The dielectric profile of water at solid surfaces and the origin of the Stern layer

Electrostatic interactions between charged objects in water, such as lipid membranes, proteins and ions, are profoundly influenced by the polarity of the water. In a macroscopic approach, the effect of the water on electrostatic interactions is quantified by means of the static dielectric tensor, which is spatially constant and diagonal in bulk. Close to an interface, however, the effect of the water is more intricate. Using atomistic molecular dynamics simulations, we calculate the space-dependent dielectric response function of water at solid surfaces.

The proximity of a surface induces spatial ordering and orientation in the first few nanometres of water. Because of the very polar nature of water molecules, this water structure directly affects the electrostatic environment, making the dielectric tensor inherently space-dependent.

At planar surfaces, the dielectric tensor has two unique components, one parallel and one perpendicular to the interface. We calculate both components at hydrophilic and hydrophobic diamond surfaces (Fig. 1) using atomistic molecular dynamics simulations [1,2]. Whereas the parallel component roughly follows the water density (Fig. 2a-b) — as expected for non-interacting polar molecules — the perpendicular component has a radically different structure (Fig. 2c-d). The curve of the inverse perpendicular component goes through zero several times, which means that the dielectric response exhibits singularities and overscreening. Interestingly, we find that the quadrupole and higher order electric multipoles contribute significantly to the dielectric response.

To study the effect of the dielectric environment on macroscopic length scales, we incorporate the perpendicular component of the dielectric tensor in mean-field continuum theory. In particular, this strategy allows us to calculate the double layer capacitance, which is formed by a charged surface and its counterion cloud. The calculated capacitance as a function of bulk salt concentration agrees exceptionally well with experimental results [1]. We also study the effect on surface forces [2], ion distributions [3] and ion solvation energies [4].

The dielectric function of water in thin interfacial layers strongly affects macromolecular interactions because of the abundance of interfacial water at small length scales. Therefore, the dielectric function is of great interest, both in the field of colloid and biological physics, and in the view of nano-technological applications. Not only can our results help understanding fundamental biological interactions, they can also provide a guide for the design of industrial applications like high power density batteries based on the double layer capacitance. As the modified dielectric properties at interfaces are traditionally contained in the so-called Stern layer, this work provides a firm theoretical footing for the Stern layer concept.