Induced long-range order in crosslinked ‘one-dimensional’ stacks of fluid monolayers

Ordinary crystals are characterized by long-range translational order in all three dimensions. In lower-dimensional systems, in contrast, translational order is destroyed through the ‘Landau–Peierls instability’ — displacements from periodic ordering due to thermal fluctuations whose amplitude increases with the size of the system1,2,3,4. This effect is well known for layered systems ordered in one dimension, such as surfactant membranes5,6, smectic (layered) liquid crystals7 and liquid crystalline polymers8, which form ordered stacks of fluid monolayers. Smectic liquid-crystal polymers can be weakly crosslinked to form percolating elastomeric networks that still allow mobility on a molecular scale9,10. In these smectic elastomers, fluctuations of the fluid layers are coupled to distortions of the underlying network, and are therefore energetically penalized11, even though the network of crosslinks has a random nature and thus no three-dimensional translational order. Here we present a high-resolution X-ray diffraction study of a smectic elastomer that reveals the effects of crosslinking on long-range ordering. We find that the introduction of a random network of crosslinks enhances the stability of the layered structure against thermal fluctuations and suppresses the Landau–Peierls instability so as to induce ‘one-dimensional’ long-range ordering at length-scales up to several micrometres.