This week I did a little bit of exploration. First, imagine Alison having this gigantic stovetop. There are all sorts of things cooking — including delicious pear jam. Well if you go about 8 rows back, you’ll find the backburner. Being the curious soul that I am, I found it appropriate to give one of those pots on the backburner a quick stir. I decided I would try to use the refractive index (n) as the polarizability-related variable in the CAF. My friend Lars Onsager, whom I go way back with, related the dielectric constant (epsilon) to the refractive index. Since the dipole density (N) is also related to the dielectric constant, it follows that the refractive index may serve a similar role. Well I popped that baby in the CAF and did a little pseudoscience to see if anything would happen. I found that I could produce surprising similar results to those results from the dipole density! The precision was much lower but the accuracy was only slightly off. Nonetheless, it was an interesting experiment. The static dielectric constant is actually related to the refractive index squared (Onsager) but when I used this new information to hopefully increase precision, it had the opposite effect.
Theories as to why it was so accurate in the first place:
- Units- When following the units for dipole density, we end up with mol cm^-3 K^-1, or # of dipoles per unit volume, which we proceed to divide by temperature. The refractive index (no units), when divided by the molecular weight (g mol^-1) yields units of mol g^-1, or # of something(?) per unit of mass, which we proceed to divide by the temperature as well. What is interesting about this is that volumetric expansion of the liquid is taken into account by using the density. Is it possible that the # of somethings per unit of mass is not taking into account deviations in the volume, thus inaccurately representing the polarizability, thus leading to lower precision? Likely not.
- Luck- Density and the refractive index have long been related in very interesting ways. Some (citation needed) have observed a linear relationship between the two. In our case, the densities and the refractive indicies were almost identical. Not purely a coincidence, but also probably a system-dependent occurrence.
It’s safe to say that we can turn this burner off.
The Seki group (Umbeyashi) who donated some lovely temperature dependent fluidity, density, and refractive index data for a family of ionic liquids.