The Configuration of Real Polymer Chains

The average configuration of polymer molecules in solution is markedly influenced by the obvious requirement, ordinarily disregarded in problems relating to molecular configuration, that two elements of the molecule are forbidden from occupying the same location in space. The influence of spatial ``interferences'' between different segments of the molecule on its average configuration has been investigated by statistical and thermodynamic methods. It is shown that if the average linear dimension of a polymer chain is to be taken proportional to a power of the chain length, that power must be greater than the value 0.50 previously deduced in the conventional ``random flight'' treatment of molecular configuration. This power should approach 0.60 for long chain molecules in good solvents. With increase in size of the solvent molecule, the influence of interference on molecular configuration diminishes, vanishing entirely in the extreme case of a solvent which is also a high polymer. The effect of a heat of interaction between solvent and polymer may also be incorporated quantitatively in the theory. A positive heat of mixing (poor solvent) tends to offset the expansive influence of interference, and the exponent referred to above tends to approach 0.50. The results are of foremost significance in the interpretation of the intrinsic viscosity and its dependence on the polymer constitution and on the solvent. It is pointed out that the spatial dimensions of the irregularly coiled polymer molecule cannot be correlated directly with hindrance to rotation about chain bonds, unless the expansion of the configuration due to interference and the effects of the heat of dilution are first of all taken into account.