(a) Consider an ATR experiment with a sample having a refractive index of 1.03 at 2000 cm-1. The ATR crystal was AgCl with a refractive index of 2.00 at this wavelength. For an angle of incidence of 45°, what is the effective penetration depth of the evanescent wave? How would the penetration depth change if the angle were changed to 60°?
(b) For the same experiment in part (a) and a 60° incidence angle, find the penetration depths for sample refractive indexes varying from 1.00 to 1.70 in steps of 0.10. Plot penetration depth as a function of refractive index. Determine the refractive index for which the penetration depth becomes zero. What happens at this point?
(c) For a sample with a refractive index of 1.37 at 2000 cm-1 and an incidence angle of 45°, plot the penetration depth versus the ATR crystal refractive index. Vary the crystal refractive index over the range of 2.00 to 4.00 in steps of 0.25. Which crystal, AgCl (nc5 2.00) or Ge (nc 5 4.00), gives the smaller penetration depth? Why?
(d) An aqueous solution with a refractive index of 1.003 is measured with an ATR crystal with a refractive index of 2.8. The incidence angle is 45°. What is the effective penetration depth at 3000 cm-1, 2000 cm-1, and 1000 cm-1? Is absorption by the aqueous solvent as much of a problem in ATR as in normal IR absorption measurements? Why or why not?
(e) Work by S. Ekgasit and H. Ishida (S. Ekgasit and H. Ishida, Appl. Spectrosc., 1996, 50, 1187; Appl. Spectrosc., 1997, 51, 461) describes a new method to obtain a depth profile of a sample surface using ATR spectroscopy. Describe the principles of this new approach. Why are spectra taken with different degrees of polarization? What is the complex index of refraction?
