Thermodynamic Model of Liquid−Liquid Phase Equilibrium in Solutions of Alkanethiol-Coated Nanoparticles

E. R. SOULÉ; C. E. HOPPE; J. BORRAJO; ROBERTO J. J. WILLIAMS

INDUSTRIAL & ENGINEERING CHEMICAL RESEARCH

AMER CHEMICAL SOC

Año: 2010 vol. 49 p. 7008 - 7016

0888-5885

A thermodynamic model for a mixture of alkanethiol-coated nanoparticles (NPs) and low molecular weight (non-polymeric) solvent is developed, and calculations of liquid-liquid phase equilibrium for different values of NP core radius, alkanethiol chain length, solvent molar volume and alkanethiol-solvent interaction parameter, are presented. The model takes into account swelling of NPs and dispersion of swollen NPs in free solvent. Swelling considers mixing of alkanethiol chains and solvent in the corona and stretching of the organic chains. Dispersion considers an entropic contribution based on Carnahan – Starling equation of state and an interaction term. Two different kinds of phase equilibrium are found. One of them, observed at high values of the interaction parameter, is the typical liquid-liquid equilibrium for compact NPs in a poor solvent where a complete phase separation is observed when cooling (increasing the interaction parameter). In diluted solutions, the miscibility of compact NPs in a poor solvent increases when increasing their size either by increasing the radius of the core or the length of the corona. This is due to the decrease of the surface interactions per unit volume between the corona and the free solvent. The second liquid-liquid equilibrium is observed at low values of the interaction parameter, where swelling of coronas is favored. In this region two different phases co-exist, one more concentrated in NPs that exhibit relatively compact coronas and the other one more diluted in NPs with extended coronas. In diluted solutions of NPs the deswelling of the fully extended coronas takes place abruptly in a very small temperature range, leading to a solution of compact NPs. This critical transition might find practical applications similar to those found for the abrupt shrinkage of hydrogels at a critical temperature.