On the validity of the Flory–Huggins approximation for semiflexible chains

Abstract

We have found exact limits on the validity of the Flory–Huggins approximate treatment of stiff chains on a lattice for small values of g, the fraction of g a u c h ebonds, by obtaining lower bounds for the total number of Hamilton walks W H (g) as a limiting case of the lattice model. The Flory–Huggins approximation underestimates the true entropy for all g<0.325. Specifically, the entropy does not become zero for g?0.227: there is a nonnegligible entropy at all g other than g=0. From this we show (1) the Flory modelc a n n o t have a first order transition from a disordered phase to a c o m p l e t e l y o r d e r e d c r y s t a l, and (2) the Gibbs–DiMarzio conclusion, that there is a second order phase transition at T 2 in the supercooled liquid phase when the state of zero entropy with g=g 0≳0 is reached, can be at best only a c o n j e c t u r e. The present analysis implies that one must use caution in predicting phase transitions when using the Flory–Huggins approximation.