Witkowski L T, Terentjev E M
Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 OHE, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Nov;80(5 Pt 1):051701. doi: 10.1103/PhysRevE.80.051701. Epub 2009 Nov 10.
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.
在这项工作中，我们研究了具有由交联引发的淬火随机无序的近晶弹性体中的层波动。该系统在连续介质模型中进行分析，并且在宏观图像中将交联作为随机场引入。在小变形和 replica 对称性的情况下，对于小于层间距的层位移，确定了沿层法线方向的 X 射线散射强度分布。在这种情况下，预计对于足够大的交联密度，固体的一阶衍射图案呈现出特征性的平方洛伦兹形式，表明在 20 纳米的长度尺度上短程有序的衰减。观察到交联通过减小相关长度使系统无序，我们表明这不是随机场的结果。预计与随机交联的耦合会阻碍相关长度的减小，因此发现它能稳定一维周期性层结构以抵抗热波动。相关长度对交联密度的依赖性使我们提出了近晶弹性体网络渗流极限的估计。
