Hybrid Molecular Dynamics – Continuum Mechanics for Polymers.
TU Darmstadt, Darmstadt
[Ph.D. Thesis], (2012)
Final.pdf - Submitted Version
Available under Creative Commons Attribution Non-commercial No Derivatives, 2.5.
Download (5MB) | Preview
|Item Type:||Ph.D. Thesis|
|Title:||Hybrid Molecular Dynamics – Continuum Mechanics for Polymers|
The interaction of polymers and a solid surface modifies the polymer properties near the surface (the so-called interphase) in comparison to those of the bulk polymers. A clear explanation of the origin of this modification in the polymer properties is still missing. The aim of my PhD thesis has been the study of the mechanical properties of nanocomposite materials and the analysis of the behavior of polymers in the interphase region under deformation. Coarse-grained simulations have been performed for a model system of silica nanoparticles (NPs) embedded in atactic polystyrene (PS). In this case molecular details are important only in a small spatial region of the interphase. The rest of the polymer has bulk-like behavior which can be described by continuum mechanics. Therefore, it is convenient to simulate the region of interest by molecular dynamics (MD) and to treat the rest of the nanocomposite by continuum mechanics methods. To fulfill this we developed a new hybrid molecular – continuum simulation method for polymers. In our model the center of the simulation box is treated by MD. This region is surrounded by a continuum domain which is described by a finite element approach. To the best of our knowledge, the present work is the first attempt to use simultaneously MD and FE methods in simulations of polymers. It has been the main motivation of this work to develop a new hybrid scheme for polymers. Coupling a MD to a FE method requires a lot of modifications in both the MD and FE domains. The introduction of my thesis contains a short review on the existing hybrid schemes and modifications needed to couple the two domains. Difficulties to couple them such as transferring the information between two domains and equilibrating the continuum domain are explained. Different methods and techniques to overcome these difficulties as well as the advantages and disadvantages of each method are described briefly. These methods, however, are limited to liquid and crystalline solid materials. They have to be modified to be capable of simulating polymers. In the present PhD thesis we have explained the technical difficulties to couple a MD to a FE model for polymers in the MD domain and how we tackled these problems. Modifications in the FE domain have been done by researchers in the Applied Mechanics Department of the University of Erlangen. The current work has involved a strong collaboration with them to integrate a modified MD domain into a FE domain. In the second chapter of the thesis, the mechanical properties of a pure polystyrene matrix as well as a polystyrene matrix filled with bare silica nanoparticles are investigated by MD simulations at the coarse-grained level. The stress-strain curve of polystyrene has been computed for a range of temperatures below and above the glass transition. The Young’s modulus of polystyrene obtained from the stress-strain curve has been compared to experimental and atomistic simulation data. By studying the local segmental orientation and the local structure of the polymer near the nanoparticle surface under deformation, we have found that the segments close to the silica nanoparticle surface are stiffer than those in the bulk. The thickness of the interphase has been estimated. We have shown that the Young’s modulus of the studied nanocomposite increases by increasing the volume fraction of the nanoparticle. The results of interphase studies under deformation as described in this section are important input parameters for the FE simulations in the present hybrid scheme; this will explained in chapter four. In hybrid simulations the usual periodic boundary conditions of MD cannot be used as the MD domain is surrounded by a FE domain. In hybrid schemes boundary conditions should allow an information transfer through the boundary region between two domains. Therefore, I developed new non-periodic boundary conditions, so-called stochastic boundary conditions (SBC), which are able to transfer information (forces and deformations) between the two domains and to minimize the artifacts in the dynamics. In the SBC ensemble we have defined a set of auxiliary particles, so-called anchor points, in the boundary region. The anchor points are harmonically coupled to the MD particles. They play an important role to transfer the information between the MD and FE domains. Particles in the boundary region are forced to mimic the bulk behavior by employing a stochastic dynamics in the boundary region. This minimizes the artificial influence of the anchor points and the vacuum on the polymers in the center of the box. The SBCs are explained in more detail in the third chapter. We have validated these boundary conditions by comparing the results of coarse-grained polystyrene melts under nonperiodic and regular periodic boundary conditions. Excellent agreement is found for thermodynamic, structural, and dynamic properties. The new hybrid molecular – continuum method for polymers is explained in more detail in chapter four. Due to the significant difference between the time steps in the two domains, we employed a staggered coupling procedure in which the continuum domain has been described as a static region while the MD domain has been treated dynamically. The Arlequin method has been used for the static coupling of the MD to the FE domain. The information transfer between them has been realized in a coupling region which contains the above mentioned anchor points. In this region two descriptions are valid, i.e., the particle and the continuum one. The total energy is blended by a weighting factor. Atactic PS and a PS silica nanocomposite have been simulated in a coarse-grained representation to validate the new hybrid scheme. The deviations between data from the hybrid method and pure FE simulations have been computed for quantities such as reaction forces and the Cauchy stress. The sources of the observed deviations are discussed in some detail. Finally, the fifth chapter summarizes the results obtained in this PhD work, and discusses possibilities to extend the current hybrid model to new problems such as larger deformations.
|Place of Publication:||Darmstadt|
|Classification DDC:||500 Naturwissenschaften und Mathematik > 540 Chemie|
|Divisions:||07 Fachbereich Chemie
07 Fachbereich Chemie > Physical Chemistry
|Date Deposited:||15 Feb 2013 10:18|
|Last Modified:||15 Feb 2013 10:18|
|Referees:||Müller-Plathe, Prof. Dr. Florian and van Der Vegt, Prof. Dr. Nico and Thiele, Prof. Dr. Christina Marie and Brunsen, Jr. Prof. Annette|
|Refereed:||3 December 2012|