Combination of monovalent and divalent sites on an associating species: Application to water

Abstract

This contribution is in honor of Professor Keith E. Gubbins, an international leader in developing advances in statistical mechanics and molecular simulation for engineering applications. The research presented here extends the SAFT model that Chapman proposed and developed while a graduate student with Professor Gubbins. In this manuscript, a thermodynamic perturbation theory within a multi-density formalism framework is extended to model species with a combination of monovalent and divalent association sites. Theory predictions are verified with Monte Carlo simulation results for different conditions of temperature, density, and angular size of the divalent site. The theory is applied to model water, where the two lone pairs of electrons on the oxygen atom are represented with a divalent site that includes cooperative hydrogen bonding. The theory results are in good agreement with experiments for saturated densities, vapor pressure, internal energy, and extent of hydrogen bonding.

Multiple insights call for revision of modern thermodynamic models to account for structural fluctuations in water

“…Figure 2 shows LDL fraction values from simulations, 12,51,60,73 two‐state model, 52 spectroscopy data 5,21 and from thermodynamic model predictions 7,46,70,72 . There is scatter from the various sources (see also Figure S1 of Supplementary Material).…”

“…An immediate conclusion is that the origin of these anomalies is not included in the models. There have been attempts to modify the models, either by including co‐operativity 72,81 or by including structural changes in the reference fluid 4 . The latter has been successful at describing some of water's anomalies, like the density maximum, but results are still very preliminary 4 …”

“…F I G U R E 5 LDL fraction isobars estimated using different methods. Solid lines are our estimations from PC-SAFT with the parameter set P2 72 and dashed lines are from simulations with the iAMOEBA water model. 60 F I G U R E 6 Variation of the average number of hydrogen bonds estimated from thermodynamic models (CPA, 70 PC-SAFT (P1), 46 ), experiments (NMR, 76 latent heat, 77 IR spectroscopy, 5 X-ray absorption, 9 pair correlation functions from X-Ray diffraction 78 ), and molecular simulations (of iAMOEBA water model).…”

“…Again, there is a clear quantitative difference for most of the bonded fractions, even though interestingly enough the set P2 has a near excellent agreement with iAMOEBA for X 3 at certain conditions. Additionally, in Supplementary Material 1 there are more comparisons of k-times bonded fractions F I G U R E 8 Fraction of water molecules (in liquid water) bonded k-times (k = 0-4) from our simulations using the iAMOEBA water model, our calculations PC-SAFT (with set P2) 72 and CPA. 70 All these calculations refer to 1 bar.…”

A modified perturbed chain‐statistical associating fluid theory equation of state for water which includes an association dependent hard sphere diameter

“…A complete equation of state for water would include both hydrogen bond cooperativity and a rigorous accounting of the structural transition toward tetrahedral symmetry. There has been progress in recent years on the inclusion of hydrogen bond cooperativity in SAFT approaches 9–11 . It was demonstrated that inclusion of hydrogen bond cooperativity can lead to accurate prediction of hydrogen bonding structure using input solely from a measured dimerization energy and quantum mechanics calculations.…”