Cooperative absorption mechanism

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. 

Although it is being found that vitamin D metaboUtes play a role ia many different biological functions, metaboHsm primarily occurs to maintain the calcium homeostasis of the body. When calcium semm levels fall below the normal range, 1 a,25-dihydroxy-vitainin is made when calcium levels are at or above this level, 24,25-dihydroxycholecalciferol is made, and 1 a-hydroxylase activity is discontiaued. The calcium homeostasis mechanism iavolves a hypocalcemic stimulus, which iaduces the secretion of parathyroid hormone. This causes phosphate diuresis ia the kidney, which stimulates the 1 a-hydroxylase activity and causes the hydroxylation of 25-hydroxy-vitamin D to 1 a,25-dihydroxycholecalciferol. Parathyroid hormone and 1,25-dihydroxycholecalciferol act at the bone site cooperatively to stimulate calcium mobilization from the bone (see Hormones). Calcium blood levels are also iafluenced by the effects of the metaboUte on intestinal absorption and renal resorption. 

Up-conversion relies on sequential absorption and luminescence with intermediate steps to generate shorter wavelengths. Hence, the presence of more than one metastable excited state is required the intermediate metastable states act as excitation reservoirs. One typical example is ground-state absorption followed by inter-mediate-state excitation, excited-state absorption, and final-state excitation to give the up-conversion (the intermediate states and final states are real states) [1, 35], There are many types of up-conversion mechanisms such as excited-state absorption, energy transfer up-conversion and cooperative up-conversion. All these up-conversion processes can be differentiated by studying the energy dependence, lifetime decay curve, power dependence, and concentration dependence by experimental measurements [36-39]. 

Figure 2. A cooperative mechanism for synergistic two-photon absorption. Molecule A ab orl>s a photon of frequency

As seen above, synergistic two-photon absorption can in principle take place by either or both of the mechanisms, where (i) each laser photon is absorbed by a different molecule (the cooperative mechanism), or (ii) both laser photons are absorbed by a single molecule (the distributi e mechanism). In each case, the energy mismatch for the molecular transitior s is transferred between the molecules by means of a virtual photon that couples with each molecule by the same electric-dipole coupling as the laser photons. The result, however, is a significant difference in the selection rules applying to the two types of processes. 

As mentioned above, there are four specific cases of bimolecular mean frequency absorption that are of special interest. These are distinguished by the type of mechanism (cooperative or distributive) involved and whether the photons absorbed have the same or different frequencies. The latter condition is in most cases determined by whether a single laser beam or two laser beams are employed for the excitation. We consider first the single-beam cases. 

Figure 5. Typical time-ordered diagrams for single-beam two-photon absorption (a) shows one of the diagrams associated with the cooperative mechanism, and (b) one of the diagrams for the distributive mechanism.

Figure 8. Typical time-ordered diagrams for the most general case of synergistic absorption with two-beam excitation of a chemically dissimilar pair of molecules (a) relates to the cooperative mechanism and (b) the distributive mechanism.

The first two terms in Eq. (5.13) arise from the cooperative mechanism, while the distributive mechanism gives rise to the third and fourth terms. Deriving the general rate for a proximity-induced two-photon absorption process from the square modulus of the result is an elaborate procedure producing sixteen terms, including cross-terms associated with quantum mechanical interference between the cooperat ve and distributive mechanisms. However, in view of the selection rules discussed earlier, it is not generally necessary to perform this calculation since each of the four specific mechanisms for two-photon absorption under consideration can, at most, have only two terms of Eq. (5.13) contributing to the matrix element. 

On casting the rate equations entirely in terms of C, it becomes evident that the result for the single-beam cooperative case contains only terms in and numerical terms, while additional terms linear in C occur in the single-beam distributive case. Hence, the odd-j terms in Eq. (7.8) only contribute to the result when circularly or elliptically polarized incident radiation is employed, and their sign is then dependent on the handedness of that incident radiation. A direct consequence of this is the exhibition of two-photon circular dichroism in the distributive absorption process for pairs of molecules with fixed mutual orientations no such effect can occur under the cooperative mechanism. 

Figure 10. Resonance energy levels for single-beam synergistic absorption. The levels indicated by dashed lines represent resonances that can be exploited in absorption based on either the cooperative or the distributive mechanism the dotted lines represent a resonance condition that applies to only the distributive case.

The synthesis of substituted polythiophenes for investigations of thermochromism has brought many examples of how the regioregular side chain substitution is central to the chromic phenomena. Some of these materials show two-phase behaviour with an isobestic point in the sequence of the spectra. As the optical absorption only reflects local properties, we have to understand what mechanism it is that will always keep the material in just two states, with no intermediate states. As the torsion of the main chain is the cause of the chromic behaviour, we have to understand more specifically what is the essential physics of a cooperative phase transition which takes the chain, or parts of the polymer chain, from one phase to the other. In many ways this might look like the falling of a row of dominoes, upon one fluctuation of one of the dominoes. In our case this would be... 

Cooper (1958) reported that the effect of sorbitol on vitamin B12 absorption did not occur when the vitamin was given in amounts equivalent to those normally found in the diet. Neither did it occur when sorbitol was given to gastrectomized rats. He makes the important point that sorbitol appears to enhance absorption only when vitamin B12 is given in the very large amounts used by Greenberg and his co-workers. Thus, sorbitol affects those rapid mechanisms of absorption of vitamin B12 which are independent of intrinsic factor. 

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