Goh Segun, Menzel Andreas M, Wittmann René, Löwen Hartmut
Theoretical Physics of Living Matter, Institute of Biological Information Processing, Forschungszentrum Jülich, 52425 Jülich, Germany.
Institut für Physik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany.
J Chem Phys. 2023 Feb 7;158(5):054909. doi: 10.1063/5.0133207.
Magnetic gels are composite materials consisting of a polymer matrix and embedded magnetic particles. Those are mechanically coupled to each other, giving rise to the magnetostrictive effects as well as to a controllable overall elasticity responsive to external magnetic fields. Due to their inherent composite and thereby multiscale nature, a theoretical framework bridging different levels of description is indispensable for understanding the magnetomechanical properties of magnetic gels. In this study, we extend a recently developed density functional approach from two spatial dimensions to more realistic three-dimensional systems. Along these lines, we connect a mesoscopic characterization resolving the discrete structure of the magnetic particles to macroscopic continuum parameters of magnetic gels. In particular, we incorporate the long-range nature of the magnetic dipole-dipole interaction and consider the approximate incompressibility of the embedding media and relative rotations with respect to an external magnetic field breaking rotational symmetry. We then probe the shape of the model system in its reference state, confirming the dependence of magnetostrictive effects on the configuration of the magnetic particles and on the shape of the considered sample. Moreover, calculating the elastic and rotational coefficients on the basis of our mesoscopic approach, we examine how the macroscopic types of behavior are related to the mesoscopic properties. Implications for real systems of random particle configurations are also discussed.
磁性凝胶是由聚合物基体和嵌入其中的磁性颗粒组成的复合材料。它们相互之间存在机械耦合，从而产生磁致伸缩效应以及对外部磁场响应的可控整体弹性。由于其固有的复合性以及由此产生的多尺度性质，一个连接不同描述层次的理论框架对于理解磁性凝胶的磁机械性能是必不可少的。在本研究中，我们将最近开发的密度泛函方法从二维空间扩展到更实际的三维系统。沿着这些思路，我们将解析磁性颗粒离散结构的介观表征与磁性凝胶的宏观连续介质参数联系起来。特别是，我们纳入了磁偶极 - 偶极相互作用的长程性质，并考虑了嵌入介质的近似不可压缩性以及相对于破坏旋转对称性的外部磁场的相对旋转。然后我们探究模型系统在其参考状态下的形状，证实了磁致伸缩效应与磁性颗粒的构型以及所考虑样品形状的相关性。此外，基于我们的介观方法计算弹性和旋转系数，我们研究宏观行为类型如何与介观性质相关。还讨论了对随机颗粒构型实际系统的影响。
