Classical van der Waals interactions between spherical bodies of dipolar fluid

The van der Waals interaction free energy $A_{\mathrm{int}}$ between two spherical bodies of Stockmayer fluid across a vacuum is calculated using molecular simulations and classical perturbation theory. The results are decomposed into their electrostatic and Lennard-Jones parts, and the former is shown to agree excellently with predictions from dielectric continuum theory. $A_{\mathrm{int}}$ is decomposed into its energetic and entropic contributions and the results are compared with analytical predictions. Finally, we expand the electrostatic part of $A_{\mathrm{int}}$ in a multipole expansion, and show that the surprisingly good agreement between the molecular and continuum descriptions is likely due to a cancellation of errors coming from the neglect of the discrete nature of the fluid within the dielectric description.

Figure 1

Schematic picture of the molecular system, together with definitions of relevant parameters.

Figure 2

(Color online) The electrostatic part $A_{\mathrm{int}}^{\left(\mathrm{el}\right)}$ of the interaction free energy, calculated using (a) Eq. (3) (black symbols) and Eq. (4) (red symbols), and (b) Eq. (6) using three values of the truncation ${\ell }_{\max }$. The solid curves represent dielectric continuum results [8], and the dotted vertical lines indicate where $D+2\delta ={\sigma }_{\mathit{LJ}}$, corresponding to the separation where particles in different bodies may start to overlap. In all cases, $\delta =0.73$ Å and $\varepsilon =80$ were used for the fittings to the dielectric continuum results. The error bars represent one standard deviation.

Figure 3

(Color online) The total (black) and attractive (red) parts of $A_{\mathrm{int}}^{\left(\mathit{LJ}\right)}$, calculated using Eq. (3). The dashed line represents the dielectric continuum results for the electrostatic interaction [black solid line in Fig. 2a], and the dotted black line as in Fig. 2. The error bars represent one standard deviation.

Figure 4

(Color online) The ratio $A_{\mathrm{int}}/U_{\mathrm{int}}$ for the electrostatic (black symbols) and LJ (red symbols) parts of the interaction. The solid black line gives analytical dielectric continuum results [8], the dotted red line shows $A_{\mathrm{int}}/U_{\mathrm{int}}=1$, and the dotted black line as in Fig. 2. The error bars represent one standard deviation.