Origin of Anomalously Large Depletion Zones in Like-Charged Colloid-Polyelectrolyte Mixtures

Depletion zones in polyelectrolyte solutions in contact with like-charged flat surfaces are investigated. Using a coupled self-consistent field and Debye-Hückel approach, an explicit expression for the thickness $\delta$ of the depletion layer is derived. It is found that $\delta \sim {\delta }_{\mathrm{n}}+c{\kappa }^{-1}$, where ${\delta }_{\mathrm{n}}$ is the depletion thickness at a neutral surface, $c$ is a function of the electrostatic characteristics of the system, and ${\kappa }^{-1}$ is the Debye length. It is argued that the theory still holds beyond the mean-field approximation, which is confirmed by quantitative agreement between our theoretical results and experiments.

Figure 1

Schematic picture of the subdivision of the interfacial region in two separate zones: an electrostatic depletion zone with characteristic thickness $d$ and an excluded volume zone with characteristic thickness $\xi$. At $x=d$ there is a phantom neutral surface.

Figure 2

The depletion thickness of a salt-free hydrolyzed polyacrylamide solution at a same-sign surface as a function of the polyelectrolyte concentration calculated using Eq. (9), with $\xi$ calculated using Eq. (1.14) of Ref. [36] with $f=0.25$ and $\sigma =0.194{\mathrm{nm}}^{-1}$ [22]. The data points are obtained from Ref. [22].

Figure 3

The depletion thickness of a salt-free NaPSS solution at a silica surface as a function of the polyelectrolyte concentration calculated using Eq. (10), with $\xi$ calculated using Eq. (1.12) of Ref. [36] with $|f|=0.01$. The dotted curve is Eq. (9) for infinite chain length. The data points are obtained from Ref. [23]. Fitting the surface charge density yielded $|\sigma |\approx 0.03{\mathrm{nm}}^{-2}$.

Figure 4

The mean-field depletion thickness in a polyelectrolyte solution at a flat wall as a function of the polyelectrolyte chain length for various ${\phi }_{\mathrm{b}}=c_{\mathrm{b}}{l}^3$. Parameters: $|f|=0.1$, $v=l^3$, 10 mM salt, and $|\sigma |=0.1{\mathrm{nm}}^{-2}$. The symbols are Scheutjens-Fleer self-consistent field computations, the solid curves are Eq. (10), and the dashed curves are Eq. (9).