A little note about chain transfer to butyl methacrylate

For good or evil, this paper, which I began writing in 1999 at the request of Professor Bob Gilbert, is finally published. It is a tremendous pleasure to finally be a co-author with David Sangster, the eminence d'or of Australian polymer science. He is the source of the quote which informs my every waking action:

'Just because the model fits the data, it doesn't mean the model is true.'

I have today (10/11/09) found a splendid biography of David Sangster on the website of the University of Sydney.

Royal Society Discussion Paper, Ocean acidification due to increasing atmospheric carbon dioxide. Part Two.

The RSC discussion paper explains the division of ocean waters between an upper zone, where calcium carbonate formation is possible, and a colder lower zone, where it is not possible. The fact that mass transport between these zones is very slow is stressed. The paper does not actually give a pH profile of the ocean, but here is one:

(The little dark dots are the data from today; the big circles are attempts to figure out the situation at various times in the past, which is what the paper I sourced this from is about.)

Note that the vast majority of the volume of the ocean is cold, and relatively acidic. This deep ocean is where an enormous amount of carbon is stored. Transport of carbon dioxide out of or into this layer will not be controlled by thermodynamics (i. e., where carbon dioxide it would most dearly love to be), but by kinetics (i. e., how fast it can get there). Thus, it does not matter to this zone whether or not we are adding carbon dioxide to the atmosphere at a rate unparalleled in Earth’s history or not, because that will not control how fast it gets there. It has to run the gauntlet of the warm water- where it may or may not be converted into calcium carbonate- first.

Remember the figures in the last post on how the carbonic acid equilibria change with temperature. I am now going to make the assertion- which I should now go out and try to verify- that the deep ocean is more acidic *because* it is cold.

To qualify this as-yet-unverified assertion of mine, I should say that I have not yet found any data on the pressure dependence of the pKa values in solutions of reasonable ionic strength, which is also likely to be important.

I suggest that the temperature gradient of the ocean is probably what generates the pH profile, and because transport of carbon dioxide into or out of the ocean is slow compared to how much is already there, it is the temperature dependence of the carbonic acid equilibria which control the speciation observed. Note also that the boundary between the carbonate-forming zone and the non-carbonate forming zone, from our figures below showing what the equilibria do, is going to be dependent both on the pH of the upper layers and their temperature.

Now… if climate change means anything, it means the oceans warming up. Heating the ocean and reducing the pH will pull the carbonate/bicarbonate equilibrium in different directions. I don’t know which is likely to be more significant.

Because the historical record does not show carbon dioxide spouting out of the ocean immediately as temperature increases, but lagging about 1000 years, I am not at all worried about degassing of carbon dioxide starting some feedback loop of badness : until that cold lower ocean where most all of the carbonic acid species are sitting warms up, there is no reason for significant amounts of carbon dioxide to leave the ocean. That is, if degassing of the ocean *is* the reason for the increase in carbon dioxide lagging historical temperature changes. It might not be.

Royal Society Discussion Paper, Ocean acidification due to increasing atmospheric carbon dioxide. Part One.

My thoughts keep returning to the ‘de-alkalinisation of the oceans’. I started thinking about this the other day, first because I came across that article on coccolithophores in Science, and second because one of my students is writing a review article on the use of polymer additives to stop scale formation in desalination plants. The main scales formed in these plants are calcium sulfate at high temperatures, but at somewhat lower temperatures calcium carbonate or magnesium hydroxide.

The first thing you want to know about, if you want to stop scale forming, is what are the characteristics of the solution it is forming from. So early on in the draft appears this table:

(TDS is ‘total dissolved solids’.)

I went back and had another look at the Royal Society discussion paper that I referenced before. This is the paper referenced everywhere in the web where people are fretting about ocean de-alkalinisation. The range of pH values quoted in this table is greater than the range shown in the pretty map in the Royal Society report. In fact, the range of pH values in this table is greater than the size of the maximum change in surface water pH they predict for Figure 5.

So my first thought was, if changes in surface seawater alkalinity are likely to cause bad effects, we ought to be able to see these effects already in ‘canary in the coalmine’ water bodies- shallow, warm places like the Persian Gulf. The reefs there don’t seem to be in particularly good shape but there doesn’t seem to be any evidence that seawater alkalinisation is contributing to their woes. Anyway, this table got me thinking about the problem again.

In discussing the formation of calcium carbonate scale, my student had to talk about the dependence of the equilibrium constants K₁ and K₂ on temperature and the total ionic strength of the solution, and had referenced this paper by Millero et al., where the following figure appears:

The Millero et al. paper also summarises data from a lot of previous work and gets it all to fall on the same line- see this, for instance:

In case you don’t remember,

pK_a = –log₁₀(K_a),

and in this case, K₁ is the equilibrium constant for the reaction:

H₂CO₃ → HCO₃^– + H⁺

and K₂ is the equilibrium constant for this reaction:

HCO₃^– → CO₃^2– + H⁺

These figures are telling us that in seawater (where I^0.5 ~ 0.83), the equilibrium position of both these reactions is further over to the right hand side than if they were happening in common or garden distilled water. And they also tell us that the warmer the water, the further the equilibrium will be over to the right hand side as well.

I plotted up a graph showing how the speciation of pH should change in seawater using the values in this paper and got this figure:

The Royal Society Figure 2 is pretty much the same as mine. It shows carbonate kicking in at a slightly lower pH, but there are different K₂ values floating around in the literature and I'm not sure what value they used.

Zooming in on the pH range important for discussing what is going on in the oceans:

Getting rid of the log scale, and looking at the carbonate/bicarbonate equilibrium only:

More to follow.

C'est la vie

A while ago the prolific Anonymous asked me:

What do you think about the de-alkalinisation of the oceans. Anything ruinously doom and gloom possible there? Is adaptation of water species quick enough by your reckoning?

I have recently been thinking about this a lot, due to work I am doing on calcium carbonate formation in desalination plants, and will offer a substantial critique of this particular bugbear soon.

But in the meantime, I came across this nifty figure in Science the other day and thought I would share it with you. If someone had asked me, 'how will marine organisms respond to changes in total carbonic acid species concentration?', I like to think I would have been prescient enough to draw a figure like this one. Find a niche and fill it: such is the way of living things!

Dialogo

Simplicio: Have you heard? The Powers wish to reduce the amount we teach, so that we will have more time for research, and thus will produce more and better research.

Sagredo: I think the second part of your syllogism does not follow from the first.

Simplicio: Why, how is that?

Sagredo: One of us cannot have more than twenty-four hours in a day. But if one has a single intelligent and dedicated postgraduate student, then one has forty-eight. If one has two, one has seventy-two, and so forth. It is the many hours that come from having many students that enable us to produce more and better research.

Simplicio: True, but I cannot see how having a few more hours for research can hurt us.

Sagredo: Where do you suppose postgraduate students come from?

Simplicio: Most of them are from places like Tartary and Hind, are they not?

Sagredo: Yes, many of them are. They are attracted from diverse foreign lands by the splendour of the learning in our land. But many other places of learning seek also to attract them, and day by day the scholars of their own lands grow wealthier and more astute, so that one day no more will come to us.

Simplicio: That would be a calamity! So where else do they come from?

Sagredo: We raise them here, by teaching undergraduates.

Simplicio: Aha! There is no problem, then. Under the new system we will surely continue to teach undergraduates.

Sagredo: Simplicio, do you suppose all undergraduates are suitable to become postgraduates?

Simplicio: I guess not. Some are damnably simple.

Sagredo: Yes, it is only the few who hunger and thirst for knowledge that are suitable to become postgraduates. If we give our undergraduates half as much as we did before, and other places of learning continue to offer a full cup of learning, where will undergraduates like that go?

Simplicio: You think they will not come here?

Sagredo: Many of them will not.

Simplicio: But surely there are many who would not leave our lovely place of learning for the City of Dreadful Night or other distant places?

Sagredo: Yes, we must pin our hopes on such as those. But consider: if we teach them half as much, what will we need to do when they commence as postgraduate students?

Simplicio: I am not sure. I recall there are forms to fill out?

Sagredo: Besides that. We must perforce teach them the other half, if they are to work as well as postgraduates in the City of Dreadful Night work. And when we have done that, what must we do?

Simplicio: I suppose we must fill in some more forms.

Sagredo: Yes, for by then the first year of their candidature will be over.

Simplicio: It would seem, then, that you think this change will diminish our chances of doing more and better research, rather than increase them?

Sagredo: Most certainly. Why would a student who would make a good postgraduate in Physics or Chemistry do an undergraduate degree at a place of learning that does not take that discipline seriously?

Simplicio: Then I suppose the Powers wish to reduce our teaching hours for some other reason?

Sagredo; That is what I had thought.

Simplicio: Perhaps it is that they must be reduced because of this thing that has come from Bologna?

Sagredo; Ah, but the places of learning that have already gone down that path teach many more hours than we do.

Simplicio: Hmm. Perhaps it is, Sagredo, that those studies they wish to cut are only those where the numbers of undergraduates have been falling, so that we may conserve our resources, as our wealth wanes?

Sagredo: That would be a sensible course of action- but you see, Simplicio, it is the studies where numbers of undergraduates are holding steady that the Powers wish to cut back.

Simplicio: Ah.I see. Perhaps- no, that makes no sense. (sighs)
I wish Salviati was here to explain what was going on.

Sagredo: So do I, Simplicio.

Simplicio: It is a pity the Powers never replaced him, when he took his renowned research group to Brescia...