This concept is presented by Farmer and Macal in Figure 4.12 in Chapter 4, Platform Molecules, Introduction to Chemicals from Biomass, Second Edition, James Clark and Fabien Deswarte (editors), Wiley, 2015.
I've created my own so-called Farmer plot with a selection of molecules of interest to folks active in the bio-plastics and bio-chemicals fields:
You can see that the aromatics and straight-chain hydrocarbons all fall on the X-axis, as they have varying amounts of hydrogen but no oxygen. As they come directly from petroleum, and as the petroleum industry doesn't like oxygen, this makes sense.
Bio-based compounds, by and large, are found in the middle of the chart as they contain both oxygen and hydrogen in varying quantities. The interesting part is that a number of petrochemical intermediates, such as mono-ethylene glycol (MEG), polyethylene terephthalate (PET) or phenol, are also oxygenated even though they originate from a pure hydrocarbon such as ethylene. Oxygenating the hydrocarbon precursor presumably requires some effort which may not be insignificant, and presumably occurs as late as possible in the petrochemical process.
So it is worth asking why you would deoxygenate a biobased molecule (lignin or cellulose, for instance) all the way to ethylene, only to oxygenate it back to, say, PET. (You would also have to hydrogenate to get to ethylene, then dehydrogenate.) The alternative, which the various people making furan-based compounds from glucose have figured out, is simply to shift the short distance directly from the bio-based molecule to the target (for example, glucose to PEF, which is the furanic substitute for PET), avoiding a whole lot of de- and re- oxygenation and hydrogenation which would be required if going all the way to ethylene or another of the six platform hydrocarbon molecules first.
The plot above shows phenol from lignin (the red line), as opposed to phenol from a lignin-derived benzene molecule (the two blue lines). Arguably the total distance between two molecules on the graph is an indication of the relative difficulty of converting one molecule to the other. Of course some reactions are going to be easier than others, and more chemistry will be needed to evaluate exactly what effort is needed, but may I suggest that the following equation, which uses Pythagoras' Theorem to calculate the distance between two points in a plane, would be a very quick and dirty first pass at flagging complicated chemistry, with a large value of D an indication of potentially complex chemistry:
where H and O are the hydrogen and oxygen coordinates, respectively, of the bio-based and petroleum-based molecules. So in the case above, we have the following:
- D[SW lignin to Phenol] = 0.0965 (red line)
- D[SW lignin to Benzene] + D[Benzene to Phenol] = 0.2669 + 0.1707 = 0.4376 (two blue lines)
Both approaches lead from SW lignin to phenol, but the first path is shorter by a factor of about 4.5, and (obviously!) must be a lot simpler. Certainly, for the non-chemist managerial type such as myself, it would be a flag to highlight when more questions need to be asked of the chemists.
So a question for the chemists out there: while admitting that this approach is crude, is it a sensible first pass at estimating complexity of a chemical transformation? If not, why not? Discuss amongst yourselves and report back to the plenary session.