Pure reorientation diffusion model

Kievan et al. (1979) measured the P T, and NOE for calf thymus nucleosomes (Table IV) and compared the results with the DNA extracted from the nucleosomes (Table I). Using the internal diffusion model [Eqs. (20) and (21)] with an isotropic tumbling time estimated from electric dichroism measurements for the overall reorientation and assuming only dipolar relaxation, the internal motion effecting P relaxation was determined to have a correlation time of 0.4 ns. That value is the same as calculated for DNA, leading to the conclusion that protein binding to DNA in nucleosomes has little effect on the internal motion. Substitution of H2O for DjO does have an influence on J, (Table IV but not much on NOE, unlike P relaxation in pure DNA which is not affected by H2O substitution. 

Models considering diffusion in the bulk as the only rate controlling process are called pure diffusion controlled. When the diffusion is assumed to be fast in comparison to the transfer of molecules between the subsurface and the interface the model is called kinetic-controlled or barrier-controlled. Both steps are taken into account in so-called mixed diffusion kinetic controlled models. Van den Tempel proposed processes within the adsorption layer to be considered instead of hypothetical adsorption barriers [18, 19, 20]. We believe that such models, which account for actual physical processes within adsorption layers, such as reorientation of molecules, their dimerisation and formation of clusters, although explanations for all known cases of anomalous adsorption kinetics do not exist yet, have to be preferred over any formal model. However, reliable experimental evidence for a slower surface tension decrease caused by aggregation within the adsorption layer does not allow the conclusion that this is an exclusive mechanism. 

For a modelling of adsorption processes the well-known integro-differential equation (4.1) derived by Ward and Tordai [3] is used. It is the most general relationship between the dynamic adsorption r(t) and the subsurface concentration e(0,t) for fresh non-deformed surfaces and is valid for kinetic-controlled, pure diffusion-controlled and mixed adsorption mechanisms. For a diffusion-controlled adsorption mechanism Eq. (4.1) predicts different F dependencies on t for different types of isotherms. For example, the Frumkin adsorption isotherm predicts a slower initial rate of surface tension decrease than the Langmuir isotherm does. In section 4.2.2. it was shown that reorientation processes in the adsorption layer can mimic adsorption processes faster than expected from diffusion. In this paragraph we will give experimental evidence, that changes in the molar area of adsorbed molecules can cause sueh effectively faster adsorption processes. 

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