Rick Shory

Offering a little something you might not otherwise have

Gibbs economics

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I was asked to review the book “Solar Hydrogen Generation: Transition Metal Oxides in Water Photoelectrolysis” in regards to alternative energy production. I loved the geeky chapters because I’m a sucker for any sort of super technical chemistry gossip. But I want to offer my perspective on the gap between such information vs. practical systems. Most people realize there are “complications”, but I would like to share my ideas on how to think of these complications in a systematic way.

I will use an economics analogy to explain a thermodynamic term called “Gibbs energy” (in older publications “Gibbs free energy”). Gibbs energy is the deal-breaker (or -maker) in a physical system, to tell whether it will “go”. It’s like a bookkeeping analysis to see if a business model is viable.

This is of course way oversimplified, but: You have raw profit, and you have organization costs. If you have enough profit, you can gloss over management. If you have a slim profit margin, your system may still work if carefully managed. There are even cases where an otherwise unprofitable system will work if you “add” enough of the right kind of organization.

Gibbs energy has two terms, which I’ll simplify to “energy” and “entropy”. Energy is the basic “bang” of the system, sometimes obvious sometimes not. Entropy is the “organization” of the system. More organized means lower entropy. In the technical thermodynamics of the Gibbs equation, the energy and entropy terms are of opposite sign. This means, conceptually, “buying” organization using energy, or vice versa.

For a simple system, like an electrochemical cell, the terms are fairly straightforward to quantify. However, any system of real relevance, such as biological life or renewable energy, is much more complex, partly because it is less definite just where the boundaries of the system are. Though harder to quantify, it can be easier to conceptualize.

For example, a pure substance is more “organized” than a mixture, thus lower entropy. Picture a gold ingot sitting beside a heap of mine tailings. The gold is more “organized” than the original state, the mountain of ore. You can see that you have to “pay” energy, effort, management to get the gold. Incidentally, the whole scene, gold plus waste rock, is now less organized, higher entropy; but that’s another story.

Back to the case of the semiconductor hydrogen reactions. At the scale of the titanium dioxide (or whatever) particles, the system “goes”. Ultraviolet light hits the slurry and activates it, splitting water into hydrogen and oxygen. (This is not technically correct. It’s actually “electrons” and “holes”, and the chemical reactions may bypass hydrogen and oxygen. But it will serve for analogy.) So far, the practical use of such systems is to get rid of some undesirable organic pollutant. The oxygen produced “burns up” the pollutant, and a little hydrogen may bubble out.

But say you want to adapt these reactions to actually get a flow of hydrogen. Now you are faced with providing a feedstock of the organic material, as well as getting rid of the “burnt” carbon dioxide. Alternatively, you could let the slurry bubble out a mixture of hydrogen and oxygen — extremely explosive. Either way, your management costs have shot up. The larger system has to be much more “organized”. Is there still enough overall energy, enough “profit”?

Say you could magically get clean hydrogen. Hydrogen is a gas, and gases are inherently high entropy, relative to liquids and solids. The atoms are flying around more freely. To bring it to a more organized, manageable state, you can see you would have to expend effort. You could compress it into high-pressure tanks. You could liquefy it at extremely low temperature. This management “costs” energy, and cuts your overall profit.

Maybe you could chemically combine hydrogen with carbon to make a fuel that would be liquid at room temperature. That’s what gasoline is, and is why such fuels are so popular. But there is yet no practical way to do that. It would take extremely organized chemical reactions. Again, the management costs.

The closest that exists so far is the work of George Olah, which has come to fruition here. At first glance, this seems like the answer. You take carbon dioxide and water and you end up with the liquid fuel methanol. Methanol is a fair substitute for gasoline, not quite as high energy density because it contains some oxygen (it’s already part “burnt”). Poisonous, to be sure, if we drink it, and will readily kill anything it’s spilled on in any quantity. In this regard, similar to gasoline. But methanol is more readily biodegraded, once dilute enough.

But peek behind the curtain, using Gibbs energy, and you see how the Iceland plant is “cheating”. The energy is geothermal, essentially free. The carbon dioxide feedstock is volcanic gases, already concentrated; that is, lower entropy. To collect the same carbon dioxide out of the atmosphere would take enormous “organization” costs of energy. Maybe someday it’ll be feasible, but not now.

I want to make a nod to the supposedly “poor” efficiency of biological life, as photosynthesis. The number is usually quoted as a sad one or two percent, compared to our even crude solar cells at 10%. But look at the outputs.

Solar cells make electricity, which must be used at the same moment it is produced. By some reckoning, it has infinite entropy. The “management” term is our huge electrical infrastructure, with all its controls, including any storage. Yes, we have made it work, but it works best for steady inputs like hydropower or fuels we can burn at will. For “higher entropy” inputs that fluctuate, like solar and wind, we have to provide ever more organization.

As an aside, I saw a blurb about future cities harvesting their own energy, the skyscrapers coated in “quantum dots”. I love it! Those would presumably be molecule-sized solar cells, each feeding into the grid. What a wonderful futuristic image, compared to the clunky ones we have now: Blocky three-by-six foot panels, weighing some forty pounds, holding arrays of hand-sized solar cells. Most people don’t realize that if even one cell in the array gets shaded, the efficiency of the whole thing plummets. (This is why solar installations look so stark. There can be no shading anywhere.) This problem could be solved, but again at an “organization” cost of more complex electronics. The management of a cityscape of quantum dots would be, well, futuristic.

But, organization is clearly the way to go. Looking again at photosynthesis, the final output is a chemically stable solid, say wood or grain. It just sits there until you’re ready to use it. This is accomplished by the extreme organization of biological life. Life just “does” it for you.

Unlike transition metal oxide systems that need scarce, high-energy ultraviolet photons, plants can get by on abundant, low-energy red photons. Plants deal with the high entropy (extreme dilution) of their feedstocks without you even noticing. They scrape together enough carbon out of the fraction-of-a-percent carbon dioxide in ambient air. From this smidgen, they build huge forest trees, continents of waving grass, fields of corn. They quietly eke out their soil mineral feedstocks in a similar way. They don’t have to go halfway around the globe for strategic metals.

Each chlorophyll molecule is essentially your quantum dot. The highly organized biochemical machinery is in place to bring that energy out into a stable carbon-based compound, such as glucose, even at the cellular level. This is done with no extreme pH sulfuric acid or potassium hydroxide electrolytes, no nightmarishly high temperatures. This energy stock can be stored locally in the cell as starch, or transported. No batteries. No spinning flywheels. No explosive pressures or high voltages. When the energy stock is to be transported, the transport system is part of the package too, in the form of the plant’s vascular system, which runs on water.

We haven’t even talked about repair, recycling and replacement of defunct equipment. For built technology, these issues are routinely swept under the rug when looking at product lifecycles. Heavy metals from electronics leach into groundwater. Plastics spiral into the oceans. Even innocuous materials have be dumped and buried in landfills.

For biological life, the recycling was all worked out millions of years ago. Dead plants just rot. Before they die and rot, they live with dust, dirt, grime, muck, random weather conditions, scarcity, breakage, etc. All the things anybody who has ever tended machinery knows can be a full time job.

Again, for real-world systems, the “management” (entropy) costs are easier to conceptualize than to quantify. But when you look at all the entropy terms that living things routinely play ball with, a one or two percent overall “efficiency” is phenomenal. Biological life is the benchmark to beat.


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