On Causation, Entropy, and Semiconductors: Friday Night Persnicketiness

Alexander,

Let us talk about a two things that interest me: causation and thermodynamics.1

I was reading a paper today that discusses the frontiers of current research in how charge transfer/separation in some two dimensional semiconductors/heterostructures works. The whole conversation in this micro-field is around the question of how we can build solar cells that are more efficient. To build these efficient solar cells we must be able to have electrons get ripped away from their happy positions in their material homes so that they can flow through wires. In reading this paper the following phrase caught my attention:

“Such an increase in DOS [density of states] with r [distance] provides an entropic driving force for charge separation.”

I would like to point out something a bit interesting in this sentence. The authors of this paper say that entropy is driving something to happen. Entropy is cast as the cause of an event. This type of language is ubiquitous in chemistry—especially in general chemistry type settings where we ask our students such questions as: “is this process entropy or enthalpy driven?”. There is something curious here, though. I made it very clear to my students when we discussed entropy that keeping track of the total entropy of the universe allows me to know if a process is possible, but it doesn’t tell me if the process will actually happen on any reasonable timescale. The common way of thinking of this goes something like: thermodynamics tells us what is not forbidden, but it doesn’t tell us if the things will actually happen.

So why were these authors so ok with saying that the entropy change of the process was driving the event? This is where the language (and thinking) of chemists (and maybe scientists/humans in general) becomes so weird. We oftentimes have a hard time correctly saying which things cause other things and which things are merely necessarily connected to the change.

I don’t think the authors are correct in saying that entropy drives charge separation. Rather there must be some sort of other physical mechanism(s) at play that cause electrons to get ripped from their positions when I shine light on a solar cell. This notion is because of something that I think is rather fundamental: thermodynamic state functions allow us to keep track of things and events, but they don’t force those things to happen. Now let us cast this statement in an analogy.

Let us think of my bank account. It is currently populated with some amount of currency. If we wanted to we could track the time evolution of my bank account by monitoring the amount of currency. Now, my paying of rent is necessarily connected with a decrease of the amount of money in my bank account. Additionally, if I have no money in my bank account I cannot pay my rent. In this way, the money in my bank account is kind of like the thermodynamic entropy change with respect to a process. I hope we can both agree that my rent being paid is not caused by or driven by the fact that my bank account has money in it. The cause of me paying my rent has its very start at my desire to continue living in my house next month. This desire won’t be fulfilled if I don’t have money in my account (that is if the entropy increase is not positive then the reaction won’t happen), but it is not caused by money being in my account! Rather the money being in the account is a necessary condition for the event to happen, but it is not a sufficient condition to be the cause of my rent check getting written.

The very notion of a cause now comes into play. How do I know when one event causes another? The hardcore Humean/empiricist will of course say that we can never ever know for sure that one event causes another, all we can know is that one event always (to our best knowledge) directly follows another event. But us pragmatic chemists that actually desire to help humanity probably shouldn’t spend all of our time thinking in this way. We want to be able to build semiconductors that make good solar cells after all. So we should probably be okay with saying some things cause other things (like billiard balls smacking into each other) because we want to be able to use these causes to inform our decision in solar cell fabrication.

To say it again, the pure empiricist doesn’t want to ever say anything causes something else. They are much happier saying that events are correlated in some way. But we humans want to 1) build concrete associations between events and 2) build solar cells. We could just build solar cells based on massive amounts of known correlations. But this makes us sad, we like thinking that we are making solar cells informed by our proposed mechanisms concerning how charge transfer happens at an interface.

It is now apparent that we scientists are all screwed up. We want to build things, but we aren’t quite absolutely sure how to build the perfect solar cell. Moreover, using our current method of inquiry we can never be sure of how to build the perfect solar cell. We can’t even know if a solar cell connected to my battery is really the reason my battery is charging… oh dear. I guess we are stuck using words like ’cause’ and ‘drive’ in an informal and imprecise way. We must be very careful with these words, though. As always, we should never confuse cause and correlation; we should never confuse the fact that a room always gets messier with the actual cause of the room getting messier—the toddler writing on the wall.2

-Darien

And now the footnotes:

  1. For those that have not taken a chemistry class in a while, the carefully defined notion of a ‘spontaneous process’ is important to have in one’s back-pocket for this post. Please see the possibly esoteric Wikipedia page on spontaneous processes. I apologize for this post going against the originally stated rules of AlkynesofPi, but it seems like we violated those within a few weeks of inception.
  2. Now, Alexander, after the above rant about causation in semiconductors I assume you have now found a little flaw in my dislike of the authors’ usage of the notion of an entropy driven process. You should be saying to me: “But Darien, maybe entropy IS actually a cause. You don’t know. It seems to be really well correlated to lots of events.” To this I sheepishly respond, the notion of entropy causing anything is rather messy. It seems like a universal truth that any change that occurs is accompanied by an increase in the total entropy of the universe. So, the authors’ noting of the entropy increase of the system and the event happening being correlated is nothing new. This is such a not-new thing that we have a universally accepted name for it — the Second Law of Thermodynamics. This not-newness maybe makes it useless in rational design of solar cells. But the flaw in my original peeve is still evident, this entropy change may indeed be the cause, I simply don’t (can’t?) know.

 

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