Road to disorder in smectic elastomers

We present a high-resolution x-ray study of the effects of disorder induced by random cross-linking side-chain smectic elastomers. The influence of variation of the concentration and stiffness of the cross-link units on the disruption of the one-dimensional translational order is reported in detail. Precise analysis of the line shape of the quasi-Bragg peaks associated with the smectic layering indicates a transition from algebraic decaying ordering to disorder. The smectic line shapes can be described by the Caille correlation function convoluted with a finite-size factor represented by a stretched Gaussian (compressed exponential). The transition to disorder is signaled by a change in the exponent of the stretched Gaussian from 1 (simple Gaussian describing finite-size domains) via 0.5 (Lorentzian describing exponentially decaying short-range correlations) to < 0.5 (stretched exponential correlations). For a flexible cross linker the changeover occurs for concentration between 0.15 and 0.20, for a stiff cross linker below about 0.10. Broadening of the higher harmonics of the x-ray peak indicates strong nonuniform strain within finite-size domains and local deformations induced by randomly distributed dislocations.