Quenched random disorder and x-ray scattering in smectic elastomers.
In this work we examine layer fluctuations in a smectic elastomer with quenched random disorder induced by crosslinks. The system is analyzed in a continuum model and crosslinks are introduced as a random field in a macroscopic picture. In the case of small deformations and replica symmetry the intensity profile for x-ray scattering along the layer normal was determined for layer displacements smaller than the layer separation. In this regime it is predicted that for large enough crosslink densities the first-order diffraction pattern of the solid assumes a characteristic squared-Lorentzian form, showing a decay of short-range order over a length scale of 20 nm. Crosslinks are observed to disorder the system by decreasing the correlation length, which we show not to be a consequence of the random field. The coupling to random crosslinks is predicted to retard the decrease in the correlation length and hence found to stabilize the one-dimensional periodic layer structure against thermal fluctuations. The dependence of the correlation length on the crosslink density leads us to propose an estimate for the percolation limit of a smectic elastomer network.
Witkowski
L T
LT
Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 OHE, United Kingdom.
Terentjev
E M
EM
D003198:Computer Simulation; D020724:Elastomers / Q000737:chemistry*; D050866:Liquid Crystals / Q000737:chemistry*; D008956:Models, Chemical; D015233:Models, Statistical; D053838:Scattering, Small Angle; D014961:X-Ray Diffraction
D020724:Elastomers