Measurement of long-ranged steric forces between polyelectrolyte layers physisorbed from $1\mathrm{M}$ $\mathrm{NaCl}$

The colloidal probe technique (CPT) is used to measure distance-dependent interaction forces between polyelectrolyte layers physisorbed from $1\mathrm{M}$ $\mathrm{NaCl}$ solution in salt solutions between $0.1\mathrm{mM}$ and $1\mathrm{M}$. Both linear polycations (poly(allylamine)hydrochloride, poly-l-lysine) and linear polyanions (poly(styrenesulfonate)) are used. The repulsive interaction energies in the range between ${10}^{-7}$ and ${10}^{-4}\mathrm{J}∕{\mathrm{m}}^2$ are described by the theory of Alexander and de Gennes for surfaces covered with neutral anchored polymers. However, the brush thickness scales with molecular area and salt concentration with a power of $-1∕3$ as known from a salted brush and reaches approximately 50% of the contour length in diluted solutions. The findings are confirmed by CPT images using a gold layer as height reference.

Figure 1

(a) Measured force between two PLL layers physisorbed from $1\mathrm{M}$ $\mathrm{NaCl}$ solution in $5\mathrm{mM}$ $\mathrm{NaCl}$ (gray dots, obtained by averaging over 1500 approach curves) and fit to the theory of Alexander and de Gennes, Eq. (1), with (solid line) and without (dashed line) the displacement parameter $\delta$. At small separations, the gray dots coincide and appear as a gray line. The inset shows a scheme of the experimental setup, together with the parameter assignment. (b) Distance-dependent forces between two PAH layers physisorbed from $1\mathrm{M}$ $\mathrm{NaCl}$ and measured in aqueous solutions with different ionic strength. The fits (solid lines) yield the brush length $L$; the average separation between pseudotails, $s$; and the separation between the silica and film surfaces, $D$ [cf. inset to 1a].

Figure 2

Polyelectrolyte brush thickness $L$ as function of the product of molecular area and ionic strength. The straight lines are power laws; the respective exponents are given in the legend. The black (gray) symbols correspond to measurements performed while lowering (raising) the salt concentration. The error bars of the PLL thickness represent twice the standard deviation. The inset shows the measured decay lengths between PLL layers physisorbed from aqueous solutions containing $1\mathrm{M}$ $\mathrm{NaCl}$ (solid circles) and no salt (open circles). The Debye length ${\kappa }^{-1}$ according to DLVO theory is also shown (dotted line).

Figure 3

Average distance between pseudotails, $s$, as function of brush thickness $L$. The shrinking and swelling is accompanied by minor structural rearrangements which are fully reversible if $5\min$ equilibration time after changing the solutions was allowed (same symbols as in Fig. 2).

Figure 4

Tapping-mode images of a surface-functionalized gold step ($50\mathrm{nm}$ high) with physisorbed PSS at different ionic strengths as indicated imaged with CP tips $(R=3\mathrm{\mu }\mathrm{m})$. With sharp tips $(R<20\mathrm{nm})$ the brushes cannot be resolved. Therefore the step height is independent of the ionic concentration and only one representative image obtained with a sharp tip is shown.