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 system 1 , 2 , 3 , 4 . This effect is well known for layered systems ordered in one dimension, such as surfactant membranes 5 , 6 , smectic (layered) liquid crystals 7 and liquid crystalline polymers 8 , 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 scale 9 , 10 . In these smectic elastomers, fluctuations of the fluid layers are coupled to distortions of the underlying network, and are therefore energetically penalized 11 , 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.