Buckling of semiflexible filaments under compression

A model for filament buckling at finite temperatures is presented. Starting from the classical worm-like chain model under constant compression, we use a mean-field approach for filament inextensibility to find the complete partition function. We find that there is a simple interpolation formula that describes the free energy of chains or filaments as a function of end-to-end separation, which spans the whole range of filament stiffnesses. Using this formula we study the buckling transition of semiflexible filaments and find that kinetics plays an important role. We propose that the filament buckling is essentially the first order transition governed by the kinetics of escaping a local free energy minimum. A simple model for the kinetics is put forward, which shows the critical buckling force for a filament is reduced by a fraction that has a universal scaling with temperature with an exponent ν = 0.56.