THE RADIUS EXPANSION FACTOR AND 2ND VIRIAL-COEFFICIENT FOR POLYMER-CHAINS BELOW THE 0 TEMPERATURE

The radius expansion factor as and second virial coefficient A2 for flexible polymers below the 0 temperature are investigated within the new framework of theory recently presented. It is then shown that the (quasi-)two-parameter scheme is still valid for alpha(s) and that the effect of chain ends can explain the observed M independence of A2 in the range of small molecular weight M for which A2 does not vanish at 0. As for as, some aspects of the coil-to-globule transition are discussed somewhat in detail. It is also shown that, if account is taken of the ternary-cluster integral beta3 along with chain stiffness, terms involving beta3 may be neglected compared to the binary-cluster integral beta2 in alpha(s) and A2, although beta3 appears separately in the third virial coefficient A3. Thus, the consideration of the effects of chain stiffness and chain ends along with beta2 and beta3 may give a consistent explanation of the observed behavior of alpha(s), A2, and A3 at, above, and below 0, while the binary-cluster approximation is actually good enough as far as only as and A2 are concerned.