Modeling Proton Dissociation and Transfer Using Dissipative Particle Dynamics Simulation

How fork-length asymmetry affects solvent connectivity and diffusion in grafted polymeric model membranes

The hydrophilic pore morphology and solvent diffusion within model (amphiphilic) polymer membranes are simulated by dissipative particle dynamics (DPD). The polymers are composed of a backbone of 18 covalently bonded A beads to which at regular intervals side chains are attached. The side chains are composed of linear Ap chains (i.e., -A1-A2…Ap) from which two branches, [AsC] and [ArC], split off (s ≤ r). C beads serve as functionalized hydrophilic pendent sites. The branch lengths (s + 1 and r + 1) are varied. Five repeat unit designs (with general formula A3[Ap[AsC][ArC]]) are considered: A2[A3C][A3C] (symmetric branching), A2[A2C][A4C], A2[AC][A5C], A2[C][A6C] (highly asymmetric branching), and A4[AC][A3C]. The distribution of water (W) and W diffusion through nanophase segregated hydrophilic pores is studied. For similar primary length p, an increase in side chain symmetry favors hydrophilic pore connectivity and long-range water transport. C beads located on the longer [ArC] branches reveal the highest C bead mobility and are more strongly associated with water than the C beads on the shorter [AsC] branches. The connectivity of hydrophilic (W and W + C) phases through mapped replica of selected snapshots obtained from Monte Carlo tracer diffusion simulations is in line with trends found from the W bead diffusivities during DPD simulations. The diffusive pathways for protons (H+) in proton exchange membranes and for hydronium (OH-) in anion exchange membranes are the same as for solvents. Therefore, control of the side chain architecture is an interesting design parameter for optimizing membrane conductivities.

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.

Anion Exchange Membranes for Fuel Cells Based on Quaternized Polystyrene-b-poly(ethylene-co-butylene)-b-polystyrene Triblock Copolymers with Spacer-Sidechain Design

This work studied the polystyrene-b-poly(ethylene-co-butylene)-b-polystyrene (SEBS) triblock copolymers functionalized by butyl quaternary ammonium (C₄Q) groups and alkyl side chains of different chain lengths (C_n, n = 0 to 24). The hydrated membrane morphology was modeled by dissipative particle dynamics simulation at hydration levels from 10 to 30. A hydroxide model was devised to characterize the diffusivity of anions under the coarse-grained framework. In general, the ionomers with alkyl side chains provided ion conductivity of a similar level at a lower ion exchange capacity. All hydrated SEBS–C₄Q–C_n ionomers showed clear phase separation of the hydrophobic and hydrophilic domains, featuring 18.6 mS/cm to 36.8 mS/cm ion conductivity. The hydrophilic channels expanded as the water content increased, forming more effective ion conductive pathways. Introducing excess alkyl side chains enhanced the nano-segregation, leading to more ordered structures and longer correlation lengths of the aqueous phase. The membrane morphology was controlled by the length of alkyl side-chains as well as their tethering positions. Ionomers with functionalized side chains tethered on the same block resulted in well-connective water networks and higher conductivities. The detailed structural analysis provides synthesis guidelines to fabricate anion exchange membranes with improved performances.

Coarse-Grained Modeling of Ion-Containing Polymers

Ion-containing polymers have continued to be an important research focus for several decades due to their use as an electrolyte in energy storage and conversion devices. Elucidation of connections between the mesoscopic structure and multiscale dynamics of the ions and solvent remains incompletely understood. Coarse-grained modeling provides an efficient approach for exploring the structural and dynamical properties of these soft materials. The unique physicochemical properties of such polymers are of broad interest. In this review, we summarize the current development and understanding of the structure-property relationship of ion-containing polymers and provide insights into the design of such materials determined from coarse-grained modeling and simulations accompanying significant advances in experimental strategies. We specifically concentrate on three types of ion-containing polymers: proton exchange membranes (PEMs), anion exchange membranes (AEMs), and polymerized ionic liquids (polyILs). We posit that insight into the similarities and differences in these materials will lead to guidance in the rational design of high-performance novel materials with improved properties for various power source technologies.

Rhamnolipid Biosurfactants for Oil Recovery: Salt Effects on the Structural Properties Investigated by Mesoscale Simulations

Rhamnolipids (RLs) are biosurfactants produced by Pseudomonas. The biodegradability and the variety of their functionality make them suitable for environmental remediation and oil recovery. We use dissipative particle dynamics simulations to investigate the aggregation behaviors of ionic RL congeners with nonane in various operating conditions. Under zero-salinity conditions, all RL congeners studied here form small ellipsoidal clusters with detectable free surfactants. When salt ions are present, the electrostatic repulsion between the ionized heads is overcome, resulting in the formation of larger aggregates of unique structures. RLs with C10-alkyl tails tend to form elongated wormlike micelles, while RLs with C16-alkyl tails tend to form clusters in spherical symmetry, including vesicles. Di-rhamnolipids (dRLs) require stronger solvation than monorhamnolipids (mRLs) to form clusters, and the resulting size of micelles is decreased. The morphology of the mixed dRL/mRL/oil systems is controlled based on the type of the congeners and the oil contents. In addition, the divalent calcium ions are found to be influential to the structure of the micelles through different mechanisms. For 5 wt % salinity, the ionic RLs can form oil-swollen micelles up to a 1:1 surfactant-to-oil ratio, suggesting that ionic RLs are superb to act as cleaning agents for petroleum hydrocarbons in the marine area. These key findings may guide the design for RL-based washing techniques in enhanced oil recovery.

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.

An Efficient Random Number Generation Method for Molecular Simulation

We propose a new random number generation method, which is the fastest and the simplest of its kind, for use with molecular simulation. We also discuss the possibility of using this method with various other numerical calculations. To demonstrate the significant increases in calculation speeds that can be gained by using our method, we present a comparison with prior methods for dissipative particle dynamics (DPD) simulations. The DPD method uses random numbers to reproduce thermal fluctuations of molecules. As such, an efficient method to generate random numbers in parallel computing environments has been widely sought after. Several random number generation methods have been developed that use encryption. In this study, we establish for the first time that random numbers with desirable properties exist in the particle coordinates used in DPD calculations. We propose a method for generating random numbers without encryption that utilizes this source of randomness. This is an innovative method with minimal computational cost, since it is not dependent on a complicated random number generation algorithm or an encryption process. Furthermore, our method may lead to faster random number generation for many other physical and chemical simulations.

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.

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.

Emulsions in external electric fields

Water is co-produced with crude oils, generally in the form of water-in-crude oil emulsions. The oil and water phases need to be separated before export. Separation is performed in gravity separators with the addition of chemical demulsifiers and, sometimes, with the application of an electric field by using an electrocoalescer. The present article reviews several aspects of electrocoalescence by considering the effect of the electric field from the molecular to a macroscopic scale: the oil-water interface, single drop effects, two drop interactions, and finally emulsions at laboratory scales. Experimental results together with Dissipative Particle Dynamics (DPD) simulation results are presented. The review begins with water-oil interface under an electric field and followed by single drop electrohydrodynamics. The electric field is shown to influence the adsorption of crude oil indigenous surface-active components (asphaltenes) due to the electrohydrodynamic (EHD) flows. The interactions between two droplets in the presence of electric field and the factors governing the drop-drop coalescence are discussed in detail. DPD simulations help to elucidate thin film breakup during (electro)-coalescence of two water droplets, where the oil film has drained out to nanometer thickness. The film is comprised of surfactant and demulsifier molecules, and the simulations capture the pores formation in the film when a DC field is applied. The results demonstrate influence of the molecular structure of the surfactant and demulsifier, and their interactions. The subsequent section describes experimental techniques to assess the resolution of crude oil emulsions at the laboratory scale. The focus is on low-field Nuclear Magnetic Resonance (LF-NMR) which allows a determination of various emulsion features such as the droplet size distribution (DSD) and the brine profile (variation of the concentration of water with the height of the emulsion sample) and their evolution with time. Application of the technique in emulsion treatment involving chemical demulsifiers and electric field is presented. The review concludes with description of commercial industrial electrocoalecers such as the Vessel Internal Electrostatic Coalescer (VIEC) and the Compact Electrostatic Coalescer (CEC).

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.

Temperature-responsive morphology formation of a PS-b-PI copolymer: a dissipative particle dynamics simulation study

Self-assembly responsiveness to stimuli of polystyrene-block-polyisoprene (PS-b-PI) diblock copolymer materials is explored by means of classical molecular dynamics (MD) and dissipative particle dynamics (DPD) simulations. A concerted relationship between the parameters achieved from atomistic and DPD simulations is obtained for this molecular recognition as clearly pronounced in a phase transition. Effects of temperature, model size and composition on the morphological formation were systematically investigated for the diblock copolymeric system. Structural changes resulting in the evolution of rheology as well as an equilibrium ordered structure were analyzed in terms of order parameters and radial distribution functions. From our models, various morphologies were observed including discrete clusters (sphere-liked morphology), connected clusters (gyroid-liked morphology), hexagonally packed cylinders (HEX), connected cylinders, irregular cylinders, perfect lamellae, perforated lamellae and defected lamellae. Based on this finding, a bottom-up multi-scale simulation of the PS-b-PI diblock copolymer provides a link between equilibrium copolymeric morphologies and the crucial parameters.

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.

Effect of the Janus Amphiphilic Wall on the Viscosity Behavior of Aqueous Surfactant Solutions

The effects of the chemical nature of an interface are one of the key parameters which can affect self-assembly and rheological behavior. To date, several studies have reported self-assembled structures and rheological behaviors in the development of various functional materials. In this study, we investigated the self-assembly and viscosity behavior of aqueous surfactant solutions confined in three types of Janus amphiphilic nanotubes (JANTs), which have two, four, and eight sequential domains, respectively, using molecular simulation. We found that the viscosity behavior depends on the surfactant concentration and the chemical nature of the wall surface. For instance, although the concentration levels of the surfactants are the same (c = 10%), completely different viscosity behaviors were observed in the two sequential domains (Newtonian-like) and the four and eight sequential domains (strong shear-thinning) of the JANTs. Our simulations demonstrated how the rheological properties of aqueous surfactant solutions, including viscosity and velocity profiles, can be controlled by the chemical nature of the JANT wall surface, effect of confinement, and their self-assembly structures. Considering the foregoing, we hope that our study offers new knowledge on nanofluid systems.

Influence of pore morphology on the diffusion of water in triblock copolymer membranes

Understanding the transport properties of water in self-assembled block copolymer morphologies is important for furthering the use of such materials as water-purifying membranes. In this study, we used coarse-grained dissipative particle dynamics simulations to clarify the influence of pore morphology on the self-diffusion of water in linear-triblock-copolymer membranes. We considered representative lamellar, cylindrical, and gyroid morphologies and present results for both the global and local diffusivities of water in the pores. Our results suggest that the diffusivity of water in the confined, polymer-coated pores differs from that in the unconfined bulk. Explicitly, in confinement, the mobility of water is reduced by the hydrodynamic friction arising from the hydrophilic blocks coating the pore walls. We demonstrate that in lamella and cylindrical morphologies, the latter effects can be rendered as a universal function of the pore size relative to the brush height of the hydrophilic blocks.

Electrocoalescence of water in oil emulsions: a DPD simulation study and a novel application of electroporation theory

Pore formation in a surfactant laden oil film between two aqueous electrolyte layers in a DC field was studied using DPD (Dissipative Particle Dynamics molecular simulation). This setting represents the final stage of an electro-coalescence process between water droplets in oil, where the oil film has drained out to nanometer thickness. We introduce a novel model for the coalescence probability based on electroporation theory for lipid bilayers, and an equation for a threshold electric potential above which coalescence is highly probable. Excess electric forcing (pinching) of the oil film occurred locally due to charge density fluctuations in the electrolyte, and this could lead to the formation of unstable, expanding pores and coalescence between the aqueous domains. Such unstable pores can form at lower electric potentials when the cohesive energy in the surfactant layer (primarily line tension) is lowered by adding demulsifier, or when demulsifier causes a morphology change in the surfactant layers with local areas that have lower surfactant density. In conclusion, higher ion concentrations in the electrolyte, higher electric field strength, and lower cohesive energy in the surfactant layer increased the coalescence probability.

Coarse-grained model of nanoscale segregation, water diffusion, and proton transport in Nafion membranes

We present a coarse-grained model of the acid form of Nafion membrane that explicitly includes proton transport. This model is based on a soft-core bead representation of the polymer implemented into the dissipative particle dynamics (DPD) simulation framework. The proton is introduced as a separate charged bead that forms dissociable Morse bonds with water beads. Morse bond formation and breakup artificially mimics the Grotthuss hopping mechanism of proton transport. The proposed DPD model is parameterized to account for the specifics of the conformations and flexibility of the Nafion backbone and sidechains; it treats electrostatic interactions in the smeared charge approximation. The simulation results qualitatively, and in many respects quantitatively, predict the specifics of nanoscale segregation in the hydrated Nafion membrane into hydrophobic and hydrophilic subphases, water diffusion, and proton mobility. As the hydration level increases, the hydrophilic subphase exhibits a percolation transition from a collection of isolated water clusters to a 3D network of pores filled with water embedded in the hydrophobic matrix. The segregated morphology is characterized in terms of the pore size distribution with the average size growing with hydration from ∼1 to ∼4 nm. Comparison of the predicted water diffusivity with the experimental data taken from different sources shows good agreement at high and moderate hydration and substantial deviation at low hydration, around and below the percolation threshold. This discrepancy is attributed to the dynamic percolation effects of formation and rupture of merging bridges between the water clusters, which become progressively important at low hydration, when the coarse-grained model is unable to mimic the fine structure of water network that includes singe molecule bridges. Selected simulations of water diffusion are performed for the alkali metal substituted membrane which demonstrate the effects of the counter-ions on membrane self-assembly and transport. The hydration dependence of the proton diffusivity reproduces semi-qualitatively the trend of the diverse experimental data, showing a sharp decrease around the percolation threshold. Overall, the proposed model opens up an opportunity to study self-assembly and water and proton transport in polyelectrolytes using computationally efficient DPD simulations, and, with further refinement, it may become a practical tool for theory informed design and optimization of perm-selective and ion-conducting membranes with improved properties.

Scission Free Energies for Wormlike Surfactant Micelles: Development of a Simulation Protocol, Application, and Validation for Personal Care Formulations

We present a scheme to calculate wormlike micelle scission free energies from a potential of mean force (PMF) derived from a weighted histogram analysis method (WHAM) applied to coarse grained dissipative particle dynamics (DPD) simulations. In contrast to previous related work, we use a specially chosen external potential based on a reaction coordinate that reversibly drives surfactants out of the nascent scission location. For the application to a model body wash formulation, we predict how addition of NaCl and small molecules such as perfume raw materials (PRMs) affect scission energies. The results show qualitative agreement and correct trends compared to recently determined scission energies for the same system; however, a more rigorous parametrization of the underlying DPD potential is required for quantitative agreement.

Theoretical analyses on water cluster structures in polymer electrolyte membrane by using dissipative particle dynamics simulations with fragment molecular orbital based effective parameters

The mesoscopic structures of polymer electrolyte membrane (PEM) affect the performances of fuel cells. Nafion® with the Teflon® backbone has been the most widely used of all PEMs, but sulfonated poly-ether ether-ketone (SPEEK) having an aromatic backbone has drawn interest as an alternative to Nafion. In the present study, a series of dissipative particle dynamics (DPD) simulations were performed to compare Nafion and SPEEK. These PEM polymers were modeled by connected particles corresponding to the hydrophobic backbone and the hydrophilic moiety of sulfonic acid group. The water particle interacting with Nafion particles was prepared as well. The crucial interaction parameters among DPD particles were evaluated by a series of calculations based on the fragment molecular orbital (FMO) method in a non-empirical way (Okuwaki et al., J. Phys. Chem. B, 2018, 122, 338–347). Through the DPD simulations, the water and hydrophilic particles aggregated, forming cluster networks surrounded by the hydrophobic phase. The structural features of formed water clusters were investigated in detail. Furthermore, the differences in percolation behaviors between Nafion and SPEEK revealed much better connectivity among water clusters by Nafion. The present FMO-DPD simulation results were in good agreement with available experimental data.

The mesoscopic structures of polymer electrolyte membrane (PEM) affect the performances of fuel cells.