Reverse Coarsening and the Control of Particle Size Distribution through Surfactant

Victor M Burlakov,Alain Goriely

doi:10.3390/app10155359

Abstract

The minimization of surface area, as a result of the minimization of (positive) surface energy, is a well-known driving force behind the spontaneous broadening of (nano) particle size distribution. We show that surfactant molecules binding to particle surfaces effectively decrease the surface energy and may change its sign. In this case, contrary to the expected broadening behavior, a minimum of free energy is achieved at the maximum surface area for all particles, i.e., when the particles are identical. Numerical simulations based on the classical Lifshitz–Slyozov–Wagner theory with surfactant-induced surface energy renormalization confirm the collapse of the particle size distribution. As the particle size evolution is much slower than particle nucleation and growth, the manipulation of surface energy with in-situ replacement of surfactant molecules provides a method for controlling particle size distribution with great potential for creating mono-disperse nanoparticles, a key goal of nanotechnology.

Highlights

The generation of identical nanoparticles [1,2,3,4,5,6,7] and fine nanostructures [8,9,10] is a key requirement for self-assembly processes in bottom-up nanotechnology
We present a thermodynamic mechanism for particle size stabilization and narrowing of a particle size distribution (PSD) by surfactant molecules binding to particle surfaces
Based on a free energy analysis, we demonstrate that there exists a range of parameters at which reverse coarsening (RC) occurs and, smaller precipitated particles grow at the expense of bigger ones

Summary

Introduction

The generation of identical nanoparticles [1,2,3,4,5,6,7] and fine nanostructures [8,9,10] is a key requirement for self-assembly processes in bottom-up nanotechnology. Known examples of PSD narrowing discussed in the literature include the so-called digestive ripening [1,2,3,22,23], inverse ripening [24,25,26,27], and size focusing during production-controlled growth [28,29] Some of these processes take place in the presence of surfactants, which are widely used in nanoparticle production, mainly to stabilize particles [30,31,32] and to tune the growth regimes towards the production of particles with required shapes and sizes [33,34,35]. Based on a free energy analysis, we demonstrate that there exists a range of parameters at which reverse coarsening (RC) occurs and, smaller precipitated particles grow at the expense of bigger ones This regime is spontaneous: i.e., it is thermodynamically driven and converts any initial distribution of particles into an array of almost identical particles [51]. The transition into this regime can be obtained by varying the surfactant concentration and/or the system’s temperature

Results and Discussion

Isolated Particle in a Binary Solution

Simulation of Reverse Coarsening in the Particle Ensemble

Conclusions