Electroresponse of weak polyelectrolyte brushes

Abstract

End-tethered polyelectrolytes are widely used to modify substrate properties, particularly for lubrication or wetting. External stimuli, such as pH, salt concentration, or an electric field, can induce profound structural responses in weak polyelectrolyte brushes, which can be utilized to further tune substrate properties. We study the structure and electroresponsiveness of weak polyacid brushes using an inhomogeneous theory that incorporates both electrostatic and chain connectivity correlations at the Debye-Hückel level. Our calculation shows that a weak polyacid brush swells under the application of a negative applied potential, in agreement with recent experimental observation. We rationalize this behavior using a scaling argument that accounts for the effect of the surface charge. We also show that the swelling behavior has a direct influence on the differential capacitance, which can be modulated by the solvent quality, pH, and salt concentration.

Fig. 1

Schematic of Ising-like configurational states for monomers and water

Fig. 2

Schematic showing the effect of Debye-Hückel correlations. (left) Like-charged ions are screened due to the local structuring from oppositely-charged ions. (right) Ionization of two adjacent monomers is unfavorable due to the intrachain repulsion

Fig. 3

Average fraction of ionized monomers on polyacid versus solution pH for various chain lengths with $p{K}_{a,0}=5.0$ and the added salt $c_{\pm }=10\text{mM}$. The mean-field result (blue) does not depend on the degree of polymerization and nearly overlaps with the $N=1$ curve with correlations. The rest of the curves include Debye–Hückel level correlations

Fig. 4

Average fraction of ionized monomers on polyacid versus solution pH for various added salt concentrations with $p{K}_{a,0}=5.0$ and chain length $N=100$. The mean-field result (blue) does not depend on the salt concentration. The rest of the curves include Debye–Hückel level correlations

Fig. 5

Comparison of bulk titration behavior across mean-field, Debye–Hückel correlations, and experiment. Experimental values are for poly(acrylic acid) are combined from Refs. [44, 45]. For calculations, an added salt concentration of 1 mM, acid monomer concentration of 1.35 mM, and $N=100$ are used. Numerical values in legend indicate value of $p{K}_{a,0}$. MF = Mean-field, DH = Debye–Hückel correlations, Exp=Experiment

Fig. 6

Density profiles near a neutral surface for different values of pH with $p{K}_{a,0}=5$. (left) Polyacid brush. (right) Net charge density from small ions. The salt concentration is 10 mM, the chain length is $N=50$ and the grafting density is ${\sigma }_g{b}^2=0.03$

Fig. 7

Average fraction of ionized monomers for a polyacid brush grafted to a neutral surface versus the solution pH with $p{K}_{a,0}=5$. (solid) Theory with Debye–Hückel correlations. (dashed) Mean-field theory (no correlations). The chain length is $N=50$ and the grafting density is ${\sigma }_g{b}^2=0.03$

Fig. 8

Polyacid brush density profile near a neutral surface for different salt concentrations at (left) pH = 5 and (right) pH = 9 with $p{K}_{a,0}=5$. The chain length is $N=50$ and the grafting density is ${\sigma }_g{b}^2=0.03$

Fig. 9

Effect of applied potential on the brush conformation and charge for $p{K}_{a,0}=5$. (left) Brush height and (right) average ionized fraction as a function of the negative of the applied electrostatic potential on the surface. Filled circles correspond to conditions of a neutral surface. The salt concentration is 100 mM, the chain length is $N=20$, and the grafting density is ${\sigma }_g{b}^2=0.01$

Fig. 10

Overall charge fraction as a function of the negative of the applied electrostatic potential on the surface with $p{K}_{a,0}=5$. Filled circles correspond to conditions of a neutral surface. The salt concentration is 100 mM, the chain length is $N=20$ and the grafting density is ${\sigma }_g{b}^2=0.01$

Fig. 11

Brush extension (top row) and differential capacitance (bottom row) as a function of the negative of the applied electrostatic potential for different solvent qualities for $p{K}_{a,0}=5$. The solvent quality includes $\beta \chi =0.5$ (left), $\beta \chi =0$ (middle) and $\beta \chi =-1$ (right). Filled circles correspond to conditions of a neutral surface. The pH is 7, the salt concentration is 100 mM, the chain length is $N=20$ and the grafting density is ${\sigma }_g{b}^2=0.01$

Fig. 12

Differential capacitance for different values of pH with salt concentrations of (left) 10 mM and (right) 1000 mM. The chain length is $N=20$ and the grafting density is ${\sigma }_g{b}^2=0.01$