Flory theory randomly branched

In the 1940s and 1950s, random branching in polymers and its effect on their properties was studied by Stockmayer, Flory, Zimm and many others. Their work remains a milestone on the subject to this day. Flory dedicated several chapters of his Principles of Polymer Chemistry to non-linear polymers. Especially important at that time was the view that randomly branched polymers are intermediates to polymeric networks. Further developments in randomly branched polymers came from the introduction of percolation theory. The modern aspects of this topic are elaborated here in the chapter by W. Burchard. 

Use a Flory theory to determine the size R of this randomly branched polymer in a good solvent with excluded volume y. What is the size of a randomly branched polymer with N— 1000, b — 3A, v = 21.6A Compare this size to the size of a linear chain with the same degree of polymerization in the same good solvent and in -solvent. 

The fractal dimension of randomly branched polymers in the polymerization reaction can be estimated using Flory theory (see Section 3.1.2). The free energy of the characteristic branched polymer consists of entropic and interaction parts ... 

Hint Use Flory theory to estimate the swelling of a randomly branched... 

If the growth of proanthocyanidin chains is a random process leading to linear chains, then classical theory predicts that P /Pn will approach a maximum of 2.0. On the other hand if chain branching occurs, achieved by double-substitution of a flavanoid A-ring (Fig. 7.7.2), then this will result in values of P /Pn>2. The extent to which the dispersivity may exceed 2 for a particular P may be predicted from the classical Flory and Stockmayer theory (82). 

Figure 11.1 Final melting temperatures of ethylene copolymers as a function of branch content ethylene copolymers containing methyl (open circles), ethyl (open square), and n-propyl (solid triangles) branches hydrogenated polybutadiene (open triangles) ethylene-vinyl acetate (solid circles). Dashed line represents Flory s equilibrium theory for random copolymers (p = Xa), as given in Equation (11.2). Reprinted with permission from Reference [12]. Copyright 1984, American Chemical Society.

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