Isotropic-cholesteric transition of a weakly chiral elastomer cylinder

When a chiral isotropic elastomer is brought to the low-temperature cholesteric phase, the nematic degree of freedom tends to order and form a helix. Due to the nematoelastic coupling, this also leads to elastic deformation of the polymer network that is locally coaxial with the nematic order. However, the helical structure of nematic order is incompatible with the energetically preferred elastic deformation. The system is therefore frustrated and appropriate compromise has to be achieved between the nematic ordering and the elastic deformation. For a strongly chiral elastomer whose pitch is much smaller than the system size, this problem has been studied by Pelcovits and Meyer, as well as by Warner. In this work, we study the isotropic-cholesteric transition in the weak-chirality limit, where the pitch is comparable to or much larger than system size. We compare two possible solutions: a helical state as well as a double-twist state. We find that the double-twist state very efficiently minimizes both the elastic free energy and the chiral nematic free energy. On the other hand, the pitch of the helical state is strongly affected by the nematoelastic coupling. As a result, this state is not efficient in minimizing the chiral nematic free energy.