Modelling Polymer Particle Deformation on Mineral Surfaces ‐ Part I: Validation of Initial Concepts

Abstract

Summary: A simple model based on elastic and attraction forces is proposed to describe the spreading of a cross-linked polymer particle on one or two surfaces. The model considers the internal elastic forces between the knots of reticulation and the external attraction forces between the particle and the mineral surface. The deformation and therefore the final shape of the particle is a resultant of the applied forces. The model is validated by fitting with experimental data of latex spreading on mineral surfaces, and the next steps towards using this knowledge to help design new particle structures and morphology are outlined.

Elastic Modulus of a Polymer Nanodroplet: Theory and Experiment

“…Two types of forces were introduced in their algorithm, governing the droplet's wetting behavior: elastic forces between the knots of reticulation, and attraction forces between each knot and the substrate. Araujo et al 22 tested their model with success against the experimental data of Lau et al 15 Engqvist et al 20 performed similar experiments to those of Lau et al, 15 investigating statics as well as dynamics of spreading. They borrowed the theoretical model of Lau et al 15 not for the purposes of testing it against their own experiments but rather for illustrating its mathematical consistency, unlike Lau et al, 15 who did compare their theory against experiment.…”

“…Whereas adsorption and deformation of isolated polymer droplets have attracted considerable attention through experimental techniques, − ranging from light scattering to scanning electron microscopy (SEM) and atomic force microscopy (AFM), theoretical and computational approaches ,− have fallen behind, with the exception of molecular dynamics − (MD) and Monte Carlo − (MC) simulations, which offer treatments from a microscopic viewpoint and are usually limited to short time scales for equilibration and to length scales in the 10 nm range . Structures usually examined in experiments can be larger by 1 order of magnitude or more, calling for an alternative approach.…”

“…Lau et al 15 also scanned profiles of latex droplets adsorbed on silica using AFM. Recently, Araujo et al 22 developed a simple computer model according to which a polymer droplet is conceptualized as a spherical spring matrix, with each spring representing a polymer chain between two knots of reticulation. Two types of forces were introduced in their algorithm, governing the droplet's wetting behavior: elastic forces between the knots of reticulation, and attraction forces between each knot and the substrate.…”

“…For the first time in the literature, we employed such a theory to predict an effective elastic modulus for adsorbed droplets of a range of nanoscopic sizes (5−100 nm) by utilizing the experimental data of Lau et al, 15 Engqvist et al, 20 and our own. Through a continuum theory approach, as opposed to a microscopic theory, we do not confine ourselves to a particular type of polymeric material, as is, for example, the case with the work of Araujo et al, 22 where their computer code specifically models the cross-linked elastomeric structure. We offer an extensive discussion of our findings.…”