Simulation of self-assembly behaviour of fluorinated phospholipid molecules in aqueous solution by dissipative particle dynamics method

In order to prepare novel biomaterials, it is essential to investigate the self-assembly behaviour of molecules containing both hydrophobic and hydrophilic groups, and to understand their structural change and morphological development. In this paper, we studied the self-assembly behaviour of fluorinated double-chain phospholipid molecules in aqueous solution at various simulation steps, concentrations, temperatures and pH values via the dissipative particle dynamics simulation method. The self-assembly behaviours of hydrogenated analogues and fluorinated single-chain phospholipids at various concentrations were also investigated for comparison. It was found that all molecules could form microsphere at low concentration, and aggregated to form various shapes with the increase of concentration. Fluorinated double-chain phospholipids were apt to form bilayer membrane more easily than hydrogenated/fluorinated single-chain phospholipids. Besides concentration, temperature and pH value of the aqueous solution also influence the self-assembly behaviour of the investigated molecules. A stable bilayer membrane could be achieved for the fluorinated double-chain phospholipids at a relatively high concentration when pH value and temperature of aqueous solution were close to physiological conditions, i.e., pH 7 and T = 37°C. This work provides a direct ‘observation’ of self-assembly behaviour in the molecular level, which is important for the development of novel biomaterials, where surface structure is required to be well controlled.     

Study of the stability of long-range-ordered lamellar structures for directed self-assembly lithography,performed using dissipative particle dynamics

We performed dissipative particle dynamics (DPD) simulations to obtain long-range-ordered lamellar structures for directed self-assembly lithography. The self-assembled structure of diblock copolymers (DBCs) depends on the length of the different blocks and the difference in their solubility parameters. In the DPD simulations, the DBCs were formed from coarse-grained particles, and the difference between the solubility parameters was represented by a repulsion parameter. We examined the phase separation morphology of the DBCs, which were confined using a trench model system. The repulsion parameter for the assembly of the lamellar structures from the DBC particles was chosen from six types of parameters. The orientation of the lamellar structure was controlled by the repulsion parameter that described the repulsion between the particles and the wall of the system. We changed the width of the trench, and examined the probability for the formation of the lamellar structure. The lamellar structure could not be obtained by increasing the width. To increase the probability, we placed a ridge at the centre of the bottom wall. It was found that the presence of the ridge increased the probability for the formation of the long-range-ordered lamellar structures.     

Microphase separation of graft-diblock copolymer by dissipative particle dynamics simulation

Microphase-separation behaviour of graft-diblock copolymers was investigated by the dissipative particle dynamics. Besides familiar totally ordered mesostructures, the simulated phase diagram also shows unfamiliar locally ordered mesostructures together with a few melted morphologies. The simulated order–disorder transition critical value is higher than the theoretically predicted value due mainly to the increasing fluctuation coming from finite chain length. The microphase-separation morphologies in graft-diblock copolymers shift away significantly from that of the corresponding linear ones with the same component volume fractions. Generally, it is more difficult to trigger microphase separation for graft-diblock copolymers than for their linear analogues, in good agreement with theoretical and experimental findings. The change of graft fraction has a significant effect on the microphase-separation behaviour of graft-diblock copolymers.     

Artificial biomembrane morphology: a dissipative particle dynamics study

Artificial membranes mimicking biological structures are rapidly breaking new ground in the areas of medicine and soft-matter physics. In this endeavor, we use dissipative particle dynamics simulation to investigate the morphology and behavior of lipid-based biomembranes under conditions of varied lipid density and self-interaction. Our results show that a less-than-normal initial lipid density does not create the traditional membrane; but instead results in the formation of a ‘net’, or at very low densities, a series of disparate ‘clumps’ similar to the micelles formed by lipids in nature. When the initial lipid density is high, a membrane forms, but due to the large number of lipids, the naturally formed membrane would be larger than the simulation box, leading to ‘rippling’ behavior as the excess repulsive force of the membrane interior overcomes the bending energy of the membrane. Once the density reaches a certain point however, ‘bubbles’ appear inside the membrane, reducing the rippling behavior and eventually generating a relatively flat, but thick, structure with micelles of water inside the membrane itself. Our simulations also demonstrate that the interaction parameter between individual lipids plays a significant role in the formation and behavior of lipid membrane assemblies, creating similar structures as the initial lipid density distribution. This work provides a comprehensive approach to the intricacies of lipid membranes, and offers a guideline to design biological or polymeric membranes through self-assembly processes as well as develop novel cellular manipulation and destruction techniques.     

Depletion phenomenon in diblock copolymer films: a dissipative particle dynamics simulation

A tentative simulation study has been carried out on the depletion phenomenon in diblock copolymer films through dissipative particle dynamics technology. Results indicate that a depletion layer appears in nearly all the systems with strong interaction between different components, accompanied with weak interaction between the component and the boundary. The system temperature plays a dominant role in the thickness of the depletion layer, on which the component fraction also has an effect to a certain extent. The findings can give support to relevant application processes.     

Structural analysis of telechelic polymer solution using dissipative particle dynamics simulations

A telechelic polymer is an amphiphilic polymer that can form micellar structures when dissolved in water. A telechelic polymer solution shows viscoelastic behaviour owing to the formation of characteristic networks, i.e. loops, bridges and dangling chains. For industrial purposes, telechelic polymers have many applications as thickening agents, such as in paints and cosmetics. Thus, it is desirable to predict and control the rheological properties of telechelic polymers. However, detailed studies at the molecular level have not yet been performed. In this study, I use the dissipative particle dynamics (DPD) method to investigate the relationship between the characteristic structural properties and the molecular structure in telechelic polymer solutions. I show that the morphology of telechelic polymer solutions depends on the concentration and chain length, the distribution of the end-to-end distance, the mean square end-to-end distance, the mean square radius of gyration and the time-averaged mean square displacement. Although an effect of entanglement is important for properties of polymer melts, the polymer chain composed of DPD particles cannot reproduce it. Therefore, I compare telechelic polymer solutions with and without the segmental repulsive potential (SRP), which can simulate the effect of entanglement in DPD simulations. The results indicate that it is necessary to include the SRP in DPD simulations to correctly analyse the behaviour of telechelic polymer solutions.     

Evaporation- and surface-induced morphology of symmetric diblock copolymer thin films: a multibody dissipative particle dynamics study

We apply the multibody dissipative particle dynamics method to exhibit evaporation- and surface-induced morphology of diblock copolymer thin films. We find that when the interactions between A components and B components of the diblock copolymer are symmetric, it is easy to obtain a lamellar morphology perpendicular to the surface. On the contrary, if the interactions between A-blocks and B-blocks are asymmetric, it is easy to obtain a lamellar morphology parallel to the surface. Spherical morphology and disorder morphology are formed when the solvent vapour and surface effect are considered. The order parameter and the film thickness are calculated during the phase-separation process for characterising the film properties. The attractive solvent vapour increases the film thickness and impacts the film morphology of the interface. The attractive surface decreases the film thickness and impacts the film morphology near the surface. Our results are partially helpful for the control of film morphology and film thickness in such kind of materials.     

A dissipative particle dynamics model of carbon nanotubes

A mesoscale dissipative particle dynamics model of single wall carbon nanotubes (CNTs) is designed and demonstrated. The coarse-grained model is produced by grouping together carbon atoms and by bonding the new lumped particles through pair and triplet forces. The mechanical properties of the simulated tube are determined by the bonding forces, which are derived by virtual experiments. Through the introduction of van der Waals interactions, tube–tube interactions were studied. Owing to the reduced number of particles, this model allows the simulation of relatively large systems. The applicability of the presented scheme to model CNT based mechanical devices is discussed.     

Simulation of heat conduction in nanocomposite using energy-conserving dissipative particle dynamics

We report on the simulation of heat conduction in nanocomposite by using a novel mesoscopic particle method, the energy-conserving dissipative particle dynamics (eDPD) method. The original eDPD method is extended to account for the interfacial thermal resistance occurs at the angstrom-wide interface between materials, and we also investigated the choice of time step in eDPD simulations. For nanocomposite with randomly dispersed nanoparticles, the eDPD simulations predict that the thermal conductivity of matrix material can be enhanced by embedding high thermal conductivity nanoparticles, but the effectiveness of such a strategy diminishes as the interfacial thermal resistance between the nanoparticle and matrix material increases. These results are in quantitative agreement with the classical Maxwell–Garnett model. Further simulations indicate that the enhancement of thermal conductivity can be affected by the alignment of nanoparticles with respect to the temperature gradient, which cannot be predicted by the classical models. These simulation results indicate that eDPD method can be a versatile method for studying thermal transport in heterogeneous materials and complex systems.     

Heat transfer simulation using energy conservative dissipative particle dynamics

Dissipative particle dynamics with energy conservation (eDPD) was used to investigate conduction heat transfer in two dimensions under steady-state condition. Various types of boundary condition were implemented to the conduction domain. Besides, 2D conduction with internal heat generation was studied and the heat generation term was used to measure the thermal conductivity and diffusivity of the eDPD system. The boundary conditions used include both the Neumann and Dirichlet boundary conditions. The Neumann boundary condition was applied via adiabatic surfaces and surfaces exposed to convection heat transfer. The DPD simulations were compared to analytical solutions and finite-difference techniques. It was found that DPD appropriately predicts the temperature distribution in the conduction regime. Details of boundary condition implementation and thermal diffusivity measurement are also described in this paper.     

Microphase separation of star-diblock copolymer melts studied by dissipative particle dynamics simulation

The microphase-separation behaviors of two types of star-diblock copolymers (A)₄(B)₄ and (AB)₄ are investigated through the dissipative particle dynamics (DPD). The simulated phase diagrams show similar ordered mesostructures as those of corresponding linear and cyclic ones, such as lamellas (LAM), perforated lamellas (PL), hexagonal (HEX) cylinders and body-centered-cubic (BCC) spheres, besides, a series of gyroid (GR) morphologies predicted by theoretical research have been identified. In the regions between the totally ordered and disordered phases, we have found some melted morphologies that can be thought as locally ordered, such as micelles (M), liquid rods (LR) and random network (RN), which have not been identified in relevant theoretical predictions. The simulated threshold for a totally ordered mesostructure to appear is higher than theoretical predictions, which can be ascribed mainly to the increasing fluctuation with finite chain length, and the star architecture can facilitate microphase separation, which is in agreement with the theoretical predictions. In addition, it is easier for the (A) _n (B) _n copolymers than for corresponding (AB) _n ones to trigger microphase separation under the same conditions. The relations between the root-mean-square radius of gyration (RMSGR) and the composition f _A in the two types of star copolymers are almost contrary, which can be attributed to the differences in their structural characteristics.     

Scaling behaviour of different polymer models in dissipative particle dynamics of unentangled melts

We present a dissipative particle dynamics (DPD) study of scaling behaviour for three polymer models. The scaling behaviour is explored for the conformational and dynamic properties of unentangled polymer melts. DPD employs a bead–spring model together with an aggressive coarse-graining to represent polymers at the mesoscale. The first model studied utilises a simple soft repulsion potential for the bead–bead interactions together with a harmonic spring potential to connect beads into a polymer chain. The second model differs from the first model by replacing the harmonic spring with a finitely extensible nonlinear elastic spring. The third model uses realistic coarse-grain potentials for the bead–bead, spring and bending interactions based on the iterative Boltzmann inversion procedure and it corresponds to a mesoscopic model of polyethylene. We systematically vary the chain length and spring constant (in the case of the first and second models), and simulate the conformational properties such as the end-to-end distance or radius of gyration, and dynamic properties such as the centre-of-mass self-diffusion coefficient or viscosity. The scaling of the conformational and dynamic properties with chain length (scaling laws) is compared with the Rouse theory, which is considered as a standard theory for unentangled polymer melts. The comparison shows that simulated scaling laws typically agree with the Rouse scaling laws for the DPD polymer models with more than 10 DPD beads. For the shorter DPD polymers, deviations from the Rouse theory exist and become significant for the dynamic properties, especially for the viscosity of the polymer melts.     

Predicting rheology of suspensions of spherical and non-spherical particles using dissipative particle dynamics (DPD): methodology and experimental validation

The rheology of non-dilute colloidal suspensions is a complex phenomenon and predictive numerical methodologies for it are still in the emerging phases. Dissipative particle dynamics (DPD), a particle-based numerical scheme for phenomena in the mesoscopic regime, has emerged as an attractive technique to tackle this problem. In this article, a practical methodology for using DPD for quantitative prediction of the rheology of non-dilute suspensions is presented and validated with focused, specific experiments. Some pertinent issues are highlighted to make DPD more amenable to being a computational tool for practical applications. The presence of solid particles of disparate sizes and non-spherical geometries poses special challenges. Methodologies to address them are presented with validations and efficient techniques are suggested to make them computationally amenable.     

Mesoscopic dynamics of colloids simulated with dissipative particle dynamics and fluid particle model

We report results of numerical simulations of complex fluids, using a combination of discrete-particle methods. Our molecular modeling repertoire comprises three simulation techniques: molecular dynamics (MD), dissipative particle dynamics (DPD), and the fluid particle model (FPM). This type of model can depict multi-resolution molecular structures (see the Figure) found in complex fluids ranging from single micelle, colloidal crystals, large-scale colloidal aggregates up to the mesoscale processes of hydrodynamical instabilities in the bulk of colloidal suspensions. We can simulate different colloidal structures in which the colloidal beds are of comparable size to the solvent particles. This undertaking is accomplished with a two-level discrete particle model consisting of the MD paradigm with a Lennard-Jones (L-J) type potential for defining the colloidal particle system and DPD or FPM for modeling the solvent. We observe the spontaneous emergence of spherical or rod-like micelles and their crystallization in stable hexagonal or worm-like structures, respectively. The ordered arrays obtained by using the particle model are similar to the 2D colloidal crystals observed in laboratory experiments. The micelle shape and its hydrophobic or hydrophilic character depend on the ratio between the scaling factors of the interactions between colloid–colloid to colloid–solvent. Unlike the miscellar arrays, the colloidal aggregates involve the colloid–solvent interactions prescribed by the DPD forces. Different from the assumption of equilibrium growth, the two-level particle model can display much more realistic molecular physics, which allows for the simulation of aggregation for various types of colloids and solvent liquids over a very broad range of conditions. We discuss the potential prospects of combining MD, DPD, and FPM techniques in a single three-level model. Finally, we present results from large-scale simulation of the Rayleigh–Taylor instability and dispersion of colloidal slab in 2D and 3D. Electronic supplementary material to this paper can be obtained by using the Springer LINK server located at http://dx.doi.org/10.1007/s00894-001-0068-3.Electronic Supplementary Material available.     

Dissipative particle dynamics simulation on the meso-scale structure of diblock copolymer under cylindrical confinement

The meso-scale structure of symmetric diblock copolymer under cylindrical confinement is studied by dissipative particle dynamics (DPD). The simulation results show that coiled cylindrical geometry is favored in the presence of larger cylinder radius (R/L ₀>～1.5), and the number of rings depends on the cylinder radius. Because of the cylinder wall's selectivity, each block can form the central core, but only the preferential block forms the outmost layer. An approximately linear relationship exists between structure transition point, which is approximately in proportion to the 3/5 exponential of chain length of copolymer and number of layers. As the cylinder radius is decreased, a helical morphology is found. Lamellae parallel to the underside of the cylinder appear when the cylinder radius is made smaller (R/L ₀ < ～1.1).     

Dissipative particle dynamics of non-spherical particles using a Gaussian density model

The Gaussian density molecular model has been adapted for dissipative particle dynamics. The model, when combined with a soft potential, is shown to be a very flexible mesoscale model exhibiting a wide range of phase behaviour. The soft potential allows relatively large time steps to be used and hence a more rapid equilibration. In addition, the model can be used to study both uniaxial and biaxial systems. We have undertaken a number of pilot studies and have demonstrated that the Gaussian model is able to identify nematic–isotropic phase transitions in liquid crystals and the formation of ordered discotic phases.     

A coarse-grained model for PCL: conformation,self-assembly of MePEG-b-PCL amphiphilic diblock copolymers

Poly-ε-caprolactone (PCL) is a biodegradable hydrophobic polyester that has been widely used in medical devices, tissue engineering and nanoparticle-based drug delivery. Coarse-grained molecular dynamics (CGMD) has been employed to study and gain insights into the conformational, structural and self-assembly behaviour of polymers, lipids and amphiphilic macromolecules. In this work, we developed a model for PCL within the framework of the MARTINI coarse-grained force field. The non-bonded interactions were based on the existing MARTINI bead types, while the bonded interactions were mapped onto a PCL rendition obtained from atomistic simulations. The model accurately reproduces the structural and dynamic properties of the PCL homopolymer and shows very reasonable temperature and solvent transferability. We also studied self-assembly of MePEG-b-PCL linear diblock copolymers using an existing MARTINI model for MePEG (Methoxy Polyethylene glycol), by analysing the critical micelle concentration (CMC), as well as the shape, size and morphology of the nano-polymeric micelles. We obtained excellent agreement of the CMC, while the size was under-predicted compared to experimental data. This robust model paves the way for CGMD modelling of PCL and serves as a starting point for future designs of PCL-related polymeric systems .     

Dissipative particle dynamics simulation of the relaxation behaviour of a triblock copolymer supramolecular network

Since block copolymers self-assemble into various nanostructures and these are widely used in soft materials such as cosmetics and paints, these continue to be the subjects of fundamental studies that progress new technologies. ABA triblock copolymers self-organise into supramolecular networks in which crosslinked structures change upon heating and other external stimulation. Supramolecular networks that consist of ABA triblock copolymers have three components: bridges, loops and dangles. These supramolecular networks have structural regions (clusters) in which end blocks of polymer chains are aggregated and connected by the internal blocks of the polymer chains. Despite of the importance of relaxation behaviour during the measurement and control of polymer materials, the molecular-level behaviour of these systems has not been addressed. We observed pull-out phenomenon that the ends of these polymers detach from clusters, and estimated characteristic detachment times by counting the number of detachments and compared it with the time of longest relaxation in that system.