Swelling of Branched Polymers
In what follows, we would like to discuss the configuration of randomly branched polymers in different environments. This configuration is accessible experimentally through light or neutron scattering experiments for instance, and some experimental results will be given. Before we come to this discussion, some words have to be said about the synthesis of these polymers, and about the influence of the experimental method itself on the conformation of the polymers. Although the detailed chemistry of the synthesis may be very involved, it is most probable that only a limited number of different classes only may be actually met. These may be characterized by the distribution of molecular weights. Hence, we will be concerned only with one such classes, which corresponds to the random percolation model1. This will be done in section II, and will provide the,distribution function. Our approach to the conformation of the polymers then will make use of a Flory — de Gennes theory2,3. Although it is not exact, this usually provides a fairly good approximation of the fractal dimensions. Thus we will consider the percolation problem from an energy point of view rather than from the usual geometric approach between any two monomers there is an interaction potential V(r), that may or may not be screened depending on the conditions. The case of a single polymer — or animal — will be considered in section III, whereas section IV deals with a polymer in the presence of many others in the reaction bath. With these results in hand, we may discuss the experimental results. In section V, we consider a sol, made of large but finite polymers below the threshold. Here the solution is heavily diluted before light scattering experiments are performed. We will argue that the screening of the interactions, which is important in the reaction bath, disappears upon dilution leading to a swelling of every individual polymer of the sol.
KeywordsFractal Dimension Weight Average Molecular Weight Single Polymer Individual Polymer Percolation Problem
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- 2.P.J. Flory, Principles of Polymer Chemistry, Cornell U. Press (1953).Google Scholar
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