Theory of phase equilibria for model aqueous solutions of chain molecules: water + alkane mixtures

Abstract

This work is the first in a series of theoretical studies of aqueous solutions. We begin by examining the phase equilibria exhibited by a number of model binary mixtures of water and alkanes. The water molecules are modelled as hard spheres with four off-centre square-well hydrogen-bonding sites representing the two hydrogen atoms and the two electron lone pairs on the oxygen atom. Dispersion forces are included, but these are treated within the mean-field approximation. The alkanes are modelled as chain molecules formed from fused hard spheres, and dispersion forces corresponding to each hard-sphere site are also included. A simple thermodynamic perturbation theory is used to develop an augmented van der Waals equation of state which incorporates the asymmetry in the attractions, which arise because of the directional hydrogen-bonding sites, and the asymmetry in the repulsions caused by the molecular shape of the chains. We are the first to use a continuum equation of state to study the effects of hydrogen bonding and chain length on the phase equilibria of model aqueous solutions. The phase diagrams and critical lines for systems of increasingly longer chain molecules are determined to give a global picture of the phase equilibria. As well as the usual gas–liquid phase separation, liquid–liquid and gas–gas phase separation, positive, negative and double azeotropes, and Bancroft points are found. The double azeotropy is of a type which has not been obtained previously using equations of state of the van der Waals type. The extent of hydrogen bonding in different regions of the phase diagram is also used to examine the nature of the liquid–liquid phase equilibria. This confirms that the large degree of liquid–liquid immiscibility found in these systems is a consequence of strong water–water hydrogen bonding, and is not due to unfavourable intermolecular dispersive interactions between the water and the alkanes. Although the model systems are not chosen to reproduce the quantitative features of the phase equilibria of water + alkane mixtures, the theory reproduces the important qualitative trends remarkably well.