Kramers theory absorption

Lynn, S., Straatemeier, J. R., and Kramers, H. Chem. Eng. Sci. 4 (1955) 49, 58, 63. Absorption studies in the fight of the penetration theory. I. Long wetted-wall columns. II. Absorption by short wetted-wall columns. III. Absorption by wetted-spheres, singly and in columns. 

Kramers (29) et al. studied the absorption of SO2 into water. This is a comparatively simple process, Ri being negligibly small and any hydrolysis reactions between CO2 or SO2 and water occurring very rapidly relative to the times of contact involved. At low fiow rates agreement with theory is satisfactory only if a surface-active agent is present in the system, though without such an agent the experimental results can be as... 

For transitions between bound states, the oscillator strength is a fundamental new quantity which quantum mechanics introduces in dispersion theory. We now have not only one characteristic frequency vq but a whole series of transition frequencies Vjk, and the presence, not only of absorption terms, but also of negative absorption terms due to stimulated emission. The theory of Kramers [130] was checked experimentally by Ladenberg and Kopfermann [131] for a line in the spectrum of Ne. 

Fig. 9. 12. Relationship between absorption rates of salicylic acid and ephedrine and bulk phase pH in the rat small intestine in vivo. Dashed lines represent curves predicted by the pH-partition theory in the absence of an unstirred layer. (From Winne D. The influence of unstirred layers on intestinal absorption in intestinal permeation. In Kramer M, Lauterbach F, eds. Workshop Conference Hoechest, vol 4. Amsterdam Excerpta Medica, 1977 58-64, with permission.)...

Christiansen tried to apply the description and the model of chain reactions to different mechanisms (Christiansen 1922) and wrote a paper with Kramers in 1923, cited previously, about unimolecular reactions confronting the activation mechanism due to thermal collisions and radiation absorption. They treated the radiation mechanism with the fundamental Einstein s quantum theory about matter-radiation interaction (Einstein 1917). Other work of Einstein and Smoluchowski will be necessary later for Christiansen-Kramers approach. After the paper the collaboration probably ended and the two researchers will reconsider separately these arguments aroxmd fifteen years later. 

Techniques for measuring the complex sound speeds and moduli of polymers are described in the section on test methods. The data shows that the real and imaginary components of the elastic moduli are frequency dependent. The frequency dependence is strongest for materials with high values of the loss factor r. Materials with frequency-dependent elastic moduli are called dispersive, and measurements and theory show that sound absorption mechanisms lead to dispersion. The real and imaginary part of an elastic modulus are related by the Kramers-Kronig relations, which are presented in the next section. 

The relationship between rotation and refractive index or between ellipticity and absorption coefficient can be represented, in analogy to dispersion theory, by the model of coupled linear oscillators or by quantum mechanical methods. ORD and CD are related to one another by equations analogous to the Kramers-Kronig equations [34]. 

Raman scattering is a two-photon process and is described by second-order perturbation theory. The cross section for a transition from initial state I I gr,) with energy Ei to a final state I I gr,/) with energy Ef through absorption of a photon with frequency co is given by the Kramers-Heisenberg-Dirac formula ... 

With a traveling fellowship awarded by Harvard, Slater spent his first postdoctoral year at Cambridge. There, he developed a theory on radiative transitions in atoms. On discussing this idea with Neils Bohr and Hans Kramers, a joint paper on the quantum theory of radiation was published in 1924. However, Bohr and Kramers altered Slater s original idea by ascribing a virtual existence to the photons in the transitions— not the real photons that Slater believed in. In early 1925, Slater was back at Harvard and published further work of his own on radiative transitions. He presented a picture of absorption and emission of real photons coupled with energy conservation in transition processes. He also established a relationship between the width of spectral lines and the lifetimes of states. 

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