![]() Staudinger, H.: Arbeitserinnerungen, Heidelberg: Hüthig Verlag 1961 Staudinger, H.: Organische Kolloidchemie, Braunschweig: Vieweg Verlag 1950 The limitation of the theory to essentially tree-like molecules and their unperturbed dimensions is outlined and the consequence of this error for the prediction of real systems is discussed. In particular, the dimensionless parameter ϱ= 1/2 〈R −1 h〉 z is shown to be a quantity of great relevance.įinally, the applicability of the cascade theory to rather complicated systems with unequal functional groups, substitution effect, vulcanization of chains and long rang correlation as a result of directed chain reactions is shown. An interpretation for the static and dynamic light scattering behavior is given, and new structure sensitive parameters are introduced by combination of the static with the dynamic light scattering data. In general, good agreement is found with the behavior predicted by the cascade theory. The second part of the article compares theory and experiment. The basis of the cascade branching theory and their rules for analytical calculations are displayed and elucidated with many examples. M w, 〈S 2〉 z, P z(q), D z etc., are uniquely determined by the extents of reaction of the various functional groups which, statistically speaking, are link probabilities. In the Flory-Stockmayer theory and the further developed cascade branching theory all average quantities which are measured by the two light scattering techniques, i.e. The representation of the molecules by rooted trees is shown to be most adequate for an extension of the theory of regularly branched chains to randomly branched polymers where statistical means have to be applied. Starting with simple regularly branched structures and ascending to the more involved randomly branched structures, the article presents various techniques for the calculation of the measurable quantities and concentrates on the polydispersity. the z-averages of the mean square radius of gyration 〈S 2〉 z, of the particle scattering factor P z(q), of the translational diffusion coefficient D z and of the reduced first cumulant Γ/q 2, as function of the weight average molecular weight M w is not possible without a comparison with special well defined models. An interpretation of the quantities measured by the two light scattering techniques, i.e. Information on the internal mobility and the translational motion of the mass centre can be obtained from the more recent technique of quasi-elastic or dynamic light scattering.Īs a result of the mostly statistical mechanism of reaction, many different isomeric structures and a broad molecular weight distribution are obtained on polymerizing monomers with more than two functional groups. The common technique for determining the shape of macromolecules is static light scattering. This article deals with branched macromolecules in dilute solution, where the individual molecules are observed. ![]() Both quantities are closely related to the architecture of the molecules. \): The time-dependent intensity of scattered light for (top) large particles and for (bottom) small particles.The striking properties of synthetic polymers and biological macromolecules are largely determined by their shape and the internal mobility. ![]()
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