# How does graphite content affect the conductivity of pencil lead?

My peers and I started an experiment to test whether we could use the conductivity of a piece of pencil lead to determine its grade (that is, whether it is 2H, HB, 3B etc.). The paper Observational Models of Graphite Pencil Materials has a helpful list of the composition of various grade pencils, while Doğa Gürgünoğlu has made some relevant measurements of conductivities in the essay Electrical conductivities of different grade lead pencil graphite.

I had assumed conductivity would be linear in graphite composition, since the other constituents like clay and wax have negligible conductivity. However, when I graphed out the data, it seems more like an exponential growth.

Anisotropy of graphite means the conductivity changes drastically depending on its orientation, as discussed here. What else could influence the conductivity of pencil lead? Is there a theoretical explanantion of this trend?

References:

• M. C. Sousa & J. W. Buchanan - Observational Models of Graphite Pencil Materials
• Doğa Gürgünoğlu - Electrical conductivities of different grade lead pencil graphite
• Guessing based on percolation theory, I suspect that at low graphite content there are few "good" pathways available for the current to be conducted through, and it looks relatively insulating. After you reach some critical graphite concentration, the conduction pathways start to connect en masse, and you see rapid increase in conductivity, until it saturates. This gives a roughly sigmoidal curve. A slight issue is that it's somewhat unexpected for the rapid growth to happen at such high graphite concentrations, but that could be a consequence of many real-world parameters. Commented Mar 16 at 12:01
• It's not linear (or any specific function like exp) because it's not some true solution. If you cover some chunk of conductor in insulator, it won't conduct at all. Here's some mixing, though, so situation is intermediate. Commented Mar 16 at 14:32
• Nicely written question and experimental data. BTW, now you can make some hand-drawn electronic circuits, and even draw the current-limiting resistor for an LED (if your instructor appreciates humor, draw it on the lab report., with a coin cell). Commented Mar 17 at 1:49
• @NicolauSakerNeto this sounds very interesting. Any chance you could write it into an answer with more details/additional readings? I'm a physics student, so theory is also welcome. Commented Mar 17 at 7:10
• @DrMoishePippik by the way, the conductivity data used is not by me, but from a high school essay I found online. Commented Mar 17 at 7:11