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-like transition governed by the kinetics of escaping a local free energy minimum. A simple model for the kinetics is put forward, which approximates the critical buckling force for a filament at non-zero temperatures. We find that the approximate value for the finite temperature buckling force is smaller that the zero temperature buckling force by a fraction that has a simple scaling with temperature.