Multiscale simulations in organic electronics

In this case study I will mainly focus on a particular example of multiscale simulations in organic electronics. We have performed [1] computer simulation study of the temperature dependence of the dynamic disorder in the crystalline lamellar arrangement of the highly crystalline conjugated polymer, poly(2,5-bis(3- tetradecylthiophen-2-yl)thieno[3,2- b]thiophene), PBTTT-C14, and established a link between the microscopic ordering and the charge-transport parameters. The structure disorder has been characterized by three order parameters: dynamic order parameter, nematic order parameter and paracrystallinity. An abrupt decrease of the side-chain dynamic order, observed around 400 K, correlates well with a sharp increase of the backbone paracrystallinity, while all nematic and dynamic order parameters of the backbone as well as the unit-cell expansion along the π-stacking direction show a monotonic linear temperature dependence. The morphological disorder leads to broadening of distributions of the electronic coupling elements and site energies. The variation in electronic couplings was found to occur on a much faster time scale (hundreds of femtoseconds) than a typical time required for a single electron-transfer event. Hence, the electronic coupling elements were preaveraged before calculating electron-transfer rates. Site energies, by contrast, were found to change on a significantly slower scale and thus could be treated as static on the time scale of charge transport. Finally, the hole mobility, reproduces well the value measured in a short-channel thin-film transistor. Preaveraging the electronic couplings (due to their fast dynamics) leads to a factor of 5 increase in the average mobility. We came to the conclusion that, in order to secure polymeric organic semiconductors with large charge-carrier mobilities, it is not enough to have large electronic coupling averages. In addition, the fast time-scale dynamics of the polymers and, even more importantly, the small energetic disorder (which evolves on a much slower than the chargecarrier dynamics time scale) are desirable. From the point of view of chemical design, it should be noted that the alkyl side chains that are added for solubility purposes can affect the backbone paracrystallinity and hence increase the energetic disorder if they do not remain in a highly crystalline state. It is therefore important that both backbones and side chains maintain good crystalline order. In this study we have used a combination of several methods for different time and length scales, so that this case can be considered as an example of multiscale computer simulations: (1) reparametrisation of bonded degrees of freedom in atomistic force field (OPLS-AA) using DFT (B3LYP) for matching potential energy surfaces; (2) atomistic molecular dynamics (NPT, Gromacs) to calculate structure and dynamics; (3) Thole model to compute electrostatic + polarization contributions to site energies for molecules as found in the morphology (distributions of site energies); (4) semi-empirical ZINDO method to calculate distributions of electronic couplings; (5) correlations between these distributions and dynamic, nematic and paracrystallinity order parameters; (6) comparison of decay times of respective autocorrelation functions with typical charge transfer times (to average or not); (7) DFT (B3LYP) to calculate reorganization energies; (8) semi-classical Marcus charge transfer theory.

[1] Poelking C., Cho E., Malafeev A., Ivanov V., Kremer K., Risko C., Brédas J.-L., Andrienko D., J. Phys. Chem. C 117, 1633−1640 (2013).