Anomalously low dielectric constant of confined water

TL;DR

Capacitance measurements reveal a low dielectric constant for atomically thin layers of water next to solid surfaces and reveal the presence of an interfacial layer with vanishingly small polarization such that its out-of-plane ε is only ~2, while the electrically dead layer is found to be two to three molecules thick.

Abstract

The dielectric constant of interfacial water has been predicted to be smaller than that of bulk water (= 80) because the rotational freedom of water dipoles is expected to decrease near surfaces, yet experimental evidence is lacking. We report local capacitance measurements for water confined between two atomically-flat walls separated by various distances down to 1 nm. Our experiments reveal the presence of an interfacial layer with vanishingly small polarization such that its out-of-plane dielectric constant is only approximately 2. The electrically dead layer is found to be two to three molecules thick. These results provide much needed feedback for theories describing water-mediated surface interactions and behavior of interfacial water, and show a way to investigate the dielectric properties of other fluids and solids under extreme confinement.

Figures (11)

• Figure 1: l Experimental setup for dielectric imaging. a Its schematic. The top layer and side walls made of hBN are shown in blue; graphite serving as the ground electrode is in black. The three-layer assembly covers an opening in a silicon nitride membrane (light brown). The channels are filled with water from the back. The AFM tip, kept always in a dry nitrogen atmosphere, served as the top electrode. b,c Cross-sectional schematics before (b) and after (c) filling the channels with water (not to scale). d Three-dimensional topography image of one of the devices. e-g AFM topography of the sagged top hBN for devices with different$h$ before filling them with water. Scale bars: $500 \mathrm{~nm} . \mathbf{h} \mathbf{- j}$ Topography profiles for the top layer (black) and the part not covered by hBN (cyan) as indicated by colorcoded lines in (d). Red curves: Same devices after filling with water.
• Figure 2: | Dielectric imaging of confined water. a-c Topographic images of the three devices in Fig. 1 after filling them with water. Scale bars: 500 nm . d-f Corresponding$d C / d z$. The shown images were obtained by applying a tip voltage of 4 V at 1 kHz (other voltages and frequencies down to 300 Hz yielded similar images). Commercial cantilevers with tips of $100-200 \mathrm{~nm}$ in radius were used to maximize the imaging sensitivity. $\mathbf{g}$ Averaged dielectric profiles across the channels in ( $\mathbf{d - f}$ ). $\mathbf{h}$ Simulated $d C / d z$ curves as a function of $\varepsilon_{\perp}$ for the known geometries of the three shown devices (Shown are the peak values in the middle of the channels). Symbols are the measured values of $d C / d z$ from (g). Their positions along the $x$-axis are adjusted to match the calculated curves. Bars and light-shaded regions: Standard errors as defined in Supplementary Information.
• Figure 3: | Dielectric constant of water under strong confinement. Symbols:$\varepsilon_{\perp}$ for water channels with different $h$. The $y$-axis error is the uncertainty in $\varepsilon_{\perp}$ that follows from the analysis such as in Fig. 2h. The $x$-error bars show the uncertainty in the water thickness including the residual sagging. Red curves: Calculated $\varepsilon_{\perp}(h)$ behavior for the model sketched in the inset. It assumes the presence of near-surface layer with $\varepsilon_{i}=2.1$ and thickness $h_{i}$ whereas the rest of the channel contains the ordinary bulk water. Solid curve: Best fit yielding $h_{i}=7.4 \mathring{\mathrm{A}}$. The dotted, dashed and dashed-dotted curves are for $h_{i}=3,6$ and $9 \mathring{\mathrm{A}}$, respectively. Horizontal lines: Dielectric constants of bulk water (solid) and hBN (dashed). The dielectric constant of water at optical frequencies (square of its refractive index) is shown by the dotted line.
• Figure 4: Fig. S1 | Devices for local dielectric imaging of confined water. a Optical micrograph of one of our devices. The top hBN layer is $\sim 45 \mathrm{~nm}$ thick and $h \approx 4 \mathrm{~nm}$. The free-standing SiN membrane appears in purple; the $\mathrm{Si} / \mathrm{SiN}$ wafer in green. The graphite layer is contacted with gold pads to serve as the ground electrode. Scale bar: $10 \mu \mathrm{~m}$. b Zoom into the central region of (a). The areas with nanochannels are shown by the two dashed rectangles. Regions with the hBN spacers not covered by the top hBN and used to measure $h$ are outlined by black dashes.
• Figure 5: Fig. S2 | Optical images of our devices after filling them with water. a Thick device ( $h \approx 242 \mathrm{~nm}$ ). Channels with water appear darker than the empty channels that are seen to the right of the image and not connected to the inlet (grey rectangle). b Thin ( $h \approx 3 \mathrm{~nm}$ ) device filled with water. Individual channels cannot be resolved on the micrograph. Scale bars: $10 \mu \mathrm{~m}$.