Romeis Dirk, Saphiannikova Marina
Leibniz-Institut für Polymerforschung Dresden e.V., Hohe Strasse 6, 01069 Dresden, Germany.
Polymers (Basel). 2021 Apr 22;13(9):1372. doi: 10.3390/polym13091372.
We consider magnetoactive elastomer samples based on the elastic matrix and magnetizable particle inclusions. The application of an external magnetic field to such composite samples causes the magnetization of particles, which start to interact with each other. This interaction is determined by the magnetization field, generated not only by the external magnetic field but also by the magnetic fields arising in the surroundings of interacting particles. Due to the scale invariance of magnetic interactions (O(r-3) in d=3 dimensions), a comprehensive description of the local as well as of the global effects requires a knowledge about the magnetization fields within individual particles and in mesoscopic portions of the composite material. Accordingly, any precise calculation becomes technically infeasible for a specimen comprising billions of particles arranged within macroscopic sample boundaries. Here, we show a way out of this problem by presenting a greatly simplified, but accurate approximation approach for the computation of magnetization fields in the composite samples. Based on the dipole model to magnetic interactions, we introduce the cascading mean-field description of the magnetization field by separating it into three contributions on the micro-, meso-, and macroscale. It is revealed that the contributions are nested into each other, as in the Matryoshka's toy. Such a description accompanied by an appropriate linearization scheme allows for an efficient and transparent analysis of magnetoactive elastomers under rather general conditions.
我们考虑基于弹性基体和可磁化颗粒内含物的磁活性弹性体样品。对这种复合样品施加外部磁场会使颗粒磁化，这些颗粒开始相互作用。这种相互作用由磁化场决定，该磁化场不仅由外部磁场产生，还由相互作用颗粒周围产生的磁场产生。由于磁相互作用的尺度不变性（在三维空间中为O(r - 3)），要全面描述局部和全局效应，需要了解单个颗粒内以及复合材料介观部分的磁化场。因此，对于包含数十亿个排列在宏观样品边界内的颗粒的标本，任何精确计算在技术上都是不可行的。在此，我们通过提出一种极大简化但准确的近似方法来计算复合样品中的磁化场，从而解决了这个问题。基于磁相互作用的偶极子模型，我们通过将磁化场在微观、介观和宏观尺度上分为三个贡献，引入了磁化场的级联平均场描述。结果表明，这些贡献相互嵌套，就像套娃玩具一样。这种描述加上适当的线性化方案，使得在相当一般的条件下能够对磁活性弹性体进行高效且透明的分析。
