Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 2 / Section G / 31 / c / ii

At room temperature, the same hard-core exclusion remains temperature independent. If the spring remains stiff, the conformational distribution remains broadly similar to the low-temperature expanded-coil distribution. Finite bond-length fluctuations increase with $\sqrt{k_{B}T/k}$ and can slightly enlarge the length scale and distribution width. The radial bond measure also favours lengths slightly above the harmonic minimum.

The comparison depends on the dimensionless stiffness $k{\sigma }^2/(k_{B}T)$, not on the word “room” alone. There is no attractive energy in this model to produce a low-temperature globule and high-temperature coil transition. Monte Carlo decorrelation speed can change with temperature and proposal scale, but the premise already stipulates adequate equilibrium sampling in both cases.