Mesoscale simulation of polymer reaction equilibrium: Combining dissipative particle dynamics with reaction ensemble Monte Carlo. I. Polydispersed polymer systems

Determination of interaction parameters in a bottom-up approach employed in reactive dissipative particle dynamics simulations for thermosetting polymers

The limitations in previous dissipative particle dynamics (DPD) studies confined simulations to a narrow resin range. This study refines DPD parameter calculation methodology, extending its application to diverse polymer materials. Using a bottom-up approach with molecular dynamics (MD) simulations, we evaluated solubility parameters and bead number density governing nonbonded interactions via the Flory-Huggins parameter and covalent-bonded interactions. Two solubility parameter methods, Hildebrand and Krevelen-Hoftyzer, were compared for DPD simulations. The Hildebrand method, utilizing MD simulations, demonstrates higher consistency and broader applicability in determining solubility parameters for all DPD particles. The DPD/MD curing reaction process was examined in three epoxy systems: DGEBA/4,4'-DDS, DGEBA/MPDA and DGEBA/DETA. Calculations for the curing profile, gelation point, radial distribution function and branch ratio were performed. Compared to MD data for DGEBA/4,4'-DDS, the maximum deviation in secondary reactions between epoxy and amine groups according to DPD simulations with Krevelen-Hoftyzer was 14.8%, while with the Hildebrand method, it was 1.7%. The accuracy of the DPD curing reaction in reproducing the structural properties verifies its expanded application to general polymeric material simulations. The proposed curing DPD simulations, with a short run time and minimal computational resources, contributes to high-throughput screening for optimal resins and investigates mesoscopic inhomogeneous structures in large resin systems.

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.

Molecular Dynamics Simulations of Ideal Living Polymerization: Terminal Model and Kinetic Aspects

Living polymerization is an important synthetic approach to achieving precise control of synthesized polymers, which is crucial for their applications. The molecular weight distribution (MWD) prescribes the macroscopic properties of polymers and hence is a key feature to characterize polymerization. In this work, we present a systematic molecular dynamics simulation study of ideal living polymerization in bulk and surface-initiated systems based on a terminal stochastic reaction model. The evolution of polymer dispersity and MWD along with the polymerization process is examined. We demonstrate that MWD is generally well captured by the Schulz-Zimm distribution for bulk and surface-initiated systems with low grafting densities. However, as the grafting density in the surface-initiated case increases, heterogeneity in chain growth emerges due to the kinetic trapping of reactive sites, which causes the starving of short chains and the thriving of minority long chains such that a shoulder region shows up in MWD. This effect can be enhanced by kinetic compressing induced by polymerization. In addition, the interplay of bonding reaction kinetics and other kinetic properties (e.g., mass transfer and polymer relaxation) is further explored, alongside the influences of bonding probability and reactant concentration. We expect that this investigation will aid in our understanding of typical kinetic aspects of living polymerization.

Reactive Martini: Chemical Reactions in Coarse-Grained Molecular Dynamics Simulations

Chemical reactions are ubiquitous in both materials and the biophysical sciences. While coarse-grained (CG) molecular dynamics simulations are often needed to study the spatiotemporal scales present in these fields, chemical reactivity has not been explored thoroughly in CG models. In this work, a new approach to model chemical reactivity is presented for the widely used Martini CG Martini model. Employing tabulated potentials with a single extra particle for the angle dependence, the model provides a generic framework for capturing bonded topology changes using nonbonded interactions. As a first example application, the reactive model is used to study the macrocycle formation of benzene-1,3-dithiol molecules through the formation of disulfide bonds. We show that starting from monomers, macrocycles with sizes in agreement with experimental results are obtained using reactive Martini. Overall, our reactive Martini framework is general and can be easily extended to other systems. All of the required scripts and tutorials to explain its use are provided online.

Molecular Weight Distribution of Branched Polymers: Comparison between Monte Carlo Simulation and Flory-Stockmayer Theory

It is challenging to predict the molecular weight distribution (MWD) for a polymer with a branched architecture, though such information will significantly benefit the design and development of branched polymers with desired properties and functions. A Monte Carlo (MC) simulation method based on the Gillespie algorithm is developed to quickly compute the MWD of branched polymers formed through step-growth polymerization, with a branched polyetherimide from two backbone monomers (4,4′-bisphenol A dianhydride and m-phenylenediamine), a chain terminator (phthalic anhydride), and a branching agent (tris[4-(4-aminophenoxy)phenyl] ethane) as an example. This polymerization involves four reactions that can be all reduced to a condensation reaction between an amine group and a carboxylic anhydride group. A comparison between the MC simulation results and the predictions of the Flory-Stockmayer theory on MWD shows that the rates of the reactions are determined by the concentrations of the functional groups on the monomers involved in each reaction. It further shows that the Flory-Stockmayer theory predicts MWD well for systems below the gel point but starts to fail for systems around or above the gel point. However, for all the systems, the MC method can be used to reliably predict MWD no matter if they are below or above the gel point. Even for a macroscopic system, a converging distribution can be quickly obtained through MC simulations on a system of only a few hundred to a few thousand monomers that have the same molar ratios as in the macroscopic system.

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.

A Simple Stochastic Reaction Model for Heterogeneous Polymerizations

The stochastic reaction model (SRM) treats polymerization as a pure probability‐based issue, which is widely applied to simulate various polymerization processes. However, in many studies, active centers were assumed to react with the same probability, which cannot reflect the heterogeneous reaction microenvironment in heterogeneous polymerizations. Recently, we have proposed a simple SRM, in which the reaction probability of an active center is directly determined by the local reaction microenvironment. In this paper, we compared this simple SRM with other SRMs by examining living polymerizations with randomly dispersed and spatially localized initiators. The results confirmed that the reaction microenvironment plays an important role in heterogeneous polymerizations. This simple SRM provides a good choice to simulate various polymerizations.

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.

Thermoset resin curing simulation using quantum-chemical reaction path calculation and dissipative particle dynamics

Thermoset resin, which is commonly used as a matrix in carbon-fiber-reinforced plastic, requires curing procedures. We propose a curing simulation technique involving a dissipative particle dynamics (DPD) simulation, which can simulate a larger system and longer time period than those of conventional all-atom molecular dynamics (AA-MD) simulations. The proposed curing DPD simulation can represent the thermoset resin exothermic reaction process precisely by considering each reactivity according to the reaction types calculated via quantum-chemical reaction path calculations. The cure reaction process given by the curing DPD simulation agrees well with that given by a conventional curing AA-MD simulation, but with run-time and computational-resource reductions of 1/480 and 1/10 times, respectively. We also conduct reverse mapping, through which the AA-MD system can be reconstructed from the DPD system, to evaluate the structural and thermomechanical properties. The X-ray diffraction pattern and thermomechanical properties of the reconstructed system agree well with those of the systems derived from the curing AA-MD simulation and experimental setup. Therefore, a cured-resin AA-MD system can be obtained from a curing DPD simulation at an extremely low computational cost, and the thermomechanical properties can be evaluated precisely using this system. The proposed curing simulation technique can be applied in high-throughput screening for better materials properties and in large system calculations.

Simulation Study of Process-Controlled Supramolecular Block Copolymer Phase Separation with Reversible Reaction Algorithm

A supramolecular diblock copolymer formed by reversible bonds between the two blocks shows a rich microphase separation behavior and has great application potential in stimuli-responsive materials. We propose a novel method to describe supramolecular reactions in dissipative particle dynamics, which includes a reversible reaction to accurately reproduce the strength, saturation, and dynamic properties of the reversible bonds in the simulations. The thermodynamic properties and dynamic processes of the supramolecular diblock copolymer melts in both equilibrium and non-equilibrium states were studied using this method. The simulation results show that the method can faithfully characterize phase behaviors and dynamic properties of supramolecular diblock copolymer melts, especially in a non-equilibrium state, which provides a novel tool to unveil self-assembly mechanism and describe the properties of supramolecular block copolymers.

Simulations of ionization equilibria in weak polyelectrolyte solutions and gels

This article recapitulates the state of the art regarding simulations of ionization equilibria of weak polyelectrolyte solutions and gels. We start out by reviewing the essential thermodynamics of ionization and show how the weak polyelectrolyte ionization differs from the ionization of simple weak acids and bases. Next, we describe simulation methods for ionization reactions, focusing on two methods: the constant-pH ensemble and the reaction ensemble. After discussing the advantages and limitations of both methods, we review the existing simulation literature. We discuss coarse-grained simulations of weak polyelectrolytes with respect to ionization equilibria, conformational properties, and the effects of salt, both in good and poor solvent conditions. This is followed by a discussion of branched star-like weak polyelectrolytes and weak polyelectrolyte gels. At the end we touch upon the interactions of weak polyelectrolytes with other polymers, surfaces, nanoparticles and proteins. Although proteins are an important class of weak polyelectrolytes, we explicitly exclude simulations of protein ionization equilibria, unless they involve protein-polyelectrolyte interactions. Finally, we try to identify gaps and open problems in the existing simulation literature, and propose challenges for future development.

Bilayer sheet protrusions and budding from bilayer membranes induced by hydrolysis and condensation reactions

Shape transformations of flat bilayer membranes and vesicles induced by hydrolysis and condensation reactions of amphiphilic molecules are studied using coarse-grained molecular dynamics simulations. The hydrolysis and condensation reactions result in the formation and dissociation of amphiphilic molecules, respectively. Asymmetric reactions between the inner and outer leaflets of a vesicle can transport amphiphilic molecules between the leaflets. It is found that the resulting area difference between the two leaflets induces bilayer sheet protrusion (BP) and budding at low reduced volumes of the vesicles, whereas BP only occurs at high reduced volumes. The probabilities of these two types of transformations depend on the shear viscosity of the surrounding fluids compared to the membrane as well as the reaction rates. A higher surrounding fluid viscosity leads to more BP formation. The inhomogeneous spatial distribution of the hydrophobic reaction products forms the nuclei of BP formation, and faster diffusion of the products enhances BP formation. Our results suggest that adjustment of the viscosity is important to control membrane shape transformations in experiments.

One-pot production of porous assemblies by PISA of star architecture copolymers: a simulation study

Porous vesicles can be produced in one-pot by the PISA of star architecture copolymers.

Polymerization-induced polymer aggregation or polymer aggregation-enhanced polymerization? A computer simulation study

In this study, using dissipative particle dynamics simulations coupled with the stochastic reaction model, we investigate the polymerization-induced polymer aggregation process and the polymer aggregation-enhanced polymerization process in a binary solution.

Computer Simulations of Static and Dynamical Properties of Weak Polyelectrolyte Nanogels in Salty Solutions

We investigate the chemical equilibria of weak polyelectrolyte nanogels with reaction ensemble Monte Carlo simulations. With this method, the chemical identity of the nanogel monomers can change between neutral or charged following the acid-base equilibrium reaction HA ⇌ A- + H⁺. We investigate the effect of changing the chemical equilibria by modifying the dissociation constant K a . These simulations allow for the extraction of static properties like swelling equilibria and the way in which charge-both monomer and ionic-is distributed inside the nanogel. Our findings reveal that, depending on the value of K a , added salt can either increase or decrease the gel size. Using the calculated mean-charge configurations of the nanogel from the reaction ensemble simulation as a quenched input to coupled lattice-Boltzmann molecular dynamics simulations, we investigate dynamical nanogel properties such as the electrophoretic mobility μ and the diffusion coefficient D.

Wang-Landau Reaction Ensemble Method: Simulation of Weak Polyelectrolytes and General Acid-Base Reactions

We present a novel method for the study of weak polyelectrolytes and general acid-base reactions in molecular dynamics and Monte Carlo simulations. The approach combines the advantages of the reaction ensemble and the Wang-Landau sampling method. Deprotonation and protonation reactions are simulated explicitly with the help of the reaction ensemble method, while the accurate sampling of the corresponding phase space is achieved by the Wang-Landau approach. The combination of both techniques provides a sufficient statistical accuracy such that meaningful estimates for the density of states and the partition sum can be obtained. With regard to these estimates, several thermodynamic observables like the heat capacity or reaction free energies can be calculated. We demonstrate that the computation times for the calculation of titration curves with a high statistical accuracy can be significantly decreased when compared to the original reaction ensemble method. The applicability of our approach is validated by the study of weak polyelectrolytes and their thermodynamic properties.

Effect of Cross-Linking on the Structure and Growth of Polymer Films Prepared by Interfacial Polymerization

Interfacial polymerization of tri- and bifunctional monomers (A3B2 polymerization) is investigated by dissipative particle dynamics to reveal an effect of cross-linking on the reaction kinetics and structure of the growing polymer film. Regardless of the comonomer reactivity and miscibility, the kinetics in an initially bilayer melt passes from the reaction to diffusion control. Within the crossover period, branched macromolecules undergo gelation, which drastically changes the scenario of the polymerization process. Comparison with the previously studied linear interfacial polymerization (Berezkin, A. V.; Kudryavtsev, Y. V. Linear Interfacial Polymerization: Theory and Simulations with Dissipative Particle Dynamics J. Chem. Phys. 2014, 141, 194906) shows similar conversion rates but very different product characteristics. Cross-linked polymer films are markedly heterogeneous in density, their average polymerization degree grows with the comonomer miscibility, and end groups are mostly trapped deeply in the film core. Products of linear interfacial polymerization demonstrate opposite trends as they are spontaneously homogenized by a convective flow of macromolecules expelled from the reactive zone to the film periphery, which we call the reactive extrusion effect and which is hampered in branched polymerization. Influence of the comonomer architecture on the polymer film characteristics could be used in various practical applications of interfacial polymerization, such as fabrication of membranes, micro- and nanocapsules and 3D printing.

Self-consistent description of electrokinetic phenomena in particle-based simulations

A new computational method is presented for study suspensions of charged particles undergoing fluctuating hydrodynamic and electrostatic interactions. The proposed model is appropriate for polymers, proteins, and porous particles embedded in a continuum electrolyte. A self-consistent Langevin description of the particles is adopted in which hydrodynamic and electrostatic interactions are included through a Green's function formalism. An Ewald-like split is adopted in order to satisfy arbitrary boundary conditions for the Stokeslet and Poisson Green functions, thereby providing a formalism that is applicable to any geometry and that can be extended to deformable objects. The convection-diffusion equation for the continuum ions is solved simultaneously considering Nernst-Planck diffusion. The method can be applied to systems at equilibrium and far from equilibrium. Its applicability is demonstrated in the context of electrokinetic motion, where it is shown that the ionic clouds associated with individual particles can be severely altered by the flow and concentration, leading to intriguing cooperative effects.

Hybrid molecular dynamics simulations of living filaments

We propose a hybrid molecular dynamics/multi-particle collision dynamics model to simulate a set of self-assembled semiflexible filaments and free monomers. Further, we introduce a Monte Carlo scheme to deal with single monomer addition (polymerization) or removal (depolymerization), satisfying the detailed balance condition within a proper statistical mechanical framework. This model of filaments, based on the wormlike chain, aims to represent equilibrium polymers with distinct reaction rates at both ends, such as self-assembled adenosine diphosphate-actin filaments in the absence of adenosine triphosphate (ATP) hydrolysis and other proteins. We report the distribution of filament lengths and the corresponding dynamical fluctuations on an equilibrium trajectory. Potential generalizations of this method to include irreversible steps like ATP-actin hydrolysis are discussed.

DISSIPATIVE PARTICLE DYNAMICS SIMULATION ON THE PREPARATION PROCESS OF MACROPOROUS STYRENE-DIVINYLBENZENE COPOLYMER

Dissipative particle dynamics (DPD) was carried out to study the copolymerization process of halogen-substituted styrene (ST-X), divinylbenzene (DVB), and dodecane (DO) in aqueous solution. The results showed that properly selecting the sizes of DO and water beads, and choosing the appropriate interaction parameters between beads are crucial in the simulation system. The influence of polymerization parameters, such as polymerization temperature, ST-X/DVB/DO/water ratio, and halogen substitution on ST on the copolymer morphology, were investigated in detail and confirmed that the simulation results can reproduce the macroscopic experimental phase separation. In addition, the pore volume of copolymers formed at different polymerization conditions is estimated, which consisted with the data measured in the experiments. Our work has demonstrated that DPD methods can be applied to study such copolymerization process.

Reaction Ensemble Monte Carlo Simulation of Complex Molecular Systems

Acceptance rules for reaction ensemble Monte Carlo (RxMC) simulations containing classically modeled atomistic degrees of freedom are derived for complex molecular systems where insertions and deletions are achieved gradually by utilizing the continuous fractional component (CFC) method. A self-consistent manner in which to utilize statistical mechanical data contained in ideal gas free energy parameters during RxMC moves is presented. The method is tested by applying it to two previously studied systems containing intramolecular degrees of freedom: the propene metathesis reaction and methyl-tert-butyl-ether (MTBE) synthesis. Quantitative agreement is found between the current results and those of Keil et al. (J. Chem. Phys. 2005, 122, 164705) for the propene metathesis reaction. Differences are observed between the equilibrium concentrations of the present study and those of Lísal et al. (AIChE J. 2000, 46, 866-875) for the MTBE reaction. It is shown that most of this difference can be attributed to an incorrect formulation of the Monte Carlo acceptance rule. Efficiency gains using CFC MC as opposed to single stage molecule insertions are presented.

STUDY ON HOMOGENEOUS PRECIPITATION OF CeO2 NANOPARTICLES BY DISSIPATIVE PARTICLE DYNAMICS SIMULATION

Dissipative particle dynamics (DPD) was carried out to study the nucleation and crystal growth process of cerium dioxide ( CeO 2) nanoparticles in alcohol/water mixed solvents by homogeneous precipitation method. The results showed that properly selecting the sizes of CeO 2 and water beads, and choosing the appropriate interaction parameters between beads are crucial in the simulation system. The nucleation and crystal growth process of CeO 2 can be classified into four stages: induction, nuclei growth, crystal forming, and crystal aggregation, which could be reproduced from different initial CeO 2 concentration and after different simulation time. The simulation results confirm that the effect of solvent on the nucleation and crystal growth of CeO 2 nanoparticles are different at four stages and cannot be simply described by Derjaguin–Landau–Verwey–Overbeek theory or nucleation thermodynamics theory as proposed in the published literatures. Our work demonstrated that DPD methods can be applied to study nanoparticle forming process.