Dielectric Fluctuations and the Origins of Noncontact Friction

Dielectric fluctuations underlie a wide variety of physical phenomena, from ion mobility in electrolyte solutions and decoherence in quantum systems to dynamics in glass-forming materials and conformational changes in proteins. Here we show that dielectric fluctuations also lead to noncontact friction. Using high sensitivity, custom fabricated, single crystal silicon cantilevers we measure energy losses over poly(methyl methacrylate), poly(vinyl acetate), and polystyrene thin films. A new theoretical analysis, relating noncontact friction to the dielectric response of the film, is consistent with our experimental observations. This work constitutes the first direct, mechanical detection of noncontact friction due to dielectric fluctuations.

Figure 1

(a) Schematic of the experiment: $d$ is the tip-sample separation and $h$ is the thickness of the polymer. The tip-sample voltage ($V_{\mathrm{ts}}$) is applied to the metal layer underlying the dielectric while the cantilever is grounded. (b) Scanning electron micrograph of a cantilever like the one used in this study. The hexagonal paddle on the shaft of the cantilever provides a target for the fiber optic interferometer. The scale bar is $10\mu \mathrm{m}$. (c) Total friction is measured by driving the cantilever at ${\omega }_c$, abruptly turning off the drive signal and recording the ensuing decay to equilibrium shown here. (d) Sample-induced friction (dots) for $d=15\mathrm{nm}$ as a function of the applied tip-sample voltage, with a quadratic fit (red line).

Figure 2

Total friction (${\Gamma }_t$) at $V_{\mathrm{ts}}=\varphi +0.5\mathrm{V}$ for films of different thicknesses on epitaxial Au(111) (symbols) with theoretical predictions based on dielectric spectroscopy measurements and calculated using Eq. (3) (lines). Note the semilog scale. (a) Poly(methyl methacrylate): 40 nm film (blue squares, blue line) and 450 nm film (black squares, black line), plotted along with measured friction over blank Au(111) (red diamonds). (b) Poly(vinyl acetate): 12 nm film (blue triangles, blue line) and 450 nm film (black triangles, black line). (c) Polystyrene: 30 nm film (blue circles, blue line) and 450 nm film (black circles, black line).

Figure 3

Electric field power spectrum for 450 nm-thick films of PMMA (squares), PVAc (triangles), and PS (circles).

Figure 4

Total friction (${\Gamma }_t$) at $V_{\mathrm{ts}}=\varphi +0.5\mathrm{V}$ plotted on a log-log scale for (a) 350 nm PMMA on a Au(111)/mica substrate (squares) and 40 nm of Au, thermally evaporated onto 350 nm of PMMA on a quartz substrate (filled squares). (b) 150 nm epitaxial Au(111) on mica (diamonds) and 30 nm PS on an Au(111)/mica substrate (circles).