Crystallization of finite-extensible nonlinear elastic Lennard-Jones coarse-grained polymers

The ability of a simple coarse-grained finite-extensible nonlinear elastic (FENE) Lennard-Jones (LJ) polymer model to be crystallized is investigated by molecular dynamics simulations. The optimal FENE Lennard-Jones parameter combinations (ratio between FENE and LJ equilibrium distances) and the optimal lattice parameters are calculated for five different perfect crystallite structures: simple tetragonal, body-centered tetragonal, body-centered orthorhombic, hexagonal primitive, and hexagonal close packed. It was found that the most energetically favorable structure is the body-centered orthorhombic. Starting with an equilibrated polymer liquid and with the optimal parameters found for the body-centered orthorhombic, an isothermal treatment led to the formation of large lamellar crystallites with a typical chain topology: folded, loop, and tie chains, and with a crystallinity of about 60%–70%, similar to real semicrystalline polymers. This simple coarse-grained Lennard-Jones model provides a qualitative tool to study semicrystalline microstructures for polymers.

Figure 1

The top views of simple tetragonal (tP), body-centered tetragonal (tI), body-centered orthorhombic (oI), hexagonal primitive (hP), and hexagonal close-packed (hcP) are represented. The $c$ axis is perpendicular to the paper sheet. The yellow atom at the center of the lattices tI and oI, and the three additional atoms of the lattice hcP compared to hP are in the plane just above or below the reference plane at $\pm c/2$.

Figure 2

(a) Side and (b) top view of the energy landscape per monomers versus the potential parameter $\sigma$ and the crystallographic parameter $a/c$ for body-centered orthorhombic (oI) structure for $c=1{\sigma }_u$. For the sake of clarity, high energies are truncated to $25{\epsilon }_u$ (top left, yellow region). In this energy landscape a valley appears with an optimum configuration.

Figure 3

Bottom of the energy valleys versus the potential parameter $\sigma$ for all the structures.

Figure 4

Thermogram starting from perfect crystal for tP, tI, oI, and hP structures. Only the enthalpy for the temperature ranging from $T=2.5$ to $4{\epsilon }_u/k_B$ is plotted.

Figure 5

Evolution and convergence over time of mean square internal distances of polymer melts for the oI parameters (see Table 1). The colors blue, red, yellow, purple, green, and cyan from bottom to top, respectively, correspond to the relaxation time $2.5\times {10}^3{\tau }_u$, $3.5\times {10}^3{\tau }_u$, $4.5\times {10}^3{\tau }_u$, $5\times {10}^3{\tau }_u$, $2.5\times {10}^4{\tau }_u$, and $1.25\times {10}^5{\tau }_u$. The dashed line shows the mean square internal distances for the “classical soft chain” parameters used by Auhl et al. [69] for $\sigma =1{\sigma }_u$ and $\epsilon =1{\epsilon }_u$.

Figure 6

Thermogram ($T=3.3$ to $2.3{\epsilon }_u/k_B$, isothermal stage of $4.5\times {10}^5{\tau }_u$, then $T=2.3$ to $T=4{\epsilon }_u/k_B$) starting from equilibrated liquid phase for body-centered orthorhombic (oI), hexagonal primitive (hP), and simple tetragonal (tP) parameters.

Figure 7

Crystallinity evolution during $4.5\times {10}^5{\tau }_u$ at $T=2.3{\epsilon }_u/k_B$ for body-centered orthorhombic (oI) and hexagonal primitive (hP) parameters.

Figure 8

Radial distribution function of perfect crystal for all optimized perfect structures (given in Table 1). The colors blue, red, yellow, and purple associated with the ends of peaks’ circle, square, cross, and point, respectively, correspond to the oI, hP, tI, and tP structures. In the insets, a more detailed description of RDF around $2{\sigma }_u$ for oI, hP, tI, and tP structures (corresponding to the first nearest neighbors) is given.

Figure 9

Radial distribution function of crystals after quenching at $T=2.3{\epsilon }_u/k_B$ and $4.5\times {10}^5{\tau }_{\mathrm{u}}$ for oI (blue line) and hP (dotted red line) structures. The two distributions are very similar. The vertical lines correspond to the radial distribution function of a perfect crystal for oI (in blue with circle ends), hP (in red with square ends), and tP (in purple with point ends) as shown in Fig. 8. The two distributions are very similar. In the insets, a more detailed description of the radial distribution function around $2{\sigma }_u$ is given.

Figure 10

Crystal nucleation and growth for the oI system during the isothermal treatment at $T=2.3{\epsilon }_u/k_B$ (from top to bottom). In blue is the amorphous phase, and in orange the crystal phase.

Figure 11

(a) Side and (b) top view of the largest crystal with oI parameters. (c) Size of the same crystal; $D$ the thickness and $L=\left(L_1+L_2\right)/2$ the average width, during its growth.

Figure 12

Cross section of two close crystals with some examples of classical type of chains detected in semicrystal: folded, loop, tie and cilia (in blue). Here only the amorphous phase of classical type of selected chains is shown to facilitate reading of the figure. This structure was obtained at $T=2.3{\epsilon }_u/k_B$ after $4.5\times {10}^5{\tau }_u$.