Surface electrostatics: theory and computations

Abstract

The objective of this work is to study the electrostatic response of materials accounting for boundary surfaces with their own (electrostatic) constitutive behaviour. The electric response of materials with (electrostatic) energetic boundary surfaces (surfaces that possess material properties and constitutive structures different from those of the bulk) is formulated in a consistent manner using a variational framework. The forces and moments that appear due to bulk and surface electric fields are also expressed in a consistent manner. The theory is accompanied by numerical examples on porous materials using the finite-element method, where the influence of the surface electric permittivity on the electric displacement, the polarization stress and the Maxwell stress is examined.

Aspects of interface elasticity theory

“…With decreasing scale follows an increasing area-to-volume ratio where interface elasticity theory plays an increasingly important role in the overall behavior of materials resulting in size effects. With the emerging applications of nanomaterials [8–13] and the utility of surface elasticity theory to capture the behavior of solids at the nano-scale and particularly the size effect [14–23] the importance of interface elasticity theory has dramatically increased. As an example, whereas the yearly number of citations to the work of Gurtin and Murdoch [6] during the period 1975–2000 amounted to a few, the yearly number of citations grew exponentially after year 2000 and the total number of citations up to 2015 exceeds 1000.…”

Size Effects in a Silica-Polystyrene Nanocomposite: Molecular Dynamics and Surface-enhanced Continuum Approaches

“…In this work, it is hypothesized that the NC's volume-fraction needs to be interpreted differently in the context of MD and SEC theories. SEC is proven to be a promising approach to consider nanoscale problems (20)(21)(22)(29)(30)(31). For both the MD and CM simulations we avoid any constraints, such as making NPs rigid (8).…”

Interface properties influence the effective dielectric constant of composites

“…Here, we briefly summarize our work in [20], that recently presented a continuum mechanics framework for surface electrostatics. The results of the theory are valid for closed material interfaces, thus in the sequel we refer directly to composites with energetic interfaces.…”

“…Variational principles allow us to express the electric displacement in the bulk, d, and on the surface, d, in terms of the internal potential energies in the bulk, V int (e), and on the surface, V int ( e), respectively, as [20] …”

“…The model identifies the effective dielectric constant (relative electric permittivity) of the composite, taking into account the independent behaviour of the interface between the particle and the matrix, in the spirit of the surface electrostatic theory presented in [20]. In contrast to the classical sphere's assemblage method, this manuscript takes the interface into account and therefore, the size effect is intrinsically inherited in this study.…”