Dissipative particle dynamics simulations of polymersomes

A DPD model of PEO-based block copolymer vesicles in water is developed by introducing a new density based coarse graining and by using experimental data for interfacial tension. Simulated as a membrane patch, the DPD model is in excellent agreement with experimental data for both the area expansion modulus and the scaling of hydrophobic core thickness with molecular weight. Rupture simulations of polymer vesicles, or "polymersomes", are presented to illustrate the system sizes feasible with DPD. The results should provide guidance for theoretical derivations of scaling laws and also illustrate how spherical polymer vesicles might be studied in simulation.     

Dissipative particle dynamics simulations of toroidal structure formations of amphiphilic triblock copolymers

In this paper, the dynamic assembly of toroidal micelle structures of amphiphilic triblock copolymers in dilute solution has been investigated using dissipative particle dynamics simulations. The amphiphilic molecule is represented by a coarse-grained model, which contains hydrophilic and hydrophobic particles. Some microstructures of complex morphology having toroidal micelles have been observed in the simulations; the toroidal micelle formation is in accordance with the theoretical prediction of the toroidal structure in cylindrical micelle suspensions by Pochan et al. (Science 2004, 306, 94). These findings are very interesting, and these complex morphologies enrich our knowledge of the potential products obtained from the self-assembly of block copolymers.     

Molecular dynamics simulations of nanoparticle self-assembly at ionic liquid-water and ionic liquid-oil interfaces

We have studied the self-assembly of hydrophobic nanoparticles at ionic liquid (IL)-water and IL-oil (hexane) interfaces using molecular dynamics (MD) simulations. For the 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF(6)])/water system, the nanoparticles rapidly approached the IL-water interface and equilibrated more into the IL phase although they were initially in the water phase. In contrast, when the nanoparticles were dispersed in the hexane phase, they slowly approached the IL-hexane interface but remained primarily in the hexane phase. Consequently, the IL-hexane interface was rather undisturbed by the nanoparticles whereas the IL-water interface changed significantly in width and morphology to accommodate the presence of the nanoparticles. The equilibrium positions of the nanoparticles were also supported and explained by potential of mean force (PMF) calculations. Interesting ordering and charge distributions were observed at the IL-liquid interfaces. At the IL-hexane interface, the [BMIM] cations preferentially oriented themselves so that they were immersed more in the hexane phase and packed efficiently to reduce steric hindrance. The ordering likely contributed to a heightened IL density and a slightly positive charge at the IL-hexane interface. In contrast, the cations at the IL-water interface were oriented isotropically unless in the presence of nanoparticles, where the cations aligned across the nanoparticle surfaces.     

Molecular dynamics simulations of charged nanoparticle self-assembly at ionic liquid-water and ionic liquid-oil interfaces

Nanoparticle self-assembly at liquid-liquid interfaces can be significantly affected by the individual nanoparticle charges. This is particularly true at ionic liquid (IL) based interfaces, where Coulombic forces play a major role. Employing 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF(6)]) as a model IL, we have studied the self-assembly of hydrophobic nanoparticles with different surface charges at the IL/water and IL/oil (hexane) interfaces using molecular dynamics simulations. In the IL/water system, the nanoparticles were initially dispersed in the water phase but quickly equilibrated at the interface, somewhat in favor of the IL phase. This preference was lessened with increased nanoparticle charge. In the IL/hexane system, all charged nanoparticles interacted with the IL to some extent, whereas the uncharged nanoparticles remained primarily in the hexane phase. Potential of mean force calculations supported the observations from the equilibrium studies and provided new insights into the interactions of the nanoparticles and ionic liquid based interfaces.     

Computer simulations of block copolymer tethered nanoparticle self-assembly

We perform molecular simulations to study the self-assembly of block copolymer tethered cubic nanoparticles. Minimal models of the tethered nanoscale building blocks (NBBs) are utilized to explore the structures arising from self-assembly. We demonstrate that attaching a rigid nanocube to a diblock copolymer affects the typical equilibrium morphologies exhibited by the pure copolymer. Lamellar and cylindrical phases are observed in both systems but not at the corresponding relative copolymer tether block fractions. The effect of nanoparticle geometry on phase behavior is investigated by comparing the self-assembled structures formed by the tethered NBBs with those of their linear ABC triblock copolymer counterparts. The tethered nanocubes exhibit the conventional triblock copolymer lamellar and cylindrical phases when the repulsive interactions between different blocks are symmetric. The rigid and bulky nature of the cube induces interfacial curvature in the tethered NBB phases compared to their linear ABC triblock copolymer counterparts. We compare our results with those structures obtained from ABC diblock copolymer tethered nanospheres to further elucidate the role of cubic nanoparticle geometry on self-assembly.     

Dissipative particle dynamics simulations in the grand canonical ensemble: applications to polymer brushes.

We have used the dissipative particle dynamics (DPD) method in the grand canonical ensemble to study the compression of grafted polymer brushes in good solvent conditions. The force-distance profiles calculated from DPD simulations in the grand canonical ensemble are in very good agreement with the self-consistent field (SCF) theoretical models and with experimental results for two polystyrene brush layers grafted onto mica surfaces in toluene.     

Molecular dynamics simulation of nanoparticle self-assembly at a liquid-liquid interface

We have used molecular dynamics simulations to investigate the in situ self-assembly of modified hydrocarbon nanoparticles (mean diameter of 1.2 nm) at a water-trichloroethylene (TCE) interface. The nanoparticles were first distributed randomly in the water phase. The MD simulation shows the in situ formation of nanoparticle clusters and the migration of both single particles and clusters from the water phase to the trichloroethylene phase, possibly due to the hydrophobic nature of the nanoparticles. Eventually, the single nanoparticles or clusters equilibrate at the water-TCE interface, and the surrounding liquid molecules pack randomly when in contact with the nanoparticle surfaces. In addition, the simulations show that the water-TCE interfacial thickness analyzed from density profiles is influenced by the presence of nanoparticles either near or in contact with the interface but is independent of the number of nanoparticles present. The nanoparticles, water molecules, and TCE molecules all exhibit diffusion anisotropy.     

Dissipative particle dynamics simulation study of the bilayer-vesicle transition

A bilayer structure is an important immediate for the vesicle formation. However,the mechanism for the bilayer-vesicle transition remains unclear. In this work,a dissipative particle dynamics(DPD) simulation method was employed to study the mechanism of the bilayer-vesicle transition. A coarse-grained model was built based on a lipid molecule termed dimyristoylphosphatidylcholine(DMPC). Simulations were performed from two different initial configurations:a random dispersed solution and a tensionless bilayer. It was found that the bilayer-vesicle transition was driven by the minimization of the water-tail hydrophobic interaction energy,and was accompanied with the increase of the position entropy due to the redistribution of water molecules. The bulk pressure was reduced during the bilayer-vesicle transition,suggesting the evolved vesicle morphology was at the relatively low free energy state. The membrane in the product vesicle was a two-dimensional fluid. It can be concluded that the membrane of a vesicle is not interdigitated and most of the bonds in lipid chains are inclined to orient along the radical axis of the vesicle.     

Conserving the linear momentum in stochastic dynamics: Dissipative particle dynamics as a general strategy to achieve local thermostatization in molecular dynamics simulations

Stochastic dynamics is a widely employed strategy to achieve local thermostatization in molecular dynamics simulation studies; however, it suffers from an inherent violation of momentum conservation. Although this short‐coming has little impact on structural and short‐time dynamic properties, it can be shown that dynamics in the long‐time limit such as diffusion is strongly dependent on the respective thermostat setting. Application of the methodically similar dissipative particle dynamics (DPD) provides a simple, effective strategy to ensure the advantages of local, stochastic thermostatization while at the same time the linear momentum of the system remains conserved. In this work, the key parameters to employ the DPD thermostats in the framework of periodic boundary conditions are investigated, in particular the dependence of the system properties on the size of the DPD‐region as well as the treatment of forces near the cutoff. Structural and dynamical data for light and heavy water as well as a Lennard–Jones fluid have been compared to simulations executed via stochastic dynamics as well as via use of the widely employed Nose–Hoover chain and Berendsen thermostats. It is demonstrated that a small size of the DPD region is sufficient to achieve local thermalization, while at the same time artifacts in the self‐diffusion characteristic for stochastic dynamics are eliminated. © 2016 Wiley Periodicals, Inc.     

Constant-pressure simulations with dissipative particle dynamics

Dissipative particle dynamics (DPD) is a mesoscopic simulation method for studying hydrodynamic behavior of complex fluids. Ideally, a mesoscopic model should correctly represent the thermodynamic and hydrodynamic properties of a real system beyond certain length and time scales. Traditionally defined DPD quite successfully mimics hydrodynamics but is not flexible enough to accurately describe the thermodynamics of a real system. The so-called multibody DPD (MDPD) is a pragmatic extension of the classical DPD that allows one to prescribe the thermodynamic behavior of a system with only a small performance impact. In an earlier paper [S. Y. Trofimov, E. L. F. Nies, and M. A. J. Michels, J. Chem. Phys. 117, 9383 (2002)] we much improved the accuracy of the MDPD model for strongly nonideal systems, which are of most practical interest. The ability to correctly reproduce the equation of state of realistic systems in turn makes simulations at constant pressure sensible and useful. This situation of constant-pressure conditions is very common in experimental studies of (soft) condensed matter but has so far remained unexplored with the traditional DPD. Here, as a proof of concept, we integrate a modified version of the Andersen barostat into our improved MDPD model and make an evaluation of the performance of the new model on a set of single- and multicomponent systems. The modification of the barostat suppresses the "unphysical" volume oscillations after a sudden pressure change and simplifies the equilibration of the system.     

Dissipative particle dynamics simulations of polymer melts. I. Building potential of mean force for polyethylene and cis-polybutadiene

We present the derivation of coarse-grained force fields for two types of polymers, polyethylene (PE), and cis-polybutadiene (cis-PB), using the concept of potential of mean force. Coarse-grained force fields were obtained from microscopic simulations for several coarse-graining levels, i.e., different number of monomers lambda per mesoscopic unit called "bead." These force fields are then used in dissipative particle dynamics (DPD) simulations to study structural and dynamical properties of polymer melts of PE and cis-PB. The radial distribution functions g(R), the end-to-end distance R0, the end-to-end vector relaxation time tau, and the chain center of mass self-diffusion D(CM), are computed for different chain lengths at different coarse-graining factor lambda. Scaling laws typical of the Rouse regime are obtained for both polymers for chain lengths ranging from 6 to 50 beads. It is found that the end-to-end distance R0 obtained from DPD simulations agree well with values obtained from both microscopic simulations and experiments. The dependence of the friction coefficient used in DPD simulations versus the coarse-graining level is discussed in view of the overall scaling of the dynamical properties.     

Finite-size effects in dissipative particle dynamics simulations

We have performed dissipative particle dynamics (DPD) simulations to evaluate the effect that finite size of transversal area has on stress anisotropy and interfacial tension. The simulations were carried out in one phase and two phases in parallelepiped cells. In one-phase simulations there is no finite-size effect on stress anisotropy when the simulation is performed using repulsive forces. However, an oscillatory function of stress anisotropy is found for attractive-repulsive interactions. In the case of liquid-liquid interfaces with repulsive interaction between molecules, there is only a small effect of surface area on interfacial tension when the simulations are performed using the Monte Carlo method at constant temperature and normal pressure. An important but artificial finite-size effect of interfacial area on surface tension is found in simulations in the canonical ensemble. Reliable results of interfacial tension from DPD simulations can be obtained using small systems, less than 2000 particles, when they interact exclusively with repulsive forces.     

Improved dissipative particle dynamics simulations of lipid bilayers

The authors introduce a new parameterization for the dissipative particle dynamics simulations of lipid bilayers. In this parameterization, the conservative pairwise forces between beads of the same type in two different hydrophobic chains are chosen to be less repulsive than the water-water interaction, but the intrachain bead interactions are the same as the water-water interaction. For a certain range of parameters, the new bilayer can only be stretched up to 30% before it ruptures. Membrane tension, density profiles, and the in-plane lipid diffusion coefficient of the new bilayer are discussed in detail. They find two kinds of finite size effects that influence the membrane tension: lateral finite size effects, for which larger membranes rupture at a smaller stretch, and transverse finite size effects, for which tensionless bilayers are more compact in larger systems. These finite size effects become rather small when the simulation box is sufficiently large.     

Atomistic molecular dynamics simulations of peptide amphiphile self-assembly into cylindrical nanofibers

Relaxation of a self-assembled structure of 144 peptide amphiphile (PA) molecules into cylindrical nanofibers is studied using atomistic molecular dynamics simulations including explicit water with physiological ion concentration. The PA for these studies includes a hydrophobic alkyl chain that is attached to the N-terminus of the sequence SLSLAAAEIKVAV. The self-assembly is initiated with PA molecules in a roughly cylindrical configuration, as suggested from previous experimental and theoretical investigations, and the cylindrical configuration that results is found to be stable during 40 ns simulations. In the converged structure of the resulting nanofiber, the cylinder radius is ～44 ?, a result that is consistent with experimental results. Water and sodium ions can penetrate into the peptide portion of the fiber but not between the alkyl chains. Even though each PA has an identical sequence, a broad distribution of secondary structure is found in the converged structure of the nanofiber. The β-sheet population for the SLSL and IKV segments of the peptide is ～25%, which is consistent with previous circular dichroism results. We also found that the epitope sequence IKVAV is located on the surface of the nanofiber, as designed for the promotion of the neurite growth. Our findings will be useful for designing new PA fibers that have improved bioactive properties.     

Dissipative particle dynamics simulation of microphase separation behaviors in graft-diblock copolymer films

Dependence of the microphase separation behaviors of graft-diblock copolymers (A _x )g(B _y ) in thin films on composition fraction, thickness of film and A–B repulsing strength is investigated preliminarily by dissipative particle dynamics. Several kinds of ordered mesostructures have been observed and the simulated phase diagrams show evident asymmetries, besides, the center of lamellas region shifts away from f _A = 0.5. Some of the mesostructures in the film can correspond to those in bulk. Decreasing the thickness of film as well as strengthening the A–B repulsion help the mesostructures enhance the degree of order.     

Mesoscopic simulation of self-assembly in surfactant oligomers by dissipative particle dynamics

Self-assembling properties of surfactant oligomers in an aqueous medium is simulated by dissipative particle dynamics (DPD). The critical micellar concentration (CMC) of dimeric (oligomerization = 2) and trimeric (oligomerization = 3) surfactant is much lower than their single-chain counterpart. All surfactants form spherical micelles at the concentration not far above their CMC. The transition from spherical to cylindrical micelles exhibits with increasing surfactant concentration. Lamellar micelles will appear with further increasing the surfactant concentration. For dimeric and trimeric surfactants, cylindrical micelles transform into extremely long “wormlike” or “threadlike” micelles before the transition to lamellar micelles. These results are in qualitative agreement with laboratory experiment. Average aggregation numbers (AN) of micelles increase with a power law of AN  c when the surfactant concentration c CMC. The self-diffusion coefficients will drop with a power law of D  c⁻ when wormlike micelles are formed.     

Brownian dynamics simulations on the self-assembly behavior of AB hybrid dendritic-star copolymers

The micellization behavior of hybrid dendritic-star copolymers with solvophilic dendritic units is studied by means of Brownian dynamics simulations. The critical micelle concentration and the micelle size and shape are examined for different solvophobic/solvophilic ratios r as a function of the number of the dendritic and linear arms. Hybrid dendritic-star copolymers with one dendritic and up to three solvophobic linear branches form spherical micelles with preferential aggregation number. Those with two dendritic arms and three solvophobic branches form micelles with wide aggregation numbers only for small values of r. For hybrid dendritic-star copolymers with three dendritic arms and two or three solvophobic linear arms, micelles with wide aggregation numbers are also formed but for slightly higher values of r. Our results for the aggregation number are compared with existing results of other architectures obtained at the same temperature, and an inequality for the aggregation number is proposed.