Critical Adsorption of Polyelectrolytes onto Charged Spherical Colloids

Abstract

The adsorption of a flexible polyelectrolyte in a salt solution onto an oppositely charged spherical surface is investigated. An analytical solution is derived, which is valid for any sphere radius and consistently recovers the result of a planar surface in the limit of large sphere radii, by substituting the Debye-Hückel potential via the Hulthén potential. Expressions for critical quantities such as the critical radius and the critical surface charge density are provide. A comparison of our theoretical results with experiments and computer simulations yields remarkable good agreement. DOI: 10.1103/PhysRevLett.96.066103 PACS numbers: 68.43.De, 82.35.Rs The complexation of charged macroions by oppositely charged polyelectrolytes is a fundamental process in biological systems and many technical applications. Particular examples are the complexation of histone proteins by DNA in nucleosomal core particles [1,2] as well as complexes of polyelectrolytes with charged colloids and micelles [3]. Industrial applications are as diverse as stabilization of colloidal suspensions, water treatment, and paper making [4].The understanding of the complexation between a polyion and a macroion surface accompanied by screening effects due to counterions and salt posses a major theoretical challenge [5]. Despite significant efforts and progresses [5][6][7][8][9][10][11], the understanding of charged complexes is still unsatisfactory and lacks behind that of neutral complexes. Certain insight into the complexation process is typically obtained by approximation schemes, e.g., variational calculations [6 -9], which, however, may lead to controversial results [12] and often apply only in limiting situations such as pointlike particles [9] or large colloidal radii [6].The theoretical studies of the adsorption behavior of polyelectrolytes onto spherical surfaces [7,10,11,13,14] lead to the observation of a phase-transition-like behavior; i.e., a bound polymer state appears at certain critical conditions which depend on, e.g., the sphere radius and screening of the Coulomb interaction. The variational calculations of Muthukumar and his co-workers [6,8] have provided useful insight into this transition in the limit of large sphere radii. Experiments on polyelectrolyte-protein and -micelle complexes [15] and computer simulations [14], however, typically yield dependencies of the critical quantities on the Debye screening length which deviate from the theoretical predictions. To understand and interpret the experimental results correctly, an analytical solution of the adsorption problem valid for any sphere radius is mandatory.In this Letter, we will present an exact solution for the critical adsorption of a flexible polyelectrolyte onto an oppositely charged spherical macroion. Expressions for critical quantities are provided, which are valid for any sphere radius. In particular, in the limit of zero macroion curvature, the results for a planar surface are obtained. In general, we find a significantly different dependence of the critica...

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

“…This is confirmed in ref. 13, by the agreement between the critical PE-sphere adsorption radius obtained from simulations and predicted by theory. However, for PE chains strongly adsorbed on surfaces, far from the adsorption-desorption transition, the self-interactions within the PE chain as well as the counterion release accompanied by a corresponding entropy gain, are likely to contribute significantly to the adsorption properties.…”

“…For PE-sphere adsorption, in contrast, its outcomes disagree with the scaling predictions from the WKB model presented above as well as from the approximate solution of PE-sphere adsorption problem in the Hulthen potential derived in ref. 13. Namely, in the limit of small ka, Muthukumar's model predicts a d c p (ka) 2 dependence, both for the rod and sphere situations.…”

“…Also, the adsorption of flexible PEs onto a spherical surface has been investigated in ref. [13][14][15] by approximating the Debye-Hu¨ckel PE-sphere attraction with the Hulthen potential that allows to determine an exact analytical solution. These results unravelled the scaling characteristics of PE adsorption, including the critical conditions for the adsorption-desorption transition and the thickness of the adsorbed PE layer.…”

Electrostatics in soft matter

“…For instance a nucleosome can be seen as an electrostatic binding between DNA and histone proteins, where the latter can be envisioned as charged spheres. ‡ Many theoreticians [95,96,97,98,99,100,101,102,92,103,104,105] have investigated these types of objects to understand the electrostatics governing those structures. Two very relevant results are: (i) the possible overcharging of the sphere by the long PE and (ii) a strong wrapping of the PE about the sphere (see figure 7 for an example).…”

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]…”