PSI - Issue 23

Yoshitaka Umeno et al. / Procedia Structural Integrity 23 (2019) 348–353 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

349

2

1. Introduction

Polycarbonate (PC), one of engineering plastics most widely used, has various excellent features, e.g., tensile strength, impact strength, ductility, thermal resistance, transparency, etc. (Williams 1984) Hence, there are a wide variety of applications of PC, from structural components to optical devices. While it is known that the mechanical properties of polymers are strongly and complexly related to their microscopic structures, the nature of such relationship is still unclear even in the case of typical polymers including PC (Wu 1990, Berger 1991, Ward and Sweeney 2013). It is therefore important to thoroughly understand the origin of the eminent mechanical properties of PC, because such knowledge can be a guideline to design new polymers. Moreover, at the first step, it is necessary to grasp atomistic behaviors during deformation, which are potentially related to the macroscopic mechanical properties. Molecular dynamics (MD) simulations based on all-atom (AA) models or coarse-grained particle (CG) models are powerful tools to enable direct observation of dynamic process of fracture and deformation. In particular, CG-MD is a suitable approach for long-time or large-scale simulations of polymers if a proper CG model is available. In the present study, we developed a CG model for PC based on an AA model, and performed MD simulations of stress-induced deformation using the developed CG model. In the framework of CG model, a typical group of atoms is regarded as one particle. Since the CG approach reduces the degree of freedom, it can deal with larger time and spatial scale than the AA models. Figure 1 shows the molecular formula of PC. A PC molecule consists of three typical groups of atoms, i.e., carbonate (Particle A in Fig. 1), phenylene (Particles B) and isopropylidene (Particle C). In this study, we regard each of three groups above as one CG particle, which reduces 33 atoms in a PC monomer to 4 CG particles. This representation includes 2 types of bond, 3 types of bond angle and 2 types of dihedral for which the inter -particle interactions are to be determined. The CG model in this study gives the potential energy as the sum of interaction between bended particles, E intra , and non-bond interaction E inter . The bonds between particles (topology of molecule) are determined beforehand and that structure is kept during the calculation. The interaction between bonded particles E intra is given as:                     dihedral : 3 1 d :angle 4 2 0 a :bond 4 2 0 b intra 1 cos      n n m m m r l l l n K K K r r E , (1) n , r 0 and θ 0 are potential parameters to be determined. The interaction between non-bonded pair E inter is given as the sum of the Coulomb potential and 9-6 type Lennard-Jones potential: where r , θ and ϕ denote bond length, bond angle and dihedral angle, respectively. Constants K b l , K a m , K d 2. Simulation method 2.1. Development of CG Model

   

   

   

9                    6 LJ LJ 3 ij  ij  ij ij r r

q q

i j  

 

,

(2)

i j

E

2





ij 

LJ

inter

r

ij

where ¯ r ij and q i denote distance between non-bonded particles i - j and charge of particle i , respectively. Constants ε LJ and σ LJ are potential parameters. The potential parameters in Eqs. (1) and (2) were determined in order that the developed CG model can reproduce the simulation results obtained with an AA model as demonstrated in our former studies (Kubo and Umeno 2016 (1, 2)). To parametrize the bonding interaction (Eq. (1)), we performed all-atom (AA) MD simulations on a 64-mer PC single chain using the COMPASS force field model (Sun et al. 1994, Sun 1998). The non-bonding interaction (Eq. (2)) was optimized to reproduce the properties of the condensed phase, e.g. , the density at room temperature.