Fiber stability analysis for in‐situ liquid crystalline polymer composites

Abstract We present a simple mathematical model based on classical theories of macroscopic elasticity that provides a fundamental description of the liquid crystal polymer (LCP) fiber break‐up instability that is observed during the annealing of in‐situ liquid crystal‐thermoplastic polymer composites. The thermodynamic model is solved using a number of consistent simplifying assumptions, and is restricted to thin liquid crystal polymer fibers. A significant feature of the liquid crystal surface energy incorporated in the model is the elastic storage due to deviations of the macroscopic orientation and of the orientational order from the preferred equilibrium values. The model predicts that thin LCP fibers are unstable to periodic surface perturbations that eventually would produce fiber break‐up and lead to an array of LCP droplets, as in the case of Rayleigh's fiber instability. The additional liquid crystalline elastic storage modes incorporated in the model, but not present in isotropic melts, tend to increase the magnitude of the critical wave‐length for fiber break‐up over that given by the Rayleigh criteria (i.e., fiber circumference) by a relatively small factor that depends on the ratio of the interfacial tension and the nematic anchoring energy.