Table 1 Potential functions and corresponding parameters of coarse-grained method Interaction Form Parameters Unit Bond k b = 6.96 (TT), k b = 6.16 (TM, MM) kcal/mol Å2 r 0 = 3.65 (TM), r 0 = 3.64 (MM) Å Angle k θ = 1.09 (TMT), k θ = 1.19 (TMM, MMM) kcal/mol θ 0 = 175.5 (TMT), θ 0 = 175 (TMM), θ 0 = 173 (TMM) Degree Non-bonded ϵ = 0.469 (TT), ϵ = 0.444 (TM), ϵ = 0.42 (MM) kcal/mol σ = 4.585 INK1197 research buy (TT), σ = 4.5455 (TM), σ = 4.506 (MM) Å r c = 15
Å (truncation radius) Carbon-CG bead 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. This process was used to construct five different polymer particles with different diameters ranging from 5 to 40 nm, indicated symbolically as D 5 through D 40. The specific details of each of the five particles are listed in Table
2. The largest particle contained over 0.4 selleck products million CG beads corresponding to about 3.6 million NVP-HSP990 atoms. Once the initial molecular structure of the CG models was established, each CG model was equilibrated for 200 ps in vacuum at T = 500 K using the Nosé-Hoover temperature thermostat and pressure barostat . After the equilibration process, the model particles were cooled down to 250 K, which is slightly lower than the glass transition temperature (280 K) of PE . The resulting average density of the models was 0.836 g/cm3, showing a good agreement Galeterone with the bulk density of linear PE (0.856 g/cm3) found in the literature [16, 20, 21]. Table 2 Characteristics of coarse-grained linear polyethylene particles Model name D 5 D 10 D 20 D 30 D 40 Number of CG beads 800 6,400 51,200 172,800 409,600 Number of molecules 4 23 256 864 2048 Diameter (nm) 5.00 10.13 20.40 30.09 40.33 Density (g/cm3) 0.854 0.822 0.805 0.846 0.833 Loading step per 20 ps (pm) 3.125 6.250 12.50 18.75 25.00 For comparison purposes, a bulk CG model of linear PE was constructed using the same potential function.
The model-building process of this bulk structure was similar to that of the particles, except that the template lattice was shaped in a cubic cell with three-dimensional periodic boundary conditions. After the same annealing process used for the spherical particles, the periodic cluster containing 20,000 CG beads reached the equilibrium simulation box dimensions of 11.8 × 11.8 × 11.8 nm3. Simulated uniaxial compression and tension deformations were applied to this model to determine the bulk elastic properties of the PE material. Figure 3 shows the virial stress-strain response from these simulations and the Poisson’s ratio for compressive strains. The Young’s modulus E of the material was calculated to be around 20 MPa for the strain range -0.1 ≤ ϵ ≤ 0.1, and the Poisson’s ratio ν was averaged as 0.