Relaxation time multistep process

First, do dynamical correlations exist in processes involving multiple saddles, such as structural changes of macromolecules in clusters and proteins In the conventional theory, it is supposed that consecutive processes of going over saddles take place independent of one another. In other words, the system loses its memory of the past immediately, since the vibrational relaxation within a well is assumed to be much faster than the escape from it and multistep processes are conventionally assumed to be Markov processes. To the contrary, when the characteristic time scale of IVR is comparable to that of the reaction, the system can keep dynamical correlations as it goes over successive saddles. 

Anianssons equations for the fast monomer relaxation process in micellar systems are explained in an elementary way. The relations which must exist between distribution curves and rate constants for the stepwise aggregation processes in order to obtain one single relaxation time are discussed. Anianssons method is finally applied to the general case of a multistep process with stepwise monomer association. 

The form of the distribution curves for any investigated system may differ from the ideal behaviour, which leads to a single relaxation time. Nevertheless, in a lot of cases only one fast relaxation time is obtained for multistep processes. Deviations from the distribution curves discussed above lead to nonexponential relaxations. (2) It Ccin be concluded that systems, which show a single fast monomer relaxation time within the experimental errors, have distribution curves not differing too much from the ideal form. 

A more rigorous approach to the description of the colloid surfactant diffusion to the interfaee was proposed by Noskov [133]. The reduced diffusion equations for micelles and monomers, which take into account the multistep nature of micellisation and the polydispersity of micelles, were derived for time intervals corresponding to the fast and slow processes using the method applied initially by Aniansson and Wall to uniform systems. Analogous equations have been derived later by Johner and Joanny [135] and also by Dushkin et al. [137]. Recently Dushkin has studied also the adsorption kinetics in the framework of a simplified model of quasi-monodisperse micelles. In this case the assumption of the existence of two kinds of micelles permits to study the main features of the surface tension relaxation in real micellar solution [138]. The main steps of the derivation of surfactant diffusion equations in micellar solutions are presented below [133, 134]. 

In this chapter we describe the common forms of viscoelastic behaviour and discuss the phenomena in terms of the deformation characteristics of elastic solids and viscous fluids. The discussion is confined to linear viscoelasticity, for which the Boltzmann superposition principle enables the response to multistep loading processes to be determined from simpler creep and relaxation experiments. Phenomenological mechanical models are considered and used to derive retardation and relaxation spectra, which describe the time-scale of the response to an applied deformation. Finally we show that in alternating strain experiments the presence of the viscous component leads to a phase difference between stress and strain. 

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