Spinodal Decomposition as an Interesting Example of the Application of Several Thermodynamic Principles

Abstract

Analysis of phase separation through spinodal decomposition and nucleation and growth.

Molecular Organization of the Early Stages of Nucleosome Phase Separation Visualized by Cryo-Electron Tomography

“…In a multicomponent system of two or more phases, the phase equilibrium criterion is that the chemical potential of a given component i must be equal in all phases where i is present: where μ i represents the chemical potential of the i th component and α, β, γ, … represent the different phases where i is present at equilibrium (Clerc and Cleary, 1995). The compositions of those two phases α and β (expressed as the mole fraction of component B in these phases in figure S25B) are fixed at a given temperature but change as a function temperature.…”

“…(B) The light gray color area is the instability region in which the system undergoes demixing through spinodal decomposition. In the area in between the binodal and spinodal, the system demix via nucleation and growth (Alberti et al, 2019; Clerc and Cleary, 1995). (C) Gibbs free energy diagram for nucleation indicating the presence of a critical nucleus ( r* ) and a nucleation barrier (ΔG * ) to overcome for growth to occur (Karthika et al, 2016).…”

“…Since the chemical potential of component i , µi , is the first derivative of the free energy with respect to the concentration of component i , ni , the equilibrium condition implies that , which can be obtained graphically at every temperature by finding the concentrations of both components for which the free energy has a common tangent (Fig. S25A) (Clerc and Cleary, 1995). The common tangent defines the points of the binodal curve, (Fig.…”

“…S25A), the mixture is said to be metastable; in this region, phase separation only happens in discrete locations throughout the mixture where some rare, large fluctuations in composition spontaneously occur, because the system must overcome an energetic barrier. These localized regions, which appear sparsely in the mixture, are called nucleation sites (Clerc and Cleary, 1995; Schmelzer et al, 2004). Classical Nucleation Theory (CNT) describes phase separation in terms of a process involving the formation of a thermodynamically unfavorable phase separated ‘nucleus’ and an increasingly thermodynamically favorable process of ‘growth’.…”

Synthetic Strategies

“…As shown in Figure 12.12, for a tiny crystal to increase its size, it must undergo an increase in its Gibbs free energy, a thermodynamically unfavorable situation. Nucleation and growth occurs in multicomponent systems such as alloys and glasses when the overall Gibbs free energy, G, versus composition, x (mole fraction), has positive concavity as shown in Figure 12.13 (Clerc and Cleary, 1995). It is not until the crystals grow beyond this critical size that further growth is thermodynamically favored.…”