Dissipative Particle Dynamics Simulation Technique Research Articles

Computer simulation study on the self-assembly of tethered nanoparticles with tunable shapes.

We built a tethered nanoparticle (TNP) model that is composed of a nanoparticle with a hydrophobic tethered polymer chain. The shape of the nanoparticle can be tuned from a pure rigid cube to a soft sphere, mimicking the increase of grafting density on the nanocube surfaces. With this model, we study the self-assembly of TNPs in dilute solution using a dissipative particle dynamics simulation technique, and especially focus on the influence of particle shape, tethered chain length, and grafting density on the self-assembly structures. Some intriguing aggregates such as spherical micelles, pearl-necklace-like structures, cubic columnar structures, handshake structures, core–shell–corona micelles, and four-patch micelles have been observed when varying the interactions between cubes and solvents and the lengths of tethered chain. Modifying the nanocube surface with some hydrophilic grafted chains helps the TNPs form small micelles. Increased steric repulsion due to chain overlapping at larger grafting densities results in shape transformation of the nanoparticle from a rigid cube to a soft sphere. In these cases, the self-assembled structures are characterized by the packing of nanoparticles on the micelle surface, and the typical packing mode turns from rectangular (typical for cubes) to hexagonal (typical for spheres).

Self-Assembly Mechanisms of Triblock Janus Particles.

We present a detailed model to study the nucleation of triblock Janus particles from solution. The Janus particles are modeled as cross-linked polystyrene spheres whose poles are patched with sticky alkyl groups and their middle band is covered with negative charges. To mimic the experimental conditions, solvent, counterions, and a substrate, on which the crystallization takes place, are included in the model. A many-body dissipative particle dynamics simulation technique is employed to include hydrodynamic and many-body interactions. Metadynamics simulations are performed to explore the pathways for nucleation of Kagome and hexagonal lattices. In agreement with experiment, we found that nucleation of the Kagome lattice from solution follows a two-step mechanism. The connection of colloidal particles through their patches initially generates a disordered liquid network. Subsequently, orientational rearrangements in the liquid precursors lead to the formation of ordered nuclei. Biasing the potential energy of the largest crystal, a critical nucleus appears in the simulation box, whose further growth crystallizes the whole solution. The location of the phase transition point and its shift with patch width are in very good agreement with experiment. The structure of the crystallized phase depends on the patch width; in the limit of very narrow patches strings are stable aggregates, intermediate patches stabilize the Kagome lattice, and wide patches nucleate the hexagonal phase. The scaling behavior of the calculated barrier heights confirms a first-order liquid-Kagome phase transition.

Precisely Controlled Incorporation of Drug Nanoparticles in Polymer Vesicles by Amphiphilic Copolymer Tethers

In this paper, we describe the fabrication of nanoparticle (NP)-embedded nanovesicles by coassembly of diblock copolymer-tethered NPs and free diblock copolymers via the dissipative particle dynamics simulation technique. We use an improved quantitative model to characterize the angular and radial distributions of NPs within vesicle walls simultaneously. In a specific circumstance, the NPs can be localized in the central portion of the vesicle walls, which is in excellent agreement with the experimental work. On the basis of this model, we find that the distributions of the NPs can be well manipulated just by three physical quantities, which are easily controlled in the experiments. For instance, the radial distributions of the NPs can be precisely controlled by changing the grafted hydrophobic chain length and the tethered arm number affects the dispersity of the NPs in the angular direction of the vesicle walls. The results provide the experimentalists with a way to design carrier-assistant drug deliver...

Mesoscale modeling of sulfonated polyimides copolymer membranes: Effect of sequence distributions

We adopt dissipative particle dynamics simulation technique and systematically study the effect of sequence distributions of hydrophobic and hydrophilic segments in individual sulfonated polyimide (SPI) copolymer on the micro-phase separated structure and the performance of proton exchange membranes (PEMs) under various water contents. The phase morphology as well as the shape and size of water channels is affected by sequence distributions. Compared to the di-block copolymer and the alt-copolymer, water channels in the multi-block copolymer are more homogenous. Additionally, the copolymer sequence distributions affect the water transport which is closely related to the proton conductivity, the dimensional stability and the mechanical properties of PEMs via tuning the phase structure. Generally, the more homogenous water channels the faster water transport. As for the dimensional stability, unlike the other two copolymers the unique shrinkage behavior of multi-block copolymer can resist the membrane swelling induced by water uptake. Moreover, the system with short block has relatively large Young's modulus and the influence of sequence distributions on Young's modulus weakens with the addition of water. Consequently, the multi-block SPI copolymer possesses fast water transport, low dimension-swelling and relatively high Young's modulus, which will make it a potentially huge application in PEM.

Flow-Induced Shape Reconfiguration, Phase Separation, and Rupture of Bio-Inspired Vesicles.

The structural integrity of red blood cells and drug delivery carriers through blood vessels is dependent upon their ability to adapt their shape during their transportation. Our goal is to examine the role of the composition of bio-inspired multicomponent and hairy vesicles on their shape during their transport through in a channel. Through the dissipative particle dynamics simulation technique, we apply Poiseuille flow in a cylindrical channel. We investigate the effect of flow conditions and concentration of key molecular components on the shape, phase separation, and structural integrity of the bio-inspired multicomponent and hairy vesicles. Our results show the Reynolds number and molecular composition of the vesicles impact their flow-induced deformation, phase separation on the outer monolayer due to the Marangoni effect, and rupture. The findings from this study could be used to enhance the design of drug delivery and tissue engineering systems.

Modeling Interactions between Multicomponent Vesicles and Antimicrobial Peptide-Inspired Nanoparticles.

We examine the interaction between peptide-inspired nanoparticles, or nanopins, and multicomponent vesicles using the dissipative particle dynamics simulation technique. We study the role of nanopin architecture and cholesterol concentration on the binding of the nanopins to the lipid bilayer, their insertion, and postembedding self-organization. We find the insertion to be triggered by enthalpically unfavorable interactions between the hydrophilic solvent and the lipophilic components of the nanopins. The nanopins are observed to form aggregates in solution, insert into the bilayer, and disassemble into the individual nanopins following the insertion process. We examine factors that influence the orientation of the nanopins in the host vesicle. We report the length of the hydrophilic segment of the nanopins to regulate their orientation within the clusters before the embedding process and in the bilayer, after the postinsertion disassembly of the aggregates. The orientation angle distribution for a given nanopin architecture is found to be driven by energy minimization. In addition, higher concentration of cholesterol is observed to constrain the orientation of the nanopins. We also report thermal fluctuations to induce transverse diffusion of nanopins with specific architectures. The incidence of transverse diffusion is observed to decrease with the concentration of cholesterol. Our results can provide guidelines for designing peptide-inspired nanoparticles or macromolecules that can interface with living cells to serve as sensors for applications in medicine, sustainability, and energy.

Self-Assembly and Critical Aggregation Concentration Measurements of ABA Triblock Copolymers with Varying B Block Types: Model Development, Prediction, and Validation.

The dissipative particle dynamics (DPD) simulation technique is a coarse-grained (CG) molecular dynamics-based approach that can effectively capture the hydrodynamics of complex systems while retaining essential information about the structural properties of the molecular species. An advantageous feature of DPD is that it utilizes soft repulsive interactions between the beads, which are CG representation of groups of atoms or molecules. In this study, we used the DPD simulation technique to study the aggregation characteristics of ABA triblock copolymers in aqueous medium. Pluronic polymers (PEG-PPO-PEG) were modeled as two segments of hydrophilic beads and one segment of hydrophobic beads. Tyrosine-derived PEG5K-b-oligo(desaminotyrosyl tyrosine octyl ester-suberate)-b-PEG5K (PEG5K-oligo(DTO-SA)-PEG5K) block copolymers possess alternate rigid and flexible components along the hydrophobic oligo(DTO-SA) chain, and were modeled as two segments of hydrophilic beads and one segment of hydrophobic, alternate soft and hard beads. The formation, structure, and morphology of the initial aggregation of the polymer molecules in aqueous medium were investigated by following the aggregation dynamics. The dimensions of the aggregates predicted by the computational approach were in good agreement with corresponding results from experiments, for the Pluronic and PEG5K-oligo(DTO-SA)-PEG5K block copolymers. In addition, DPD simulations were utilized to determine the critical aggregation concentration (CAC), which was compared with corresponding results from an experimental approach. For Pluronic polymers F68, F88, F108, and F127, the computational results agreed well with experimental measurements of the CAC measurements. For PEG5K-b-oligo(DTO-SA)-b-PEG5K block polymers, the complexity in polymer structure made it difficult to directly determine their CAC values via the CG scheme. Therefore, we determined CAC values of a series of triblock copolymers with 3-8 DTO-SA units using DPD simulations, and used these results to predict the CAC values of triblock copolymers with higher molecular weights by extrapolation. In parallel, a PEG5K-b-oligo(DTO-SA)-b-PEG5K block copolymer was synthesized, and the CAC value was determined experimentally using the pyrene method. The experimental CAC value agreed well with the CAC value predicted by simulation. These results validate our CG models, and demonstrate an avenue to simulate and predict aggregation characteristics of ABA amphiphilic triblock copolymers with complex structures.

Harnessing steric hindrance to control interfacial adsorption of patchy nanoparticles onto hairy vesicles

Via the Dissipative Particle Dynamics simulation technique we investigate the interfacial adsorption of nanoparticles with a binding site onto a hairy vesicle encompassing phospholipids and lipids functionalized with oligo ethylene glycol (OEG) chain. The functionalized nanoparticles are modeled as patchy spherical particles. We examine the relation between the relative concentration and size of the OEG chains, the adsorption kinetics, life-time and post-adsorption dynamics of the nanoparticles. We also draw correspondence with experimental studies on the adsorption of proteins onto the surface of colloidal particles. Results from our investigations can elucidate the fundamental factors and mechanisms controlling the adsorption of functionalized nanoparticles onto colloidal particles.

Efficient and Large-Scale Dissipative Particle Dynamics Simulations on GPU

In this paper, we introduce a complete implementation for efficient and large-scale dissipative particle dynamics (DPD) simulation on Graphics Processing Unit (GPU). The implementation is designed and optimized according to the nature of DPD simulation technique and also takes fully advantage of the computational power of GPUs. From studies of benchmarks, we show that the GPU-based implementation can predict the results correctly and provide nearly 60 times speedup over LAMMPS on a single Central Processing Unit (CPU) core. By using a novel divide-and-conquer (D&C) algorithm to reduce the memory requirement in simulation, our implementation has the capability to perform large-scale DPD simulations with some ten millions of particles on a single current GPU. Furthermore, the thermal fluctuation analysis of a superior large-scale lamellar system (11,059,200 particles) is presented as an important example of practical application of our implementation, and a scaling law at large wavelengths that is inaccessible to small simulation system, is observed. As a result, our GPU-based DPD implementation is very promising for studying various interesting phenomena, which often take place on the mesoscopic length and time scales and are not easily addressed by a conventional CPU-based implementation.

Dissipative particle dynamics simulation of onion phase in star-block copolymer

A dissipative particle dynamics simulation technique was used to investigate the effect of molecular architecture of star-block copolymer on the patterned structure in a nanodroplet. With increasing the ratio of solvophilic to block length to solvophobic block length(RH/T), solvophobic sphere, ordered hexagonal phase, onion phase, perforated onion phase and flocculent phase are formed, respectively. Since onion phase has potential application in controlled drug release, it has received wide attention experimentally and theoretically. Our simulation indicates onion phase forms at a certain RH/T(close to but less than 1). A star-block copolymer molecule has two conformations in onion phase: either fully located in a shell or shared by two neighboring shells. Central structure affects onion’s final shape. The molecular number of the copolymer in each shell is a quadratic function of the shell’s radius. The arm number of star-block copolymer has little influence on onion’s structure, but slightly affects the solvent content. Additionally, we studied the influence of arm length on onion’s structure.

Perpendicular Domain Orientation in Dense Planar Brushes of Diblock Copolymers

Dense planar brushes of diblock copolymers physically attached to the substrate by end groups are studied by the dissipative particle dynamics simulation technique. We predict stability of spatially ordered perpendicularly oriented domains which are separated from the substrate and the free surface of the film by homogeneous layers of different type. Depending on composition of the copolymer, various structures including hexagonally ordered “golf holes”, parallel “gullies” and “ridges”, and “stalactites” ordered with the symmetry of hexagonal lattice can be stable. We analyze regimes of good and poor solvents for both blocks (nonselective solvents). Physical reasons for perpendicular domain orientation are discussed. In the case of low “grafting” density, our results coincide with those reported in the literature.

DISSIPATIVE PARTICLE DYNAMICS IN SOFT MATTER AND POLYMERIC APPLICATIONS — A REVIEW

Computer simulations and in particular mesoscopic simulation techniques such as the dissipative particle dynamics (DPD) technique, enable researchers to study the complexities of soft material and polymeric systems by performing in silico experimentations alongside in vivo experiments. In addition, these mesoscopic simulations allow scientists and engineers to characterize and optimize the actual experiments in a more efficient manner. The DPD is one the most reliable mesoscopic simulation techniques for phenomenological investigation of soft matter and polymeric systems. In this review, which is complimentary to an earlier review also by the present authors on DPD methodology and complex fluid application (Moeendarbary et al., 2009), we categorize and review the notable published works, and document efforts that applied the DPD simulation technique to various important soft matter and polymeric applications, over the last decade.

Microphase Transitions of Perforated Lamellae of Cyclic Diblock Copolymers under Steady Shear

The dissipative particle dynamics simulation technique is used to study the microphase transitions of perforated lamellae of cyclic diblock copolymers under steady shear. The perforated lamellae are transformed to perfect lamellae, and the layer normal is aligned to the direction parallel to the gradient of the velocity under weak shear, whereas they undergo a phase transition to form perfect lamellae whose normal is aligned to the direction perpendicular to the gradient of the velocity due to strong shear. Subjected to the moderate shear, the perforated lamellae are transformed to hexagonally ordered cylinders. By examining the microphase morphologies in the shearing process, we find shear thinning in general, which is reflected by the reorientation of the lamellae, and shear-induced thickening when hexagonally ordered cylinders appear. The calculated shear viscosity basically decreases with increasing shear rate but shows a local maximum at the shear rate that induces hexagonally ordered cylinders.

Understanding Multicompartment Micelles Using Dissipative Particle Dynamics Simulation

AbstractMulticompartment micelles are a new class of nanomaterials that may find wide applications in the fields of drug delivery, nanotechnology and catalysis. Due to their structural complexity, as well as the wide parameter space to explore, experimental investigations are a difficult task, to which molecular simulation may contribute greatly. In this paper, the application of the dissipative particle dynamics simulation technique to the understanding of multicompartment micelles is introduced, illustrating that DPD is a powerful tool for identifying new morphologies by varying block length, block ratio and solvent quality in a systematic way. The formation process of multicompartment micelles, as well as shear effects and the self‐assembly of nanoparticle mixtures in multicompartment micelles, can also be studied well by DPD simulation. The present work shows that DPD, as well as other simulation techniques and theories, can complement experiments greatly, not only in exploring properties in a wider parameter space, but also by giving a preview of phenomena prior to experiments. DPD, as a mesoscopic dynamic simulation technique, is particularly useful for understanding the dynamic processes of multicompartment micelles at a microscopic level.magnified image

Novel Two‐Compartment Micelles Formed by Self‐Assembly of Linear Pentablock Copolymers in Selective Solvents

AbstractIn this work, the formation of two‐compartment micelles from symmetric pentablock copolymers in selective solvents was studied using the dissipative particle dynamics simulation technique, and the effects of block lengths and solvent quality were investigated. The simulations revealed several new morphologies and their formation mechanisms were elucidated at the molecular level, providing useful information that may contribute to the future rational design and synthesis of novel multicompartment micelles with tailored structures.magnified image

The dependence of nanostructures on the molecule rigidity of A2(B4)2-type miktoarm block copolymer

Using the dissipative particle dynamics simulation technique, we have studied the influence of the molecule rigidity on the nanostructures of the A2(B4)2-type miktoarm block copolymers. A typical spherical micellar ordered structure is obtained for a coil-coil miktoarm block copolymer in melt. By introducing a bond angle potential in our model to enhance the molecule rigidity systematically, we find, respectively, a hexagonal cylindrical structure and a parallel ellipsoid in lamellae structure which is discovered for the first time.

Simulation Studies of Protein-Induced Bilayer Deformations, and Lipid-Induced Protein Tilting, on a Mesoscopic Model for Lipid Bilayers with Embedded Proteins

Biological membranes are complex and highly cooperative structures. To relate biomembrane structure to their biological function it is often necessary to consider simpler systems. Lipid bilayers composed of one or two lipid species, and with embedded proteins, provide a model system for biological membranes. Here we present a mesoscopic model for lipid bilayers with embedded proteins, which we have studied with the help of the dissipative particle dynamics simulation technique. Because hydrophobic matching is believed to be one of the main physical mechanisms regulating lipid-protein interactions in membranes, we considered proteins of different hydrophobic length (as well as different sizes). We studied the cooperative behavior of the lipid-protein system at mesoscopic time- and lengthscales. In particular, we correlated in a systematic way the protein-induced bilayer perturbation, and the lipid-induced protein tilt, with the hydrophobic mismatch (positive and negative) between the protein hydrophobic length and the pure lipid bilayer hydrophobic thickness. The protein-induced bilayer perturbation was quantified in terms of a coherence length, ξP, of the lipid bilayer hydrophobic thickness profile around the protein. The dependence on temperature of ξP, and the protein tilt-angle, were studied above the main-transition temperature of the pure system, i.e., in the fluid phase. We found that ξP depends on mismatch, i.e., the higher the mismatch is, the longer ξP becomes, at least for positive values of mismatch; a dependence on the protein size appears as well. In the case of large model proteins experiencing extreme mismatch conditions, in the region next to the so-called lipid annulus, there appears an undershooting (or overshooting) region where the bilayer hydrophobic thickness is locally lower (or higher) than in the unperturbed bilayer, depending on whether the protein hydrophobic length is longer (or shorter) than the pure lipid bilayer hydrophobic thickness. Proteins may tilt when embedded in a too-thin bilayer. Our simulation data suggest that, when the embedded protein has a small size, the main mechanism to compensate for a large hydrophobic mismatch is the tilt, whereas large proteins react to negative mismatch by causing an increase of the hydrophobic thickness of the nearby bilayer. Furthermore, for the case of small, peptidelike proteins, we found the same type of functional dependence of the protein tilt-angle on mismatch, as was recently detected by fluorescence spectroscopy measurements.

Equilibrium structure and lateral stress distribution of amphiphilic bilayers from dissipative particle dynamics simulations

The equilibrium structure and lateral stress profile of fluid bilayer membrane patches are investigated using the Dissipative Particle Dynamics simulation technique. Although there are no attractive forces between the model amphiphiles, they spontaneously aggregate into planar bilayers under suitable conditions of concentration and amphiphile architecture. Pure bilayers of single-chain and double-chain amphiphiles are simulated, and the amphiphile architecture and interaction parameters varied. We find that a strong chain stiffness potential is essential to create the lamellar order typical in natural lipid membranes. Single-chain amphiphiles form bilayers whose lamellar phase is destabilized by reductions in the tail stiffness. Double-chain amphiphiles form bilayers whose rigidity is sensitive to their architecture, and that remain well-ordered for smaller values of their tail stiffness than bilayers of single-chain linear amphiphiles with the same hydrophobic tail length. The lateral stress profile across the bilayers contains a detailed structure reflecting contributions from all the interaction potentials, as well as the amphiphile architecture. We measure the surface tension of the bilayers, and extract estimates of the membrane area stretch modulus and bending rigidity that are comparable to experimental values for typical lipid bilayers. The stress profile is similar to that found in coarse-grained Molecular Dynamics simulations, but requires a fraction of the computational cost. Dissipative Particle Dynamics therefore allows the study of the equilibrium behavior of fluid amphiphilic membranes hundreds of times larger than can be achieved using Molecular Dynamics simulations, and opens the way to the investigation of complex mesoscopic cellular phenomena.

Simulating the rheology of dense colloidal suspensions using dissipative particle dynamics

The rheological properties of colloidal suspensions of spheres, rods, and disks have been studied using a mesoscopic simulation technique, known as dissipative particle dynamics (DPD). In DPD, a suspension is modeled as a system of large colloidal particles in a liquid of interacting point particles. For the calculation of hydrodynamic interactions, this method is computationally more efficient than conventional techniques using a continuum model for the solvent. Applying a steady-shear rate to the particulate suspensions, we have measured the viscosity as a function of shear rate and volume fraction of the suspended particles. The viscosity of a 30 vol % suspension of spheres displays characteristic shear-thinning behavior as a function of increasing shear rate. The values for the high- and low-shear viscosity are in good agreement with experimental data. For higher particulate densities good results are obtained for the high-shear viscosity, although the viscosity at low-shear rates shows a dependence on the size of the suspended spheres that we attribute to finite size effects. Dilute suspensions of rods and disks show intrinsic viscosities which are in excellent agreement with theoretical predictions. For concentrated suspensions of both rods and disks, the viscosity increases with the third power of the volume fraction. We find the same scaling behavior as predicted by Doi and Edwards [M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Oxford University Press, New York, 1986)] for rod suspensions in the semidilute regime. The DPD simulation technique emerges as a useful tool for studying the rheology of particulate suspensions.

Computer simulation of rheological phenomena in dense colloidal suspensions with dissipative particle dynamics

The rheological properties of colloidal suspensions of spheres and rods have been studied using dissipative particle dynamics (DPD). We have measured the viscosity as a function of shear rate and volume fraction of the suspended particles. The viscosity of a 30 vol% suspension of spheres displays characteristic shear-thinning behaviour as a function of shear rate. The values for the low- and high-shear viscosity are in good agreement with experimental data. For higher particulate densities, good results are obtained for the high-shear viscosity, although the viscosity at low shear rates shows a dependence on the size of the suspended spheres. Dilute suspensions of rods show an intrinsic viscosity which is in excellent agreement with theoretical results. For concentrated rod suspensions, the viscosity increases with the third power of the volume fraction. We find the same scaling behaviour as Doi and Edwards for the semidilute regime, although the explanation is unclear. The DPD simulation technique therefore emerges as a useful tool for studying the rheology of particulate suspensions.