Shear-induced martensitic transformations in crystalline polyethylene: Direct molecular-dynamics simulations

I. A. Strelnikov and E. A. Zubova

Phys. Rev. B 99, 134104 – Published 15 April 2019

Abstract

We carry out molecular-dynamics simulation of shear-induced martensitic phase transitions between the orthorhombic and nonorthorhombic (triclinic and monoclinic) phases of crystalline polyethylene (PE) in the framework of a realistic all atom model of the polymer. We show that the variation of the shear rate allows observing on a nanosample both a strongly nonequilibrium phase transition occurring by random nucleation and irregular growth of a new phase (“civilian” way, for rapid deformations) and the coherent, or “military,” kinetics (generally considered as usual for martensitic transformations). We induce transitions from the orthorhombic to the triclinic phase according to two transformation modes observed in experiment on PE single crystals. Rapid deformation favors the transition directly to the triclinic phase, slow deformation—first to the intermediate monoclinic, and only then—to the triclinic phase. The second way corresponds to the experiment on extended chain PE. We explain this result and analyze the competition between different transformation and plastic deformation modes. Rotations of PE chains around their axes necessary for the transition between the orthorhombic and nonorthorhombic phases are executed by short twist defects diffusing along the chains. The transition between the monoclinic and triclinic phases occurs through half-chain-period translations of the chains along their axes, mostly collectively, as crystallographic slips.

Received 25 January 2018

DOI:https://doi.org/10.1103/PhysRevB.99.134104

Physics Subject Headings (PhySH)

Crystal defects Crystal forms Nonequilibrium & irreversible thermodynamics Phase transitions

Macromolecules Single crystal materials

Molecular dynamics

Condensed Matter, Materials & Applied PhysicsPolymers & Soft Matter

Authors & Affiliations

I. A. Strelnikov and E. A. Zubova^*

N.N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, 4 Kosygin Street, Moscow 119991, Russia

^*zubova@chph.ras.ru

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Issue

Vol. 99, Iss. 13 — 1 April 2019

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Images

Figure 1
Crystalline lattices known in alkanes and PE: triclinic (T, $A 2 / m)$ , monoclinic (M, $P 2_{1} / m)$ , and orthorhombic (O, $P n a m)$ . We show the projection onto the $(x y)$ plane orthogonal to the chain axes. For the phases, we use the terminology by Kitaigorodskii [1] adopted in the book [2] by Wunderlich. We use the term triclinic for the T lattice because its unit cell (containing two ${CH}_{2}$ groups of one chain) is triclinic, although a monoclinic crystallographic cell containing four ${CH}_{2}$ groups (belonging to two neighboring chains) is often used for the description of this lattice, and it is the projection of this cell which is shown in the figure.
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Figure 2
Orientation relations of the parent and product phases in transitions between the M, T, and O phases. We show invariant planes (dashed lines) and shear directions calculated by method suggested by Acton et al. [19] for the lattices at 300 K in the Amber force field. Bracketed quantities are the magnitudes of shear $s$ for the modes $(s$ is equal approximately to the ratio of the shift of a molecule parallel to the invariant plane to the height above this plane). Here we showed only some particular modes, and (unlike Bevis et al. [18]) we numbered the modes dropping the unrealistic ones which do not shear all molecules to their correct positions.
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Figure 3
Setting of MD experiments (simulation of $O \to T$ transition according to mode O-T $T 2_{1}$ in a small sample). The plane orthogonal to $y$ axis is close to the invariant (shear) plane for mode $T 2_{1}$ . The upper “lid” (molecules on the gray substrate, which will not be shown on the subsequent figures) was fixed. The bottom “lid” (made of rigid molecules) was shifted in the direction of the $x$ axis (the gray arrow). The color of a molecule depends on its setting angle [the angle between the $x$ axis and the projection of the plane of the zigzag ...-C-C-C-... on $(x y)$ plane]. At the top of the figure: the first nucleus of the T phase (the blue chain within a square). At the bottom: the final stage of the deformation. We show (in gray) the boundaries between the parent O and the product T and M phases. Comparing the relative orientations of the unit cells of the phases one can see (Fig. 2) that the transformation modes are O-T $T 2_{1}$ for the T phase and O-M $T 3_{1}$ for the M phase.
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Figure 4
Structure of the samples in the process of phase transitions. The observed transformation modes are shown below every sample. (a) Rapid $O \to T T 2$ transition: competing T (mode $T 2_{1})$ and M (mode $T 3_{1})$ phases (sample with long chains). (b) “Regular” $O \to T T 2$ transition: “military” propagation of the T phase; the domain boundaries are advancing to the upper and bottom edges of the sample, parallel to the invariant plane of the transformation mode $T 2_{1}$ . (c) “Civilian” kinetics of the rapid $O \to T T 1$ transition: random nucleation and irregular growth of both the intermediate M and T phases. (d) The reverse $T \to O T 2$ transition at “regular” rate: parasitic M phase.
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Figure 5
Twiston accomplishing localized rotation of a PE chain through $90^{\circ}$ .
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Figure 6
Energies of defects in O lattice with parameters corresponding to 300 K. On the left: energies of T and M defects obtained under periodic boundary conditions with the chains consisting of 12 and $50 {CH}_{2}$ groups (in the samples with 12 and 48 chains correspondingly). In the first case, the transition path lies through rotation of the chain as a whole. In the second case – through generation of a pair of twistons which move in opposite directions. After the twistons have been created, the energy of the system rises linearly as one ${CH}_{2}$ group rotates after another. When all the groups have been turned, the twistons annihilate. On the right: the dependence of the minimum energy path on shear.
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