Grasinger Matthew, Dayal Kaushik
Department of Civil and Environmental Engineering, Carnegie Mellon University, USA.
Soft Matter. 2020 Jul 15;16(27):6265-6284. doi: 10.1039/d0sm00845a.
Polymeric materials that couple deformation and electrostatics have the potential for use in soft sensors and actuators with applications ranging from robotic, biomedical, energy, aerospace and automotive technologies. In contrast to the mechanics of polymers that has been studied using statistical mechanics approaches for decades, the coupled response under deformation and electrical field has largely been modeled only phenomenologically at the continuum scale. In this work, we examine the physics of the coupled deformation and electrical response of an electrically-responsive polymer chain using statistical mechanics. We begin with a simple anisotropic model for the electrostatic dipole response to electric field of a single monomer, and use a separation of energy scales between the electrostatic field energy and the induced dipole field energy to reduce the nonlocal and infinite-dimensional statistical averaging to a simpler local finite-dimensional averaging. In this simplified setting, we derive the equations of the most likely monomer orientation density using the maximum term approximation, and a chain free energy is derived using this approximation. These equations are investigated numerically and the results provide insight into the physics of electromechanically coupled elastomer chains. Closed-form approximations are also developed in the limit of small electrical energy with respect to thermal energy; in the limit of small mechanical tension force acting on the chain; and using asymptotic matching for general chain conditions.
将形变与静电相结合的聚合材料有潜力用于软传感器和致动器，应用范围涵盖机器人技术、生物医学、能源、航空航天和汽车技术等领域。与运用统计力学方法研究了数十年的聚合物力学不同，形变和电场作用下的耦合响应在很大程度上仅在连续介质尺度上进行了唯象建模。在这项工作中，我们运用统计力学研究了电响应聚合物链的耦合形变和电响应的物理机制。我们从一个简单的各向异性模型开始，该模型用于描述单个单体对电场的静电偶极响应，并利用静电场能量和感应偶极场能量之间的能量尺度分离，将非局部和无限维的统计平均简化为更简单的局部有限维平均。在这种简化情况下，我们使用最大项近似推导了最可能的单体取向密度方程，并利用该近似推导了链自由能。对这些方程进行了数值研究，结果为机电耦合弹性体链的物理机制提供了见解。还在电能相对于热能较小的极限情况下、作用在链上的机械张力较小的极限情况下以及使用一般链条件的渐近匹配方法，开发了封闭形式的近似解。
