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Well, I have been inspired to learn how to insert fancy math equations into my blog posts.  Kudos to the good folks at codecogs for providing this.  To test the power of the website, I decided to enter the Kramers-Kronig transform between the s-polarized reflectivity, Rs and the phase angle, δ.

The P stands for the Cauchy principle value and I is a constant for using this in an ATR experiment.  The value of I is given as

From this  one may go on to calculate the optical constants of a material.  Pretty cool!  My only complaint is the box that is drawn around them, but I will hold off on fixing that for now.


I am working on a paper that describes room temperature molten salts in terms of a quasi-crystalline lattice.  The preservation of the lattice-like structure in the ionic liquid results in some pretty neat features in the IR spectrum, specifically the presence of transverse optic/longitudinal optic (TO/LO) modes.  TO/LO modes commonly occur in the solid-state due to the coupling of incident IR photons with the phonon states of the material to produce polaritons.  In the absence of any anharmonicity among the constituent vibrational modes, the incident photons are completely reflected.  It is fascinating that a room temperature molten salt supports optical phonons, resulting in TO/LO mode splitting in the IR spectra.  This can provide tremendous insight into the fundamental interactions among the constituent ions composing the ionic liquid.

The TO/LO splitting can also be used to calculate the dipole moment derivative for the vibrational motions responsible for a given band.  This requires the use of dipolar coupling theory, which relates the dipole moment derivative to the magitude of the TO/LO splitting.  The theory also requires some knowledge of the particle density of the compound.  My current task is to support the result derived from dipolar coupling theory by estimating the optical constants of the ionic liquid.  Integration of the extinction coefficient can give another measure of band intensity.  This may then be related to the dipole moment derivative.

This is my first foray into calculating optical constants or dipolar coupling theory.  I also learned a tremendous amount writing the portion of polaritons.  I think this article may have done more to expand my expertise in molecular spectroscopy than some classes I had in graduate school.  This post would be much clearer if I could insert some of the equations, but I don’t know how to do that yet.  If I figure it out, I will come back and edit it some.

In my previous post, I articulated my view on the limits of scientific inquiry by focusing on how scientists “do science.”  I also explored three implications that result if this picture of science is adopted.  Here, I examine one objection against this position: naturalism must be correct because modern scientific theories work. Read the rest of this entry »