Multi-scale Simulation Method Based On The Dissipative Particle Dynamics

Because of the long chain characteristics of polymers, the physical properties of which are multiscaled on both the length and the time scales. On different scales, there are a series of well developed simulation techniques, such as molecular dynamics (MD) and Monte-Carlo (MC) on the microscopic scale, dissipative particle dynamics (DPD), lattice Boltzmann method (LBM), dynamic density functional theory (DDFT), and field-theoretic polymer simulation (FTPS) on the mesoscale. These simulation methods are all focused on a specific scale, therefore it is an urgency to build up a multiscale simulation method that can simulate on a larger time and length scale and keep enough microscopic information simultaneously.The thesis is dedicated to develop the multi-scale simulation method of polymers: including bridging the gap between the micro- and the meso-scale and between the meso- and the macro-scale simulation techniques.(1) Micro- and meso-scale simulations are connected by mapping the RDF of the coarse-grained PE bead from the Lowe-Andersen temperature-controlling method (LA) onto the target one from detailed molecular dynamics simulation. LA is selected in this research because this method is fast, stable, and easy to tune for a better temperature control. In the first step by fitting the RDF, we obtain a modified numerical coarse-grained potential. This potential, substituting the analytical conservative potential originally used in LA, is updated iteratively until the two RDFs are consistent with each other within error. This numerical potential can be applied in larger systems and the properties of PE on the mesoscale can be obtained. Because the potentials are always coupled with one another, it is difficult to fit the RDFs when there are too many potentials to be operated in one system. The advantage of the present coarse-graining scheme is that there are only two kinds of potentials to be fitted, i.e., the nonbonded conservative potential and the bonded spring potential in a polymer chain, so it is easier to implement. After simulating the mesoscale PE systems using LA with the numerical coarse-grained potential, we can further fill the beads with atomistic details, i.e., do a fine-graining. By fixing bond lengths and bond angles, the atoms are regrown according to a scheme similar to Rosenbluth sampling. Because the system is already in equilibrium, only tens of picoseconds of MD run is needed to alleviate the local tension arising from the chain regrowing procedure. In this way one may fast equilibrate the system by mesoscale simulation and still keep its atomistic details in a fine-graining step. Finally the coarse-grained potentials are tested. We simulated the miscibility of the blends of LLDPE/HDPE and found that it conforms to the experiment result. We also investigated the scaling behavior of PE in bulk applying the coarse-grained potential and found that it still obeys the Rouse scaling.(2) Connection between the meso- and macro-scale simulation. (a) Macro-scale simulation of polymer melts is one of the most important scope of computational fluid dynamics. The differential equations goverening the flow behavior of fluids include the continuity equation controlling the mass conservation, and the momentum equation controlling the momentum conservation. When the physical properties, such as density and viscosity depend on the temperature, the goverening equations of fluid dynamics also include the energy equation controlling the conservation of energy. The goverening equations of fluid dynamics usually are a set of non-linear partial differential equations. They can only be sovled numerically in most of the cases. There exist many methods to solve the partial differential equations numerically, the finite difference method and finite element method are the most widely applied methods among them. Computational fluid dynamics is not an addition—it also often apply these two methods. The finite element method is based on variational principle(when the functional exists)or method of weighted residual and combine with the block approaching skill, forms the systematic numerical computing method. It is good at dealing with problems such as potential flux in complex geometry domains, and viscous incompressible and compressible flow problems. In this thesis we applied the finite element method to compute the momentum equation, i.e., the Navier-Stokes equation. (b) When calculating the governing equation of fluid dynamics by finite element method, the fluid in every element can be taken as homogenous. The fluid in each element is taken as the study object of meso-scale simulation, for example, the dependence of the shear viscosity on the shear rate derived from meso-scale simulation can be input in the finite element simulation in solving the Navier-Stokes equation, the distributions of velocity and pressure of the whole fluid can be obtained. Thus the connection between the meso- and macro-scale simulation can be established. (c) The fluid properties, such as viscosity, are obtaioned from meso-scale simulation by non-equilibrium simulation. By applying the Lees-Edwards periodic boundary condition in the equilibrium LA method, we get the non-equilibrium LA. Tuning the Schmidt number large enough so as to model the real polymer. (d) We are going to apply the coase-grained potential for PE in the non-equilibrium LA simulation to derive the shear viscosity of PE melt. Then we can get the informations about the velocity and the pressure distributions of PE melt by finite element calculating of the momentum equation. So the meso- and macro-scale simulations of polymers can be connected.(3) Isotropic-to-nematic transition simulation of polymers.Liquid crystals have been the subject of significant scientific and technological interest because of their''tunable''optical, rheological, and structural properties. The uniqueness of such properties derives from a combination of translational molecular mobility (fluidlike characteristic) and long range orientational order (solidlike characteristic). Liquid-crystalline (nematic, cholesteric, and smectic) phases of semiflexible polymers play an important role both in biological and in synthetic materials. Composite materials consisting of polymers and low molar mass liquid crystals have attracted much attention due to their applications in electro-optical devices and flat panel displays. For example, the main advantage of PDLC (polymer-dispersed liquid crystals) devices is their simplicity of operation. By matching the refractive index of the polymer and the ordinary refractive index of the LC (liquid crystal), PDLC films can be switched from a translucent"off"to a transparent"on"state by application of an electric field. Unlike more conventional LC displays, they require neither complex surface treatments, nor polarisers. Because of the good performance and wide application of the LC and composites consisting of LC and polymers, it is necessary to analyse the mechanism controlling the formation of them by computer simulations.We tried to simulate the isotropic-to-nematic transition of polymers on the meso-scale. In addition to the translational degrees of freedom we introduce the rotational degrees of freedom into the system. We applied the anisotropic potential, i.e., added an anisotropic attractive potential into the"soft"repulsive conservative potential of DPD model. The DPD thermostat will disturb the originally oriented beads, we therefore adopt the Brendsen thermostat. By doing so we can simulate the nematic transition of polymers. The mono-bead system are simulated and only local ordered domains are found. So this work is just at its beginning, there are a lot of problems to be settled. It can be applied to the homogeneous polymer system, or to the hetetogeneous copolymer system or polymer blends so that the competition between phase separation and nematic transition can be studied. Furthermore, this method can be combined with non-equilibrium simulation by applying a field to the system, which can manifest the field induced ordering in this complex system.