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Homogeneous droplet nucleation has been studied for almost a century but hasnot yet been fully understood. In this work, we used the density gradienttheory (DGT) and considered the influence of capillary waves (CW) on thepredicted size-dependent surface tensions and nucleation rates for selected$n$-alkanes. The DGT model was completed by an equation of state (EoS) based onthe perturbed-chain statistical associating fluid theory (PC-SAFT) and comparedto the classical nucleation theory and the Peng--Robinson EoS. It was foundthat the critical clusters are practically free of CW because they are so smallthat 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 surfacetension. 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 fortuitouscoincidence their predictions are similar in the relevant range of criticalcluster sizes. The difference of the DGT predictions to the classicalnucleation theory computations is important but not decisive. Of the effectsinvestigated, the most pronounced is the suppression of the CW which causes asizable decrease of the predicted nucleation rates. The major differencebetween experimental nucleation rate data and theoretical predictions remainsin the temperature dependence. For normal alkanes, this discrepancy is muchstronger than observed, e.g., for water. The theoretical corrections developedhere have a minor influence on the temperature dependency. We provide empiricalequations correcting the predicted nucleation rates to values comparable withexperiments.

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