(599d) A Combined Model to Study Conductive Properties of Polymers with Atomic Resolution

Since certain polymers were first found to be able to conduct electricity, several applications have been implemented and many more envisioned. Applications include transistors, capacitors, Transducers, filters, sensors, displays, switches, etc. The two main advantages of organic conductors and semiconductors, over traditional metals or semiconductors, is their electronic and mechanical flexibility that makes it possible to tune their conductivity by, for instance, mechanically process them in a variety of ways in addition to regulating the level of doping. Paradoxically, their non rigid structure is a limiting factor for their conductivity, particularly conductivity is found to decrease with disorder. Most of the models for conductivity currently in use are analogous to known models for semiconductors, for instance, current densities are predicted to be proportional to mobility and charge carrier density as in regular solids. The connection between these macroscopic-type of variables and the local or nanoscopic nature of polymers is made through models for charge carrier mobility based on probabilistic theories that accounts for the charge transport as a hopping mechanism. In this type of models, charge carrier density is often represented by an effective value. Those models are certainly valid in the sense that they produce more than acceptable predictions for conduction in polymer, but they tend to overlook the atomic nature of the polymer in favor of a bulk-type of conduction what makes it more difficult to make a connection between the local properties and conductivity. HOMO-LUMO gap (HLG) and in general polymer electronic structure determines conductivity and photoconductivity in polymers. Molecular level simulations are able to predict the relationship between geometry and composition of polymers and their electronic properties, information that can be of great help to experimentalist in the design of polymer-based devices. In addition, many polymer-based devices are built by assembling polymers in a variety of configurations, thus it is important to address possible interference between polymers that may modify their performance. In this project we combine semiempirical methods and Density Functional Theory (DFT) to study the evolution of the electronic structure and geometrical configurations of different polymers with the number of units in the chain. PA, PAH, and MEH-PPV were studied. Energy levels predicted by each of the methods were plotted as a function of the polymer chain size that clearly shows the evolution from molecular levels to bands. The results above show that semiempirical methods provide a good estimation for the geometrical structure of polymer but they perform poorly when electronic structures are of interest. Particularly, energy of unoccupied levels is greatly overestimated and thus HLG is very poorly predicted. Comparison of the predicted HLG between semiempirical results and DFT results for short chains, show a good qualitative agreement, but semiempirical methods overpredict this properties by several eVs. This disagreement is unacceptable if we expect to be able to calculate conductive and photoconductive properties of polymer. DFT seems to asymptotically converge to the right results, when compared to experimentally available values. We have then a method that would allow calculation of a large chain but will not be accurate and a method which is accurate but will not work on large systems. Here we combined both methods using the fact that semiempirical do indeed produce accurate geometries. We first optimize the geometry at a semiempirical level and then use that geometry to calculate electronic structure at a DFT level. The figure below show results for PA, the hollow diamond, square and triangle show the results obtained when DFT was used after a geometry optimization done at a semiempirical level. The full circle shows the results for full DFT optimization. It must be pointed out that the simulation time decreased tremendously when both methods are combined, for the larger chains, the semiempirical optimization took about 30secs while the DFT electronic calculation took less an hour in all cases. The full DFT optimization took several hours (up to 14 hs in the worse case). The gain is obvious. Conductive characteristics are calculated in two steps. On one step a Green Function's approach, developed by one of the authors of this work for small molecules, is used to calculate current vs. voltage characteristics. Conduction through polymers is studied here using a Green's-function-based technique widely used to predict conductivity in small molecules. In order to study conductivity in molecules, molecules are usually attached to contacts, thus the first step is to obtain a Hamiltonian for the molecule extended by the addition of a few metallic atoms at each end (Extended Molecule). The atoms added to the molecule are of the atomic type in the contacts the molecule will be attached to. For simplicity, from now on we will refer as ?molecule's atoms? or ?polymer's atoms? those belonging to the molecule of interest, and ?contact's atoms? those added to it to represent the contacts. Notice that the interaction molecule-contact is at atomic level, from the molecular point of view, the contact is not just flat surfaces, but a group of atoms; in addition, a single molecule will bond to only a few atoms in the surface. Also notice that in many polymeric devices, polymers lie parallel to the contact surface and the conduction is perpendicular to the polymer backbone. In this work we will follow attachment strategies appropriate to each case. Polymeric devices are then modeled by using the hoping model implemented with a Monte Carlo technique. Parameters needed for the hoping model are obtained from the simulations using Green Function's formalism. Parameter for conduction along the backbone and interpolymer conduction are determined and used within the hopping model. A circle is thus closed, precise quantum mechanical calculations are conducted to obtain information on the electronic structure of small to medium size systems; this information is then fed into a Green Function's-based transport model that provides conductivity information needed for our Monte Carlo code able to produce conductive information in an entire device. As part of this work we will show a comparison with available experimental information or polymeric systems of interest. In addition to calculating conductive properties, predictions from the electronic structure calculations can be directly compared to experimental results; particularly, the HLG, a key factor determining activation threshold for photoconductors, can be directly compared with the band gap measured experimentally. It is also possible to predict the valence band width; although calculations are carried out at 0 K and important temperature dependant effect cannot be accounted for. In this presentation we will also show our prediction on the HLG for MEH-PPV that show to be within the optical range thus explaining absorption and emission within that range observed in experiment carried out by colleagues here at the Institute for Micromanufacturing.