Conditions of Spontaneous Dispersion and Formation of Thermodynamically Stable Colloid Systems

Abstract

The macrophase dispersion is thermodynamically favorable if the free energy change due to dispersion (isolation of n particles with radius r, at sufficiently low interfacial energy σ) is negative, i.e., ΔF = n4πr ²σ − TΔS < 0, where ΔS(C) is the entropy gain and C is the concentration. If there is a factor opposing dispersion to molecular dimension b, a negative minimum of ΔF at r > b may occur, i.e., formation of a thermodynamically stable colloid system takes place. In this article, the analysis of the ΔF = ΔF(r, σ, n, C ) function behavior for three different conditions is proposed: (i) C = constant, with a virtual maximum; (ii) r = constant, with a negative minimum; and (iii) n = constant, when this function is monotonic, in all cases, for monodisperse systems, with broad variation of σ. In all the three cases, the equation ΔF = 0 serves as a necessary condition for spontaneous dispersion and formation of a thermodynamically stable, lyophilic colloid system. Under normal temperatures and low concentrations, this needs small r∼10⁻⁶ cm and low σ∼10⁻²–10⁻¹ mJ/m². These conditions become “easier” for dispersion of an aggregate (e.g., σ on the order of units), and “more difficult” for highly concentrated systems (with σ decreasing to 10⁻³ mJ/m²). Essential changes and complications can be connected with polydispersity accounting. A special attention is paid to real physical systems corresponding to considered versions of the ΔF behavior.

Keywords:

• Spontaneous dispersion
• Thermodynamic stability
• Lyophilic systems

Acknowledgments

With a great gratitude, the author appeals to the memory of his teacher Peter A. Rehbinder, who established the founding principles of this doctrine. The author is indebted to A.V. Pertsov and L.A. Kochanova, the main participants in developing these ideas; to A.I. Rusanov, for fruitful discussions; to E.A. Amelina, V.V. Yaminsky, A.M. Parfenova, and N.P. Fedoseeva, who provided many experimental data cited in this article; and to Ch.R. O'Melia and A.S. Zelenev, for valuable assistance in editing the English text.