Generalized interface models for transport phenomena: unusual scale effects in composite nanomaterials

TL;DR

This paper introduces a generalized interface model for transport in nanomaterials, revealing unusual non-monotonic size effects and intrinsic length scales affecting effective conductivity.

Contribution

It develops a unified formalism combining classical interface models and captures complex behaviors observed in nanoscale composite structures.

Findings

Unusual non-monotone scale effect with a peak in conductivity at specific particle sizes

Introduction of intrinsic length scales governing universal scaling laws

Application to particle dispersion structures demonstrating complex size-dependent transport properties

Abstract

The effective transport properties of heterogeneous nanoscale materials and structures are affected by several geometrical and physical factors. Among them the presence of imperfect interfaces plays a central role being often at the origin of the scale effects. To describe real contacts between different phases some classical schemes have been introduced in literature, namely the low and the high conducting interface models. Here, we introduce a generalized formalism, which is able to take into account the properties of both previous schemes and, at the same time, it implements more complex behaviors, already observed in recent investigations. We apply our models to the calculation of the effective conductivity in a paradigmatic structure composed of a dispersion of particles. In particular we describe the conductivity dependence upon the size of the inclusions finding an unusual non-monotone scale effect with a pronounced peak at a given particle size. We introduce some intrinsic length scales governing the universal scaling laws.