Polyelectrolyte adsorption onto oppositely charged interfaces: unified approach for plane, cylinder, and sphere

Abstract

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.

The numerical study of the adsorption of flexible polyelectrolytes with the annealed charge distribution onto an oppositely charged sphere by the self-consistent field theory

“…[12][13][14][15][16][17][18][19][20][21][22][23][24][25] An important aspect of PE adsorption is the charge inversion, that is, the total amount of charges on adsorbed PE chains overcompensates that of the surface charges of the object. Other interesting issues regarding the PE adsorption, such as the critical condition for the adsorption, the thickness of the polymer layer, the addition of the salt ions, and the difference between planar and curved (cylindrical, spherical) charged objects, have also attracted the research attention.…”

“…It has been shown by the scaling law, analytical and computational studies that, the thickness of the adsorbed polymer layer scales with both the linear charge density or average charge fraction of PE chains and the surface charge density as a power law, with the scaling exponent of about −1/3. 20,[22][23][24][25]51 Another interesting finding is that, at relatively low ionic strength, a curved convex surface entails a much higher surface charge density to trigger the PE adsorption than does a planar surface. [22][23][24] The adsorption of PEs with an annealed charge distribution on oppositely charged surfaces has been studied to a less extent compared to PEs with a smeared charge distribution.…”

“…20,[22][23][24][25]51 Another interesting finding is that, at relatively low ionic strength, a curved convex surface entails a much higher surface charge density to trigger the PE adsorption than does a planar surface. [22][23][24] The adsorption of PEs with an annealed charge distribution on oppositely charged surfaces has been studied to a less extent compared to PEs with a smeared charge distribution. This disparity in research efforts is partly due to the additional complexity brought about by the acid-base ionization equilibrium for PE chains with the annealed charge distribution.…”

Sensing Viruses by Mechanical Tension of DNA in Responsive Hydrogels

“…Without external forces and melting, the electrostatically driven adsorption-desorption transition of unconstrained polyelectrolyte chains such as DNA onto oppositely charged curved surfaces has been examined in detail theoretically [51,52] and by computer simulations [53]. The scaling laws for the critical adsorption transition were obtained experimentally as functions of polyelectrolyte chain-surface adhesion strength, salt conditions, surface curvature, and chain stiffness [54].…”

Global analysis of the ground-state wrapping conformation of a charged polymer on an oppositely charged nano-sphere

“…Recent analytical studies [35,[46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62] and numerical simulations [12,13,36,[63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78] have provided very useful insight into the essential role that electrostatic interactions play in determining the structural properties of charged polymer-sphere complexes. It was shown that a minimal chain-sphere model for nucleosome core particles [37][38][39][40][41]51] can closely predict the experimentally observed [79][80][81][82][83][84]…”