A quantum mechanical derivation of Beer's Law is presented. The expression includes a term for the probability of radiationless energy transfer during gas-kinetic collisions. The theory indicates that this effect is the major contributor to the pressure intensity enhancement observed in the infrared spectra of small gaseous molecules in the presence of a foreign (non-absorbing) gas. Further investigation of the phenomenon shows that it is due to deactivation of the 1st excited vibrational state by inter-molecular collisions. The derived equation is: ln(Io/I)= Bmn C'd-2 ln [(z+(1-Tt) Amn)/(Z+(1-To)Amn)] where Bmn is the Einstein coefficient of induced absorption, C' is the concentration, d is the pathlength, Z is the probability of radiationless energy transfer, Amn is the Einstein coefficient of spontaneous emission, andTt and To are the fractional transmissions of the transmitted and incident light respectively. The effect is studied by reference to a number of small gaseous molecules (CH4, C2H6, C2H4, C2H2, CO, CO2 NO, HCN, HC1 and CH3Br) in the foreign gases N2, 02, He and CO2 using a grating spectrometer equipped with a pair of 40 metre long path gas cells. The investigation involves the following stages: (a) measurement of the observed pressure enhancement factors (b) determination of the absolute intensity of individual vibration-rotation bands. (c) calculation of the Einstein probability coefficients Bmn and Amn (d) computation of the collisional deactivation probabilities (Z), relaxation times (Y) and Napier numbers (Z10) for each transition. The mechanism of vibration - translation and rotation - translation energy conversion is discussed, the relationships between various molecular parameters and the observed spectra are examined, and comparison is made between measured and literature values obtained by acoustical experiments. Some areas of interest for future research are discussed.
|Date of Award||1975|