# Predictions of homogeneous nucleation rates for $n$-alkanes accounting for the diffuse phase interface and capillary waves

## TL;DR

This study improves the prediction of homogeneous nucleation rates for n-alkanes by incorporating capillary wave effects and a density gradient theory, addressing discrepancies with experimental data.

## Contribution

It introduces a correction for capillary wave effects on surface tension within the density gradient theory for n-alkanes, enhancing nucleation rate predictions.

## Key findings

- Capillary waves decrease surface tension and nucleation rates.
- Critical clusters are nearly free of capillary wave effects.
- Theoretical corrections have minor impact on temperature dependence.

## Abstract

Homogeneous droplet nucleation has been studied for almost a century but has not yet been fully understood. In this work, we used the density gradient theory (DGT) and considered the influence of capillary waves (CW) on the predicted size-dependent surface tensions and nucleation rates for selected $n$-alkanes. The DGT model was completed by an equation of state (EoS) based on the perturbed-chain statistical associating fluid theory (PC-SAFT) and compared to the classical nucleation theory and the Peng--Robinson EoS. It was found that the critical clusters are practically free of CW because they are so small that even the smallest CW wavelengths do not fit into their finite dimensions. The CW contribute to the entropy of the system and thus decrease the surface tension. A correction for the effect of CW on the surface tension is presented. The effect of the different EoSs is relatively small because by a fortuitous coincidence their predictions are similar in the relevant range of critical cluster sizes. The difference of the DGT predictions to the classical nucleation theory computations is important but not decisive. Of the effects investigated, the most pronounced is the suppression of the CW which causes a sizable decrease of the predicted nucleation rates. The major difference between experimental nucleation rate data and theoretical predictions remains in the temperature dependence. For normal alkanes, this discrepancy is much stronger than observed, e.g., for water. The theoretical corrections developed here have a minor influence on the temperature dependency. We provide empirical equations correcting the predicted nucleation rates to values comparable with experiments.