Dielectric Profile of Interfacial Water and its Effect on Double-Layer Capacitance

The framework for deriving tensorial interfacial dielectric profiles from bound charge distributions is established and applied to molecular dynamics simulations of water at hydrophobic and hydrophilic surfaces. In conjunction with a modified Poisson-Boltzmann equation, the trend of experimental double-layer capacitances is well reproduced. We show that the apparent Stern layer can be understood in terms of the dielectric profile of pure water.

Figure 1

Snapshots from the simulations of the (a) hydrophilic and (b) hydrophobic surfaces and (c)–(d) corresponding water density profiles $n(z)$ without an external electric field. All graphs have the same $z$ scale, with $z=0$ fixed at the outermost carbon atoms for the hydrophobic and at the oxygen atoms of the hydroxyl groups for the hydrophilic surface.

Figure 2

The parallel dielectric function ${\epsilon }_{\parallel }$ next to a (a) hydrophilic and a (b) hydrophobic diamond calculated from polarization fluctuations [Eq. (6), solid lines] and for an external electric field $E_{\parallel }=0.05\mathrm{V}/\mathrm{nm}$ [Eq. (5), dashed lines]. The inverse perpendicular dielectric function ${\epsilon }_{\perp }^{-1}$ next to a (c) hydrophilic and a (d) hydrophobic diamond from fluctuations [Eq. (8), solid lines] and for an external electric field $D_{\perp }/{\epsilon }_0=\pm 0.5\mathrm{V}/\mathrm{nm}$ [Eq. (7), dashed lines]. The dotted lines denote the dipole contribution for an applied external field.

Figure 3

Double-layer capacitance from Eq. (10) in the limit ${\sigma }_0\to 0$, using ${\epsilon }_{\perp }^{-1}(z)={\epsilon }_{\mathrm{bulk}}^{-1}$ (black lines), ${\epsilon }_{\perp }^{-1}(z)$ from MD (solid colored lines), and the sharp-kink-approximation using $z_{\perp }^{\mathrm{DDS}}$ (broken lines). The blue lines correspond to hydrophilic and the red lines to hydrophobic surfaces. Circles denote experimental data [18]. (a) Surface charge ${\sigma }_0$ located at $z=0$. The dotted lines include a soft ion repulsion $\mu (z)=\alpha \exp [1-z/\lambda ]$ and use ${\epsilon }_{\mathrm{bulk}}^{-1}$ (black) or the sharp-kink approximation (red and blue). (b) Surface charge located at $z=-0.1\mathrm{nm}$ with ${\epsilon }_{\perp }^{-1}=1$ for $z<0$, using ${\epsilon }_{\perp }^{-1}(z)={\epsilon }_{\mathrm{bulk}}^{-1}$ for $z>0$ (solid line) and the sharp-kink approximation (dashed lines).