Adsorption and encapsulation of flexible polyelectrolytes in charged spherical vesicles

Abstract

We present a theory of adsorption of flexible polyelectrolytes on the interior and exterior surfaces of a charged vesicle in an electrolyte solution. The criteria for adsorption and the density profiles of the adsorbed polymer chain are derived in terms of various characteristics of the polymer, vesicle, and medium, such as the charge density and length of the polymer, charge density and size of the vesicle, electrolyte concentration and dielectric constant of the medium. For adsorption inside the vesicle, the competition between the loss of conformational entropy and gain in adsorption energy results in two kinds of encapsulated states, depending on the strength of the polymer-vesicle interaction. By considering also the adsorption from outside the vesicle, we derive the entropic and energy contributions to the free energy change to transfer an adsorbed chain in the interior to an adsorbed chain on the exterior. In this paper, we have used the Wentzel-Kramers-Brillouin (WKB) method to solve the equation for the probability distribution function of the chain. The present WKB results are compared with the previous results based on variational methods. The WKB and variational results are in good agreement for both the interior and exterior states of adsorption, except in the zero-salt limit for adsorption in the exterior region. The adsorption criteria and density profiles for both the interior and exterior states are presented in terms of various experimentally controllable variables. Calculation of the dependencies of free energy change to transfer an adsorbed chain from the interior to the exterior surface on salt concentration and vesicle radius shows that the free energy penalty to expel a chain from a vesicle is only of the order of thermal energy.

Manipulation of Confined Polyelectrolyte Conformations through Dielectric Mismatch

“…The system minimizes its potential energy with trivalent counterions-monomer Coulombic attractions, and simultaneously gains additional translational entropy of the released monovalent counterions. 12 13 14…”

“…The influence of spatial confinement on polyelectrolytes has been extensively investigated. − The equilibrium conformation of a highly charged polymer chain confined in a cavity is evidently governed by the interplay between energetic and entropic factors coming from the confinement shape and size relative to the chain length, the chain bending stiffness, the electrostatic interaction between the charged monomers, counterions, and the solvent, as well as their configurational entropy. For short flexible polyelectrolytes confined in a neutral spherical cavity, Kumar and Muthukumar using self-consistent field theory demonstrated that, for a given radius of the spherical cavity and fixed charge density along the backbone of the chain, solvent and small ion entropies dominate over all other contributions to the free energy.…”

Selective Adsorption of Confined Polymers: Self-Consistent Field Theory Studies

“…Previous theories mainly focus on the adsorption of homopolymer corresponding to the nonselective adsorption. The conventional polymer adsorption problem can be in broad terms rationalized as the tug of war between the attractive interaction of the polymer to the surface and the conformational entropy loss of the polymer as it is being adsorbed to the interface. ,− As one of the typical examples of nonselective adsorption, the adsorption of homogeneous polyelectrolytes by oppositely charged surfaces has been widely studied, − including the effects of solution salinity, charge density, length and stiffness of polyelectrolytes, and curvature and charge distribution of surfaces.…”

Spontaneous Injection of Polymer into a Spherical Cavity from a Narrow Tube

“…While, for sufficiently strong attraction, the chain was in an adsorbed state. 40 Furthermore, the translocation time was increased due to the confinement effect of the sphere but was reduced by the polymer−sphere attraction. The two effects offset each other at a special polymer−sphere attraction, which is dependent on the sphere size, the polymer length, and the driving force.…”