Recent work on hexabenzocoronene (HBC) derivatives and semi-triangular discotic molecules showed that classical MD simulations are of key importance in deter­mining the influence of structure and dynamics on the conductivity of DLCs [22—25]. MD simulations are capable of predicting the conductivity of the meso — phases and reveal how local conformation, disorder, and dynamics affect efficient charge-transfer along the one-dimensional column pathway. However, to realize the possibility for rational design of compounds with optimal structure-mobility rela­tionships, it is necessary to verify that the MD simulations describe the real liquid- crystalline phase correctly. DLC structures from MD simulations were successfully compared to experiments on lattice constants, density, phase-transition tempera­tures, order parameter, and mutual orientation (twist angle) in specific cases. Fur­thermore, a more thorough and efficient analysis such as Rietveld refinement of crystalline structures can be performed. HAT6 exhibits a rather limited charge — carrier mobility of about 10 4 cm2 V 1 s 1 as measured with pulse-radiolysis time — resolved microwave conductivity [26]. The question is to relate this to the much better mobilities in larger molecules such as HBC.

By comparing classical MD simulations with NPD measurements, and probing dynamics using QENS [27] along with considering the above first-principles DFT calculations (Sect. 6.3.1.1), we can go beyond the identification of the local molecular conformation, structural defects, and thermal motions in HAT6 by investigating and discussing their effect on the charge transport.

In the columnar phase, the neutron diffraction (ND) pattern of a discotic liquid crystal can be conveniently subdivided into three regions, as illustrated in the case of the neutron-diffraction pattern of deuterated HAT6 (Fig. 6.10, left).[7] The red area indicates a region with three sharp peaks originating from the two-dimensional hexagonal lattice, the (100) peak corresponding to an average column-column distance. The blue region originates from the broad distribution in tail-tail distances. The intra-columnar distances correspond to the broad yellow shoulder around 3.65 A. The tail-tail region and shoulder disappear almost completely for the fully — protonated sample. Thus, the shoulder represents intra-columnar distances between whole molecules rather than only the core-core separation.

The crystal structure predicted by the MD simulations[8] reproduces the three regions in the diffraction pattern (Fig. 6.11b). The dynamical behaviour of the liquid-crystalline phase is included in the comparison of the MD simulations with the experimental observations. The dynamic behaviour was included by calcu­lating the anisotropic displacements (Fig. 6.11b). The experimentally-observed

diffraction pattern is intermediate between the simulated patterns of the models. The order in intra-columnar distances and the intensity of the (210) peak is overestimated in both cases. Despite these differences, both the diffraction pattern of TWIST60 and TWIST25 show remarkable agreement with the experimental pattern, while the relaxed structures stem from entirely different starting config­urations (details of the models TWIST60 and TWIST25 are given in the caption of Fig. 6.10). Both models converge to comparable minima in configuration space, close to the actual liquid-crystalline structure, considering the agreement with the experimental diffraction pattern. The competition between the mutual van der Waals interactions of the cores with the steric repulsion of the tails causes a high disorder in the core-core distances, rather than a uniform shift of the core-core distance distribution to higher distances. The tails tend to orient toward the open spaces formed by these core-core defects, since the whole-molecule peak lies at a higher distance than the core-core peak. The inferred values of the twist-angle distribution are found to be around 36°, which is close to the to the DFT-estimated minimum-energy twist angle of 30° [28].

To characterize the dynamical processes on the picosecond timescale, the MD simulations are compared with QENS[9] experiments [27]. In the analyses of the experiments, it was consistently found that in addition to the elastic peak, at least two Lorentzian functions are required to fit the data. The peak widths corresponded to time scales of about 0.2 and 7 ps timescale. The incoherent-scattering function can be extracted from the MD simulation and compared with the measured function (Fig. 6.12, left). The agreement is satisfactory, and the essential observation is that the MD models compare well with the measured temporal and spatial dynamics (Fig. 6.12, right). By examining the simulation trajectories more closely the underlying thermal motions can be characterized. Further, the typical amplitudes of molecular motion on the 0.2 and 7 ps can be estimated.

Figure 6.13 illustrates the characteristic translational and tilt motions for a single molecule on the 0.2 ps timescale. The twist-angle deviations are negligible on this timescale with amplitudes smaller than 0.1°. Apparently, the tilt movement of the molecular core is too fast to be followed by the aliphatic tails. On the 7 ps timescale, the rotational motions are much more prominent: the aliphatic tails start to follow the rotations of the core. A step further towards the understanding of the hot carriers relaxation would be to follow closely the dynamics of both the core and tails at the vibrational level and investigate how the molecular vibrations in the ground and excited electronic-states behave.