Coarse-graining scheme for simulating uniaxial stress-strain response of glassy polymers through molecular dynamics

Simulation of the deformation of polymers below their glass transition through molecular dynamics provides an useful route to correlate their molecular architecture to deformation behavior. However, present computational capabilities severely restrict the time and length scales that can be simulated when detailed models of these macromolecules are used. Coarse-graining techniques for macromolecular structures intend to make bigger and longer simulations possible by grouping atoms into superatoms and devising ways of determining reasonable force fields for the superatoms in a manner that retains essential macromolecular features relevant to the process under study but jettisons unnecessary details. In this work we systematically develop a coarse-graining scheme aimed at simulating uniaxial stress-strain behavior of polymers below their glass transition. The scheme involves a two step process of obtaining the coarse grained force field parameters above glass transition. This seems to be enough to obtain “faithful” stress-strain responses after quenching to below the glass transition temperature. We apply the scheme developed to a commercially important polymer polystyrene, derive its complete force field parameters and thus demonstrate the effectiveness of the technique.

Figure 1

(a) Chemical structure of the PS molecule along with the optimum structure of its all atom and united atom monomers; (b) Schematic representation of coarse grained PS.

Figure 2

United atom model of PS with labeled atoms to facilitate description of the detailed force field.

Figure 3

(Color online) (a) Variation in the specific volume $v_f$ with temperature for the united atom PS sample cooled from 500 to 100 K at $\dot{T}=1\text{K}/\text{ps}$. (b) Stress-strain response of the detailed sample at 100 K pulled in incompressible tension at a rate of $0.005{\text{ps}}^{-1}$. Deformed configurations at the strain marked by square symbols are superposed.

Figure 4

The (a) nonbonded force and (b) potential $\mathcal{U}\left(R\right)$ for the equivalent CG polystyrene obtained by the force matching technique.

Figure 5

The (a) normalized probability distribution $P_s\left(R\right)$ of CG bond lengths and (b) the corresponding Boltzmann inverted potential ${\mathcal{U}}_s\left(R\right)$ for CG bond stretching. Also shown is the fit using the harmonic potential.

Figure 6

Comparison between the nonbonded rdfs of the detailed and CG samples of PS contaning 14 chains of 80 monomer each.

Figure 7

Comparison of block averaged pressure variation at 500 K under $NVT$ control for a detailed and a CG sample, (a) before and (b) after simplex optimization.

Figure 8

Comparison of rdfs between the detailed and the simplex optimized CG samples.

Figure 9

Comparison between the stress-strain response of detailed and two CG polystyrene samples deformed at a rate of $0.005{\text{ps}}^{-1}$ at 100 K.