# Generalized Kinetic Monte Carlo Framework for Organic Electronics
## 3 kMC Framework for Organic Materials and Devices
### Modeling of the Organic Material
#### 3.1.2 Polymer Chains  
Organic materials used in organic devices can be distinguished into two separate categories, small molecules and polymers. Polymers are composed of repeating macromolecules called monomers forming long chains. One prominent example for polymers used in OSCs is poly(3-hexylthiophene) (P3 HT) [3]. In this section, we briefly emphasize the importance of the correct model of polymer chains in our kMC model and present the algorithm for the chain morphology generation. The spatial overlap of molecular orbitals leads to weaker bound and less localized electron states along polymer chains [50]. Therefore, charge transport along polymer chains, called intrachain transport, is faster than charge transport between two separate polymer chains, which we refer to as inter-chain transport [51; 52; 53]. [PERSON] et al. showed that crystallization of P3 HT increases the mobility [54]. [PERSON] et al. have demonstrated that the mobility strongly depends on the orientation of the micro-crystalline domains in semi-crystalline P3 HT [55; 56]. In situ grazing incidence X-ray scattering techniques can be exploited to gain information on the polymer crystallization and ordering [57]. Many present kMC models treat every site as an independent localized state, and charge transport to all of its neighbors is described with the same mechanism [6; 58]. Multi-scale simulation models combining molecular dynamics and kMC include the distance dependence and directionality captured in the coupling integrals calculated from MD simulations, but did not investigate the effect of polymer chains on mobility [42; 43]. [PERSON] et al. model single charge transport between crystalline regions based on kMC along a generated polymer chain and investigate the impact of the electric field on the single charge mobility [44]. However, the probability of leaving the chain is modeled with an effective, field-dependent exit rate and does not account for neighboring chains. To account for both inter-chain and intra-chain transport, it is necessary to generate a morphology in which all the sites belonging to a polymer chain are connected. The algorithm for the chain morphology generation is based on a self-avoiding random walk [59]. It starts at a random free site, a node that is not yet part of a polymer chain. Then, all free neighbors of the site are determined. Free neighbors are next-neighbors, which are not already part of another polymer chain. One of these free neighbors is randomly chosen and connected to the chain. Every node stores a link to the previous and next chain element. From this newly-added node, again, the free neighbors are determined, and one is added to the chain. This procedure is repeated until the desired chain length is reached or there are no longer any free neighbors. Then, a new free site is searched, and the next polymer chain is generated until the whole simulation box is filled with chains. In our model, we assume that the chain length in organic materials follows a Gaussian distribution. Therefore, the average chain length \(l_{c}\) and its standard deviation \(\sigma\) are necessary input parameters for the algorithm. The desired chain length for every single chain will then be calculated according to the Gaussian distribution function. Chain length and distribution can be measured experimentally using, e.g., gel permeation chromatography [60] or static light scattering [61]. According to [PERSON] and [PERSON] [51], the orientation of the polymer chains is of great importance for the overall transport characteristics of organic materials. Therefore, we account for a preferred direction and the amount of orientation of the polymer chains, including three distinguished chain models. Gaussian chains are flexible and show no preferred orientation. They are obtained by the random walk algorithm described above. Rigid chains are entirely directed polymers pointing in one direction.