The dilution wave in polymer crystallization is described by Fisher’s reaction-diffusion equation

Monodisperse long-chain alkanes such as C198H398 form lamellar crystals in both extended- and folded-chain forms. Folded-chain crystals are in a meta-stable equilibrium with polymer solution at a concentration CF. The crystal growth rate is virtually zero at this point, due to the self-poisoning phenomenon. If extended-chain crystallization is initiated from this state, a wave of crystallization proceeds through the solution, termed the dilution wave. The solution concentration falls as the wave passes, until a value CE is reached that is in equilibrium with the extended-chain crystal phase. We write down a reaction-diffusion equation to describe the dilution wave, and show that this is equivalent to Fisher’s equation, which has previously been used to describe many other traveling wave phenomena. Numerical solutions of the equation are used to show examples of the wave shape.