Partial volume of a polymer

With the help of the above-described apparatus, Francois et al.16 discovered a characteristic effect in linear polymer solutions. A preliminary study had already shown to these authors that the partial volume per mass and the branching ratio are related. A measurement of partial volumes per mass should in principle show a chain-end effect. This effect was observed however, another unexpected effect appeared. 

Problems concerning end-effects for long chains have already been mentioned in Chapter 1. The chemical structure of a chain with polymerization degree N can be represented by 

In the following, (N + 2) will be replaced by N, but before discussing this formula, let us consider the process which leads to the determination of v. 

The quantities measured in the experiment are the mass per volume of solution pt and the mass per volume of pure solvent °p0. The apparent partial volume per mass of polymer is deduced from these (measured) quantities by applying eqn (5.2.6). The partial volume per mass is itself a function of w, and 

The authors quoted above determined the apparent partial volume per mass of polymer wt. However, they did not obtain the real volume per mass w,. Therefore, we shall only consider the apparent volume of the chain 

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Vo = no/ris, no being the number of I.MWl. moles, ns the number of moles of the lattice cells, V, the molar volume of the ith polymer homologue, Vq the molar volume of LMWL, Vp the specific partial volume of a polymer in solution (in a polynary mixture). 

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