Absorption homogeneous

Pretreating wet DG with S02 (experiment 2) resulted in higher solubilization of residual carbohydrates than uncatalyzed steam explosion (experiment 1), however, higher yields and conversions are possible if homogeneous absorption of the acid gas can be accomplished. Careful examination of the S02-pretreated residue indicated nonhomogeneous pretreatment because the S02 appears to have been absorbed only at the surface of the particles and did not penetrate far into the interior. However, less expensive pretreatment reactors are possible if S02 is used as the catalyst, as opposed to dilute-acid pretreatment, because exotic alloys may not be needed. 

If molecules are embedded in solid hosts (e.g., in glassy or crystalline states) and temperatures are sufficiently low, sharp homogeneous absorption bands begin to show up within the broad inhomogeneous absorption band of the dopant [61]. A solute molecule and its noncovalently bonded solvent shell can be classified as a supermolecule [62]. Each solute molecule will thus create a unique supermolecule with its own arrangement of the solvent shell. Each supermolecule exists in a local energy well with a potential energy barrier which caimot be overcome at low temperatures. These supermolecules can show different physical properties— specifically, a spread in their absorption. In essence every supermolecule is different and can be addressed individually. 

Fig. 2.7 Comparison of the saturation of a homogeneous absorption line profile (a) and an inhomogeneous profile (b) in a standing-wave field, (c) The traveling saturating wave is kept 2ita) = a)o and a weak probe wave is tuned across the line profile...

As mentioned before, an increase in temperature activates low frequency modes of the matrix (phonons) or the molecule (librations) which lead to a broadening and a frequency shift of the homogeneous absorption line. In experiments with ensembles of molecules the homogeneous optical linewidth and its temperature dependence... 

The index of refraction n(v) is related to the absorption coefficient a v) of a homogeneous absorption profile by the dispersion relation... 

Note The difference to the homogeneous absorption profile where a co) is reduced by frequency-dependent factor S(co)) see (3.79) and Fig. 3.24. 

If the off-diagonal matrix elements that describe the coherence between a ground state and an excited electronic state decay exponentially with time, the homogeneous absorption line should have a Lorentzian shape (Figs. 10.6 and 10.7 Eqs. (2.70) and (10.35)). More generally, as we discussed in Sect. 10.6, the spectral lineshape is the Fourier transform of the relaxation function ... 

Here, no and ni are the numbers of unexcited and excited chromophores, F is the rate of the spontaneous optical transitions from the excited electronic level, and the rates k and k of the induced optical transitions are related to the fiinctions I and I which describe homogeneous absorption and fluorescence bands as follows ... 

The shapes of realistic homogeneous absorption and fluorescence spectra can be described by... 

Fig.3.19a-c. Saturation by a monochromatic standing wave, (a) Population distribution n(v ) for 03 coq. (b) Absorption coefficient a(o3) of an in-homogeneously broadened line, as obtained when tuning the frequency U3 of the standing wave across the line profile, (c) Saturation of a homogeneous absorption profile... 

The effective S values were determined from the homogeneous absorption line-shapes calculated using a thermally averaged Green s function approximation method... 

---