Institute of Complex Systems, ICS-2, Forschungszentrum Jülich, 52425 Jülich, Germany.
Phys Chem Chem Phys. 2011 Jun 28;13(24):11686-93. doi: 10.1039/c1cp20749k. Epub 2011 May 20.
A universal description is presented for weak adsorption of flexible polyelectrolyte chains onto oppositely charged planar and curved surfaces. It is based on the WKB (Wentzel-Kramers-Brillouin) quantum mechanical method for the Green function equation in the ground state dominance limit. The approach provides a unified picture for the scaling behavior of the critical characteristics of polyelectrolyte adsorption and the thickness of the adsorbed polymer layer formed adjacent to the interface. We find, particularly at low-salt conditions, that curved convex surfaces necessitate much larger surface charge densities to trigger polyelectrolyte adsorption, as compared to a planar interface in the same solution. In addition, we demonstrate that the different surface geometries yield very distinct scaling laws for the critical surface charge density required to initiate chain adsorption. Namely, in the low-salt limit, the surface charge density scales cubical with the inverse Debye screening length for a plane, quadratic for an adsorbing cylinder, and linear for a sphere. As the radius of surface curvature grows, the parameter of critical chain adsorption onto a rod and a sphere turns asymptotically into that of a planar interface. The transition occurs when the radius of surface curvature becomes comparable to the Debye screening length. The general scaling trends derived appear to be consistent with the complex-formation experiments of polyelectrolyte chains with oppositely charged spherical and cylindrical micelles. Finally, the WKB results are compared with the existing theories of polyelectrolyte adsorption and future perspectives are outlined.
提出了一种通用描述，用于描述柔性聚电解质链在带相反电荷的平面和曲面上的弱吸附。它基于 WKB（Wentzel-Kramers-Brillouin）量子力学方法，用于基态主导极限下的格林函数方程。该方法为聚电解质吸附的临界特性和与界面相邻的吸附聚合物层的厚度的标度行为提供了统一的图像。我们发现，特别是在低盐条件下，与相同溶液中的平面界面相比，弯曲凸面需要更大的表面电荷密度才能引发聚电解质吸附。此外，我们证明，不同的表面几何形状对于引发链吸附所需的临界表面电荷密度产生非常不同的标度定律。即，在低盐极限下，对于平面，表面电荷密度与逆德拜屏蔽长度的立方成正比，对于吸附圆柱，与二次方成比例，对于球体，与线性成比例。随着表面曲率半径的增大，棒和球上的临界链吸附参数渐近地变成平面界面的参数。当表面曲率半径变得与德拜屏蔽长度相当时，就会发生这种转变。得出的一般标度趋势似乎与带相反电荷的球形和圆柱形胶束的聚电解质链的复杂形成实验一致。最后，将 WKB 结果与现有的聚电解质吸附理论进行了比较，并概述了未来的研究方向。
