Brownian dynamics simulations of polyelectrolyte adsorption onto charged patterned surfaces

The adsorption of single polyelectrolyte molecules onto surfaces decorated with periodic arrays of charged patches was studied using Brownian dynamics simulations. A free-draining, freely jointed bead-rod chain was used to model the polyelectrolyte, and electrostatic interactions were incorporated using a screened Coulombic potential with the excluded volume accounted for by a hard-sphere potential. The simulations predicted that the polyelectrolyte lies close to the adsorbing surface if the patch length, surface charge density, and screening length are sufficiently large. Chain conformations were found to be very sensitive to patch length, patch spacing, and the nature of the charge on adjacent patches. This is due both to the size of the polymer relative to patch length and spacing and to the structure of the electric field near the surface. In some cases, the component of the radius of gyration parallel to the surface can be made smaller than its free-solution value, which is contrary to what is observed for a uniformly charged surface. Isolated charged patches were also considered, and significant adsorption was observed above a critical surface charge density. The results demonstrate how polyelectrolyte conformations can be controlled by the design of the charged patches and may be useful for applications in which adsorbed polyelectrolyte films play a key role.     

Phase diagram for the adsorption of weak polyelectrolytes at a soft charged surface

We have experimentally studied the adsorption of polyelectrolytes at oppositely charged surfaces. A weak flexible polyelectrolyte, poly(acrylic acid), was adsorbed from dilute solutions on a Langmuir film of a cationic amphiphile, dimethyldioctadecylammonium bromide. The polymer surface coverage, Gamma, at equilibrium was measured by two reflectivity techniques-ellipsometry and polarization modulated infrared reflection absorption spectroscopy (PM-IRRAS)-as a function of the surface charge density, sigma, and of the polymer ionization degree, alpha. Different adsorption regimes were evidenced. For weakly charged surfaces, sigma < sigma sat, Gamma increases with sigma and with 1/alpha, as expected for a neutralization of the surface by the adsorbed polymers. For highly charged surfaces, sigma > sigma sat, the adsorption of polyelectrolytes saturates. The mean orientation of the adsorbed chains also depends on the value of sigma: it is parallel to the surface for sigma < sigma (< sigma sat) and orthogonal to the surface for sigma > sigma. We have measured the values of sigma sat and sigma as a function of alpha and compared the results with existing theories.     

Brownian dynamics simulations of polyelectrolyte adsorption onto topographically patterned surfaces

The effect of patterned surface topography on the adsorption of single polyelectrolyte molecules is explored using Brownian dynamics simulations. The polyelectrolyte is modeled as a free-draining, freely jointed bead-rod chain, and electrostatic interactions are incorporated using a screened Coulombic potential with excluded volume interactions accounted for by the repulsive part of a Lennard-Jones potential. Topography consisting of periodically spaced valleys of square cross section separated by flat hills is considered. Chain conformations are characterized for a wide range of valley widths, depths, and spacings as well as for several different types of surface charge distributions. Depending on the parameter values describing the topography, the chains are found to adopt conformations ranging from flat and extended to those associated with bridge-, brush-, or semi-bridge-like structures. The formation of these structures is rationalized on the basis of a free-energy model that takes into account the increase in free energy due to entropic confinement, excluded volume interactions, and chain stretching as well as the decrease in free energy due to bead-surface electrostatic attraction. The results of this work are expected to be useful in designing patterned surface topography to control the conformations of adsorbed polyelectrolyte molecules.     

Nonrandom adsorption of polyelectrolyte chains on finite regularly charged surfaces

Adsorption phenomena are relevant in a wide variety of subjects, from biophysics to technological applications. Different aspects, such as molecular recognition, multilayer deposition, and dynamics of polymer adsorption have been addressed. The methodologies used range from analytical and numerical methods to molecular dynamics or Monte Carlo simulations. In this work, a coarse‐grained model is used to explore the adsorption of charged backbones to oppositely charged regions of a surface. These regions encompass those small enough to prevent complete adsorption, but extend to surfaces sufficiently large to promote adsorption with minimal effect on the three‐dimensional conformation in bulk. Apart from the different surface areas explored, variations on the surface charge density, polyelectrolyte chain length, and chain stiffness were also considered. The degree of compaction of the polyelectrolyte, on adsorption, is different from that found in the bulk. Also, results indicate an nonuniform adsorption pattern on regularly charged surfaces. © 2013 Wiley Periodicals, Inc.     

Polyelectrolyte–particle complex formation. Polyelectrolyte linear charge density and ionic concentration effects. Monte Carlo simulations

The influence of the linear charge density (LCD) of a polyelectrolyte on its adsorption on an oppositely charged colloidal particle is investigated by Monte Carlo simulations. Adsorption characteristics are studied at different linear charge densities and ionic concentrations and for a given polyelectrolyte/particle size ratio so that particle curvature has full effect. The isolated polyelectrolyte goes through a smooth transition from a collapsed structure to an extended rod-like conformation with increasing the linear charge density in the low ionic concentration regime. In the high ionic concentration regime, the polyelectrolyte is less sensitive to the increase in the linear charge density and adopts a coil conformation. We found that complex formation is promoted by decreasing the ionic concentration and increasing the linear charge density and that large changes in the polymer dimensions are observed at the adsorption-desorption limit. By adjusting the linear charge density and ionic strength, we demonstrate that the adsorption-desorption limit corresponds to a sharp transition from non-adsorbed to adsorbed conformations and that the mean adsorption energy per monomer has to be less than -0.4 kT to achieve adsorption. We calculated that the linear charge density at the adsorption-desorption limit is related to the Debye-Hückel length according to LCD^crit ~3². At small values of the linear charge density and low ionic strength (no adsorption is observed at high ionic strength), a large amount of monomers are present in loops and tails. By increasing LCD, the amount of monomers in trains reaches a maximum value and the polyelectrolyte adopt flat conformation at the surface of the particle.     

Brownian dynamics simulations of polyelectrolyte adsorption in shear flow: effects of solvent quality and charge patterning

We probe the effects of solvent quality and charge patterning on polyelectrolyte adsorption in shear flow using Brownian dynamics simulations with hydrodynamic interaction (HI). The polyelectrolyte is modeled as a freely jointed bead-rod chain, and electrostatic and non-electrostatic interactions are accounted for by using screened Coulombic and Lennard-Jones potentials, respectively. In the absence of flow, the conformation of a polyelectrolyte molecule adsorbed onto a uniformly charged surface changes from flat to globular with an increase in bead-bead attraction (hydrophobicity), consistent with prior experimental observations. In the presence of flow, migration due to bead-wall HI and, as a consequence, desorption decrease with an increase in bead-bead attraction, implying that flow-induced desorption is more difficult under poor-solvent conditions. When bead-bead non-electrostatic attraction is strong, desorption can be enhanced by increasing bead-bead electrostatic repulsion. Analogous to the effect of bead-surface electrostatic attraction, an increase in the strength of bead-surface non-electrostatic attraction reduces desorption. We also study the effect of shear flow on the adsorption of a polyelectrolyte molecule onto surfaces decorated with periodic arrays of charged patches. An increase in patch periodicity increases desorption even when the effective surface charge density is kept the same. The results of this work suggest mechanisms for controlling the desorption of polyelectrolyte molecules in shear flows.     

On the theory of polyelectrolyte adsorption : The effect on adsorption behavior of the electrostatic contribution to the adsorption free energy

A theory has been developed for the adsorption of polyelectrolytes on charged interfaces from an aqueous salt solution. This adsorption is determined by the electrical charge density of the polyelectrolyte, the adsorption energy, the salt concentration, the molecular weight, solubility, flexibility, and concentration of polymer. The theory relates these parameters to the properties of the adsorbed polymer layer, i.e., the amount of polymer adsorbed, the fraction of the adsorbent interface covered, the fraction of the segments actually adsorbed on the interface versus the fraction of the segments in the dangling loops, the final surface charge density, and the thickness of the adsorbed layer. As polyelectrolyte adsorption should resemble nonionic polymer adsorption at high ionic strength of the solution or low charge density on the polymer, this work is an extension of the nonionic polymer adsorption theory to polyelectrolyte adsorption. The following effects are taken into account: (a) the conformational change upon adsorption of a coil in solution into a sequence of adsorbed trains interconnected by loops dangling in solution; (b) the interactions of the adsorbed trains with the interface and with each other; (c) the interaction of the dangling loops with the solvent; (d) the change in surface charge density of the adsorbent due to adsorption of charged trains and the accompanying changes in the electrical double layer which contains “small” ions as well as charged loops; (e) the (induced) dipole interaction of the adsorbed trains with the charged adsorbent interface. The theory is worked out for low potentials (Debye—Hückel approximation); in Appendix B an outline of a more complete treatment is given. The predicted adsorption isotherms have the experimentally observed high-affinity character. A relation between the adsorption energy, the surface charge density on the adsorbent, the degree of dissociation of the polymer, and the salt concentration predicts the conditions under which no adsorption will occur. For adsorbent and polymer carrying the same type of charge (both positive or both negative) the adsorption is predicted to decrease with increased charge density on polymer or adsorbent and to increase with salt concentration. If adsorbent and polymer carry different type charges, the adsorption as a function of the degree of dissociation, α, goes through a maximum at a relatively low value of α and, depending on the adsorption energy, an increase in the salt concentration can then increase or decrease the adsorption. At finite polymer concentration in solution the number of adsorbed segments and the fraction of the interface covered practically do not change with an increase in polymer concentration, whereas the total number of polymer molecules adsorbed increases slightly, as does the average fraction of segments in loops. The experimental results for polyelectrolyte adsorption have been reviewed in general and, as far as data are available, the predictions of the theory seem to follow the experimentally observed trends quite closely, except for the thickness of the adsorbed layer. This thickness is systematically overestimated by the theory and two reasons for this are given. The theoretical model implies a not too low ionic strength of the solution. Extrapolation of results to solutions of very low ionic strength is not warranted.     

Interactions between Adsorbed Layers of a Low Charge Density Cationic Polyelectrolyte on Mica in the Absence and Presence of Anionic Surfactant

Interactions between two negatively charged mica surfaces across aqueous solutions containing various amounts of a 10% charged cationic polyelectrolyte have been studied. It is found that the mica surface charge is neutralized when the polyelectrolyte is adsorbed from a 10–50 ppm aqueous solution. Consequently no electrostatic double-layer force is observed. Instead an attractive force acts between the surfaces in the distance regime 250–100 Å. We suggest that this attraction is caused by bridging. Additional adsorption takes place when the polyelectrolyte concentration is increased to 100 and 300 ppm, and a long-range repulsion develops. This repulsive force is both of electrostatic and steric origin. The polyelectrolyte layer adsorbed from a 50 ppm solution does not desorb when the polyelectrolyte solution is replaced with an aqueous polyelectrolyte-free solution. Injection of sodium dodecyl sulfate (SDS) into the measuring chamber to a concentration of about 0.01 CMC (8.3 × 10⁻⁵M) does not affect the adsorbed layers or the interaction forces. However, when the SDS concentration is increased to 0.02 CMC (0.166 mM) the adsorbed layer expands dramatically due to adsorption of SDS to the polyelectrolyte chains. The sudden swelling suggests a cooperative adsorption of SDS to the preadsorbed polyelectrolyte layer and that the critical aggregation concentration between the polyelectrolyte and SDS at the surface is about 0.02 CMC. The flocculation behavior of the polyelectrolyte in solution upon addition of SDS was also examined. It was found that 0.16–0.32 mol SDS/mol charged segments on the polyelectrolyte is enough to make the solution slightly turbid.     

Adsorption of cationic starch on cellulose studied by QCM-D

The adsorption of cationic starch (CS) from aqueous electrolyte solutions onto model cellulose film has been investigated by the quartz crystal microbalance with dissipation monitoring (QCM-D) and X-ray photoelectron spectroscopy (XPS). The influence of the electrolyte composition and charge density of CS was examined. The adsorption of CS onto cellulose followed the general trends expected for polyelectrolyte adsorption on oppositely charged surfaces, with some exceptions. Thus, as result of the very low surface charge density of the cellulose surface, highly charged CS did not adsorb in a flat conformation even at low ionic strength. The porosity of the film, however, enabled the penetration of coiled CS molecules into the film at high electrolyte concentrations. Differences between the adsorption behavior of CS on cellulose and earlier observations of the adsorption of the same starches on silica could be explained by the different morphologies and acidities of the hydroxyl groups on the two surfaces.     

The relationship between polymer/substrate charge density and charge overcompensation by adsorbed polyelectrolyte layers

This work examines polyelectrolyte adsorption (exclusively driven by electrostatic attractions) for a model system (DMAEMA, polydimethylaminoethyl methacrylate, adsorbing onto silica) where the adsorbing polycation is more densely charged than the substrate. Variations in the relative charge densities of the polymer and substrate are accomplished by pH, and the polycation is of sufficiently low molecular weight that the adsorbed conformation is generally flat under all conditions examined. We demonstrate, quantitatively, that the charge overcompensation observed on the isotherm plateau can be attributed to the denser positive charge on the adsorbing polycation and that the ultimate coverage obtained corresponds to the adsorption of one oligomer onto each original negative silica charge, when the silica charge is most sparse, at pH 6. This limiting behavior breaks down at higher pHs where the greater silica charge density accommodates single chains adsorbing onto multiple negative sites. As a result of the greater substrate charge density and reduced polycation charge at higher pHs, the extent of charge overcompensation diminishes while the coverage increases on the plateau of the isotherm. Ultimately at the highest pHs, a regime is approached where the coil's excluded surface area, not surface charge, limits the ultimate coverage. In addition to quantifying the crossover from the charge-limiting to the area-limiting behaviors, this paper quantitatively reports adsorption-induced changes in bound counterion density and ionization at the interface, which were generally found to be independent of coverage for this model system.     

Poisson-Boltzmann theory of the charge-induced adsorption of semi-flexible polyelectrolytes

A model is suggested for the structure of an adsorbed layer of a highly charged semi-flexible polyelectrolyte on a weakly charged surface of opposite charge sign. The adsorbed phase is thin, owing to the effective reversal of the charge sign of the surface upon adsorption, and ordered, owing to the high surface density of polyelectrolyte strands caused by the generally strong binding between polyelectrolyte and surface. The Poisson-Boltzmann equation for the electrostatic interaction between the array of adsorbed polyelectrolytes and the charged surface is solved for a cylindrical geometry, both numerically, using a finite element method, and analytically within the weak curvature limit under the assumption of excess monovalent salt. For small separations, repulsive surface polarization and counterion osmotic pressure effects dominate over the electrostatic attraction and the resulting electrostatic interaction curve shows a minimum at nonzero separations on the Angstrom scale. The equilibrium density of the adsorbed phase is obtained by minimizing the total free energy under the condition of equality of chemical potential and osmotic pressure of the polyelectrolyte in solution and in the adsorbed phase. For a wide range of ionic conditions and charge densities of the charged surface, the interstrand separation as predicted by the Poisson-Boltzmann model and the analytical theory closely agree. For low to moderate charge densities of the adsorbing surface, the interstrand spacing decreases as a function of the charge density of the charged surface. Above about 0.1 M excess monovalent salt, it is only weakly dependent on the ionic strength. At high charge densities of the adsorbing surface, the interstrand spacing increases with increasing ionic strength, in line with the experiments by Fang and Yang [J. Phys. Chem. B 101, 441 (1997)].     

In-situ investigation of the adsorption of globular model proteins on stimuli-responsive binary polyelectrolyte brushes

Binary brushes constituted from two incompatible polymers can be used in the form of ultrathin polymeric layers as a versatile tool for surface engineering to tune physicochemical surface characteristics such as wettability, surface charge, chemical composition, and morphology and furthermore to create responsive surface properties. Mixed brushes of oppositely charged weak polyelectrolytes represent a special case of responding surfaces that are sensitive to changes in the pH value of the aqueous environment and therefore represent interesting tools for biosurface engineering. The polyelectrolyte brushes used for this study were composed of two oppositely charged polyelelctrolytes poly(2-vinylpyridine) (P2VP) and poly(acrylic acid) (PAA). The in-situ properties and surface characteristics such as as surface charge, surface tension, and extent of swelling of these brush layers are functions of the pH value of the surrounding aqueous solution. To test the behavior of the mixed polylelctrolyte brushes in contact with biosystems, protein adsorption experiments with globular model proteins were performed at different pH values and salt concentrations (confinement of counterions) of the buffer solutions. The influence of the pH value, buffer salt concentration, and isoelectric points (IEP) of the brush and protein on the adsorbed amount and the interfacial tension during protein adsorption as well as the protein adsorption mechanism postulated in reference to recently developed theories of protein adsorption on polyelectrolyte brushes is discussed. In the salted regime, protein adsorption was found to be similar to the often-described adsorption at hydrophobic surfaces. However, in the osmotic regime the balance of electrostatic repulsion and a strong entropic driving force, "counterion release", was found to be the main influence on protein adsorption.     

Brownian dynamics simulations of polyelectrolyte adsorption in shear flow with hydrodynamic interaction

The adsorption of single polyelectrolyte molecules in shear flow is studied using Brownian dynamics simulations with hydrodynamic interaction (HI). Simulations are performed with bead-rod and bead-spring chains, and electrostatic interactions are incorporated through a screened Coulombic potential with excluded volume accounted for by the repulsive part of a Lennard-Jones potential. A correction to the Rotne-Prager-Yamakawa tensor is derived that accounts for the presence of a planar wall. The simulations show that migration away from an uncharged wall, which is due to bead-wall HI, is enhanced by increases in the strength of flow and intrachain electrostatic repulsion, consistent with kinetic theory predictions. When the wall and polyelectrolyte are oppositely charged, chain behavior depends on the strength of electrostatic screening. For strong screening, chains get depleted from a region close to the wall and the thickness of this depletion layer scales as N(1/3)Wi(2/3) at high Wi, where N is the chain length and Wi is the Weissenberg number. At intermediate screening, bead-wall electrostatic attraction competes with bead-wall HI, and it is found that there is a critical Weissenberg number for desorption which scales as N(-1/2)kappa(-3)(l(B)|sigmaq|)(3/2), where kappa is the inverse screening length, l(B) is the Bjerrum length, sigma is the surface charge density, and q is the bead charge. When the screening is weak, adsorbed chains are observed to align in the vorticity direction at low shear rates due to the effects of repulsive intramolecular interactions. At higher shear rates, the chains align in the flow direction. The simulation method and results of this work are expected to be useful for a number of applications in biophysics and materials science in which polyelectrolyte adsorption plays a key role.     

Stabilization of Liposomes by Polyelectrolytes: Mechanism of Interaction and Role of Experimental Conditions

ζ-potential measurements on LUVs allow to evidence the influence of pH, ionic salt concentration, and polyelectrolyte charge on the interaction between polyelectrolyte (chitosan and hyaluronan) and zwitterionic lipid membrane. First, chitosan adsorption is studied: adsorption is independent on the chitosan molecular weight and corresponds to a maximum degree of decoration of 40% in surface coverage. From the dependence with pH and independence with MW, it is concluded that electrostatic interactions are responsible of chitosan adsorption which occurs flat on the external surface of the liposomes. The vesicles become positively charged in the presence of around two repeat units of chitosan added per lipid accessible polar head in acid medium down to pH = 7.2. Direct optical microscopy observations of GUVs shows a stabilization of the composite liposomes under different external stresses (pH and salt shocks) which confirms the strong electrostatic interaction between the chitosan and the lipid membrane. It is also demonstrated that the liposomes are stabilized by chitosan adsorption in a very wide range of pH (2.0 < pH < 12.0). Then, hyaluronan (HA), a negatively charged polyelectrolyte, is added to vesicles; the vesicles turn rapidly negatively charged in presence of adsorbed HA Finally, we demonstrated that hyaluronan adsorbs on positively charged chitosan-decorated liposomes at pH < 7.0 leading to charge inversion in the liposome decorated by the chitosan-hyaluronan bilayer. Our results demonstrate the adsorption of positive and/or negative polyelectrolyte at the surface of lipidic vesicles as well as their role on vesicle stabilization and charge control.     

Simultaneous tailoring of surface topography and chemical structure for controlled wettability

Wettability was controlled in a rational manner by individually and simultaneously manipulating surface topography and surface chemical structure. The first stage of this research involved the adsorption of charged submicrometer polystyrene latex particles to oppositely charged poly(ethylene terephthalate) (PET) film samples to form surfaces with different topographies/roughness; adsorption time, solution pH, solution ionic strength, latex particle size, and substrate charge density are external variables that were controlled. The introduction of discrete functional groups to smooth and rough surfaces through organic transformations was carried out in the second stage. Amine groups (-NH(2)) and alcohol groups (-OH) were introduced onto smooth PET surfaces by amidation with poly(allylamine) and adsorption with poly(vinyl alcohol) (PVOH), respectively. On latex particle adsorbed surfaces, a thin layer of gold was evaporated first to prevent particle redistribution before chemical transformation. Reactions with functionalized thiols and adsorption with PVOH on patterned gold surfaces successfully enhanced surface hydrophobicity and hydrophilicity. Particle size and biomodal particle size distribution affect both hydrophobicity and hydrophilicity. A very hydrophobic surface exhibiting water contact angles of 150 degrees /126 degrees (theta(A)/theta(R)) prepared by adsorption of 1-octadecanethiol and a hydrophilic surface with water contact angles of 18 degrees /8 degrees (theta(A)/theta(R)) prepared by adsorption of PVOH were prepared on gold-coated surfaces containing both 0.35 and 0.1 microm latex particles. The combination of surface topography and surface-chemical functionality permits wettability control over a wide range.     

Interactions between charged surfaces immersed in a polyelectrolyte solution

With grand canonical simulations invoking a configurationally weighted scheme, we have calculated interactions between charged surfaces immersed in a polyelectrolyte solution. In contrast to previous simulations of such systems, we have imposed full equilibrium conditions (i.e., we have included diffusive equilibrium with a bulk solution). This has a profound impact on the resulting interactions: even at modest surface charge densities, oppositely charged chains will, at sufficiently large separations, adsorb strongly enough to overcompensate for the nominal surface charge. This phenomenon, known as charge inversion, generates a double-layer repulsion and a free-energy barrier. Simpler canonical approaches, where the chains are assumed to neutralize the surfaces perfectly, will not capture this stabilizing barrier. The barrier height increases with the length of the polyions. Interestingly enough, the separation at which the repulsion becomes attractive is independent of chain length. The short chains here are unable to reach across from one surface to the other. We therefore conclude that the transition to an attractive regime is not provided by the formation of such "intersurface" bridges. With long chains and at large separations, charge inversion displays decaying oscillatory behavior (i.e., the apparent surface charge switches sign once again). This is due to polyion packing effects. We have also investigated responses to salt addition and changes in polyelectrolyte concentration. Our results are in qualitative and semiquantitative agreement with experimental findings, although it should be noted that our chains are comparatively short, and the experimental surface charge density is poorly established.     

Patterned polyelectrolyte multilayer: surface modification for enhancing selective adsorption

This paper describes the use of surface chemical modification to enhance the difference of the surface charge on a patterned polyelectrolyte multilayer, which can be used for selectively adsorbing functional materials. We fabricated a patterned multilayer by combining the layer-by-layer self-assembly technique and photolithography and taking advantage of the different solubility of polyelectrolyte multilayers of diazo resins (DAR)/poly(acrylic acid) before and after UV irradiation. This patterned surface can be used as a matrix for selective adsorption of small molecular dyes, such as Methylene Blue. However the difference in surface charge on the patterned surface was not enough when we used it to selectively adsorb polystyrene (PS) nanoparticles using electrostatic force as the driving force. Therefore, we modified the patterned surface by interfacial chemistry. After modification, the patterned polyelectrolyte multilayer can be used as a good matrix for selective adsorption of PS nanoparticles with both positive and negative charges.     

Coadsorption and surface forces for selective surfaces in contact with aqueous mixtures of oppositely charged surfactants and low charge density polyelectrolytes

The coadsorption of a positively charged polyelectrolyte (with 10% of the segments carrying a permanent positive charge, AM-MAPTAC-10) and an anionic surfactant (sodium dodecyl sulfate, SDS) on silica and glass surfaces has been investigated using optical reflectometry and a noninterferometric surface force technique. This is a selective coadsorption system in the sense that the polyelectrolyte does adsorb to the surface in the absence of surfactant, whereas the surfactant does not adsorb in the absence ofpolyelectrolyte. It is found that the total adsorbed amount goes through a maximum when the SDS concentration is increased. Maximum adsorption is found when the polyelectrolyte/surfactant complexes formed in bulk solution are close to the charge neutralization point. Some adsorption does occur also when SDS is present in significant excess. The force measured between AM-MAPTAC-10-coated surfaces on approach in the absence of SDS is dominated at long range by an electrostatic double-layer force. Yet, layers formed by coadsorption from solutions containing both polyelectrolyte and surfactant generate long-range forces of an electrosteric nature. On separation, adhesive interactions are found only when the adsorbed amount is low, i.e., in the absence of SDS and in a large excess of SDS. The final state of the adsorbed layer is found to be nonhysteretic, i.e., independent of the history of the system. The conditions for formation of long-lived trapped adsorption states from mixed polymer-surfactant solutions are discussed.     

Encapsulation of a polyelectrolyte chain by an oppositely charged spherical surface

Using the ground state dominance approximation and a variational theory, we study the encapsulation of a polyelectrolyte chain by an oppositely charged spherical surface. The electrostatic attraction between the polyelectrolyte and the surface and the entropy loss of the encapsulated polyelectrolyte chain dictate the optimum conditions for encapsulation. Two scenarios of encapsulation are identified: entropy-dominated and adsorption-dominated encapsulation. In the entropy-dominated encapsulation regime, the polyelectrolyte chain is delocalized, and the optimum radius of the encapsulating sphere decreases with increasing the attraction. In the adsorption-dominated encapsulation regime, the polyelectrolyte chain is strongly localized near the surface, and the optimum radius increases with increasing the attraction. After identifying a universal encapsulation parameter, the dependencies of the optimum radius on the salt concentration, surface charge density, polymer charge density, and polymer length are explored.