Cooperative absorption

Using a cooperative adsorption isotherm developed by Ling (5) to derive a cooperative absorption isotherm that explicitly relates intracellular potassium content to external potassium concentration, Reisin and Gulati (4) have expressed the cooperative isotherm for the intracellular potassium as a function of Kex/Naex. This isotherm Ka(j is defined... 

Similar features arise in the theory of multiphoton absorption [68-70] and also single-photon cooperative absorption [71,72]. In connection with second-harmonic generation, the result has added significance since most species that can support P(—2m m,m), and thereby have the potential for frequency doubling, are, indeed, polar (see previous section). 

Thus by the cooperative absorption of the photon pair, the total energy absorbed is (E q + o)> tbe sum of the two molecular transition energies, and overall energy conservation is therefore achieved. 

By introducing the formalism of virtual photon coupling, the timescale for cooperative absorption, t, can be interpreted in terms of a range of propagation for which the exchanged photon has virtual character. Thus the distance R between two molecules that cooperate in the absorption process must be subject to the condition... 

However in most samples of chemical interest there is normally more than one pair of molecules to consider. With N molecules, there are clearly jN N — 1) pairs which can participate in a cooperative absorption process, but N N — 1) to participate in a distributive process. Hence, overall the photon statistics do not provide a basis for differentiating the significance of the two mechanisms. However, as shown below, the selection rules for the two processes differ markedly, and often result in a single mechanism being exclusively operative. 

APTE effect 2.step cooperative absorption sensitization... 

Alternatively, there may be cooperative absorption of the analyte so that, as the amount of analyte increases, the concentration in the stationary phase increases more rapidly than would otherwise be predicted. The plot of C ob against Cjiat consequently curves upward in a shape known as an anti-Langmuir sorption isotherm (Figure 2.13). This is less common than saturation of the stationary phase, but as some solutes (e.g., some acids) are absorbed in the stationary phase, they alter its nature so that they have... 

However, reality is not that simple and different up-conversion processes may exist simultaneously, or their effects can be tentatively reinforced reciprocally. For instance, two-photon absorption and cooperative absorption have been theoretically investigated (Rios Leite and de Araujo 1980). Also SHG and cooperative luminescence have been considered simultaneously, in order to increase SHG by the partial resonance of cooperative luminescence (Bonneville and Auzel 1976, Ovsyankin and Fedorov 1981). 

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