Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany.
J Chem Phys. 2019 Sep 21;151(11):114906. doi: 10.1063/1.5118875.
Magnetic gels and elastomers are promising candidates to construct reversibly excitable soft actuators, triggered from outside by magnetic fields. These magnetic fields induce or alter the magnetic interactions between discrete rigid particles embedded in a soft elastic polymeric matrix, leading to overall deformations. It is a major challenge in theory to correctly predict from the discrete particle configuration the type of deformation resulting for a finite-sized system. Considering an elastic sphere, we here present such an approach. The method is in principle exact, at least within the framework of linear elasticity theory and for large enough interparticle distances. Different particle arrangements are considered. We find, for instance, that regular simple cubic configurations show elongation of the sphere along the magnetization if oriented along a face or space diagonal of the cubic unit cell. Contrariwise, with the magnetization along the edge of the cubic unit cell, they contract. The opposite is true in this geometry for body- and face-centered configurations. Remarkably, for the latter configurations but the magnetization along a face or space diagonal of the unit cell, contraction was observed to revert to expansion with decreasing Poisson ratio of the elastic material. Randomized configurations were considered as well. They show a tendency of elongating the sphere along the magnetization, which is more pronounced for compressible systems. Our results can be tested against actual experiments for spherical samples. Moreover, our approach shall support the search of optimal particle distributions for a maximized effect of actuation.
磁凝胶和弹性体是构建可在外磁场触发下实现可逆激发的软致动器的有前途的候选材料。这些磁场会引起或改变嵌入软弹性聚合物基质中的离散刚性颗粒之间的磁相互作用，从而导致整体变形。从离散颗粒构型正确预测有限尺寸系统产生的变形类型是理论上的一个主要挑战。考虑到弹性球体，我们在这里提出了这样一种方法。该方法原则上是精确的，至少在线性弹性理论的框架内，并且对于足够大的颗粒间距离是如此。考虑了不同的颗粒排列。例如，我们发现，如果沿立方单胞的面或空间对角线取向，则规则的简单立方构型会使球体沿磁化方向伸长。相反，如果沿立方单胞的边缘取向，则会收缩。对于体心和面心构型，在这种几何形状中则相反。值得注意的是，对于后一种构型，但磁化方向沿单胞的面或空间对角线，随着弹性材料泊松比的减小，收缩会恢复为膨胀。还考虑了随机配置。它们显示出沿磁化方向拉长球体的趋势，对于可压缩系统，这种趋势更为明显。我们的结果可以与球形样品的实际实验进行对比。此外，我们的方法将支持寻找最佳的颗粒分布，以实现最大的致动效果。
