Abstract
What are the fundamental laws for the adsorption of charged polymers onto oppositely charged surfaces, for convex, planar, and concave geometries? This question is at the heart of surface coating applications, various complex formation phenomena, as well as in the context of cellular and viral biophysics. It has been a long-standing challenge in theoretical polymer physics; for realistic systems the quantitative understanding is however often achievable only by computer simulations. In this study, we present the findings of such extensive Monte-Carlo in silico experiments for polymer-surface adsorption in confined domains. We study the inverted critical adsorption of finite-length polyelectrolytes in three fundamental geometries: planar slit, cylindrical pore, and spherical cavity. The scaling relations extracted from simulations for the critical surface charge density σc-defining the adsorption-desorption transition-are in excellent agreement with our analytical calculations based on the ground-state analysis of the Edwards equation. In particular, we confirm the magnitude and scaling of σc for the concave interfaces versus the Debye screening length 1/κ and the extent of confinement a for these three interfaces for small κa values. For large κa the critical adsorption condition approaches the known planar limit. The transition between the two regimes takes place when the radius of surface curvature or half of the slit thickness a is of the order of 1/κ. We also rationalize how σc(κ) dependence gets modified for semi-flexible versus flexible chains under external confinement. We examine the implications of the chain length for critical adsorption-the effect often hard to tackle theoretically-putting an emphasis on polymers inside attractive spherical cavities. The applications of our findings to some biological systems are discussed, for instance the adsorption of nucleic acids onto the inner surfaces of cylindrical and spherical viral capsids.
Highlights
What are the fundamental laws for the adsorption of charged polymers onto oppositely charged surfaces, for convex, planar, and concave geometries? This question is at the heart of surface coating applications, various complex formation phenomena, as well as in the context of cellular and viral biophysics
We study the effects of the chain length, the polymer persistence, and systematically of the confinement size and solution salinity on the critical surface charge density sc
We examined the dependence of the critical adsorption conditions for semiflexible chains in all three adsorption geometries
Summary
Weak PE adsorption onto surfaces of different geometries at varying conditions has been investigated in a number of recent theoretical,[5,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42] experimental,[43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58] and computer simulation[59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78] studies. Edwards equation for polymer conformations in the attractive Debye–Huckel potential of the interface.[17] In addition, some ES chain stiffening at low-salt conditions takes place impeding the PE–surface adsorption The experimental observations of critical PE adsorption are based on the complex formation of various polymers with oppositely charged particles and micelles of spherical and cylindrical geometry.[47] These experimental findings indicate a weaker dependence of sc on ka for more ‘‘convex’’ surfaces, as the adsorbing interfaces transfer from the planar to the cylindrical and to the spherical shape. For a PE inside spherical cavities in the low salt limit the value of dc tends to saturate to a plateau[39] dscp,inv B 3C2 These functional dependencies on ka are in stark contrast to the fast and monotonically increasing dc for the adsorption of PEs on the outside of cylindrical and spherical interfaces (eqn (3) and (4)).
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