Outline 3 Dynamic Scattering

The foundations of the modem tireory of elementary gas-phase reactions lie in the time-dependent molecular quantum dynamics and molecular scattering theory, which provides the link between time-dependent quantum dynamics and chemical kinetics (see also chapter A3.11). A brief outline of the steps hr the development is as follows [27],... 

The paper is organized in the following way In Section 2, the principles of quasi-elastic neutron scattering are introduced, and the method of NSE is shortly outlined. Section 3 deals with the polymer dynamics in dense environments, addressing in particular the influence and origin of entanglements. In Section 4, polymer networks are treated. Section 5 reports on the dynamics of linear homo- and block copolymers, of cyclic and star-shaped polymers in dilute and semi-dilute solutions, respectively. Finally, Section 6 summarizes the conclusions and gives an outlook. 

The prerequisite for an experimental test of a molecular model by quasi-elastic neutron scattering is the calculation of the dynamic structure factors resulting from it. As outlined in Section 2 two different correlation functions may be determined by means of neutron scattering. In the case of coherent scattering, all partial waves emanating from different scattering centers are capable of interference the Fourier transform of the pair-correlation function is measured Eq. (4a). In contrast, incoherent scattering, where the interferences from partial waves of different scatterers are destructive, measures the self-correlation function [Eq. (4b)]. 

The equations for dynamic LS require a more detailed outline. Here a time correlation function (TCE) of the scattering intensity is measured that is given as [60]... 

The semiclassical mapping approach outlined above, as well as the equivalent formulation that is obtained by requantizing the classical electron-analog model of Meyer and Miller [112], has been successfully applied to various examples of nonadiabatic dynamics including bound-state dynamics of several spin-boson-type electron-transfer models with up to three vibrational modes [99, 100], a series of scattering-type test problems [112, 118, 120], a model for laser-driven... 

In Chapter 3 we went as far as we could in the interpretation of rocking curves of epitaxial layers directly from the features in the curves themselves. At the end of the chapter we noted the limitations of this straightforward, and largely geometrical, analysis. When interlayer interference effects dominate, as in very thin layers, closely matched layers or superlattices, the simple theory is quite inadequate. We must use a method theory based on the dynamical X-ray scattering theory, which was outlined in the previous chapter. In principle that formrrlation contains all that we need, since we now have the concepts and formtrlae for Bloch wave amplitude and propagatiorr, the matching at interfaces and the interference effects. 

In order to indicate the theoretical ideas involved in LEED crystallography, we now outline the main dynamical (i.e., multiple-scattering) methods used to compute 1-V curves for comparison with the experiment (cf., also References 2a and 2f). 

It is our objective in this chapter to outline the basic concepts that are behind sedimentation and diffusion. As we see in this chapter, gravitational and centrifugal sedimentation are frequently used for particle-size analysis as well as for obtaining measures of solvation and shapes of particles. Diffusion plays a much more prevalent role in numerous aspects of colloid science and is also used in particle-size analysis, as we see in Chapter 5 when we discuss dynamic light scattering. The equilibrium between centrifugation and diffusion is particularly important in analytical and preparative ultracentrifuges. 

First, we will describe briefly the biology of secretory cells in general and goblet cells in particular. Next, we will outline our earlier studies on the conformation of mudn networks using dynamic laser scattering. Short discussions on the Donnan swelling properties of the mucin network will bring us to the application of the theory of polymer gel phase transition to explain condensation and decondensation in secretion. 

Combination of static and dynamic laser light scattering is also useful to determine not only the size distribution but also the particle structure of polymer colloids such as the adsorbed surfactant layer thickness [73] and the formation of nanoparticles [74,75]. A recently developed method of determining the density of polymer particles is outlined below to illustrate the usefulness of laser light scattering as a powerful analytical tool for investigating more sophisticated colloidal problems [76-78]. 

Tanaka, Hocker, and Benedek first realized this essential nature of gds and developed a theory of the dynamics of gel networks [16]. According to their theory the quasi-elastic light scattering from gel networks became one of the standard methods of studying polymer gels. Here we briefly outline the theory of the dynamics of gels. 

The criterion outlined previously clearly expresses statisticality as a property of continuum states, and as such has little to do with bound-state dynamics. However, if the process is dominated by a resonance, or a number of resonances, then contact can be made with chaotic behavior in bound systems.75 Denoting Q as a projection operator onto a bound manifold and P = I - Q as its orthogonal projector (which includes the unbound manifold), it is always possible to express E,n"> in terms of the scattering solutions in the P space, as [with G = (E - ie - PHP)- ] ... 

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