Past exam of the quantum condensed matter course of the University of Cambridge / 2007 / Section A / A3 / b / Solution

Here $R$ denotes a typical chain size, such as an rms end-to-end distance of a polymer chain, rather than the mean end-to-end vector of an isotropic solution, which is zero. The Flory approximation gives $R\sim a{N}^{3/5}$ in a good solvent, an ideal chain has $R\sim a{N}^{1/2}$ in a theta solvent, and a compact polymer globule has size $R\sim a{N}^{1/3}$ in a strongly poor solvent. These are scaling estimates with order-one prefactors omitted, treating the stated $N$ as the segment count associated with the supplied statistical length.