Modelling the thermodynamic properties of the mixture of water and polyethylene glycol (PEG) with the SAFT-γ Mie group-contribution approach

The SAFT-gamma Mie group-contribution (GC) equation of state (EoS) is employed to describe the thermodynamic properties of aqueous mixtures of polyethylene glycol (PEG), a polyether of great industrial and scientific interest. This prototypical system is chosen due to the intrinsic complexity of hydrogen-bonding polymers, and represents a critical test of the theory. Water is modelled as a single Mie segment with four association sites and PEG as a linear heteronuclear chain of three types of segments: the associating hydroxymethyl end group (CH2OH); the associating oxygen (cO); and the modified methylene group (CH2OE), which incorporates the effects that the proximity of an electronegative atom has on the electronic environment of the methylene group. The SAFT-gamma Mie model parameters characterizing the newly-defined group interactions are estimated to reproduce the liquid-liquid equilibrium (LLE) closed-loop miscibility gaps observed in the orthobaric phase diagram of PEG + water mixtures. The resulting model allows one to predict miscibility gaps in a temperature range between 350 K and 600 K, capturing both the UCST and the LCST within a 2% error with a close description of the overall phase behaviour. The predictive capability of the model is assessed by comparing the calculations with the experimental density of pure PEG, the enthalpy of mixing, and vapour-liquid equilibrium properties of PEG + water mixtures, with a good overall agreement. By coupling the present SAFT model with a recent thermodynamic model describing solubility in semi-crystalline polymers, the solubility of water in PEG below its melting point is semi-quantitatively captured both in the low- and high-humidity regimes. In particular, deliquescence - the melting of semi-crystalline PEG at high relative humidity - is predicted by simply accounting for the melting enthalpy of PEG crystals.