Example of possible structure of the hybrid models for polyethylene (top) and polystyrene (bottom) chain: the black filled circles represent the centres of mass of the coarse-grained beads while the black filled triangles represent the position of the virtual sites in the atomistic fragment of the polymer chain. In this example the polymer chain is formed by six coarse-grained (solid line) and four atomistic (dotted line) resolved monomers (i.e., and ). The labels i, j, l, and l ′ indicate the particles involved in the bonded force field interactions (see Eq. (2) in the text).
End-to-end distance (Ree) (a) and radius of gyration (Rg) (b) for the polystyrene hybrid models PS-1 (black), PS-2 (red), and PS-3 (green). The dashed and dotted lines refer to the mean value obtained from the AA and CG model, respectively.
End-to-end distance (Ree) (a) and radius of gyration (Rg) (b) for the polyethylene hybrid models PE-1 (black), PE-2 (red), and PE-3 (green). The dashed and dotted lines refer to the mean value obtained from the AA and CG model, respectively.
Comparison between intra-radial distribution function (RDF). g(r), obtained for the pure atomistic and the hybrid model. The intra-RDF of the hybrid simulation is calculated by considering only the atomistic part in each chain. From top to bottom: (a) polystyrene (PS-1 only), (b) polyethylene (PE-1 only). The blue solid line indicates the pure atomistic model. The red dashed line indicates the hybrid model.
Mean squared internal distance calculated for the pure coarse-grained model (solid blue line), PE-1 and PS-1 model (black, dash-pointed line), PE-2 and PS-2 (dashed red line), and PE-3 and PS-3 (green pointed line). From left to right: (a) polystyrene, (b) polyethylene.
Comparison between inter-radial distribution function (RDF), g(r), obtained for the pure coarse-grained and the hybrid model. The inter-RDF of the hybrid model is calculated by coarse-graining the atomistic part of each chain. From the top (a) polystyrene (PS-1 only), (b) polyethylene (PE-1 only). In the plot the blue solid line indicates the pure CG model, the red dashed line indicates the hybrid model.
Intra and inter-radial distribution functions g(r) calculated on the hybrid models (PS-1 (a), PE-1 (b)) between virtual sites and all the coarse-grained sites (red line), all coarse-grained site and all coarse-grained sites (green line), beads and all coarse-grained sites (blue line).
The IBI coarse-grained potential between polystyrene beads (dotted red line) and polyethylene beads (solid blue line).
Numerical density profile across the simulation box along the x-axis calculated separately for the coarse-grained beads (blue diamonds) and virtual sites (red circles). The results refer to the PS-2 (a) and PE-2 (b) model.
Particle number (N) fluctuation across the simulation box along the x-axis for pure atomistic (red circles), pure coarse-grained (blue diamonds) and hybrid (green triangles) model of polystyrene PS-2 (a), and polyethylene PE-2 (b). For the hybrid model both CG beads and virtual sites have been included in the calculation. The results obtained for the full atomistic model have been obtained from a trajectory of 16 ns and 10 ns, respectively, for polystyrene and polyethylene.
List of systems simulated in this work. In the table: Nm AA and Nm CG represent, respectively, the number of atomic and coarse-grained resolved monomers per chain.
Radius of gyration (Rg) and end-to-end distance (Ree) of the various systems simulated. The averaged values have been calculated over the last part of the trajectory.
Article metrics loading...
Full text loading...