The main feature of discotic liquid crystals is that they form columnar phases, where the molecules stack on top of each other and the columns arrange in a regular lattice. The self-organization into stacks with aromatic cores surrounded by saturated hydrocarbons results in predominantly one-dimensional charge transport within the core, along the columns. By modifying the periphery and the shape of the core it is possible to obtain materials with small charge trapping and recombination.

The spacial arrangement of stacks is, however, never perfect: the columns can be misaligned, tilted, or form various types of topological defects. In addition, the local alignment of molecules in columns can be different for different compounds, changing the overlap of the pi-orbitals and affecting the efficiency of the charge transport in a single column.

Using atomistic molecular dynamics simulations we study solid and liquid crystalline columnar discotic phases formed by alkyl-substituted hexabenzocoronene mesogens. Correlations between the molecular structure, packing, and dynamical properties of these materials are established.

Studied systems

All systems consist of a central flat aromatic core and six side chains. We considered several types of side chains: alkyl chains of different lengths, Cn, with n = 10, 12, 14, 16; branched side chains, C_(10-6); and dodecylphenyl-substituted PhC_12. In our simulation we adopt the united atom approach, and consider explicitly only the hydrogen atoms belonging to the aromatic rings of the central core, since the charge on these hydrogens is responsible for the multipole of the core of the molecule and the interaction of the side chains with aromatic cores is not important in the columnar phase.

Simulation snapshots

An equilibrated snapshot of one of the systems at T=400K. One can see that the aromatic cores are well aligned and the columns are arranged in an almost perfect hexagonal lattice, with the axially symmetric distribution of the side chains. At T=300K the columns are arranged in a rectangular lattice and the cores are also well aligned.

Mesophase Ordering

The two-dimensional radial distribution function g_xy has a large peak around r=0, which is because of the molecules in the same column. The other peak is due to the in-plane nearest neighbors and provides us with the lattice constant of hexagonal (or square) arrangement of the columns.

g_z(r) provides information about the arrangement of the molecules in the planes parallel to the director n, which in our case is the direction of the columns (along the z axis). In other words, g_z (r), is the probability to find a molecule at a distance (n*r) from the reference molecule. It has a series of narrow peaks, which indicates the ordered stacking of the molecules in the columns. For linear side chains the peaks are sharp and well-defined, with a constant distance between molecules in the columns. It is interesting that the separation is not affected by the length of the chain (of course, in the range studied).

Order parameter

The order parameter Q and the average tilt angle of the unit vector n (given by the projection onto the z-axis) The systems with linear side chains C10-C16 are well ordered: the order parameter is close to its maximum value, Q=1; in addition, there is no tilt of the molecules in the columns. The system with the dodecylphenyl-substituted side chains, PhC12, has slightly lower ordering (but still rather high, Q ~ 0.95, and a small average tilt of the molecules in the columns. Finally, the system with the branched chains, C_(10-6), has the worst ordering: the order parameter is quite low and varies much from column to column; there is also a significant tilt of the molecules in the columns.