement with experimental data, and we find that these boundaries can shift as a result of varying the number of ethoxy groups. Varying the ethoxy groups has a significant effect on the micellar shape and crystalline spacing, with a reduction leading to more nonspherical micelles and decreased periodic spacing of the hexagonal and lamellar phases. Finally, while typical commercial products contain a distribution of ethoxy groups, computational work tends to focus on simulations containing a single chain length. We show that it is valid to use monodisperse simulations to infer behavior about solutions with a polydisperse chain length, based on its mean molecular length.

Comprehensive review of the interfacial behavior of water/oil/surfactant systems using dissipative particle dynamics simulation

A comprehensive understanding of interfacial behavior in water/oil/surfactant systems is critical to evaluating the performance of emulsions in various industries, specifically in the oil and gas industry. To gain fundamental knowledge regarding this interfacial behavior, atomistic methods, e.g., molecular dynamics (MD) simulation, can be employed; however, MD simulation cannot handle phenomena that require more than a million atoms. The coarse-grained mesoscale methods were introduced to resolve this issue. One of the most effective mesoscale coarse-grained approaches for simulating colloidal systems is dissipative particle dynamics (DPD), which bridges the gap between macroscopic time and length scales and molecular-scale simulation. This work reviews the fundamentals of DPD simulation and its progress on colloids and interface systems, especially surfactant/water/oil mixtures. The effects of temperature, salt content, a water/oil ratio, a shear rate, and a type of surfactant on the interfacial behavior in water/oil/surfactant systems using DPD simulation are evaluated. In addition, the obtained results are also investigated through the lens of the chemistry of surfactants and emulsions. The outcome of this comprehensive review demonstrates the importance of DPD simulation in various processes with a focus on the colloidal and interfacial behavior of surfactants at water-oil interfaces.

Flow-induced scission of wormlike micelles in nonionic surfactant solutions under shear flow

We investigate flow-induced scission of wormlike micelles with dissipative particle dynamics simulations of nonionic surfactant solutions under shear flow. To understand flow-induced scission in terms of micellar timescales, we propose a method to evaluate the longest relaxation time of unentangled surfactant micelles from the rotational relaxation time and the average lifetime at equilibrium. The mean squared displacement of surfactant molecules provides evidence that the longest relaxation time estimated by the proposed method serves as the characteristic timescale at equilibrium. We also demonstrate that the longest relaxation time plays an essential role in flow-induced scission. Using conditional statistics based on the aggregation number of micelles, we examine the statistical properties of the lifetime of wormlike micelles. We then conclude that flow-induced scission occurs when the Weissenberg number defined as the product of the longest relaxation time and the shear rate is larger than a threshold value.

Modeling Alkyl Aromatic Hydrocarbons with Dissipative Particle Dynamics

Building on previous work studying alkanes, we develop a dissipative particle dynamics (DPD) model to capture the behavior of the alkyl aromatic hydrocarbon family under ambient conditions of 298 K and 1 atmosphere. Such materials are of significant worldwide industrial importance in applications such as solvents, chemical intermediates, surfactants, lubricating oils, hydraulic fluids, and greases. We model both liquids and waxy solids for molecules up to 36 carbons in size and demonstrate that we can correctly capture both the freezing transition and liquid-phase densities in pure substances and mixtures. We also demonstrate the importance of including specialized bead types into the DPD model (rather than solely relying on generic bead types) to capture specific local geometrical constructs such as the benzene ring found in the benzyl chemical group; this can be thought of as representing subtle real-world many-body effects via customized pairwise non-bonded potentials.

Estimating Preferred Alkane Carbon Numbers of Nonionic Surfactants in Normalized Hydrophilic-Lipophilic Deviation Theory from Dissipative Particle Dynamics Modeling

The preferred alkane carbon number (PACN) in the normalized hydrophilic-lipophilic deviation (HLD_N) theory is a numerical parameter and a transferable scale to characterize the amphiphilicity of surfactants, which is usually measured experimentally using the fish diagram or phase inversion temperature (PIT) methods, and the experimental measurement can only be applied to existing surfactants. Here, for the first time, we propose a procedure to estimate the PACN of C_iE_j nonionic surfactants directly from dissipative particle dynamics (DPD) simulation. The procedure leverages the method of moment concept to quantitatively evaluate the bending tendency of nonionic surfactant monolayers by calculating the torque density. Seven nonionic surfactants, C_iE_j (C₆E₂, C₆E₃, C₈E₃, C₈E₄, C₁₀E₄, C₁₂E₄, and C₁₂E₅), with known PACNs are modeled. Two surfactants, C₁₀E₄ and C₆E₂, were first selected to train and test the interaction parameters, and the relationship between interaction parameters and torque density was mapped for the C₁₀E₄-octane-water system using the artificial neural network (ANN) fitting approach to derive the interaction parameters giving zero torque density, then the interaction parameters were tested in the C₆E₂-dodecane-water system to get the final tuned interaction parameters for PACN estimation. With this procedure, we reproduce the PACN values and their trend of seven nonionic surfactants with reasonable accuracy, which opens the door for quantitative comparison of surfactant amphiphilicity and surfactant classification in silico using the PACN as a transferrable scale.

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.

DPD Modelling of the Self- and Co-Assembly of Polymers and Polyelectrolytes in Aqueous Media: Impact on Polymer Science

This review article is addressed to a broad community of polymer scientists. We outline and analyse the fundamentals of the dissipative particle dynamics (DPD) simulation method from the point of view of polymer physics and review the articles on polymer systems published in approximately the last two decades, focusing on their impact on macromolecular science. Special attention is devoted to polymer and polyelectrolyte self- and co-assembly and self-organisation and to the problems connected with the implementation of explicit electrostatics in DPD numerical machinery. Critical analysis of the results of a number of successful DPD studies of complex polymer systems published recently documents the importance and suitability of this coarse-grained method for studying polymer systems.

First-principles prediction of critical micellar concentrations for ionic and nonionic surfactants

The concentration of surfactant in solution for which micelles start to form, also known as critical micelle concentration is a key property in formulation design. The critical micelle concentration can be determined experimentally with a tensiometer by measuring the surface tension of a concentration series. In analogy with experiments, in-silico predictions can be achieved through interfacial tension calculations. We present a newly developed method, which employs first principles-based interfacial tension calculations rooted in COSMO-RS theory, for the prediction of the critical micelle concentration of a set of nonionic, cationic, anionic, and zwitterionic surfactants in water. Our approach consists of a combination of two prediction strategies for modelling two different phenomena involving the removal of the surfactant hydrophobic tail from contact with water. The two strategies are based on regular micelle formation and thermodynamic phase separation of the surfactant from water and both are required to take into account a wide range of polarity in the hydrophilic headgroup. Our method yields accurate predictions for the critical micellar concentration, within one log unit from experiments, for a wide range of surfactant types and introduces possibilities for first-principles based prediction of formulation properties for more complex compositions.

Interactions of Crosslinked Polyacrylic Acid Polyelectrolyte Gels with Nonionic and Ionic Surfactants

The morphology and stability of surfactant-loaded polyelectrolyte gels are of great interest for a variety of personal care, cosmetic, and pharmaceutical products. However, the mechanisms of surfactant interactions with gel-forming polymers are poorly understood and experimentally challenging. The aim of this work is to explore in silico the specifics of surfactant absorption within polyelectrolyte gels drawing on the examples of typical non-ionic octaethylene glycol monooctyl ether (C₈E₈) and anionic sodium dodecyl sulfate (SDS) surfactants and polyacrylic acid modified with hydrophobic sidechains mimicking the practically important Carbopol polymer. Using the systematically parameterized coarse-grained dissipative particle dynamics models, we generate and characterize the equilibrium conformations and swelling of the polymer films in aqueous solutions with the surfactant concentrations varied up to the critical micelle concentration (cmc). We discover the striking difference in interactions of Carbopol-like polymers with nonionic and ionic surfactants under mildly acidic conditions. The sorption of C₈E₈ within the polymer film is found substantial. As the surfactant concentration increases, the polymer film swells and, close to cmc, becomes unstable due to the formation and growth of water pockets filled with surfactant micelles. Sorption of SDS at the same bulk concentrations is found much lower, with only about 1% of surfactant mass fraction achieved at cmc. As the SDS concentration increases further, a lamellae structure is formed within the film, which remains stable. Reduced swelling and higher stability indicate better prospects of using SDS-type surfactants with Carbopol-based gels in formulations for detergents and personal care products.

Dissipative particle dynamics simulations in colloid and Interface science: a review

Dissipative particle dynamics (DPD) is one of the most efficient mesoscale coarse-grained methodologies for modeling soft matter systems. Here, we comprehensively review the progress in theoretical formulations, parametrization strategies, and applications of DPD over the last two decades. DPD bridges the gap between the microscopic atomistic and macroscopic continuum length and time scales. Numerous efforts have been performed to improve the computational efficiency and to develop advanced versions and modifications of the original DPD framework. The progress in the parametrization techniques that can reproduce the engineering properties of experimental systems attracted a lot of interest from the industrial community longing to use DPD to characterize, help design and optimize the practical products. While there are still areas for improvements, DPD has been efficiently applied to numerous colloidal and interfacial phenomena involving phase separations, self-assembly, and transport in polymeric, surfactant, nanoparticle, and biomolecules systems.

Effects of metal-polymer complexation on structure and transport properties of metal-substituted polyelectrolyte membranes

Morphological and transport properties of hydrated metal-substituted Nafion membranes doped with metal ions of different valency and coordination strength are explored using coarse-grained dissipative particle dynamics simulations. To incorporate the effects of metal-polymer complexation, we introduce a novel metal ion complexation model, in which the charged central metal ion is surrounded by dummy sites that coordinate with ligands. The model parameters are determined by matching the metal-ligand running coordination numbers and the diffusion coefficients obtained from atomistic simulations and/or experiments. The increase of valency and coordination strength is found to strongly influence both the morphology and transport characteristics of the membrane at all hydration levels. The membrane segregation into hydrophobic and hydrophilic sub-phases is affected by metal-sulphonate coordination induced crosslinking at the hydrophilic/hydrophobic interface. The simulation results indicate that the interfacial crosslinking influences the interfacial tension and thereby affect the growth and coalescence of water clusters upon the increase of hydration. Multivalent complexation hinders water and ion mobility and causes anomalous sub-diffusion and dramatic decrease of the water permeability and ionic conductivity. Our DPD model is found efficient in elucidating the mechanisms of coordination-induced cross-linking and complexation and predicting on a semi-quantitative level the morphological and transport properties of metal-substituted Nafion membranes depending on the ion valency and coordination strength. The proposed model can be further advanced and adopted for other polyelectrolyte systems, such as sulfonated block-copolymers, polysaccharide solutions and composites, and biopolymer assemblies.

Structural properties of cationic surfactant-fatty alcohol bilayers: insights from dissipative particle dynamics

Bilayers, self-assembled by cationic surfactants and fatty alcohols in water, are the basic units of lamellar gel networks - creamy formulations extensively used in cosmetics and pharmaceutics. Mesoscopic modelling and study of the bilayers formed by single- or double-tail cationic surfactants (CTAC or DHDAC), and fatty alcohols (FAs) in the lamellar fluid and gel phases were employed. Fatty alcohols with alkyl tail equal to or greater than the surfactant alkyl tail, i.e., C₁₆FA or C₁₈FA and C₂₂FA, were considered. A model formulation was explored with the FA concentration greater than that of the surfactant and the structure of the fluid and gel bilayers in tensionless state characterised via the density profiles across the bilayers, orientational order parameters of the surfactant and FA chains, intrinsic analysis of the bilayer interfaces, and bending rigidity. The intrinsic analysis allows identification and quantification of the coexistence of the interdigitated and non-interdigitated phases present within the gel bilayers. The FA chains were found to conform the primary scaffolding of the bilayers while the surfactant chains tessellate bilayer monolayers from their water-hydrophobic interface. Further, the overlap of the FA chains from the apposed monolayers of the fluid bilayers rises with increasing FA length. Finally, the prevalence of the non-interdigitated phase over the interdigitated phase within the gel bilayers becomes enhanced upon the FA length increase with a preference of the surfactant chains to reside in the non-interdigitated phase rather than the interdigitated phase.

Micellization of Rhamnolipid Biosurfactants and Their Applications in Oil Recovery: Insights from Mesoscale Simulations

The dissipative particle dynamics (DPD) mesoscopic method is used to investigate the self-assembly of rhamnolipid congeners and their aggregation behaviors with paraffins including nonane and pentadecane. The coarse-grained force field is parameterized by combining molecular dynamics (MD) simulations, COSMOtherm calculations, and available experimental data. This model reproduces the vesicular formation of α-l-rhamnopyranosyl-β-hydroxydecanoyl-β-hydroxydecanoate (Rha-C10-C10) reported by all-atom MD simulations. The vesicle composed of Rha-C10-C10 is found to be most stable at a surfactant concentration of 100-146 mM based on asphericity analysis. The architecture of rhamnolipid congeners affects the morphology of their aggregates. Di-rhamno-di-lipidic dRha-C16-C16 forms vesicles with a thicker unilamellar layer of 3.2 nm. Rha-C16-C16 forms vesicles at a lower concentration of 70 mM, but the enclosed water space collapses when the surfactant concentration increases. dRha-C10-C10 forms wormlike micelles, which agglomerate into a torus and interconnected network at higher concentrations. In the presence of alkane molecules, dRha-C10-C10 maintains its wormlike micellar morphology with alkane molecules wrapped inside the aggregates. For Rha-C10-C10, Rha-C16-C16, and dRha-C16-C16, nonane molecules are distributed in the hydrophobic subdomain formed by rhamnolipid molecules. Spherical vesicles are formed at a surfactant concentration of 50 mM and then develop into ellipsoidal vesicles when the concentration increases to 125 mM. When mixed with pentadecane, the alkane molecules are aggregated and surrounded by surfactants forming a core-shell structure at a low surfactant concentration of 20 mM. At higher alkane and surfactant concentrations, the morphologies develop into disk micelles, wormlike micelles, and vesicles, with pentadecane molecules being distributed and packed with rhamnolipids. The obtained simulation results suggest that these biosurfactants have potential as environmental remediation agents.

Closed-Form Coexistence Equation for Phase Separation of Polymeric Mixtures in Dissipative Particle Dynamics

To date, no extensive study of the phase diagram for binary fluid mixtures in dissipative particle dynamics (DPD) has been published. This is especially pertinent for newer parameterization schemes where the self-self interaction, or the effective volume, of different particle types is varied. This work presents an exhaustive study of the parameter space concerning DPD particles with soft interaction potentials. Moreover, we propose a closed-form coexistence equation or binodal curve that is inspired by the Flory-Huggins model. This equation describes the phase diagram of all binary mixtures made up out of monomers, homopolymers, and the mixtures thereof when self-self interactions are varied. The mean absolute percentage error (MAPE) of the equation on simulated data, including validation simulations, is 1.02%. The equation can a priori predict the phase separation of mixtures using only DPD interaction parameters. The proposed coexistence equation can therefore be used to directly validate interaction parameters resulting from novel parameterization schemes, including coarse graining and equations of state, without the need for additional simulations. Finally, it is shown that the choice of bond potential markedly influences phase behavior.

Critical Micelle Concentrations in Surfactant Mixtures and Blends by Simulation

We explore the use of coarse-grained dissipative particle dynamics simulations to predict critical micelle concentrations (CMCs) in polydisperse surfactant mixtures and blends. By fitting pseudo-phase separation models (PSMs) to aqueous solutions of binary surfactant mixtures at selected compositions above the CMC, we avoid the need for expensive simulations of more complex multicomponent mixtures performed as a function of dilution. The approach is demonstrated for sodium laureth sulfate (SLES) surfactants with polydispersity in the ethoxylate spacer. For this system, we find a modest degree of cooperativity in micelle formation, which we attribute to the reduced repulsion between charged headgroups for surfactants with dissimilar ethoxylate spacer lengths. However, this is insufficient to explain the lowered CMC often observed in commercial SLES samples, which we attribute to the presence of small amounts of unsulfated alkyl ethoxylates and/or traces of salt.

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.

Designing Highly Conductive Block Copolymer-Based Anion Exchange Membranes by Mesoscale Simulations

Hydroxide ion conductivity is a key aspect of anion exchange membranes and is mainly determined by the nanoscale membrane morphologies. Fundamental understanding of the structural and transport properties of membranes in terms of polymer architectures is crucial for future development of membrane-based applications. Using mesoscale simulations, this work predicts the mesostructure of the hydrated triblock copolymers; the designed polymers are composed of aromatic (polyphenylene oxide, PPO) or aliphatic (polystyrene-ethylene-butylene-styrene, SEBS) backbones, with cationic side chains being modified by hydrophobic or hydrophilic spacers. For PPO-based polymers, using octyl spacers creates a meshlike water network, yielding ion conductivity equal to 30.6 mS/cm at room temperature. For SEBS-based polymers, the nonmodified form is sufficient to produce ion-conducting pathways. Adding hydrophobic spacers further enhances the nanosegregation, and the membranes provide similar conductivity at a lower ion exchange capacity and water content. Adding hydrophilic spacers, however, has negative impacts on the ion transport. The side chains are in the stretched configurations, which sterically hinder the mobility of water and hydroxide ions. Such a resistance can be overcome by adapting multication side-chain designs, where large water channels are formed, yielding ion conductivity as high as 32.8 mS/cm.

Wax Formation in Linear and Branched Alkanes with Dissipative Particle Dynamics

We present a dissipative particle dynamics (DPD) model for wax formation (i.e., the freezing transition) in linear and branched alkanes at room temperature (298 K) and atmospheric pressure. We parametrize the model using pure liquid phase densities and the onset of wax formation as a function of alkyl chain length. Significant emphasis is placed on building an accurate representation of the underlying molecular architecture by careful consideration of bond lengths and angles, aided by distributions obtained from molecular dynamics simulation. Using the derived model, we observe wax formation in n-alkanes when the alkyl chain length is greater than 18 (n-octadecane), in excellent agreement with experimental observations. Further, we reproduce the behavior of branched alkanes and mixtures including solubilities of heavy alkanes in light alkane solvents.

Model for the Simulation of the CnEm Nonionic Surfactant Family Derived from Recent Experimental Results

Using a comprehensive set of recently published experimental results for training and validation, we have developed computational models appropriate for simulations of aqueous solutions of poly(ethylene oxide) alkyl ethers, an important class of micelle-forming nonionic surfactants, usually denoted C_nE_m. These models are suitable for use in simulations that employ a moderate amount of coarse graining and especially for dissipative particle dynamics (DPD), which we adopt in this work. The experimental data used for training and validation were reported earlier and produced in our laboratory using dynamic light scattering (DLS) measurements performed on 12 members of the C_nE_m compound family yielding micelle size distribution functions and mass-weighted mean aggregation numbers at each of several surfactant concentrations. The range of compounds and quality of the experimental results were designed to support the development of computational models. An essential feature of this work is that all simulation results were analyzed in a way that is consistent with the experimental data. Proper account is taken of the fact that a broad distribution of micelle sizes exists, so mass-weighted averages (rather than number-weighted averages) over this distribution are required for the proper comparison of simulation and experimental results. The resulting DPD force field reproduces several important trends seen in the experimental critical micelle concentrations and mass-averaged mean aggregation numbers with respect to surfactant characteristics and concentration. We feel it can be used to investigate a number of open questions regarding micelle sizes and shapes and their dependence on surfactant concentration for this important class of nonionic surfactants.

The Role of Chemical Heterogeneity in Surfactant Adsorption at Solid-Liquid Interfaces

Chemical heterogeneity of solid surfaces disrupts the adsorption of surfactants from the bulk liquid. While its presence can hinder the performance of some formulations, bespoke chemical patterning could potentially facilitate controlled adsorption for nanolithography applications. Although some computational studies have investigated the impact of regularly patterned surfaces on surfactant adsorption, in reality, many interesting surfaces are expected to be stochastically disordered and this is an area unexplored via simulations. In this paper, we describe a new algorithm for the generation of randomly disordered chemically heterogeneous surfaces and use it to explore the adsorption behavior of four model nonionic surfactants. Using novel analysis methods, we interrogate both the global surface coverage (adsorption isotherm) and behavior in localized regions. We observe that trends in adsorption characteristics as surfactant size, head/tail ratio, and surface topology are varied and connect these to underlying physical mechanisms. We believe that our methods and approach will prove useful to researchers seeking to tailor surface patterns to calibrate nonionic surfactant adsorption.

The Relationship between Wormlike Micelle Scission Free Energy and Micellar Composition: The Case of Sodium Lauryl Ether Sulfate and Cocamidopropyl Betaine

The scission energy is the difference in free energy between two hemispherical caps and the cylindrical region of a wormlike micelle. This energy difference determines the logarithm of the average micelle length, which affects several macroscopic properties such as the viscosity of viscoelastic fluids. Here we use a recently published method by Wang et al. ( Langmuir, 2018, 34, 1564-1573) to directly calculate the scission energy of micelles composed of monodisperse sodium lauryl ether sulfate (SLES_nEO), an anionic surfactant. Utilizing dissipative particle dynamics (DPD), we perform a systematic study varying the number of ethoxyl groups (n) and salt concentration. The scission energy increases with increasing salt concentration, indicating that the formation of longer micelles is favored. We attribute this to the increased charge screening that reduces the repulsion between head groups. However, the scission energy decreases with increasing number of ethoxyl groups as the flexibility of the head group increases and the sodium ion becomes less tightly bound to the head group. We then extend the analysis to look at the effect of a common cosurfactant, cocamidopropyl betaine (CAPB), and find that its addition stabilizes wormlike micelles at a lower salt concentration.

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.

Tuning the Properties of Nanogel Surfaces by Grafting Charged Alkylamine Brushes

Nanogels are chemically crosslinked polymeric nanoparticles endowed with high encapsulation ability, tunable size, ease of preparation, and responsiveness to external stimuli. The presence of specific functional groups on their surfaces provides an opportunity to tune their surface properties and direct their behavior. In this work, we used mesoscale modeling to describe conformational and mechanical properties of nanogel surfaces formed by crosslinked polyethylene glycol and polyethyleneimine, and grafted by charged alkylamine brushes of different lengths. Simulations show that both number of chains per area and chain length can be used to tune the properties of the coating. Properly selecting these two parameters allows switching from a hydrated, responsive coating to a dried, highly charged layer. The results also suggest that the scaling behavior of alkylamine brushes, e.g., the transition from a mushroom to semi-dilute brush, is only weakly coupled with the shielding ability of the coating and much more with its compressibility.

Utilizing Machine Learning for Efficient Parameterization of Coarse Grained Molecular Force Fields

We present a machine learning approach to automated force field development in dissipative particle dynamics (DPD). The approach employs Bayesian optimization to parametrize a DPD force field against experimentally determined partition coefficients. The optimization process covers a discrete space of over 40 000 000 points, where each point represents the set of potentials that jointly forms a force field. We find that Bayesian optimization is capable of reaching a force field of comparable performance to the current state-of-the-art within 40 iterations. The best iteration during the optimization achieves an R² of 0.78 and an RMSE of 0.63 log units on the training set of data, these metrics are maintained when a validation set is included, giving R² of 0.8 and an RMSE of 0.65 log units. This work hence provides a proof-of-concept, expounding the utility of coupling automated and efficient global optimization with a top down data driven approach to force field parametrization. Compared to commonly employed alternative methods, Bayesian optimization offers global parameter searching and a low time to solution.

Prediction of Partition Coefficients of Environmental Toxins Using Computational Chemistry Methods

The partitioning of compounds between aqueous and other phases is important for predicting toxicity. Although thousands of octanol-water partition coefficients have been measured, these represent only a small fraction of the anthropogenic compounds present in the environment. The octanol phase is often taken to be a mimic of the inner parts of phospholipid membranes. However, the core of such membranes is typically more hydrophobic than octanol, and other partition coefficients with other compounds may give complementary information. Although a number of (cheap) empirical methods exist to compute octanol-water (log k _OW) and hexadecane-water (log k _HW) partition coefficients, it would be interesting to know whether physics-based models can predict these crucial values more accurately. Here, we have computed log k _OW and log k _HW for 133 compounds from seven different pollutant categories as well as a control group using the solvation model based on electronic density (SMD) protocol based on Hartree-Fock (HF) or density functional theory (DFT) and the COSMO-RS method. For comparison, XlogP3 (log k _OW) values were retrieved from the PubChem database, and KowWin log k _OW values were determined as well. For 24 of these compounds, log k _OW was computed using potential of mean force (PMF) calculations based on classical molecular dynamics simulations. A comparison of the accuracy of the methods shows that COSMO-RS, KowWin, and XlogP3 all have a root-mean-square deviation (rmsd) from the experimental data of ≈0.4 log units, whereas the SMD protocol has an rmsd of 1.0 log units using HF and 0.9 using DFT. PMF calculations yield the poorest accuracy (rmsd = 1.1 log units). Thirty-six out of 133 calculations are for compounds without known log k _OW, and for these, we provide what we consider a robust prediction, in the sense that there are few outliers, by averaging over the methods. The results supplied may be instrumental when developing new methods in computational ecotoxicity. The log k _HW values are found to be strongly correlated to log k _OW for most compounds.

Invariance of experimental observables with respect to coarse-graining in standard and many-body dissipative particle dynamics

Dissipative particle dynamics (DPD) is a well-established mesoscale simulation method. However, there have been long-standing ambiguities regarding the dependence of its (purely repulsive) force field parameter on temperature as well as the variation of the resulting experimental observables, such as diffusivity or surface tension, with coarse-graining (CG) degree. Here, we rederive the temperature dependence of DPD interaction parameter and revisit the role of the CG degree in standard DPD simulations. Consequently, we derive a scaling of the input variables that renders the system properties invariant with respect to CG degree and illustrate the versatility of the method by computing the surface tensions of binary solvent mixtures. We then extend this procedure to many-body dissipative particle dynamics and, by computing surface tensions of the same mixtures at a range of CG degrees, demonstrate that this newer method, which has not been widely applied so far, is also capable of simulating complex fluids of practical interest.

Simulations of Interfacial Tension of Liquid-Liquid Ternary Mixtures Using Optimized Parametrization for Coarse-Grained Models

In this work, liquid-liquid systems are studied by means of coarse-grained Monte Carlo simulations (CG-MC) and Dissipative Particle Dynamics (DPD). A methodology is proposed to reproduce liquid-liquid equilibrium (LLE) and to provide variation of interfacial tension (IFT), as a function of the solute concentration. A key step is the parametrization method based on the use of the Flory-Huggins parameter between DPD beads to calculate solute/solvent interactions. Parameters are determined using a set of experimental compositional data of LLE, following four different approaches. These approaches are evaluated, and the results obtained are compared to analyze advantages/disadvantages of each one. These methodologies have been compared through their application on six systems: water/benzene/1,4-dioxane,water/chloroform/acetone, water/benzene/acetic acid, water/benzene/2-propanol, water/hexane/acetone, and water/hexane/2-propanol. CG-MC simulations in the Gibbs (NVT) ensemble have been used to check the validity of parametrization approaches for LLE reproduction. Then, CG-MC simulations in the osmotic (μ_soluteN_solventP _zzT) ensemble were carried out considering the two liquid phases with an explicit interface. This step allows one to work at the same bulk concentrations as the experimental data by imposing the precise bulk phase compositions and predicting the interface composition. Finally, DPD simulations were used to predict IFT values for different solute concentrations. Our results on variation of IFT with solute concentration in bulk phases are in good agreement with experimental data, but some deviations can be observed for systems containing hexane molecules.

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, C_iE_j. 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.

Micelle Formation in Alkyl Sulfate Surfactants Using Dissipative Particle Dynamics

We use dissipative particle dynamics (DPD) to study micelle formation in alkyl sulfate surfactants, with alkyl chain lengths ranging from 6 to 12 carbon atoms. We extend our recent DPD force field [ J. Chem. Phys. 2017 , 147 , 094503 ] to include a charged sulfate chemical group and aqueous sodium ions. With this model, we achieve good agreement with the experimentally reported critical micelle concentrations (CMCs) and can match the trend in mean aggregation numbers versus alkyl chain length. We determine the CMC by fitting a charged pseudophase model to the dependence of the free surfactant on the total surfactant concentration above the CMC and compare it with a direct operational definition of the CMC as the point at which half of the surfactant is classed as micellar and half as monomers and submicellar aggregates. We find that the latter provides the best agreement with experimental results. Finally, with the same model, we are able to observe the sphere-to-rod morphological transition for sodium dodecyl sulfate (SDS) micelles and determine that it corresponds to SDS concentrations in the region of 300-500 mM.