A new type of Maxwell stress in soft materials due to quantum mechanical-elasticity coupling

Abstract

All dielectrics deform when subjected to an electric field. This behavior is attributed to the so-called Maxwell stress and the origins of this phenomenon can be traced to geometric deformation nonlinearities. In particular, the deformation is large when the dielectric is elastically soft (e.g. elastomer) and negligible for most "hard"materials. In this work, we develop a theoretical framework which shows that a striking analog of the electrostatic Maxwell stress also exists in the context of quantum mechanical-elasticity coupling. The newly derived quantum-elastic Maxwell stress is found to be significant for soft nanoscale structures (such as the DNA) and underscores a fresh perspective on the mechanics and physics of polarons. We discuss potential applications of the concept for soft nano-actuators and sensors and the relevance for the interpretation of opto-electronic properties.

Quantum Coherent States and Path Integral Method to Stochastically Determine the Anisotropic Volume Expansion in Lithiated Silicon Nanowires

“…which is the product of electromagnetic intensity I(r) (Equations (14) and (15)) and the volume of the silicon cubic lattice [34]. The probability amplitude of U ij is part of the quantum harmonic oscillator and therefore is in a dynamic state.…”

“…It is defined as the probability of an electron occupying the upper conduction band . The average number of electrons in the upper conduction band is defined as = × ħ e (27) which is the product of electromagnetic intensity I(r) (Equations (14) and (15)) and the volume of the silicon cubic lattice [34]. The probability amplitude of U is part of the quantum harmonic oscillator and therefore is in a dynamic state.…”

“…In this application, the magnetic field is negligible which results in 𝜇 𝑖𝑗 being defined as unity or one. Equation ( 5) is also known as the Maxwell stress tensor [14,15]. When i = j, the three orthogonal directions that were discussed in the introduction, namely <110>, <111> and <112>, will be given by the matrix elements 𝜀 11 , 𝜀 22 and 𝜀 33 , respectively and are called the electric susceptibilities 𝜀 𝑖𝑗 for lithiated silicon.…”