Xing Xiangjun, Baskaran Aparna
Department of Physics, Syracuse University, Syracuse, New York 13244, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Aug;78(2 Pt 1):021709. doi: 10.1103/PhysRevE.78.021709. Epub 2008 Aug 19.
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.
当手性各向同性弹性体进入低温胆甾相时，向列自由度倾向于有序排列并形成螺旋结构。由于向列弹性耦合，这也会导致聚合物网络发生弹性变形，该变形在局部与向列序同轴。然而，向列序的螺旋结构与能量上更有利的弹性变形不相容。因此，系统处于受挫状态，必须在向列有序和弹性变形之间达成适当的折衷。对于螺距远小于系统尺寸的强手性弹性体，Pelcovits和Meyer以及Warner已经研究过这个问题。在这项工作中，我们研究弱手性极限下的各向同性 - 胆甾相转变，此时螺距与系统尺寸相当或远大于系统尺寸。我们比较了两种可能的解：螺旋态和双扭曲态。我们发现双扭曲态能非常有效地使弹性自由能和手性向列自由能都最小化。另一方面，螺旋态的螺距受到向列弹性耦合的强烈影响。因此，这种状态在使手性向列自由能最小化方面效率不高。
