Frozen Topology: Entanglements Control Nucleation and Crystallization in Polymers

Chuanfu Luo and Jens-Uwe Sommer

Phys. Rev. Lett. 112, 195702 – Published 16 May 2014

Abstract

Polymer chains form lamellar structures during crystallization which display a memory of thermal history. Using molecular dynamics simulations and primitive path analysis, we show a direct dependence of both density and crystalline stem length on the local entanglement length. The slow relaxation of the entanglement state after a change of external conditions can directly explain the role of thermal history for polymer crystallization, in particular memory effects. The analysis of the local entanglement state can be used to predict the occurrence of nucleation events. Our results present a fresh insight of the nonequilibrium properties of polymer crystals which might be identified as “frozen topology” of polymer melts.

Received 27 January 2014

DOI:https://doi.org/10.1103/PhysRevLett.112.195702

Authors & Affiliations

Chuanfu Luo^1,* and Jens-Uwe Sommer^1,2

¹Leibniz-Institut für Polymerforschung Dresden, Hohe Strasse 6, 01069 Dresden, Germany
²Institut für Theoretische Physik, Technische Universität Dresden, Zellescher Weg 17, 01062 Dresden, Germany

^*luo@ipfdd.de

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Vol. 112, Iss. 19 — 16 May 2014

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Images

Figure 1
(a) Average density ( $\bar{ρ}$ ), average entanglement length ( ${\bar{N}}_{e}$ , weighted average, in number of monomers), and crystallinity ( $Φ_{c}$ ) during continuous cooling. Here, vertical dashed lines mark three characteristic temperatures: $T_{s} = 439 K$ (red) determined by the onset of crystallization, $T_{c} = 434 K$ (blue) determined by the peak position of heat flux, and $T_{e} = 429 K$ (black) at which homogeneous crystallization has finished and further increase of crystallinity is due to reorganization. (b) In situ correlation of $N_{e} (T)$ and stem lengths at three reference temperatures [ $d (T_{s})$ , $d (T_{c})$ , and $d (T_{e})$ ]. The red vertical dashed line marks $T_{s}$ . (c) In situ dependencies of $d$ and $ρ$ on $N_{e} (T_{s})$ . The color bars are shown on the top. The $x$ axis is the sorted $N_{e} (T_{s})$ , the entanglement length at $T_{s}$ (439 K, the red dashed horizontal line). (d) Stem length ( $d$ ) at different temperatures against the reference $N_{e}$ . This plot is a projected view of (c) at different $T$ . The horizontal and vertical dashed black lines mark the criterion of crystallized stems ( $d \geq 15$ is used to calculate the crystallinity) and the corresponding $N_{e}$ at the end of homogeneous crystallization ( $T_{e}$ ), respectively.
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Figure 2
(a) Snapshots of the crystallized stems and the contour profiles of less entangled regions ( $N_{e} \geq 60$ ) during the heating of a single crystal at 550 K (highly above the apparent melting temperature, 506 K, of this single crystal at a heating rate of $31.4 K μ s^{- 1}$ ). The images in the upper and lower panels are from two different viewpoints to give a better 3D understanding. The red stems are crystallized stems with $d \geq 15$ . The regions inside the green isosurfaces ( $N_{e} = 60$ ) are less entangled. (b) Temperature profile of the “self-seeding.” Here, the relaxation time and quench time are denoted as $t_{r}$ and $t_{q}$ . (c) Snapshots of the recrystallized stems during quench after different $t_{r}$ . Here, the red stems are the crystallized stems take from a certain quench time as marked on the top of each image. The green isosurfaces with $N_{e} = 60$ are taken from the initial single crystal ( $t_{r} = 0$ ) to show the memory effect. The different $t_{q}$ selected here are corresponding to the maximum memory effect during the quench. All 3D images are prepared by the software VMD [31].
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Figure 3
(a) Average entanglement length ( ${\bar{N}}_{e}$ ) and its self-correlation ( $X (N_{e})$ ) of the single crystal during the relaxation at 550 K. (b) Crystallinity ( $Φ_{c}$ ) and self-correlation of density [ $X (ρ)$ ] during relaxation. In both (a) and (b), the self-correlation is against to the initial state ( $t_{r} = 0$ ): $X (N_{e}) = σ [N_{e} (t_{r}), N_{e} (t_{0})] / σ [N_{e} (t_{r})] σ [N_{e} (t_{0})]$ and $X (ρ) = σ [ρ (t_{r}), ρ (t_{0})] / σ [ρ (t_{r})] σ [ρ (t_{0}]$ . Four different states after different relaxation time ( $t_{r}^{1} - t_{r}^{4}$ ) are selected to do following quenches, which are corresponding to the snapshots show in Fig. 2. (c) Memory effects of position and orientation during the quenches after four relaxation times ( $t_{r}^{1} - t_{r}^{4}$ ). Here, $m$ and $f_{2}$ are defined to measure the positional and orientational memory effects, respectively. The horizontal dashed lines are drawn to guide the eyes for nonmemory values of $m$ and $f_{2}$ . (d) In situ dependence of $d (t_{q}, N_{e} |_{t_{q} = 0})$ for quench simulations after different relaxation times ( $t_{r}^{1} - t_{r}^{4}$ ).
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