Past exam of the soft condensed matter course of the University of Cambridge / 2022 / Section B / 5 / e / Solution

For a small opposing force, the relevant parameter is $q=\beta F\delta \ll 1$. A Taylor series givessoIn particular the zero-force rate is finite, despite the numerator and denominator of the original expression both vanishing.

For $q\gg 1$, the exponential dominates the denominator:Opening a monomer-sized gap is exponentially rare at high opposing force. The algebraic $F^2$ prefactor belongs to this first-passage model and must not be discarded when quoting the leading asymptotic rate.