Cross sections of n-alkane solid phases viewed down the molecular c axis with a and b axes as shown (red, first subfigure). Colored lines show molecule orientation (average projection of C-C bonds onto a-b plane). Color is based on Ising (light/dark) and Potts (red/green/blue) states discussed in Sec. II. (a) Orthorhombic herringbone crystal. (b) Monoclinic crystal. (c) Orthorhombic RI phase. (d) Hexagonal RII phase. (From Ref. 6.)
Lattice labeling scheme for hexagonal array of molecules.
Potts, Ising, and monoclinic order parameters versus temperature during a heating scan, as described in main text. White and gray shading indicates approximate region of stability of observed phases (orthorhombic, monoclinic, RI, RII).
Potts, Ising, and monoclinic order parameters versus temperature during a cooling scan, as described in main text. White and gray shading indicates approximate region of stability of observed phases (monoclinic, RI, RII).
In-plane orientations and molecular positions for typical configurations of observed phases in temperature scans on heating [(a), orthorhombic; (b), monoclinic; (c), RI; (d), RII] and cooling [(g), RII; (f), RI; (e), monoclinic].
Typical snapshot of a single row of molecules in the (a) orthorhombic, (b) monoclinic, (c) RI, and (d) RII phases. Alternating hydrogens have been colored green and blue to highlight molecular twisting.
Joint probability distribution P(θ, Δz) for azimuthal angles θ (radians) and vertical displacements Δz (nm) for the (a) orthorhombic, (b) RI, and (c) RII phases. Note the expanded Δz scale in (a).
(a) Definition of orientation angles θ1 and θ2 relative to separation vector r 12 between monomers at the same height on neighboring molecules. (b) Left, example “head-to-tail” favorable arrangements; right, corresponding favorable ranges of orientation angles. (c) Left, example “head-to-head” collisions between hydrogens at same z coordinates (solid against solid, or transparent against transparent); right, corresponding unfavorable range of orientation angles.
Intensity plot of frequency of occurrence (red = low, violet = high) of relative orientation angles θ1 and θ2 for neighboring molecules (see Fig. 8 for definition of θ1 and θ2) for (a) orthorhombic, (b) monoclinic, (c) RI, and (d) RII phases. Black dots are expected arrangements for ideal phase geometries. In (c) and (d), reddish regions indicate avoidance of “head-to-head” collisions between hydrogens on neighboring molecules.
In-plane Potts correlation function C(r) versus distance r (in units of near-neighbor separation) at the RII–RI transition on cooling (T = 327 K).
Correlation length ξ(T) versus temperature T on cooling, in units of the near-neighbor distance.
Simulation results for scattering intensity log (S(q)) from orthorhombic, monoclinic, RI, and RII phases. 110, 200, and 210 peaks are marked for the orthorhombic crystal phase. Curves offset for clarity, with temperature increasing from bottom to top.
Energy per molecule U for systems heated (red) and cooled (blue) at 4 K/ns. Lines along the top axis indicate, from left to right, experimental transition temperatures crystal–RI, RI–RII, and RII–melt.
C23 phase transition temperatures on heating and cooling from simulation and experiment.
Heat capacity c p in kJ/(mol K) for simulated phases, from fitting U vs. T on heating, over the temperature range T fit (Kelvin), versus experimental c p values at temperatures T exp . (See Ref. 7.)
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