Titlebook: Excluded Volume Effects in Polymer Solutions; as Explained by the Lothar Schäfer Book 1999 Springer-Verlag Berlin Heidelberg 1999 Critical

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From a Microscopic Description to Simple Models: Some Folk-Lores little to do with a realistic microscopic description of macromolecules in a solvent. Indeed we use a kind of of ‘spring and bead’ model, where the macromolecule is replaced by a sequence of elastic springs connecting small (point-like) beads, which repel each other. Of all the microscopic structu

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Grand Canonical Description of Solutions at Finite Concentratione molecules contained in volume . is allowed to fluctuate. We only control the average concentration . via the chemical potential μ.. This has great technical advantages, allowing for a very simple analysis of the thermodynamic limit. In contrast, in the canonical ensemble, where the particle number

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Breakdown of the Expansions in the Excluded Volume Regionsired. We want to examine here whether this theory is indeed valid in all the parameter space of interest. We first consider quantities involving only a few chains, to be treated by the cluster expansion as derived in Chap. 4.

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Continuous Chain Model and Naive Two Parameter Theorymost naturally is formulated in terms of Edwards’ continuous chain model [Edw65, Edw66]. In the context of our general presentation of renormalization group theory this is not an essential topic, but in explicit calculations to be presented later we make use of the simplifications brought about by t

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The Renormalization Group: Fundamental Aspects involves a large amount of arbitrariness. Thus there should exist a mapping from segments of size ℓ = ℓ. to segments of size ℓ. which does not change macroscopic observables. It also should not affect the basic structure of the model, viz. Gaussian segments interacting via some local two-body repul

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