Energetics of twisted spindle-shaped polymer nematics

During deswelling, initially spherical bipolar polymer microparticles with nematic ordering become elongated spindle shapes in which the polymer chains are observed to follow a twisted pattern. Using geometric arguments, we have previously shown that this twisting pattern follows curves that are well-described by a type of spiral called a loxodrome, for which the angle between the principal directions of the surface and tangent vector to the spiral is constant. In this talk, I will discuss an energetic model of this loxodrome twisting and show that the observed behavior can be captured by the Frank free energy along with an additional term that constrains the length of the integral curves in the system, a key constraint in the geometric model. I will demonstrate that the model predicts distinct regimes for the expected twisting behavior that depend on the relative values of the Frank elastic constants of the system.