Stable in bulk low-temperature phases in the PE models used. We show the view of six neighboring chains in the projection onto a plane orthogonal to the chain axes. Radii of the balls are equal to van der Waals radii of the corresponding atoms (carbon, hydrogen, and “united” ones). At the top: T, M, and O phases present in the all atom PE model. At the bottom: T, M2, and O2 phases present in the UA PE model G4. In the UA PE model G1, there is only one monoclinic phase. It is close to the T phase of the model G4 in the arrangement of the chains, but all the chains are identically placed relative to the projection plane.
Definition of local setting angle α n for nth carbon (or united) atom in a zigzag chain (Sec. II F).
Structure of the phases observed in the sample [–C800H1600–]×30 during heating: orthorhombic (“herringbone” packing), monoclinic (“parallel” packing), and columnar (C). At the top, we present snapshots of the projections of six neighboring chains onto the plane orthogonal to chain axes. Only the bonds between carbon atoms are depicted. For the C phase, we used three different colors to separate neighboring chains. At the bottom, we present sketches of the phases. A line represents an average projection of C–C bonds in a chain, an arrow shows the direction from the nearest atom of the chain under the plane to the nearest atom above the plane. For the C phase, such representation is impossible, and we only denote the projections of centers of masses of the chains by crosses. The (average) periods of the lattices along the x and y axes are a and b. We also show the setting angle of a chain α.
Temperature dependence of the density of the sample [–C800H1600–] ×30. Different symbols indicate different phases appearing on heating. At high temperatures, there is an area of hysteresis where both the monoclinic and columnar phases exist on our time scale (<1000 ps).
Structure of the herringbone packing in the sample [–C800H1600–]×30 at different temperatures: projection of two neighboring chains having different setting angles onto the plane orthogonal to chain axes. We show only the bonds between atoms of carbon (C–C) and carbon and hydrogen (C–H).
Change of the lattice parameters a and b (Fig. 3) and the density of the sample [–C800H1600–] ×30 during the transition between the O and high-temperature M phases at T = 550 K. The initial state of the sample was the equilibrium state at the temperature T = 510 K.
The distribution of (local) setting angles in rotating molecules during the transition between the O and high-temperature M phases (between 100 ps and 400 ps at T = 550 K) in the sample [–C800H1600–] × 30. For this sample, the x-axis runs along the [1 0 0] crystallographic direction in the initial O lattice, as shown in Fig. 3 at the bottom.
Point topological structural defect of the chain rotation through ∼70°. The temperature of the sample [–C800H1600–] ×30 is 550 K. On the graph, we show the setting angles of the atoms belonging to a part of the sixth chain after 160 ps of heating (the initial state of the sample was at T = 510 K). The inset at the top displays a snapshot of the same part of the chain. For the sake of clarity, only carbon atoms and bonds between them are shown.
Time dependence of the longitudinal period of chains at different temperatures in the area of hysteresis at the phase transition from the monoclinic (M) phase to the columnar (C) phase in the sample [–C800H1600–] ×30. The initial states of the crystal are the M phase at T = 550 K (black lines) or the C phase at T = 600 K (grey lines). One can see that at T = 580 K there is no transition at available times (this is also true for T = 550 K, 560 K, and 570 K), while at T = 590 K and T = 600 K, one can observe the transition starting at 600 ps and 100 ps, correspondingly. Note that the rate of the transition itself is the same at both temperatures.
Time dependence of the position of the center of mass of one chain relative to the center of mass of the whole sample [–C800H1600–] ×30 at different temperatures.
Snapshots of one chain in the columnar phase in the united atom model (the sample G1[–A800–] ×30) (at the top) and in the all atom model (the sample [–C800H1600–] ×30) (at the bottom) at the temperatures T = 650 K and T = 600 K, correspondingly. On the left, we displayed a view along the chain. For both the models, only the bonds between united (or carbon) atoms are shown.
Comparison of the frequency distributions of the setting and torsion angles in the orthorhombic (O) and columnar (C) phases at T = 600 K in the sample [–C800H1600–] ×30. We put an orthorhombic sample equilibrated at T = 510 K into the thermostat at T = 600 K and observed a series of transitions to the monoclinic (during 100 ps) and then to the columnar (during the next 150 ps) phases. The plot shows the frequency distributions of the angles at t =10 ps (O phase) and t = 500 ps (C phase). The x-axis runs along the [1 0 0] direction in the initial O lattice.
The distribution of the (local) setting angles during the transition from the monoclinic phase to the columnar phase at T = 590 K (between the time moments t = 600 ps and t = 760 ps - see Fig. 9) in the sample [–C800H1600–] ×30.
The distribution of the torsion angles during the transition between the monoclinic phase and the columnar phase at T = 590 K (between the time moments t = 600 ps and t = 760 ps) in the sample [–C800H1600–]×30.
Distribution of the (local) setting angles during quick heating of the sample [–C20H40–]×120. For this sample, the x-axis was parallel to the crystallographic direction [1 1 0] (the axes are shown in Fig. 3), therefore the peaks of the distribution at lower temperatures are at −77° and 10°.
Domain structure (four domains of parallel packing) observed in the sample G4[–A80–] ×120 at T = 500 K. As in Fig. 3, we present snapshots of the projections of chains onto the plane orthogonal to chain axes (the xy plane); only the bonds between carbon atoms are depicted; and we draw the boundaries between domains.
Temperature dependence of the density of the sample G1[–A800–] ×30. The upper part of the curve corresponds to the monoclinic (M) phase, the lower onecorresponds to the columnar phase. The density jump is about 0.25%, but the transition is still of the first order. The inset shows the cross-section plane of the M phase in the model G1 at a low temperature. The arrows, as in Fig. 3, show the direction from the nearest atom of the chain under the plane to the nearest atom above the plane. We also show the setting angle of a chain α.
The temperature dependence of the distribution of the (local) setting angles α (Fig. 17) during the transition from the monoclinic to the columnar phase in the sample G1[–A800–] ×30.
Potentials of interactions between atoms in our all atom PE model (C-carbon, H-hydrogen).
Potentials of interactions between atoms in the UA PE models used. If we give only one numerical value for a parameter, it means that this value was adopted in both the models G1 and G4. Otherwise, we give the value for the model G1, and, in brackets, for the model G4. The force constants are close to those used in Ref. 29, the rigidity of torsion angles has the maximal reasonable value (see discussion in Sec. II B).
Summary of the PE crystalline samples simulated in the present article and in Refs. 20 and 27, and 35. Designation of a sample (the first column) includes the number of carbon (C) and hydrogen (H) (or united (A)) atoms in its chain (with one dash on the left and one dash on the right if the chains are “infinite” according to periodic boundary conditions, otherwise it is a linear alkane) and the number of chains in the sample. G1 or G4 means the set of geometric parameters used in the UA model (see Sec. II B). We list the temperatures (in K) at which the samples lose one or another positional order. The order along the chain axis is lost when the longitudinal diffusion of chains starts. At higher temperatures, the distribution of local setting angles becomes uniform, and the conformational order may also be lost. A dash means the absence of the corresponding disorder within the investigated temperature interval on the time scale used.
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