Wednesday, November 25, 2009

Deconstructing charge transport in complex materials

Consider a material in which there are two distinct charge carriers (e.g., electrons and protons or electrons and oxygen vacancies). A measurement of the conductivity of a sample will just yield the sum of the conductivities of the two individual charge carriers. Given that the physical conduction mechanism for the two carriers may be distinctly different (e.g., small polaron hopping vs. vacancy diffusion) the temperature, pressure, and composition dependence of the two components may be completely different. Is there a way to extract for each of the carriers the conductivity, density of carriers, and mobility? A few weeks ago I thought this was hopeless, but I was wrong.

So my favourite paper for this week has the weighty title
by Wei Lai and Sossina Haile from Caltech.
The paper is in a journal I have never looked at before, Journal of the American Ceramic Society (n.b. that is Ceramic not Chemical!)

The physics underlying the impedance technique is fascinating. It makes use of the concept of chemical capacitance:
The chemical capacitance has certain similarities to conventional dielectric capacitance. While the latter is a measure of the ability of the system to store electrical energy in the form of polarized electric dipoles, the former is a measure of the ability of the system to store chemical energy in the form of changes in stoichiometry
One measures the frequency dependence of the impedance of a sample of finite thickness. The sample acts like a circuit with a finite RC time constant, but the capacitance is due to the chemical capacitance. One then plots the imaginary part of the impedance vs. the real part (this is known as a Nyquist plot). Qualitatively it should look like one of the plots below.

The left one is what one obtains for a mixed ionic and electronic conductor where the two specifies have distinctly different conductivities. The right one occurs when the two components have comparable conductivities.

Lai and Haile apply the technique to a solid oxide fuel cell material (samaria doped cerium oxide at a range of oxygen partial pressures). They extract a considerable amount of information about the electronic and ionic conduction which is of great interest to Elvis Shoko, Michael Smith and myself. Elvis brought the paper to our attention.

I wonder whether this technique would also be useful for understanding charge transport in hydrated melanin, Gratzel cells, and conjugated polymers with charged functional groups and counterions.

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