Nullius in verba (take nobody's word) is the motto of the Royal Society, and it should be the motto of every scientist. The problem is, it is not. An alternative way of expressing this comes from Aristotle: the fallacy ad verecundiam. Just because someone says so, that does not mean it is right. We have to ask questions of both our logic and of nature, and I am far from convinced we do this often enough. What initiated this was an article in the August Chemistry World where it was claimed that the “unexpected” properties of elements such as mercury and gold were due to relativistic effects experienced by the valence electrons.
 
If we assume the valence electrons occupy orbitals corresponding to the excited states of hydrogen (i.e. simple solutions of the Schrödinger equation) the energy E is given by E = Z²E_o/n²h². Here, E_o is the energy given by the Schrödinger equation, n gives the quanta of action associated with the state, and Z is a term that at one level is an empirical correction. Thus without this, the 6s electron in gold would have an energy 1/36 that of hydrogen, and that is just plain wrong. The usual explanation is that since the wave function goes right to the nucleus, there is a probability that the electron is near the nucleus, in which case it experiences greater electric fields. For mercury and gold, these are argued to be sufficient to lead to relativistic mass enhancement (or spacetime dilation, however you wish to present the effects), and these alter the energy sufficiently that gold has the colour it has, and both mercury and gold have properties unexpected from simple extrapolation from earlier elements in their respective columns in the periodic table. The questions are, is this correct, or are there alternative interpretations for the properties of these elements? Are we in danger of simply hanging our hat on a convenient peg without asking, is it the right one? I must confess that I dislike the relativistic interpretation, and here are my reasons.
 
The first involves wave-particle duality. Either the motion complies with wave properties or it does not, and the two-slit experiment is fairly good evidence that it does. Now a wave consistent with the Schrödinger equation can have only one frequency, hence only one overall energy. If a wave had two frequencies, it would self-interfere, or at the very least would not comply with the Schrödinger equation, and hence you could not claim to be using standard quantum mechanics. Relativistic effects must be consistent with the expectation energy of the particle, and should be negligible for any valence electron. 
 
The second relates to how the relativistic effects are calculated. This involves taking small regions of space and assigning relativistic velocities to them. That means we are assigning specific momentum enhancements to specific regions of space, and surely that violates the Uncertainty Principle. The Uncertainty Principle argues the uncertainty of the position multiplied by the uncertainty of the momentum is greater or equal to the quantum of action. In fact it may be worse than that, because when we have stationary states with nh quanta, we do not know that that is not the total uncertainty. More on this in a later blog.
 
On a more personal note, I am annoyed because I have published an alternative explanation [ Aust. J. Phys. 40 : 329 -346 (1987)] that proposes that the wave functions of the heavier elements do not correspond exactly to the excited states of hydrogen, but rather are composite functions, some of which have reduced numbers of nodes. ( The question, “how does an electron cross a nodal surface?” disappears, because the nodes disappear.) The concept is too complicated to explain fully here, however I would suggest two reasons why it may be relevant.
 
The first is, if we consider the energies of the ground states of atoms in a column of elements, my theory predicts the energies quite well at each end of a row, but for elements nearer the centre, there are more discrepancies, and they alternate in sign, depending on whether n is odd or even. The series copper, silver and gold probably show the same effect, but more strongly. The “probably" is because we need a fourth member to be sure. However, the principle remains: taking two points and extrapolating to a third is invalid unless you can prove the points should lie on a known line. If there are alternating differences, then the method is invalid. Further, within this theory, gold is the element that agrees with theory the best. That does not prove the absence of relativistic effects, but at least it casts suspicion.
 
The second depends on calculations of the excited states. For gold, the theory predicts the outcomes rather well, especially for the d states, which involve the colour problem. Note that copper is also coloured. (I shall post a figure from the paper later. I thought I had better get agreement on copyright before I start posting it, and as yet I have had no response. The whole paper should be available as a free download, though.) The function is not exact, and for gold the p states are more the villains, and it is obvious that something is not quite right, or, as I believe, has been left out. However, the point I would make is the theoretical function depends only on quantum numbers, it has no empirical validation procedures and depends only on the nodal structure of the waves. The only interaction included is the electron nucleus electric field so some discrepancies might be anticipated. Now, obviously you should not take my word either, but when somebody else produces an alternative explanation, in my opinion we should at least acknowledge its presence rather than simply ignore it.

Some time ago I had posts on biofuels, and I covered a number of processes, but for certain reasons (I had been leading a research program for a company on this topic, and I thought I should lay off until I saw where that was going) I omitted what I believe is more optimal. The process I had eventually landed on is hydrothermal liquefaction, for reasons as follows.
 
The first problem with biomass is that it is dispersed, and it does not travel easily. How would you process forestry wastes? The shapes are ugly, and if you chip onsite, you are shipping a lot of air. If you are processing algae, either you waste a lot of energy drying it, or you ship a lot of water. There is no way around this problem initially, so you must try to make the initial travel distance as short as possible. Now, if you use a process such as Fischer Tropsch, you need such a large amount of biomass that you must harvest over a huge area, and now your transport costs rise very fast, as does the amount of fuel you burn shipping it. Accordingly, there are significant diseconomies of scale. The problem is, as you decrease the throughput, you lose processing economies of scale. What liquefaction does is reduce the volume considerably, and in turn, liquids are very much easier to transport. But to get that advantage, you have to process relatively smaller volumes. Transportation costs are always less for transport by barge, so that gives marine algae an increased desirability factor.
 
A second advantage of liquefaction is that you can introduce just about any feedstock, in any mix, although there are disadvantages in having too much variation. Liquefaction produces a number of useful chemicals, but they vary depending on the feedstock, and to be useful they have to be isolated and purified, and accordingly, the more different feedstocks included, the harder this problem. Ultimately, there will be the issue of “how to sell such chemicals” because the fuels market is enormously larger than that for chemicals, but initially the objective is to find ways to maximize income while the technology is made more efficient. No technology is introduced in its final form.
 
Processing frequently requires something else. Liquefaction has an advantage here too. If you were to hydrogenate, you have to make hydrogen, and that in turn is an unnecessary expense unless location gives you an advantage, e.g. hydrogen is being made somewhere nearby for some other purpose. In principle, liquefaction only requires water, although some catalysts are often helpful. Such catalysts can be surprisingly cheap, nevertheless they still need to be recovered, and this raises the more questionable issue relating to liquefaction: the workup. If carried out properly, the water waste volumes can be reasonably small, at least in theory, but that theory has yet to be properly tested. One advantage is that water can be recycled through the process, in which case a range of chemical impurities get recycled, where they condense further. There will be a stream of unusable phenolics, and these will have to be hydrotreated somewhere else.
 
The advantages are reasonably clear. There are some hydrocarbons produced that can be used as drop-in fuels following distillation. The petrol range is usually almost entirely aromatic, with high octane numbers. The diesel range from lipids has a very high cetane number. There are a number of useful chemicals made, and the technology should operate tolerably cheaply on a moderate scale, whereupon it makes liquids that can be cheaply transported elsewhere. In principle, the technology is probably the most cost-effective.
 
The disadvantages are also reasonably clear. The biggest is that the technology has not been demonstrated at a reasonable scale, so the advantages are somewhat theoretical. The costs may escalate with the workup, and the chemicals obtained, while potentially very useful, e.g. for polymers, are often somewhat different from the main ones currently used now, so their large-scale use requires market acceptance of materials with different properties.
 
Given the above, what should be done?  As with some of the other options, in my opinion there is insufficient information to decide, so someone needs to build a bigger plant to see whether it lives up to expectations. Another point is that unlike oil processing, it is unlikely that any given technology will be the best in all circumstances. We may have to face a future in which there are many different options in play.

I devoted the last post to the question, could we provide biofuels? By that, I mean, is the land available. I cited a paper in which it showed fairly conclusively that growing corn to make fuel is not really the answer, because to get the total US fuel consumption, based on that paper you would need to multiply the total area of existing ground under cultivation in the US by a factor of 17. And you still have to eat. Of course, the US could still function reasonably well while consuming significantly less liquid fuel, but the point remains that we still need liquid fuels. The authors of this paper could also have got this wrong and have made an error in their calculations, but such errors go either way, and as areas get larger, the errors are more likely to be unfavourable than favourable because the transport costs of servicing such large areas have to be taken into account. On the other hand, the area required for obtaining fuels from microalgae is less than five per cent of current area. Again, that is probably an underestimate, although, as I argued, a large amount of microalgae could be obtained from sewage treatment plants, and they are currently in place.
 
One problem with growing algae, however, is you need water, and in some places, water availability is a problem (although not usually for sewage treatment). Water itself is hardly a scarce resource, as anyone who has flown over the Pacific gradually realizes. The argument that it is salty is beside the point as far as algae go because there are numerous algae that grow quite nicely in seawater. One of what I consider to be the least well-recognized biofuel projects from the 1970s energy crisis was carried out by the US navy. What they did was to grow Macrocystis on rafts in deep seawater. The basic problem with seawater far from a shore is that it is surprisingly deficient in a number of nutrients, and this was overcome by raising water from the ocean floor. Macrocystis is one of the fastest growing plants, in fact under a microscope you can watch cell division proceeding regularly. You can also mow it, so frequent replanting is not necessary. The US navy showed this was quite practical, at least in moderately deep water. (You would not want to raise nutrients from the bottom of the Kermadec trench, for example, but there is plenty of ocean that does not go to great depths.)
 
The experiment itself eventually failed and the rafts were lost in a storm, in part possibly because they were firmly anchored and the water-raising pipe could not stand the bending forces. That, however, is no reason to write it off. I know of no new technology that was implemented without improvements on the first efforts at the pilot/demonstration level. The fact is, problems can only be solved once they are recognized, and while storms at sea are reasonably widely appreciated, that does not mean that the first engineering effort to deal with them is going to be the full and final one. Thus the deep pipe does not have to be rigid, and it can be raised free of obstructions. Similarly, the rafts, while some form of anchoring is desirable, do not have to be rigidly anchored. So, why did the US Navy give up? The reasons are not entirely clear to me, but I rather suspect that the fact that oil prices had dropped to the lowest levels ever in real terms may have had something to do with it.

In previous posts I have discussed the possibility of biofuels, and the issue of greenhouse gases. One approach to the problem of greenhouse gases, or at least the excess of carbon dioxide, is to make biofuels. The carbon in the fuels comes from the atmosphere, so at least we slow down the production of greenhouse gases, and additionally we address, at least partially, the problem of transport fuels. Sooner or later we shall run out of oil, so even putting aside the greenhouse problem, we need a substitute. The problem then is, how to do it?
 
The first objections we see come from what I believe is faulty analysis and faulty logic. Who has not seen the argument: "Biofuels are useless? All you have to do is to see the energy balances and land requirements for corn." This argument is of the "straw man" type; you choose a really bad example and generalize. An alternative was published recently in Biomass and Bioenergy. 56: 600-606. These authors provided an analysis of the land area required to provide 50% of the US transport fuels. Corn came in at a massive 846% of current US cropping area, i.e. to get the fuels, the total US cropping area needed to be multiplied by a factor greater than 8. Some might regard that as impractical! However, microalgae came in at between 1.1 and 2.5% of US cropping area. That is still a lot of area, but it does seem to be more manageable.
 
There is also the question of how to grow things, fuel needed, fertilizer needed, pesticides needed, etc. Corn here comes out very poorly, in fact some have argued that you put more energy in the form of useful work in growing it than you get out. (The second law bites again!) Now, I must show my bias and confess to having participated in a project to obtain chemicals and fuels from microalgae grown in sewage treatment water. It grows remarkably easily: no fertilizer requirements, no need to plant it or look after it; it really does grow itself, although there may be a case for seeding the growing stream to get a higher yield of desirable algae. Further, the algae removes much of the nitrogen and phosphate that would otherwise be an environmental nuisance, although that is not exactly a free run because when finished processing, the phosphates in particular remain. However, good engineering can presumably end up with a process stream that can be used for fertilizer.
 
One issue is that microalgae in a nutrient rich environment, and particularly in a nitrogen rich environment, tend to reproduce as rapidly as possible. If starved of nitrogen, they tend to use the photochemical energy and store its reserves of lipids. It is possible, at least with some species, to reach 75% lipid content, while rapidly growing microalgae may have only 5% extractible lipids.
 
That leaves the choice of process. My choice, biased that I am, uses hydrothermal liquefaction. Why? Well, first, harvesting microalgae is not that easy, and a lot of energy can be wasted drying it. With hydrothermal liquefaction, you need an excess of water, so "all you have to do" is to concentrate the algae to a paste. The quotation marks are to indicate that even that is easier said than done. As an aside, simple extraction of the wet algae with an organic solvent is not a good idea: you can get some really horrible emulsions. Another advantage of hydrothermal liquefaction is, if done properly, not only do you get fuel from the lipids, but also from the phospholipids, and some other fatty acid species that are otherwise difficult to extract. Finally, you end up with a string of interesting chemicals, and in principle, the chemicals, which are rich in nitrogen heterocycles, would in the long run be worth far more than the fuel content.
 
The fuel is interesting as well. If done under appropriate conditions, the lipid acids mainly either decarboxylate or decarbonylate, to form linear alkanes or alkenes one carbon atom short. There is a small amount of the obvious diketone formed as well. The polyunsaturated acids fragment, and coupled with some deaminated aminoacid fragments, make toluene, xylenes, and interestingly enough, ethyl benzene and styrene. Green polystyrene is plausible.
 
As you may gather, I am reasonably enthusiastic about this concept, because it simultaneously addresses a number of problems: greenhouse gases, "green" chemicals, liquid fuels, and sewage treatment, with perhaps phosphate recovery thrown in. There are a number of other variations on this theme; the point of what I am trying to say is there are things we can do. I believe the answer to the question is yes. Certainly there are more things to do, but no technology is invented mature.