Ben Hoffman, a student in my group, reported Monday on a Nature Materials article (link here, subscription required) that combines optical spectroscopy, carrier mobility, and X-ray diffraction measurements to help understand how strongly disordered polymer films transport charge.
I consider disorder to be the most intellectually interesting aspect of organic electronics so having this paper presented was high on my list of priorities for the journal club. In almost any organic film, relatively weak intermolecular interactions lead to a low energetic cost for creating defects, polymorphs, etc. In the extreme case, organic solids may be essentially amorphous glasses. However, even in the case where materials are semicrystalline (or have semicrystalline regions) disorder is crucial to consider for modeling charge transport. Seminal work by Bassler showed how it can impact the electric field and temperature dependence of carrier mobility. Noriega and Salleo, two authors of the paper from Monday, have a pretty good book chapter on these topics in chapter 3 here. In addition, a longer review aimed at a theoretical audience is given by Tessler. Baldo and Forrest and later Burin and Ratner illustrated important impacts of disorder on charge injection at contacts.
The paper presented this week touches on most of the important concepts relating to disorder in solids. This includes the idea (that I love) that a simple 1D tight binding model can be used as an insightful tool to study disordered solids. If you allow the tight binding matrix elements to be random, you recover important results such as eigenvector localization and "gap states" as shown for a specific case in Figure 3 of the paper.
This paper introduced me to the concept of "paracrystallinity" (compare with paramagnetism). This is essentially a measure of the statistical spread in lattice spacings in a disordered solid. For example, on a 1D lattice, if the site spacings are pulled from a Gaussian statistical distribution with mean a and standard deviation s, then the paracrystallinity is s/a (see work from some of the same authors in ref 32).
Overview:
The motivation for this paper is a set of recent observations indicating that even strongly disordered polymeric solids can have quite high field effect mobilities (1cm2/Vs or larger). How can this be since strong disorder is known to lead to "localized" wave functions that don't transport charge very well? This is mysterious enough that Nature Materials published a perspective article accompanying the paper that Ben presented this week.
The answer, supported in part by the paper Ben presented, may be that transport is dominated by charge motion along the polymer backbone. Polymer materials with high molecular weight are strongly disordered but have lots of long backbones for good transport. This invokes the usual picture of conjugated polymers as "molecular wires".
Methods:
The paper begins with an optical and optoelectronic study of mixtures of pre-aggregated regioregular P3HT with regiorandom P3HT. Particular attention is paid to electroluminescence spectroscopy since this measurement requires the motion of polarons injected electrically from contacts (i.e. like an OLED) which then recombine to give off light.
It then illustrates a tight-binding calculation for paracrystalline pi stacks of P3HT. This consists of diagonalizing a fairly large random matrix and evaluating the statistical distribution of eigenvalues and eigenvector decay lengths. It uses DFT results as input for the tight-binding matrix elements. (this is the downside of tight-binding: you need additional inputs from either experiment or first-principles theory to get any numbers out).
Finally, the paper uses a somewhat non-standard (but internally validated) method of extracting paracrystallinity from diffraction peak widths. This sounds trivial but is really the bane of diffraction people studying organics. It is really hard to deconvolve intrinsic disorder from domain size effects, as I understand it. Typically one uses higher order diffraction peaks, but this is not always possible with polymer films so the authors had to do something slightly different. I do not understand this and have not yet had the motivation to work at it.
Results:
The paper opens with a stunning result: In a blend that is 90% disordered P3HT and 10 % aggregated P3HT electroluminescence ONLY occurs from the aggregated material at low currents (~ 1mA). A weak electroluminesence from the disordered matrix occurs only at large currents. By contrast, photoluminesence occurs from all of the regions.
I have the following view of what happens, which I admit was hard to extract directly from the paper: We see in Figure 1a that EL from neat RRa films occurs even at the low current of 1 mA. To explain Figure 1b (90:10 RRa:RR mixture) we have to say that transfer from RRa to RR is quite efficient, but that when it happens the recombination rate in RR is high enough that most emission occurs from there. (i.e. charges are more likely to recombine that to go back to the RRa domain - this is the barrier to charges moving back to RRa that the paper mentions).
Next the paper moves on to apply the well-known (see Ch. 11 of Plischke and Bergerson) 1D disordered tight binding model to the case of P3HT pi stacks. They show that the usual results of strongly localized gap states are obtained for values of paracrystallinity approaching 10%, implying essentially amorphous material.
The final results are a new study of different P3HT films and an extensive survey of the polymer electronics literature that correlates disorder (extracted from WAXS line shapes) with molecular weight (MW) and also carrier mobility with molecular weight. Both paracrystallinity and mobility start to saturate at about the same MW. This suggests a dominant role for long conjugated chains in providing electrical connections across a polymer device.
Nevertheless, the penultimate section of the paper is called "paracrystallinity governs charge transport". How do we reconcile this with Figure 4 where the causal variable seems to be MW ? I think this section is pointing out that disorder and paracrystallinity still plays a significant role in determining activation barriers to charge migration. It is still clear, despite this caveat,that the key to good mobility in dosordered materials is the necessity of long conjugated chains to interconnect aggregates across the film. The barrier part is relatively minor in comparison.
I happen to be very interested in small molecules and the authors include one case (TIPS-pentacene) in their survey of paracrystallinity to show that a "monomeric" film has small paracrystallinity. It is important to note that this material has a field effect mobility of more than 1cm^2/Vs in solution-cast FET's. This is far from the mobility trend for polymers in Figure 4. The whole mechanism of backbone transport is NOT operative for such a material and so the picture encoded in the correlations in Figure 4 doesn't capture much about transport in small molecules, as far as I can tell.
Conclusions:
The paper concludes that high molecular weight polymers exhibit increased disorder, but also increased carrier mobility. This is attributed to very mobile transport along conjugated chains. An important by-product of this conclusion is that pi stacking is NOT necessarily the crucial determining factor in charge carrier mobility for polymer films. One can have very good mobilities with very poor pi stacking if transport along polymer backbones is efficient. The authors are careful to remark that " no single microsctructural feature is entirely responsible for electronic performance". However, I consider the diminished impact of pi-stacking an important conclusion that needs to be considered. Ade group members have commented to me that this idea has been floating around the polymer world for a while.
Criticism:
The data in Figure 1 is extremely interesting, but I cannot identify a clear connection to the conclusions about molecular weight and the message of the rest of paper. The new result really seems to be that rapid charge migration from RRa to RR occurs (but not the reverse due to rapid recombination in RR).
Conclusive results related to the main message of the paper would need to expand Figure 1 to consider the effect of molecular weight on the EL physics (similar to the MW study for P3HT in Figure 4).
As usual, I hope for comments on this article.
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