  Despite its limitations, mainly due to its simplicity, Flory theory has been
extended to many other important cases, e.g., linear chains with stiffness and
polymers of various topology in a confined space. Surprisingly, the severe
limitations of the applicability of the Flory-type free energy for cylindrical
confinement have not been well noticed. In this note, we present a simple
"renormalized" form of Flory energy for 1D system, from which one can obtain
the following three quantities consistently: the equilibrium end-to-end
distance of the chain, the confinement free energy, and the effective "Hookian"
spring constant of the chain. Our result has practical implications for many
experimental studies concerning DNA molecules in nano-/micro-channels.
