Electrical properties of very simple systems can be calculated using NEGF. Is there a way to calculate the resistance (and other electrical properties) of a conjugated polymer, as a function of degree of polymerization (DP)?
Short answer: No.
First off, the degree of polymerization does not directly relate to the charge transport properties of conducting polymers (more below). You can find highly conductive oligomers.
Secondly, in my opinion, NEGF is not a suitable method to understand the charge transport in polymers. It works for nanoscale devices and molecular wires, but most polymer devices are on the ~100 nm to micron scale.
That's not to say that different oligomer and polymer lengths don't have different transport properties. Absolutely, different molecular weight polymers have different charge mobility, etc. The effects are usually due to a number of hard to characterize factors:
- Concentration of defects and traps
- Morphology of the film (e.g., higher MW might yield smoother or more ordered films)
- Polydispersity (e.g., broader MW distribution is often problematic)
- Effective conjugation length
The electronic structure of oligomers and conjugated polymers can be simulated fairly well using first-principals methods, including DFT. This can often predict components like the energy levels, band gaps, band dispersion, etc. for crystals and parameters for amorphous films such as the Marcus reorganization energy which is often related to the charge mobility in many of these materials.
What you usually find is that as a function of chain length, charges become more delocalized and the reorganization energy drops (increasing mobility). In reality, this trend should saturate, although most DFT methods incorrectly delocalize charges completely.
Also, most devices with conjugated polymers are amorphous or polycrystalline, making device performance predictions difficult. Transport is not usually band-like, but some form of variable-range hopping between chains or sites within a chain.