The concentration dependence of the chain dimensions of cubic lattice model chains under Θ-conditions

✍ Scribed by Olaj, Oskar Friedrich ;Pelinka, Kurt Heinz

• Publisher: Wiley (John Wiley & Sons)
• Year: 1976
• Weight: 294 KB
• Volume: 177
• Category: Article
• ISSN: 0025-116X
• DOI: 10.1002/macp.1976.021771127

✦ Synopsis

All existing theories on the concentration dependence of the dimensions of a linear macromolecule-a recent review of which has been given by Yamakawa"-qualitatively agree that the size of the polymer chain (e.g. expressed as the mean square distance between chain ends) should decrease with increasing concentration when the polymer forms an athermal solution with the solvent, or, more generally, the solvent is a good or at least a moderately good one. This qualitative prediction has been confirmed experimentally by neutron small angle scattering techniq~es'.~' on the one side, and model calculations with self-avoiding athermal lattice chains (chains without finite attraction or repulsion) on the other4'. Unfortunately, most of the existing theories express the relative decrease in size in form of a series expansion in an argument containing the binary cluster integral p of segmentsegment interaction as a factors-@. Due to the large value of [ j for athermal systems this leads to an extremely slow convergence of the series expansion, so that no quantitative comparison with the experimental or numerical findings could be carried However, all these theories agree inasmuch, as they predict a zero concentration dependence for [I = 0, namely for @-conditions. From a numerical study of the pair distribution function G(R) of model lattice chains at the @-state we had to learn" that,contrary to what has been assumed hitherto, G(R) is not unity, whichever the distance between the centers of mass of the two chains, R , might be, but is much lower than ' )