Diffusiophoresis of core–shell structured (nano)particles in solution of general electrolytes

Abstract

This work addresses limitations in existing diffusiophoresis theories for soft particles, which have traditionally focused on colloids with a hard (impermeable) core and a permeable polyelectrolyte shell. Many core–shell (nano)particles feature however more complex structures with differentiated ion and fluid flow permeabilities in both their core and shell. We present here a comprehensive framework to describe how the diffusiophoretic motion of such composite particles depends on the electrostatic and hydrodynamic properties of their core and shell components. The derivations are based on the Debye-Hückel and flat-plate frameworks, which are suitable for particles with moderate charge and sizes significantly larger than the Debye layer thickness. Our theory is further applicable to a large spectrum of electrolyte types, including binary valence-symmetric and valence-asymmetric mixtures. The chemiphoretic and electrophoretic contributions to diffusiophoretic velocity are explicitly identified and analyzed, and we explore how electrolyte composition, as well as the hydrodynamic and electrostatic softness of the core and shell, influence particle motion direction. We also demonstrate how the limits of our closed-form expressions for particle diffusiophoretic velocity align with literature results for systems with restricted core and shell permeabilities to ions and/or fluid flow. Overall, our formulation provides a better understanding of the processes governing the diffusiophoresis of complex core–shell (nano)particles.