Size-dependent mechanical behavior of nanoscale polymer particles through coarse-grained molecular dynamics simulation

Table 1 Potential functions and corresponding parameters of coarse-grained method

Interaction	Form	Parameters	Unit
Bond	$E = \frac{1}{2} k_{b} {(r_{b} - r_{0})}^{2}$	k_b = 6.96 (TT), k_b = 6.16 (TM, MM)	kcal/mol Å²
Bond	$E = \frac{1}{2} k_{b} {(r_{b} - r_{0})}^{2}$	r₀ = 3.65 (TM), r₀ = 3.64 (MM)	Å
Angle	$E = \frac{1}{2} k_{θ} {(θ - θ)}^{2}$	k_θ = 1.09 (TMT), k_θ = 1.19 (TMM, MMM)	kcal/mol
Angle	$E = \frac{1}{2} k_{θ} {(θ - θ)}^{2}$	θ₀ = 175.5 (TMT), θ₀ = 175 (TMM), θ₀ = 173 (TMM)	Degree
Non-bonded	$E = (\frac{27 ϵ}{4}) [{(\frac{σ}{r})}^{9} - {(\frac{σ}{r})}^{6}]$	ϵ = 0.469 (TT), ϵ = 0.444 (TM), ϵ = 0.42 (MM)	kcal/mol
		σ = 4.585 (TT), σ = 4.5455 (TM), σ = 4.506 (MM)	Å
		r_c = 15 Å (truncation radius)
Carbon-CG bead	$E = - \frac{A}{r^{6}}$	A = -583.81 (CT, CM)	kcal/mol
		r_c = 10 Å (truncation radius)

T is a CH₃-CH₂-CH₂- bead, and M is a -CH₂-CH₂-CH₂- bead. The potentials (CT and CM) between carbon atom and CG bead are for the contact of the polymer particle with the loading plates.