Reply to “Comment on ‘Simple improvements to classical bubble nucleation models’ ”

We reply to the Comment by Schmelzer and Baidakov [Phys. Rev. E 94, 026801 (2016)]. They suggest that a more modern approach than the classic description by Tolman is necessary to model the surface tension of curved interfaces. Therefore we now consider the higher-order Helfrich correction, rather than the simpler first-order Tolman correction. Using a recent parametrization of the Helfrich correction provided by Wilhelmsen et al. [J. Chem. Phys. 142, 064706 (2015)], we test this description against measurements from our simulations, and find an agreement stronger than what the pure Tolman description offers. Our analyses suggest a necessary correction of order higher than the second for small bubbles with radius $\lesssim 1$ nm. In addition, we respond to other minor criticism about our results.

Figure 1

Parameters in Eq. (3) as a function of the temperature $T^{*}(=k_{\mathrm{B}}T/\epsilon )$ obtained by Wilhelmsen et al. [6], where $T$, $k_{\mathrm{B}}$, and $\epsilon$ are the temperature, the Boltzmann constant, and the binding energy in the Lennard-Jones potential, respectively. The parameters obtained at $r_c=2.5\sigma \left(6.0\sigma \right)$ are shown as open (filled) symbols. The surface energies ${\gamma }_0$ in Ref. [7] are also shown as cross marks.

Figure 2

Comparison of surface tension between the MD simulations [3, 7] and theoretical models using Eqs. (1) and (3), as a function of the critical bubble radius, $r$. (a) Surface energy ratio $\gamma /{\gamma }_0$, obtained by our MD simulation (open symbols) and from Ref. [7] (filled symbols) with various temperatures. The Tolman equation, Eq. (1), with ${\delta }_T=0.3\sigma$ is shown by the solid curve. (b) Our MD simulations at $T^{*}=k_{\mathrm{B}}T/\epsilon =0.6,0.7,0.8$, and 0.855 (open symbols) and the theoretical model with Eq. (3) (solid curves). (c) Results by Baidakov and Bobrov [7] (filled symbols) and with Eq. (3) (solid curves).