Brushes of flexible, semiflexible, and rodlike diblock polyampholytes: Molecular dynamics simulation and scaling analysis

Planar brushes of flexible, semiflexible, and rodlike diblock polyampholytes are studied using molecular dynamics simulations in a wide range of the grafting density. Simulations show linear dependence of the average thickness on the grafting density in all cases regardless of different flexibility of anchored chains and the brushes’ different equilibrium conformations. Slopes of fitted lines to the average thickness of the brushes of semiflexible and rodlike polyampholytes versus the grafting density are approximately the same and differ considerably from that of the brushes of flexible chains. The average thickness of the brush of flexible diblock polyampholytes as a function of the grafting density is also obtained using a simple scaling analysis, which is in good agreement with our simulations.

Figure 1

(Color online) Sample snapshots of brushes of (a) flexible $\left(l_p=5\sigma \right)$, (b) semiflexible $\left(l_p=25\sigma \right)$, and (c) rodlike $\left(l_p=200\sigma \right)$ diblock polyampholytes at grafting density ${\rho }_a{\sigma }^2=0.08$. Neutral, positively, and negatively charged monomers are shown by white, red (dark), and blue (black) spheres, respectively (see also Fig. 5). Counterions are not shown and periodic boundary condition is removed for clarity.

Figure 2

(Color online) The average thickness of the brushes formed by flexible ($k_{bend}=0$ and $5k_{B}T$), semiflexible $\left(k_{bend}=25k_{B}T\right)$, and rodlike $\left(k_{bend}=200k_{B}T\right)$ diblock polyampholytes versus dimensionless grafting density, ${\rho }_a{\sigma }^2$. The lines are linear fits to our simulation data. The slopes of solid, dashed, dotted and dash-dotted lines are 41.6, 40.2 and 22.7 and 20.0, respectively. The size of the symbols corresponds to the size of error bars.

Figure 3

(Color online) Histogram of the average end-to-end distance of the chains for brushes formed by flexible, semiflexible, and rodlike diblock polyampholytes at grafting densities (a) ${\rho }_a{\sigma }^2=0.02$, (b) ${\rho }_a{\sigma }^2=0.06$, and (c) ${\rho }_a{\sigma }^2=0.10$.

Figure 4

(Color online) Histogram of the average distance of the end monomers of the chains from the grafting surface for the brushes of flexible, semiflexible and rodlike diblock polyampholytes at grafting densities (a) ${\rho }_a{\sigma }^2=0.02$, (b) ${\rho }_a{\sigma }^2=0.06$, and (c) ${\rho }_a{\sigma }^2=0.10$.

Figure 5

(Color online) The blob picture of a flexible diblock polyampholyte brush. The blobs of positive charge are more probably surrounded by blobs of negative charge. Positively and negatively charged monomers are shown by red $(+)$ and blue $(-)$ sphere, respectively. The neutral monomers are not shown for clarity. $h$ and $\xi$ are the brush thickness and correlation blob size, respectively.