# Nucleation Rates of Water Using Adjusted SAFT-0 EOS

## TL;DR

This study uses an adjusted SAFT-0 equation of state to accurately predict water nucleation rates, improving agreement with experimental data by accounting for anomalous density behavior below 277.15 K.

## Contribution

The paper introduces a modified SAFT-0 EOS for water that enhances nucleation rate predictions by incorporating temperature-dependent segment diameter adjustments.

## Key findings

- Adjusted SAFT-0 EOS significantly improves nucleation rate calculations.
- Nucleation rates increased by factors of 500 (GT) and 100 (CNT) after adjustment.
- GT predictions scale well with experimental data using Hale's model.

## Abstract

The SAFT-0 is an equation of state (EOS) that considers the effects of molecular association based on the statistical association fluid theory (SAFT). This EOS recently showed relatively successful calculations of the phase-equilibrium properties and the classical and nonclassical nucleation rates of methanol. Motivated by methanol results, we use the SAFT-0 EOS for water, in particular within the temperature range of anomalous density behavior below T_{max}=277.15 K. To do so, we adjust the effective temperature-dependent segment diameter in terms of the association energy in a way that the SAFT-0 EOS reproduces the water vapor-liquid equilibria and the vapor pressures, particularly in the temperature range where the data of nucleation rates of water are available (220-260 K). The Gibbsian form of classical nucleation theory (CNT) (known as the P-form) and nonclassical gradient theory (GT) calculations were carried out using the SAFT-0 EOS with and without including this adjusted diameter. Calculated rates were compared to the experimental values of W\"olk and Strey [J. Phys. Chem. B 2001, 105, 11683-11701]. In addition to the phase-equilibrium properties, this adjustment improved the nucleation rates from both GT and CNT by factors of 500 and 100, respectively. To explore this further, the GT and experimental rates were analyzed using Hale's scaled model [J. Chem. Phys., 2005, 122, 204509]. This analysis shows that the predictions of GT scale relatively well with those of the experimental data.