Interactions of polyelectrolyte brushes with oppositely charged surfactants

Using Brownian dynamics simulations, we study the effect of the charge ratio, the surfactant length, and the grafting density on the conformational behavior of the complex formed by the polyelectrolyte brush with oppositely charged surfactants. In our simulations, the polyelectrolyte chains and surfactants are represented by a coarse-grained bead-spring model, and the solvent is treated implicitly. It is found that varying the charge ratio induces different morphologies of surfactant aggregates adsorbed onto the brush. At high charge ratios, the density profiles of surfactant monomers indicate that surfactant aggregates exhibit a layer-by-layer arrangement. The surfactant length has a strong effect on the adsorption behavior of surfactants. The lengthening of surfactant leads to a collapsed brush configuration, but a reswelling of the brush with further increasing the surfactant length is observed. The collapse of the brush is attributed to the enhancement of surfactants binding to polyelectrolyte chains. The reswelling is due to an increase in the volume of adsorbed surfactant aggregates. At the largest grafting density investigated, enhanced excluded volume interactions limit the adsorption of surfactant within the polyelectrolyte brush. We also find that end monomers in polyelectrolyte chains exhibit a bimodal distribution in cases of large surfactant lengths and high charge ratios.     

Electrostatic binding of oppositely charged surfactants to spherical polyelectrolyte brushes

We use Brownian dynamics (BD) simulations to investigate the formation and structural characteristics of the complex between a spherical polyelectrolyte brush (SPB) and oppositely charged surfactants. Increasing the amount of added surfactants leads to a collapsed conformation of the SPB and the number of adsorbed surfactants exhibits a linear dependence. Nevertheless, the surfactant uptake into the SPB does not increase with further addition of surfactants. It is found that the surfactant length has a strong influence on the SPB conformation and the adsorption properties of surfactant. Upon changing the surfactant length from 3 to 11, the SPB undergoes a swelling-deswelling-reswelling conformational transition. The brush deswelling is due to the increase in the surfactant uptake. The increasing size of adsorbed aggregates is a main reason for reswelling of the SPB. A non-linear relationship between the brush thickness and the grafting density is observed. Especially at intermediate grafting densities, increasing the number of grafted chains has a weak effect on the brush thickness. We also find that a completely collapsed brush conformation occurs at high surfactant/SPB charge ratios or large surfactant lengths, while the brush layer is in a partly collapsed or extended state at an intermediate charge ratio and surfactant length.     

Counterion localization in solutions of starlike polyelectrolytes and colloidal polyelectrolyte brushes: a self-consistent field theory

A quantitative analysis of the distribution of counterions in salt-free solutions of colloidal polyelectrolyte brushes and starlike polyelectrolytes is performed on the level of the Poisson-Boltzmann approximation. Exact numerical solutions are obtained for starlike polyelectrolyte molecules composed of f = 20, . . ., 50 arms with a fixed fractional charge alpha per segment by applying the self-consistent field method of Scheutjens and Fleer (SF-SCF). The Wigner-Seitz cell dimension defines the concentration of polyelectrolyte stars in the system. The numerical results are compared to predictions of an analytical mean field theory and related to experimental observations on the osmotic pressure in solutions of starlike polyelectrolytes and colloidal polyelectrolyte brushes.     

Adsorption of weakly charged polyelectrolytes onto oppositely charged spherical colloids

The adsorption of a long weakly charged flexible polyelectrolyte in a salt solution onto an oppositely charged spherical surface is investigated. An analytical solution for Green's function 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 like the critical radius and the critical surface charge density are provided. In particular, we find a universal critical line for the sphere radius as a function of the screening length separating adsorbed from desorbed states. Moreover, results for the monomer density distribution, adsorbed layer thickness, and the radius of gyration are presented. A comparison of our theoretical results with experiments and computer simulations yields remarkably good agreement.     

Adsorption of highly charged polyelectrolytes onto an oppositely charged porous substrate

The adsorption behavior of highly charged cationic polyelectrolytes onto porous substrates is electrostatic in nature and has been shown to be highly dependent on the polyelectrolyte properties. Copolymers of acrylamide (AM) and diallyldimethylammonium chloride (DADMAC) were synthesized to have a range of macromolecular properties (i.e., charge density and molecular mass). Traditional titration methods have been complemented by fluorescence labeling techniques that were developed to directly observe the extent that fluorescently labeled poly(AM- co-DADMAC) adsorbs into the pore structure of a cellulosic substrate. Although contributing to the electrostatic driving force, the charge density acts to limit adsorption to the outermost surface under electrolyte-free conditions. However, adsorption into the pores can occur if both the molecular mass and charge density of poly(AM- co-DADMAC) are sufficiently low. Adsorption initially increases as the electrolyte concentration is increased. However, the electrostatic persistence length of poly(AM- co-DADMAC) restricts the polyelectrolyte from entering the pores. Therefore, changes in the adsorption behavior at moderate electrolyte concentrations have been attributed to swelling of the polyelectrolyte layer at the fiber exterior. The adsorption behavior changes again at high electrolyte concentrations such that poly(AM- co-DADMAC) could adsorb into the pore structure. This occurred when the electrolyte concentration was sufficient to screen the electrostatic persistence length of poly(AM- co-DADMAC), provided that the entropic driving force for adsorption still existed. It is suggested that adsorption into the pore structure is a kinetic process that is governed by localized electrostatic interactions between poly(AM- co-DADMAC) and the charges located within the pores.     

Binary oppositely charged polyelectrolyte brushes for highly selective electroless deposition of bimetallic patterns

Binary polymer brushes consisting of two oppositely charged polyelectrolytes are grafted on one substrate via two-step surface-initiated atomic transfer radical polymerization from contact printed initiator monolayer. The polymeric structures provide robust and effective platforms for highly selective loadings of catalytic-active ionic moieties with opposite charges [PdCl₄^2? and Pd(NH₃)₄²⁺] that can be used for electroless deposition (ELD) of metals in the subsequent steps. Binary metallic Cu/Ni patterns can thus be built up with high site-selectivity when the deposition was carried out in the order of Cu and Ni.     

Strong and weak adsorptions of polyelectrolyte chains onto oppositely charged spheres

We investigate the complexation of long thin polyelectrolyte (PE) chains with oppositely charged spheres. In the limit of strong adsorption, when strongly charged PE chains adapt a definite wrapped conformation on the sphere surface, we analytically solve the linear Poisson-Boltzmann equation and calculate the electrostatic potential and the energy of the complex. We discuss some biological applications of the obtained results. For weak adsorption, when a flexible weakly charged PE chain is localized next to the sphere in solution, we solve the Edwards equation for PE conformations in the Hulthen potential, which is used as an approximation for the screened Debye-Huckel potential of the sphere. We predict the critical conditions for PE adsorption. We find that the critical sphere charge density exhibits a distinctively different dependence on the Debye screening length than for PE adsorption onto a flat surface. We compare our findings with experimental measurements on complexation of various PEs with oppositely charged colloidal particles. We also present some numerical results of the coupled Poisson-Boltzmann and self-consistent field equation for PE adsorption in an assembly of oppositely charged spheres.     

Binding of oppositely charged surfactants to spherical polyelectrolyte brushes: a study by cryogenic transmission electron microscopy

The formation of a complex between an anionic spherical polyelectrolyte brush (SPB) and the cationic surfactant cetyltrimethylammonium bromide (CTAB) is investigated. The SPB consists of long chains of the strong polyelectrolyte poly(styrene sulfonate) (PSS), which are bound chemically to a solid poly(styrene) core of 56 nm in radius. The SPB are dispersed in water, and the ionic strength is adjusted by addition of NaBr. The resulting complexes are investigated in dilute solution by dynamic light scattering, by electrophoretic light scattering, and by cryogenic transmission electron microscopy (cryo-TEM). The formation of the complex between the SPB and the surfactant can be monitored by a strong shrinking of the surface layer when adding CTAB to dilute suspensions (0.01 wt %) and by a decrease of the effective charge of the complexes. Complex formation starts at CTAB concentrations lower than the critical micelle concentration of this surfactant. If the ratio r of the charges on the SPB to the charge of the added surfactant is exceeding unity, the particles start to flocculate. Cryo-TEM images of the complexes at r = 0.6 measured in salt-free solution show that the surface layer composed of the PSS chains and the adsorbed CTAB molecules is partially collapsed: A part of the chains form a dense surface layer while another part of the chains or aggregates thereof are still sticking out. This can be deduced from the cryo-TEM micrographs as well as from the hydrodynamic radius, which is still of appreciable magnitude. The 1:1 complex (r = 1.0) exhibits a fully collapsed layer formed by the PSS chains and CTAB. If the complex is formed in the presence of 0.05 M NaBr, r = 0.6 leads to globular structures directly attached to the surface of the core particles. All structures seen in the cryo-TEM images can be explained by a collapse transition of the surface layer brought about by the hydrophobic attraction between the polyelectrolyte chains that became partially hydrophobic through adsorption of CTAB.     

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.     

Development of the theory of a self-consistent field for polyelectrolyte solutions

A new theoretical approach to calculating the thermodynamic and structure functions of polyelectrolyte solutions is proposed, based on the method of Gaussian equivalent representation for calculating the functional integrals. Formulas for the mean-force potential, osmotic pressure, and complete monomer-monomer pair distribution functions are presented. A sodium polystyrene sulfonate solution with NaCl additives is considered as an example.     

On the mechanism of uptake of globular proteins by polyelectrolyte brushes: a two-gradient self-consistent field analysis

We present model calculations for the interaction of a protein-like inhomogeneously charged nanoscale object with a layer of densely grafted polyelectrolytes ("polyelectrolyte brush"). The motivation of this work is the recent experimental observation that proteins that carry an overall negative charge are absorbed into negatively charged polyelectrolyte brushes. Two-gradient self-consistent field (2G-SCF) calculations have been performed to unravel the physical mechanism of the uptake of protein thus effected. Our results prove that an overall neutral, protein-like object can electrostatically be attracted and therefore spontaneously driven into a polyelectrolyte brush when the object has two faces (patches, domains), one with a permanent positive charge and the other with a permanent negative charge. Using a 2G-SCF analysis, we evaluate the free energy of insertion, such that the electric dipole of the inclusion is oriented parallel to the brush surface. An electroneutral protein-like object is attracted into the brush because the polyelectrolyte brush interacts asymmetrically with the charged patches of opposite sign. At high ionic strength and low charge density on the patches, the attraction cannot compete with the repulsive excluded-volume interaction. However, for low ionic strengths and sufficiently high charge density on the patches, a gain on the order of k(B)T per charge becomes possible. Hence, the asymmetry of interaction for patches of different charges may result in a total attractive force between the protein and the brush. All results obtained herein are in excellent agreement with recent experimental data.     

Reswelling of polyelectrolyte hydrogels by oppositely charged surfactants

The interactions between charged alkylacrylamide gels of varying hydrophobicity and charge density and the oppositely charged surfactant hexadecyltrimethylammonium (C16TA+) have been investigated to determine the conditions necessary to induce excess surfactant binding (beyond charge neutralization) and resolubilization of the polymer-surfactant complex. In all cases, an initial gel collapse occurred due to neutralization of the charges in the gel, and the volume of the collapsed gel was smaller than that of the corresponding neutral gel at the same surfactant concentration, as a result of the formation of interchain micellar cross-links. For gels containing neutral repeating units that were found previously to bind C16TA+, a subsequent sharp reswelling of the gel network occurred, beginning at a critical surfactant concentration called the cac(2). The reswelling is due to binding of excess surfactant, which results in the gels becoming recharged. For gels whose neutral repeating units do not bind C16TA+, there was no reswelling behavior (no cac(2)), but there was a gradual increase of the swelling back to that of the equivalent neutral gel with increasing surfactant concentration. The results are interpreted in terms of the expected surfactant binding isotherm.     

Directed motion of a polyelectrolyte micelle along tethered chains of oppositely charged polyelectrolyte brush

The complexation of different single polyelectrolyte (PE) micelles formed by linear diblock copolymers with oppositely charged brushes with varying grafting densities and charge content was studied by means of molecular dynamics simulations using the primitive model. We found that all micelles perform a directed motion along the vertical z axis on the grafted surface where they trapped while on the other axes the motion is restricted in a circle in which the diameter decreases with the increase of the hydrophilic length of the linear diblock copolymer. The motion of micelles is characterized as super diffusion inside brushes with low densities and low charge content. At high grafting densities and charge content the diffusion becomes Fickian or slightly subdiffusive. The number of the absorbed brush chains on the micelle corona increases almost monotonically with the increase of brush grafting density or with the decrease of charge content. The distance from the surface in which the micelle is trapped can be controlled by the charge density along the grafted PE chain. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 621–631     

Adsorption of polyelectrolyte versus surface charge: in situ single-molecule atomic force microscopy experiments on similarly, oppositely, and heterogeneously charged surfaces

We have studied the effect of the pH and surface charge of mica on the adsorption of the positively charged weak polyelectrolyte (PE) poly(2-vinylpyridine) (P2VP) using atomic force microscopy (AFM) single-molecule experiments. These AFM experiments were performed in situ directly under aqueous media. If the mica's surface and the PE are oppositely charged (pH > 3), the PE forms a flat adsorbed layer of two-dimensionally (2D) equilibrated self-avoiding random walk coils. The adsorbed layer's structure remains almost unchanged if the pH is decreased to pH 3 (the mica's surface is weakly charged). At pH 2 (the mica surface is decorated by spots of different electrical charges), the polyelectrolyte chains take the form of a 2D compressed coil. In this pH range, at an increased P2VP concentration in solution, the PE segments preferentially adsorb onto the top of previously adsorbed segments, rather than onto an unoccupied surface. We explain this behavior as being caused by the heterogeneous character of the charged surface and the competitive adsorption of hydronium ions. The further increase of polymer concentration results in a complete coverage of the mica substrate and the charge overcompensation by P2VP chains adsorbed on the similarly charged substrate, due to van der Waals forces.     

Monte Carlo simulations of cross-linked polyelectrolyte gels with oppositely charged macroions

The volume and structural changes upon replacement of oppositely charged network counterions for oppositely charged macroions in cross-linked polyelectrolyte gels have been investigated by Monte Carlo simulations using a coarse-grained model. Initially, the gel deswells, but after an approximately equivalent amount of macroions, the gel starts to swell again. The deswelling effect is greatest for small and highly charged macroions. The role of different network properties on the deswelling has also been examined. The initial deswelling is understood in terms of a replacement of confined counterions with macroions, thereby reducing the osmotic pressure originating from the counterions. At these conditions, macroions are located near network nodes with various degrees of network chains wrapping them. At charge equivalence, a profound change in the network structure has appeared. At these conditions, the cohesive electrostatic interaction and the excluded volume effect of the macroions strongly influence the equilibrium volume of the gel. Our model system reproduces many characteristic experimental observations of polyelectrolyte gels containing oppositely charged surfactants.     

Molecular bottle brushes in a solution of semiflexible polyelectrolytes and block copolymers with an oppositely charged block: a molecular dynamics simulation

Using a coarse-grained model, we performed molecular dynamics simulations of the electrostatically driven self-assembly of strongly charged polyelectrolytes and diblock copolymers composed of oppositely charged and neutral blocks. Stoichiometric micelle-like complexes formed in a dilute solution represent cylindrical brushes whose conformation is determined by the linear charge density on the polyelectrolyte and by temperature. The core-shell morphology of the cylindrical brushes is proven. The core of these anisotropic micelles consists of an insoluble complex coacervate formed by the ionic chains and a shell made up of the neutral solvophilic blocks. As the concentration of macromolecules increases, the orientational ordering of ionic micelles takes place. The complexation can induce effective steric stiffening of the polyelectrolyte chains.     

The model of a polyelectrolyte solution with explicit account of counterions within a self-consistent field theory

A theoretical approach to calculating the thermodynamic and structural functions of solutions of polyelectrolytes based on Gaussian equivalent representation for the calculation of functional integrals is proposed. It is noted that a new analytical result of this work is the direct assumption of counterions, along with an equation for the gyration radius of a polymer chain as a function of the concentrations of monomers and added low-molecular salt. An equation of state is obtained within the proposed model. Our theoretical results are used to describe the thermodynamic and structural properties of an aqueous solution of sodium polystyrene sulfonate with additions of NaCl.     

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.     

Absorption of ionic amphiphils by oppositely charged polyelectrolyte gels

Slightly cross-linked polyelectrolytes absorb oppositely charged surfactants in aqueous media. Transfer of amphiphilic ions from solution into the swollen network proceeds as a frontal heterogeneous cooperative reaction causing a collapse of the original polyelectrolyte gel. Small and wide angle X-ray diffraction data show that electrostatic complex formed as a result of the reaction consists of lamellar type surfactant micelles embedded in a polyelectrolyte network. It is also shown that such complexes contain equimolar amount of surfactant ions and ionized polyelectrolyte units paired with amphiphil head groups. In other words a charged network is not able to bind surplus oppositely charged surfactant ions. However, it is still able to solubilize a substantial amount of a nonionized surfactant. Chemical structure of surfactants strongly affect internal structure of lamellae and stability of the complexes.     

Adsorption of proteins onto charged surfaces: A Monte Carlo approach with explicit ions

A computer model has been developed to simulate the adsorption of proteins onto charged surfaces displaying an electric double layer. Coadsorption of ions onto the surface is included by means of explicit ions. Only electrostatic interactions are considered. Monte Carlo simulations in the canonical ensemble of the enzyme cutinase and 15 variants (modeled from the X-ray tertiary structure of the wild-type) were performed. Adsorption free energies for all variants were calculated by the thermodynamic integration method. Distributions of the electric moment and the vector pointing toward the protein active site and parallel to its central β-sheet were determined to elucidate the mean orientation of the protein with respect to the surface as a function of its distance from the surface. It was found that the free energy of adsorption varied linearly with the total charge of the protein, while the electric moment (dipole moment) had a second-order but significant effect. Though an increase of the electric moment generally resulted in a slightly increased affinity of the protein for the surface, close to the surface the mean force acting on the protein clearly varied linearly with the strength of the electric moment, such that a clear correlation between the latter and the protein orientation with respect to the surface could be established. Wild-type cutinase displayed the highest affinity for the charged surface amongst all proteins having the same total charge, even though it did not have the largest electric moment. © 1996 by John Wiley & Sons, Inc.