Figure 1
2D illustration of a bead-spring network with characteristic defects highlighted: in cyan dangling structures and chains, in blue free structures and chains, in pink a secondary loop and in purple a primary loop. The cross-links are shown enlarged with a black border. The distribution of functionalities, end-to-end distances and defects are for illustration purposes only and do not necessarily represent a realistic polymer network [22].
Figure 2
Illustration of a slip-link in orange. The other colors serve as a reference of the surrounding polymer beads.
Figure 3
Illustration of a slip-spring in orange. The other colors serve as a reference of the surrounding polymer beads.
Figure 4
An illustration of the dangers of the common periodic boundary conditions for optimization procedures implemented in pylimer-tools: when strands are converted into single springs, if the strands are longer than half the box size, the springs might collapse (step 3) even if they should not have. To prevent this, the initial state is used to derive multiples of the box to be used as offsets when computing the spring lengths. In this example, the vector r1 from A to B would have an offset of negative one box length.
| NOTATION | DESCRIPTION | SYMBOL |
|---|---|---|
| ΦD | mass fraction of dangling chains | ΦD |
| Φel | mass fraction of network backbone | Φel |
| f | cross-link functionality | f |
| pgel | gelation point | pgel |
| p | extent of reaction | p |
| r | stoichiometric imbalance | r |
| wdang | dangling chain fraction | wdang |
| wsol | soluble chain fraction | wsol |
| COGNAC | COarse-Grained molecular dynamics program by NAgoya Cooperation [13] | |
| CP2K | CP (Car-Parrinello = ab initio MD) code for the new Millennium; note that CP2K [15] didn’t implement the CP method | |
| DPD | dissipative particle dynamics | |
| equilibrium shear modulus | stress relaxation modulus for a viscoelastic solid [52] | Geq |
| GROMACS | GROningen MAchine for Chemical Simulations [12] | |
| KG | Kremer-Grest | |
| LAMMPS | Large-scale Atomic/Molecular Massively Parallel Simulator [11] | |
| MC | Monte Carlo | |
| MD | molecular dynamics | |
| MEHP | Maximum Entropy Homogenization Procedure | |
| MMT | Miller-Macosko Theory | |
| OCTA | Open, flexible and expandable system OCTA [14] | |
| PBC | periodic boundary conditions | |
| PSP | Polymer Structure Predictor [20] | |
| SI | système international (d’unités) |