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Quenched random disorder and x-ray scattering in smectic elastomers.

L T Witkowski¹, E M Terentjev

¹Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 OHE, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 7, 2010

Summary

This study reveals how crosslinks in smectic elastomers create disorder, affecting layer fluctuations. Increased crosslinks stabilize the material

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Area of Science:

Materials Science
Soft Matter Physics
Polymer Science

Background:

Smectic elastomers exhibit unique layer fluctuations influenced by quenched random disorder.
Crosslinks, introduced as a random field in a continuum model, are key to understanding this disorder.

Purpose of the Study:

To analyze layer fluctuations in smectic elastomers with disorder induced by crosslinks.
To investigate the impact of crosslink density on the material's structural properties and stability.

Main Methods:

Analysis using a continuum model with crosslinks represented as a random field.
Determination of the x-ray scattering intensity profile along the layer normal under small deformations and replica symmetry.
Examination of layer displacements smaller than the layer separation.

Main Results:

A characteristic squared-Lorentzian form is predicted for the diffraction pattern at sufficient crosslink densities, indicating short-range order decay over 20 nm.
Crosslinks decrease the correlation length, a phenomenon not solely due to the random field.
The coupling to random crosslinks retards the decrease in correlation length, stabilizing the layer structure.

Conclusions:

Crosslinks significantly influence the order and stability of smectic elastomer layer structures.
The study provides insights into the relationship between crosslink density and correlation length.
An estimate for the percolation limit of smectic elastomer networks is proposed based on correlation length dependence.