Length dependence of rate constants for end-to-end association and dissociation of equilibrium linear aggregates

A semi-quantitative analysis is given of the length dependence of the rate constant for association (annealing) of two long linear aggregates in solution. The equilibrium constant for this process, or its inverse (fragmentation or dissociation), is relatively easy to formulate from appropriate partition functions. From these two ingredients, the length dependence of the rate constant for spontaneous fragmentation can be deduced. Numerical examples are included.