Predicting what porphyrin nanorods are going to do

Porphyrins are a class of organic molecules that show up a lot in biology. But it’s not just their biological properties that are interesting. They also have really fascinating physical properties. Those are exactly what I studied this summer. There’s one kind of porphyrin (TPPS4) that self-assembles into long and skinny cylinders called nanorods. Complicated things happen when you shine light on them and run electricity through them at the same time. So many complicated things happen, in fact, that you probably don’t want to hear about all of them. I’ll just tell you about the one interesting thing that I worked on.

If you shine light on a freshly made nanorod, not much happens. But if you run electricity through the nanorod for a little while beforehand, it will produce its own electricity (called a “solar current”) when you do finally shine a light on it. It probably produces the solar current for a reason similar to the reason that other solar cells—like the kind that people put on their roof—produce electricity when you shine light on them. The unusual thing it is that you can control which direction the nanorod will produce an electric current in by changing the direction in which you run electricity through it beforehand. The direction of the nanorod’s own electricity will be the opposite of the direction of the electricity you ran through it. The process of running electricity through the nanorod beforehand is called training. The whole phenomenon is, appropriately enough, then called the trainable solar cell effect.

This summer, I worked some on the theory behind the trainable solar cell effect. A couple of years ago, Katherine van Aken—another student working in the same lab—helped come up with a tentative theory to explain the effect. The idea is that training must produce some asymmetry between the two ends of the nanorods, and then that asymmetry is what allows the nanorods to produce their own current. Van Aken proposed that maybe the asymmetry is in the amount of oxygen sticking to the two ends of the nanorod. Maybe the end that was positive during training ends up with more oxygen on it than the other end. That would become the end that the nanorod’s own current flows out of.

One of the things I did was to make predictions using the model. The more predictions we have, the better we’ll be able to design experiments to test the model. In the rest of this post, I will detail the most interesting of these.

 

Background

The Smith group studies the optoelectronic properties of TPPS4 nanorods by putting a large number of them in parallel electrically. This collection of nanorods in parallel is referred to as the sample. A voltage source and ammeter are also in the circuit:

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The nanorods exhibit a wide variety of interesting optoelectronic properties (Schwab et al. 2004; Riley et al. 2010). One of these is the trainable solar cell effect, which has been studied primarily by Schwab et al. (2004), van Aken (2012), Myint (2012), and Wang (2016). If a sample is trained by applying a voltage across it for several hours, it will develop a disposition to produce an electromotive force in the direction opposite to the training voltage whenever it is illuminated with a laser of the proper wavelength. The short-circuit current that results from this electromotive force is termed the solar current. Myint (2012) observed solar current growth and decay that looked something like this:

solar-over-time-export-1

One of the models proposed by Van Aken (2012) to explain this effect is called the adsorbed oxygen model. Consider the electronic structure of the metal – porphyrin – metal system:

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Suppose a lot of oxygen is adsorbed on the nanorods and is acting as a p-type semiconductor. Then there will be concave-down band bending. It will be symmetric prior to training because there is roughly the same amount of oxygen adsorbed on either side.

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But if the left electrode is held at a higher potential than the right electrode for several hours, then the negatively charged oxygen will move towards the left electrode. This will make the Schottky barriers thinner on the left than on the right, as shown below:

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When a photon of the proper frequency is absorbed, an electron is promoted to the valence band, and a hole is left in the conduction band. Both of these species move about randomly, sometimes moving into one of the electrodes. The asymmetry of the barriers does not produce a very large asymmetry in the rate at which electrons move into the two electrodes: The Schottky barriers are just downhill slides for the electrons. The holes, on the other hand, can only pass through the barriers by thermally assisted tunneling. The rate of tunneling is highly dependent on width. Thus the rate at which holes tunnel into the left electrode is higher than the rate at which they tunnel into the right one. The solar current is just the movement of charge through the external circuit to fill the extra holes.

 

Qualitative Predictions

In order to test the adsorbed oxygen model, it is necessary to make predictions from it. This requires a more detailed analysis of the entities and processes that play a role in the theory. The oxygen could accumulate on the left side either by sliding along the surface of the porphyrin or by the equilibrium constant for adsorption becoming position-dependent. I will assume that it is primarily by the equilibrium constant for adsorption becoming position-dependent.

Recall how the solar current exhibits asymptotic growth during training. The model makes predictions for how the magnitude of that asymptote depends on the partial pressure of oxygen in the sample’s environment. The fraction  of adsorption sites that are filled is positively correlated with the pressure of oxygen. In fact, the limit as the pressure goes to zero is zero, and the limit as the pressure goes to infinity is unity (Webb 2003, eqn. 5). If none of the sites are filled, then there can be no asymmetry, and hence there can be no solar current. If all of the sites are filled, then there can be no asymmetry either. The density of sites does not depend on position, nor does the function that always returns unity. Multiply these two together, and you find that the amount adsorbed is the same everywhere. Therefore, the solar current approaches zero both as the pressure approaches zero and as the pressure approaches infinity.

It is only at moderate pressures that the solar current is nonzero. Since the solar current vs. pressure function is continuous, it will look something like the sketch below:

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The plot will increase up to some pressure, and then it will start to decrease. This prediction would be confirmed if letting the solar current asymptote at a variety of pressures revealed both an increasing section and a decreasing section. Myint (2012) found a decreasing section. His data suggest that the maximum is located at a pressure below 0.16 Torr. An increasing section remains to be found.

 

 

 

Qualitative Predictions from Irreversible Adsorption

The question of whether oxygen adsorption on the nanorods is reversible or irreversible is not yet settled. There is some evidence on both sides. All predictions already discussed hold in both cases. The only qualification is that irreversibility would require one to refresh the sample by exposure to lots of oxygen in between trainings.

The irreversible adsorption hypothesis permits the model to make some further predictions that it does not make with the reversible adsorption hypothesis. Training has been conducted successfully both in constant illumination and in the dark, under about 0.8 torr of oxygen (Schwab 2004). It has only ever been attempted under ultra-high vacuum (UHV) in constant illumination. The reversible adsorption hypothesis predicts that training in the dark would work at any pressure—it would just be a bit slower than training under illumination. The irreversible adsorption hypothesis, on the other hand, predicts that training in the dark under UHV would not work at all. This is because photodesorption (see Morrison p. 345) is required for any change to occur in the amount of oxygen adsorbed.

Irreversible adsorption also predicts that a solar current which is trained under illumination will decay faster under illumination than in the dark. The fraction of sites filled starts out much higher than the equilibrium fraction under UHV. During training, photodesorption removes oxygen from the negative end. Symmetry can best be regained by removing oxygen from the positive end—requiring light.

Further Reading

This discussion was intended as just a taste of my project, for someone casually browsing Speaking of Science. If you are interested in all the gory details, I can send you a copy of my paper on this topic. Just email me at:

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References

Van Aken, K. L. “Trainable Solar Cell Effect in TPPS4 Nanowires.” Undergraduate Thesis. Haverford College. Spring 2012.

Lower, S. “The Road is Downhill: Free Energy and Equilibrium.” In Thermodynamics of Chemical Equilibrium: All About Entropy and Free Energy. Virtual Textbook. Accessed June 2, 2016. Last Updated 2007. URL = <www.chem1.com/acad/webtext/thermeq/TE5.html#SEC2&gt;.

Morrison, S. R. The Chemical Physics of Surfaces, Second Edition. New York: Plenum Press, 1990.

Myint, P. “Trainable Solar Cell Effect in TPPS4 Nanorwires [sic].” Unpublished Typescript. Haverford College. August 23, 2012.

Riley, C. K., E. A. Muller, B. E. Feldman, C. M. Cross, K. L. van Aken, Danvers E. Johnston, Y. Lu,  A. T. Johnson, J. C. de Paula, and W. F. Smith. “Effects of O2, Xe, and Gating on the Photoconductivity and Persistent Photoconductivity of Porphyrin Nanorods.” J. Phys. Chem. C, vol. 114, pp. 19227-19233. Autumn 2010.

Schwab, A. D., D. E. Smith, B. Bond-Watts, D. E. Johnston, J. Hone, A. T. Johnson, J. C. de Paula, and W. F. Smith. “Photoconductivity of Self-Assembled Porphyrin Nanorods.” Nano Letters, vol. 4, no. 7, pp. 1261-1265. Summer 2004.

Webb, P. A. “Introduction to Chemical Adsorption Analytical Techniques and their Applications to Catalysis.” MIC Technical Publications. Norcross, Georgia: Micromeritics Instrument Corp., January 2003. Accessed May 28, 2016. URL = <www.particletesting.com/Repository/Files/introduction_to_chemical_adsorption_analytical_techniques.pdf&gt;.

Wang, T. “Trainable Solar Cell Effects of Self-Assembled TPPS4 Nanorods.” Undergraduate Thesis. Haverford College. Spring 2016.