Statistical field theory of polarizable polymer chains with nonlocal dipolar interactions
Statistical field theory of polarizable polymer chains with nonlocal dipolar interactions
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DOI：
10.1103/physreve.109.044501
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发表时间：
2024-04-03
影响因子：
2.4
通讯作者：
Dayal，Kaushik
中科院分区：
文献类型：
--
作者：
Khandagale，Pratik;Garcia-Cervera，Carlos;Dayal，Kaushik
聚合物软物质对外加电场的机电响应具有基本的科学兴趣，并且与传感和致动技术相关。几个现有的理论和数值方法的极化聚合物的组合施加电场和拉伸是基于离散的单体模型。在这些模型中，由于这些相互作用的非局部性，考虑单体上的诱导偶极子之间的相互作用是具有挑战性的。另一方面，统计场论的框架提供了一个连续的描述聚合物链，可能使一个易于处理的方式来考虑这些相互作用。然而，使用该框架的现有制剂已被限制到单体极化率的弱各向异性的情况。本文制定了一个通用的方法，统计场理论的框架内，占的偶极相互作用的非局部性质没有任何限制的各向异性或非线性的极化率的单体。该方法基于三个关键要素：（1）统计场论框架，其中离散单体被正则化为连续偶极子分布，（2）用连续偶极子分布作为强迫的局部静电偏微分方程代替非局部偶极子-偶极子相互作用，以及（3）极化和局部电场之间的完全一般关系的使用。场论中的连续描述使计算上易于处理的非局域到局域变换成为可能，而不是直接处理偶极-偶极相互作用。此外，它使得能够使用现实的物理机械系综，其中规定了平均远场施加的电场，而不是规定在聚合物域中的每个点处施加的场。应用该模型，使用有限元方法，研究的机电响应的聚合物链在合奏与固定的远场施加电场和固定链拉伸。非局部偶极相互作用被发现增加，在偶极-偶极相互作用被忽略的情况下，由数量级的极化和电场的大小，以及显着改变它们的空间分布。其次，研究了外加场与链的相对取向对局域电场和极化的影响。该模型预测，聚合物链的弹性响应是线性的，与高斯近似一致，并且在很大程度上不受所施加的电场的方向，虽然极化和局部电场分布显着的影响。
The electromechanical response of polymeric soft matter to applied electric fields is of fundamental scientific interest as well as relevant to technologies for sensing and actuation. Several existing theoretical and numerical approaches for polarizable polymers subject to a combined applied electric field and stretch are based on discrete monomer models. In these models, accounting for the interactions between the induced dipoles on monomers is challenging due to the nonlocality of these interactions. On the other hand, the framework of statistical field theory provides a continuous description of polymer chains that potentially enables a tractable way to account for these interactions. However, prior formulations using this framework have been restricted to the case of weak anisotropy of the monomer polarizability. This paper formulates a general approach based in the framework of statistical field theory to account for the nonlocal nature of the dipolar interactions without any restrictions on the anisotropy or nonlinearity of the polarizability of the monomer. The approach is based on three key elements: (1) the statistical field theory framework, in which the discrete monomers are regularized to a continuous dipole distribution, (2) a replacement of the nonlocal dipole-dipole interactions by the local electrostatics partial differential equation with the continuous dipole distribution as the forcing, and (3) the use of a completely general relation between the polarization and the local electric field. Rather than treat the dipole-dipole interactions directly, the continuous description in the field theory enables the computationally tractable nonlocal-to-local transformation. Further, it enables the use of a realistic statistical-mechanical ensemble wherein the average far-field applied electric field is prescribed, rather than prescribing the applied field at every point in the polymer domain. The model is applied, using the finite element method, to study the electromechanical response of a polymer chain in the ensemble with fixed far-field applied electric field and fixed chain stretch. The nonlocal dipolar interactions are found to increase, over the case where dipole-dipole interactions are neglected, the magnitudes of the polarization and electric field by orders of magnitude as well as significantly change their spatial distributions. Next, the effect of the relative orientation between the applied field and the chain on the local electric field and polarization is studied. The model predicts that the elastic response of the polymer chain is linear, consistent with the Gaussian approximation, and largely unchanged by the orientation of the applied electric field, though the polarization and local electric field distributions are significantly impacted.