Electric-Field-Induced Friction Reduction and Control

Friction is always present when surfaces in contact are set in motion. In this work I describe how a precise, active control of the global friction is possible by adjusting the local molecular conformation of a polyelectrolyte coating via the application of an alternating electric field. The intensity of the applied field determines the degree of interpenetration between polymer brushes in contact, regulating chain stretching while sliding, which is the process at the origin of the global friction. The dynamics of the problem is controlled by the relaxation times of the polyelectrolyte.

Figure 1

Interaction forces between mica surfaces (thickness $4.018\mu \mathrm{m}$) coated with a brush layer of ${\mathrm{PS}}_{36}{\mathrm{PAA}}_{125}$ immersed in water $p\mathrm{H}$ 10.1 (a) Normal force $F$ (normalized by the radius of curvature of the surfaces $R$) vs surface separation $D$. The force profiles were measured during quasistatic approach (closed circles) and separation (open circles) of the surfaces, and upon application of an alternating voltage (crosses, 450 Hz, $20{\mathrm{V}}_{p\mathrm{\text{−}}p}$), measured 30 min after the application of the potential difference was started. For compressions outside the hatched zone, friction was below the detection limit of our instrument. Inset: Log-linear representation. The model described in the text (dashed line) fails to fit the data at high compressions. Adding a term proportional to $D^{-3}$ (red dotted line) provides an accurate description of the data. (b) Friction forces. A dramatic reversible reduction in $F_f$ is immediately observed upon the application of a potential difference between silver electrodes deposited in the back side of the surfaces (square wave, 450 Hz, $20{\mathrm{V}}_{p\mathrm{\text{−}}p}$). $V=0.3\mu \mathrm{m}/\mathrm{s}$, $L=1.85\mathrm{mN}$. Lower panel: Relative velocity between the surfaces in contact. Reciprocating motion (responsible for the alternating sign of the friction signal) is necessary due to the finite displacement range. (c) Voltage dependence of $F_f$ reduction. Fine control of friction can be achieved by changing the magnitude of the applied voltage. $L=5.56\mathrm{mN}$, $V=0.3\mu \mathrm{m}/\mathrm{s}$. Dashed line is a guide to the eye. Inset: Crossed-cylinder geometry used in the surface forces apparatus.

Figure 2

Load dependence of $F_f$ between mica surfaces coated with a layer of ${\mathrm{PS}}_{36}\mathrm{\text{−}}{\mathrm{PAA}}_{125}$ with (circles) and without (squares) an externally applied electric field. At low $L$ the PE layers oppose very small resistance to shear because of the limited layer interpenetration. Lubrication is substantially worsened at larger loads. $F_f$ is greatly reduced when the external field is applied (alternating square wave voltage, 450 Hz, $20{\mathrm{V}}_{p\mathrm{\text{−}}p}$). $V=0.3\mu \mathrm{m}/\mathrm{s}$. Mica thickness $4.018\mu \mathrm{m}$

Figure 3

$F_f$ variation with the frequency of the applied field $\nu$ (red circles). $F_f$ is similar before (open squares) and after (closed squares) application of the field (alternating square wave voltage, $20{\mathrm{V}}_{p\mathrm{\text{−}}p}$, $V=0.3\mu \mathrm{m}/\mathrm{s}$, $L=0.62\mathrm{mN}$). Continuous line is a guide to the eye. The schematic on the right illustrates the variation of polymer configuration with surface charge. At low $\nu$ the brush alternates between the neutralized ${\delta }_N$ (negatively charged electrode) and contracted ${\delta }_{+}$ (positively charged electrode) states. At high $\nu$ slow neutralization does not occur, and the PE oscillates between the contracted, ${\delta }_{+}$ and the stretched ${\delta }_{-}$ states.

Figure 4

(a) Variation of resonance frequency $\Delta f$ (solid line) and “dissipation factor” $\Delta D$ (dashed line) for the third harmonic ($n=3$) of a silica-coated quartz crystal covered by a polymer brush of ${\mathrm{PS}}_{36}{\mathrm{PAA}}_{125}$ when the $p\mathrm{H}$ of the media is switched between 10.5 and 3.5, as indicated. The zero values are chosen at $p\mathrm{H}$ 3.5. $D\equiv Q^{-1}=2\Gamma /f$, where $Q$ is the quality factor and $\Gamma$ the bandwidth of the resonance peak of frequency $f$. Similar qualitative response was observed for the different odd overtones ($n=1$ to $n=13$). (b) Shift of resonance frequencies (circles) and dissipation (squares) upon $p\mathrm{H}$ changes between 3.5 and 10.5 for the different overtones, and corresponding fits (crosses) obtained by viscoelastic modeling of the adsorbed polymer brush. The best possible fit was obtained for a thickness difference of $2.9\pm 0.2\mathrm{nm}$ (assuming film density $1\mathrm{g}/\mathrm{ml}$) between the neutralized and charged states. The calculated viscosity and overtone-dependent shear modulus of the layer in the charged state are $\eta =(1.32\pm 0.02)\times {10}^{-3}\mathrm{Pa}\mathrm{s}$ and $\mu =(0.156\pm 0.003)\mathrm{MPa}\times n^{-0.66\pm 0.02}$, respectively.