ATR II : Depth of Penetration

The depth of penetration (DP) in an ATR experiment is a measure of how far the evanescent wave penetrates into a sample. Understanding the variables that determine DP tell us a lot about how the technique works, why ATR spectra look the way they do, and the sorts of interesting applications that can be pursued via ATR. The equation for depth of penetration in an ATR experiment is (the envelope please):

DP = 1/2πWnc(sin2θ – n2sc)1/2

(please pardon the appearance of the equation, it had a rough night...and blogger does not allow subscripts and superscripts. Red is for superscripts, blue is for subscripts.)

Where
DP = Depth of Penetration (in cm)
W = Wavenumber in cm-1
nc = Refractive index of ATR crystal
θ = Angle of incidence of IR beam with crystal surface
nsc = refractive index of sample divided by refractive index of crystal

Note that all the paramaters in the DP equation are in the denominator, so when any of them goes up, DP goes down. The next several blog posts will cover the different parameters in this equation and what they teach us about the ATR experiment.