Figure 1

Force ($F/R$) vs separation ($D$) profiles (both approaching and receding), between curved mica sheets (radius $R$) following attachment from ${10}^{-4}\mathrm{g}\mathrm{m}/\mathrm{m}\mathrm{l}$ solution of PEP-X molecules in cyclohexane (Merck, Spectroscopic grade). Different symbols are for different runs and experiments, including data (○) taken immediately following a shear measurement. The upper inset shows ($F/R$) vs $D$ in a ${10}^{-4}\mathrm{g}\mathrm{m}/\mathrm{m}\mathrm{l}$ solution of unfunctionalized PEP ($M=290\mathrm{K}$): the absence of any long-ranged repulsion in this case demonstrates that PEP-X attaches to the surface by its zwitterion-terminated end—X only; the solid curve corresponds to the profile with the end-functionalized chains from the main plot. The lower inset illustrates schematically the SFB configuration, with the corresponding structure of the PEP-X brush, where $L_0=48\pm 3\mathrm{n}\mathrm{m}$ corresponds to half the onset distance for the interaction and the mean interanchor spacing $s=8.4\mathrm{n}\mathrm{m}$ is evaluated from adsorbance measurements [14]. The solid curve in the main figure corresponds to the Alexander–de Gennes model [15] with the values of $s$ and $L_0$ above. Using the Milner-Witten-Cates self-consistent field model [16] with the same $s$ and $L_0$ parameters gives a similarly good fit to the data.Reuse & Permissions

Figure 2

Shear forces between PEP-X brush-bearing surfaces at separation $D=7.0\pm 0.4\mathrm{n}\mathrm{m}$. Upper trace: Applied lateral motion ($\Delta x_0$) of top mica surface; Lower trace: Shear force $F_s$ transmitted to the lower mica surface. The horizontal broken line represents the midpoint between the shear forces on the back and forth cycles, and is therefore the position of zero shear force when the shear springs are unbent. Inset (i) illustrates the chain configuration in the initial force-rise regime $a\to b$. Inset (ii) illustrates the relaxation of a chain following cessation of the applied motion at point $d$ (lower trace): the thick part is as yet unrelaxed, while the thin part has relaxed by arm retraction as described in the text.Reuse & Permissions

Figure 3

Variation at $D=15\mathrm{n}\mathrm{m}$ of $F_{s(\max )}$ (◆) and $F_{\mathrm{k}\mathrm{i}\mathrm{n}}$ (●) with rest period ${\tau }_{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}}$ between shearing cycles (Fig. 2). Inset: Variation of the kinetic friction $F_{\mathrm{k}\mathrm{i}\mathrm{n}}$ with sliding velocity $v_s$ at different strong compressions of the PEP-X brushes. (▲): $D=4.1\pm 0.4\mathrm{n}\mathrm{m}$; ●: $D=6.2\pm 0.4\mathrm{n}\mathrm{m}$. The cartoon indicates the interpenetration zone, whose width $\delta$ increases with increasing waiting time ${\tau }_{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}}$, but decreases with increased shear velocity $v_s$ (inset), as discussed in the text.Reuse & Permissions

Figure 4

The relaxation regime for the region marked $d\to e$ on the right-hand side of the trace in Fig. 2, on an expanded scale, plotted as $[F_s(0)-F_s(t)]/F_s(0)$ vs $\ln [t]$ where $F_s(0)=0.9\mu \mathrm{N}$ is the value of $F_s$ at the point $d$; the straight line is a best fit and has a slope 0.038 (see text).Reuse & Permissions