Phase behavior of monomeric mixtures and polymer solutions with soft interaction potentials

Construction of Multiscale Dissipative Particle Dynamics (DPD) Models from Other Coarse-Grained Models

We present a general scheme for converting coarse-grained models into Dissipative Particle Dynamics (DPD) models. We build the corresponding DPD models by analogy with the de novo DPD coarse-graining scheme suggested by Groot and Warren (J. Chem. Phys., 1997). Electrostatic interactions between charged DPD particles are represented though the addition of a long-range Slater Coulomb potential as suggested by González-Melchor et al. (J. Chem. Phys., 2006). The construction is illustrated by converting MARTINI models for various proteins into a DPD representation, but it not restricted to the usual potential form in the MARTINI model-viz., Lennard-Jones potentials. We further extended the DPD scheme away from the typical use of homogeneous particle sizes, therefore faithfully representing the variations in the particle sizes seen in the underlying MARTINI model. The accuracy of the resulting construction of our generalized DPD models with respect to several structural observables has been benchmarked favorably against all-atom and MARTINI models for a selected set of peptides and proteins, and variations in the scales of the coarse-graining of the water solvent.

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.

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.

Molecularly Informed Field Theories from Bottom-up Coarse-Graining

Polymer formulations possessing mesostructures or phase coexistence are challenging to simulate using atomistic particle-explicit approaches due to the disparate time and length scales, while the predictive capability of field-based simulations is hampered by the need to specify interactions at a coarser scale (e.g., χ-parameters). To overcome the weaknesses of both, we introduce a bottom-up coarse-graining methodology that leverages all-atom molecular dynamics to molecularly inform coarser field-theoretic models. Specifically, we use relative-entropy coarse-graining to parametrize particle models that are directly and analytically transformable into statistical field theories. We demonstrate the predictive capability of this approach by reproducing experimental aqueous poly(ethylene oxide) (PEO) cloud-point curves with no parameters fit to experimental data. This synergistic approach to multiscale polymer simulations opens the door to de novo exploration of phase behavior across a wide variety of polymer solutions and melt formulations.

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.

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.

Diffusive transport of nanoscale objects through cell membranes: a computational perspective

Diffusion is an essential and fundamental means of transport of substances on cell membranes, and the dynamics of biomembranes plays a crucial role in the regulation of numerous cellular processes. The understanding of the complex mechanisms and the nature of particle diffusion have a bearing on establishing guidelines for the design of efficient transport materials and unique therapeutic approaches. Herein, this review article highlights the most recent advances in investigating diffusion dynamics of nanoscale objects on biological membranes, focusing on the approaches of tailored computer simulations and theoretical analysis. Due to the presence of the complicated and heterogeneous environment on native cell membranes, the diffusive transport behaviors of nanoparticles exhibit unique and variable characteristics. The general aspects and basic theories of normal diffusion and anomalous diffusion have been introduced. In addition, the influence of a series of external and internal factors on the diffusion behaviors is discussed, including particle size, membrane curvature, particle-membrane interactions or particle-inclusion, and the crowding degree of membranes. Finally, we seek to identify open problems in the existing experimental, simulation, and theoretical research studies, and to propose challenges for future development.

A new equation of state for homo-polymers in dissipative particle dynamics

A chain-revised Groot-Warren equation of state (crGW-EOS) was developed and tested to describe systems of homo-oligomeric chains in the framework of dissipative particle dynamics (DPD). First, thermodynamic perturbation theory is applied to introduce correction terms that account for the reduction in pressure with an increasing number of bonds at constant bead number density. Then, this EOS is modified by introducing a set of switching functions that yields an accurate second virial coefficient in the low-density limit. The crGW-EOS offers several improvements over the revised Groot-Warren equation of state and Groot-Warren equation of state for chain molecules. We tested the crGW-EOS by using it to predict the pressure of oligomeric systems and the B₂ virial coefficient of chain DPD particles for a range of bond lengths. Additionally, a method is developed for determining the strength of cross-interaction parameters between chains of different compositions and sizes and for thermal and athermal mixtures. We explored how different levels of coarse-graining affect the upper-critical solution temperature.

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.

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.

Stable micelles based on a mixture of coiled-coils: the role of different oligomeric states

Homomeric micelles with tunable size, shape and stability have been extensively studied for biomedical applications such as drug carriers. However, designing the local valency and self-assembled morphology of nanophase-separated multicomponent micelles with varied ligand binding possibilities remains challenging. Here, we present micelles self-assembled from amphiphilic peptide-PEG-lipid hybrid conjugates, where the peptides can be either a 3-helix or 4-helix coiled-coil. We demonstrate that the micelle size and sphericity can be controlled based on the coiled-coil oligomeric state. Using theory and coarse-grained dissipative particle dynamics (DPD) simulations in an explicit solvent simulation, we studied the distribution of 3-helix and 4-helix conjugates within the mixed micelles and observed self-organization into nanodomains within the mixed micelle. We discovered that the phase separation behavior is dictated by the geometry mismatch in the alkyl chain length from different coiled-coil oligomeric states. Our analyses of the self-assembly tendency and drug delivery potency of mixed micelles with controlled multivalency provide important insights into the assembly and formation of nanophase-separated micelles.

Alpha-linolenic acid-loaded oil/water microemulsion: Effects of phase behaviour simulation and environmental stress on phase stabilizing and anti-oxidation capacity

α-Linolenic acid (ALA)-loaded microemulsion (ME) was prepared from isoamyl acetate, polyoxyethylene ether 35 (EL-35), ethanol and water. The dynamic phase behaviour was simulated using dissipative particle dynamics (DPD), which showed that spherical ME was formed at water/oil ratios of 1:9 and 9:1, while a lamellar structure with distinctive water-course and oil layer appeared at ratios of 3:7, 5:5, and 7:3. Phase stabilizing and anti-oxidation effect of environmental stresses on ALA-loaded microemulsion were investigated. Results showed that the ME region was large and had good environmental tolerance. Subsequently, the investigation of anti-oxidation stability revealed that more than 60% ALA of ALA-loaded ME could be protected from oxidation under environmental stresses. Furthermore, ALA-loaded ME was applied in aqueous-based foods. The transparency, precipitate, stratification and phase separation were used to evaluate influence of ME on product properties, confirming great feasibility and stability of ALA-loaded ME for practical applications.

Fragment Molecular Orbital Based Parametrization Procedure for Mesoscopic Structure Prediction of Polymeric Materials

In the analyses of miscibility behaviors of macromolecules and polymers, dissipative particle dynamics (DPD) simulations are generally performed. In these simulations, the so-called χ parameters describing the effective interactions among particles are crucial. It has been known that such parameters can be obtained within the classical or empirical force field frameworks. However, there is a potential problem that charge transfer and polarization occasionally occur. Additionally, satisfactory reference parameters are not available for some cases. Therefore, we developed a new procedure to evaluate the set of parameters by using the ab initio fragment molecular orbital (FMO) method which can provide the set of interaction energies among segments as polymer units. Moreover, we evaluated the anisotropy of molecules by using the FMO-based effective interaction parameters for three standard binary mixture systems (hexane-nitrobenzene, polyisobutylene-diisobutyl ketone, and polyisoprene-polystyrene). The calculated values showed good agreement with the experimental values with about 10% errors.

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.

Dissipative Particle Dynamics Simulations for Phospholipid Membranes Based on a Four-To-One Coarse-Grained Mapping Scheme

In this article, a new set of parameters compatible with the dissipative particle dynamics (DPD) force field is developed for phospholipids. The coarse-grained (CG) models of these molecules are constructed by mapping four heavy atoms and their attached hydrogen atoms to one bead. The beads are divided into types distinguished by charge type, polarizability, and hydrogen-bonding capacity. First, we derive the relationship between the DPD repulsive force and Flory-Huggins χ-parameters based on this four-to-one CG mapping scheme. Then, we optimize the DPD force parameters for phospholipids. The feasibility of this model is demonstrated by simulating the structural and thermodynamic properties of lipid bilayer membranes, including the membrane thickness, the area per lipid, the lipid tail orientation, the bending rigidity, the rupture behavior, and the potential of mean force for lipid flip-flop.

Prediction of solvent-induced morphological changes of polyelectrolyte diblock copolymer micelles

Self-assembly processes of polyelectrolyte block copolymers are ubiquitous in industrial and biological processes; understanding their physical properties can also provide insights into the design of polyelectrolyte materials with novel and tailored properties. Here, we report systematic analysis on how the ionic strength of the solvent and the length of the polyelectrolyte block affect the self-assembly and morphology of the polyelectrolyte block copolymer materials by constructing a salt-dependent morphological phase diagram using an implicit solvent ionic strength (ISIS) method for dissipative particle dynamics (DPD) simulations. This diagram permits the determination of the conditions for the morphological transition into a specific shape, namely vesicles or lamellar aggregates, wormlike/cylindrical micelles, and spherical micelles. The scaling behavior for the size of spherical micelles is predicted, in terms of radius of gyration (R(g,m)) and thickness of corona (Hcorona), as a function of solvent ionic strength (c(s)) and polyelectrolyte length (NA), which are R(g,m) ∼ c(s)(-0.06)N(A)(0.54) and Hcorona ∼ c(s)(-0.11)N(A)(0.75). The simulation results were corroborated through AFM and static light scattering measurements on the example of the self-assembly of monodisperse, single-stranded DNA block-copolynucleotides (polyT50-b-F-dUTP). Overall, we were able to predict the salt-responsive morphology of polyelectrolyte materials in aqueous solution and show that a spherical-cylindrical-lamellar change in morphology can be obtained through an increase in solvent ionic strength or a decrease of polyelectrolyte length.

Morphological transformations in polymer brushes in binary mixtures: DPD study

Morphological transformations in polymer brushes in a binary mixture of good and bad solvents are studied using dissipative particle dynamics simulations drawing on a characteristic example of polyisoprene natural rubber in an acetone-benzene mixture. A coarse-grained DPD model of this system is built based on the experimental data in the literature. We focus on the transformation of dense, collapsed brush in bad solvent (acetone) to expanded brush solvated in good solvent (benzene) as the concentration of benzene increases. Compared to a sharp globule-to-coil transition observed in individual tethered chains, the collapsed-to-expanded transformation in brushes is found to be gradual without a prominent transition point. The transformation becomes more leveled as the brush density increases. At low densities, the collapsed brush is highly inhomogeneous and patterned into bunches composed of neighboring chains due to favorable polymer-polymer interaction. At high densities, the brush is expanded even in bad solvent due to steric restrictions. In addition, we considered a model system similar to the PINR-acetone-benzene system, but with the interactions between the solvent components worsened to the limit of miscibility. Enhanced contrast between good and bad solvents facilitates absorption of the good solvent by the brush, shifting the collapsed-to-expanded transformation to lower concentrations of good solvent. This effect is especially pronounced for higher brush densities.

The Self-Assembly of an Amphiphilic Block Copolymer: A Dissipative Particle Dynamics Study

The self-assembly of a poly(ethylene oxide)-block-poly(propylene oxide)-block-poly(ethylene oxide) blockcopolymer (EO13PO30EO13) in the presence of water was investigated. The phases have been studied with the mesoscopic simulation technique Dissipative Particle Dynamics (DPD). The micellar, hexagonal, lamellar, bicontinuous and inverse micellar phase have been identified with this method and showed remarkable agreement with the experimental phase behavior. This work showed that the Dissipative Particle Dynamics simulations are also suitable for complicated polymer systems such as the EO13PO30EO13 triblock copolymer.

Prediction of the Critical Micelle Concentration of Nonionic Surfactants by Dissipative Particle Dynamics Simulations

Micellization of surfactant solutions is a ubiquitous phenomenon in natural systems and technological processes, and its theoretical description represents one of the cornerstone problems in the physical chemistry of colloidal systems. However, successful attempts of quantitative modeling confirmed by experimental data remains limited. We show, for the first time, that the dissipative particle dynamics with rigorously defined soft repulsion interaction and rigidity parameters is capable of predicting micellar self-assembly of nonionic surfactants. This is achieved due to a novel approach suggested for defining the interaction parameters by fitting to the infinite dilution activity coefficients of binary solutions formed by reference compounds that represent coarse-grained fragments of surfactant molecules. Using this new parametrization scheme, we obtained quantitative agreement with the experimental critical micelle concentration and aggregation number for several typical surfactants of different chemical structures. The proposed approach can be extended to various colloidal and polymeric systems beyond nonionic surfactant solutions.