Polyelectrolyte adsorption: electrostatic mechanisms and nonmonotonic responses to salt addition

The main question addressed in this work is as follows: Under pure electrosorption conditions, that is, disregarding nonelectrostatic effects, how does the net adsorption of a polyelectrolyte at an oppositely charged surface respond to the addition of simple salt? Previous simulations and mean-field calculations have suggested that the polymers will desorb. However, we will demonstrate that an increased adsorption also is possible, even for pure electrosorption, at low and intermediate levels of salt. As this is a correlation-driven effect, mean field approaches will fail to capture it. Using simulations, one will in general need to simulate large systems and relatively long polymers. Also important is the presence of a proper bulk solution, with a finite and well-defined polyelectrolyte concentration. We have performed a theoretical study of polyelectrolyte adsorption, assuming screened Coulomb interactions between monomers; that is, the salt is implicit. This work focuses on the effects from ionic screening and polymer length. Specifically, the adsorption at a weakly charged colloidal particle, with a diameter of 200 nm, is monitored for various salt concentrations, in the presence of highly charged chains. Using simulations, we investigate polymers with two different degrees of polymerization: 40 and 160, respectively. These simulations are complemented by predictions from classical polymer density functional theory, utilizing a recently developed correlation-correction (Forsman, J.; Nordholm, S. Langmuir, in press). The agreement with corresponding simulations is semiquantitative, and because the calculations run many orders of magnitude faster than the simulations, longer and more realistic polymers could be studied with this approach. However, switching off the correlation-correction leads to a mean-field theory, which fails to even qualitatively reproduce the simulated response to screening.     

Poisson-Boltzmann theory of pH-sensitive (annealing) polyelectrolyte brush

We present a self-consistent field analytical theory of a polymer brush formed by weakly charged pH-sensitive (annealing) polyelectrolytes tethered to a solid-liquid interface and immersed in buffer solution of low molecular weight salt. We use the Poisson-Boltzmann framework, applied by us previously to polyelectrolyte (PE) brushes with quenched charge (Zhulina, E. B.; Borisov, O. V. J. Chem. Phys. 1997, 107, 5952). This approach allows for detailed analysis of the internal structure of annealing PE brush in terms of polymer density distribution, profiles of electrostatic potential and of local degree of chain ionization as a function of buffer ionic strength and pH without any assumptions on mobile ion distribution imposed in earlier scaling-type models. The presented analytical theory recovers all major asymptotic dependences for average brush properties predicted earlier. In particular, a nonmonotonic dependence of brush thickness on ionic strength and grafting density is confirmed and specified with accuracy of numerical coefficients including crossover regions. Moreover, the theory predicts qualitatively new effects, such as, e.g., disproportionation of tethered polyions into weakly charged concentrated proximal and strongly charged sparse distal brush domains at low salt and moderate grating densities. The presented results allow us to quantify responsive features of annealing PE brushes whose large-scale and local conformational properties can be manipulated by external stimuli.     

Cylindrical cell model for the electrostatic free energy of polyelectrolyte complexes

Associative phase separation (complex coacervation) in a mixture of oppositely charged polyelectrolytes can lead to different types of (inter-)polyelectrolyte complexes (soluble micelles, macroscopic precipitation). In a previous report [Langmuir 2004, 20, 2785-2791], we presented a model for the electrostatic free energy change when (weakly charged) polyelectrolyte forms a homogeneous complex phase. The influence of ionization of the polymer on the electrostatic free energy of the complex was incorporated but the influence of complex density neglected. In the present effort, cylindrical cells are assumed around each polyelectrolyte chain in the complex, and on the basis of the Poisson-Boltzmann equation, the electrostatic free energy is calculated as a function of the complex density. After combination with Flory-Huggins mixing free energy terms and minimization of the total free energy, the equilibrium complex density is obtained, for a given ratio of polycations to polyanions in the complex. The analysis is used in an example calculation ofpolyelectrolyte film formation by alternatingly applying a polycation and a polyanion solution. The calculation suggests that the often observed exponential growth of a polyelectrolyte film when the polymer is weakly charged has a thermodynamic origin: the polyelectrolyte complex shifts repeatedly between two equilibrium states of different densities and compositions. However, when the polyelectrolytes are strongly charged the difference in the compositions between the two equilibrium states is very small, and exponential growth by an absorption mechanism is no longer possible.     

Microphase separation of weakly charged block polyelectrolyte solutions: Donnan theory for dynamic polymer morphologies

A mean-field dynamic density functional theory for the phase behavior of concentrated weakly charged block polyelectrolyte solutions is developed, using the Donnan membrane equilibrium approach to account for electrostatic interactions. In this limit all long-range electrostatic interactions are canceled and the net charge density in any region on a coarse-grained scale is zero. The phase diagram of a model triblock polyelectrolyte in solution as a function of the charge of the solvophilic block and the solvent concentration is established. Different mesoscopic structures (lamellar, bicontinuous, hexagonal, micellar, and dispersed coexisting phases) are formed depending on the copolymer charge asymmetry. It is found that upon changing the charge of the solvophilic copolymer block the polyelectrolyte solution does not follow the lyotropic sequence of phases of this polymer. Upon increase in the charge of the solvophilic blocks, changes in copolymer morphology take place by means of change in curvature of polymeric domains.     

Electrophoresis of soft particles: analytic approximations

An approximate analytic expression is derived for the electrophoretic mobility of a weakly charged spherical soft particle (i.e., a hard particle covered with a weakly charged polyelectrolyte layer) on the basis of the general mobility expression for soft particles (Ohshima, H., J. Colloid Interface Sci. 2000, 228, 190-193). The obtained mobility expression, which reproduces various approximate results so far derived and gives some new mobility formulas, covers all types of weakly charged soft particles with arbitrary values of the thickness of polymer layer, the radius of the particle core, the electrophoretic softness, and the Debye length, including spherical polyelectrolytes with no particle core as well as spherical hard particles with no polyelectrolyte layer.     

Interplay of ionic and nonionic interactions in weakly charged polyelectrolytes

We describe the results of theoretical and experimental studies of the regular heterogeneities on a nanometer scale which are formed in the systems containing weakly charged polyelectrolytes due to the competition of ionic and hydrophobic interactions. In particular, we consider the effect of microphase separation in poor solvent polyelectrolyte solutions and gels and nano-self-assemblies emerging in the complexes of polyelectrolyte gels with oppositely charged surfactants. The practically important application connected with metal nanoparticles formation in regular microstructures in polyelectrolyte systems is considered as well.     

Single ion diffusive transport within a Poly(styrene sulfonate) polymer brush matrix probed by fluorescence correlation spectroscopy

Diffusive transport within complex environments is a critical piece of the chemistry occurring in such diverse membrane systems as proton exchange and bilayer lipid membranes. In the present study, fluorescence correlation spectroscopy was used to evaluate diffusive charge transport within a strong polyelectrolyte polymer brush. The fluorescent cation rhodamine-6G was used as a counterion probe molecule, and the strong polyelectrolyte poly(styrene sulfonate) was the polymer brush. Such strong polyelectrolyte brushes show promise for charge storage applications, and thus it is important to understand and tune their transport efficiencies. The polymer brush demonstrated preferential solvation of the probe counterion as compared to solvation by the aqueous solvent phase. Additionally, diffusion within the polymer brush was strongly inhibited, as evidenced by a decrease in diffusion constant of 4 orders of magnitude. It also proved possible to tune the transport characteristics by controlling the solvent pH, and thus the ionic strength of the solvent. The diffusion characteristics within the charged brush system depend on the brush density as well as the effective interaction potential between the probe ions and the brush. In response to changes in ionic strength of the solution, it was found that these two properties act in opposition to each other within this strong polyelectrolyte polymer brush environment. A stochastic random walk model was developed to simulate interaction of a diffusing charged particle with a periodic potential, to show the response of characteristic diffusion times to electrostatic field strengths. The combined results of the experiments and simulations demonstrate that responsive diffusion characteristics in this brush system are dominated by changes in Coulombic interactions rather than changes in brush density. More generally, these results support the use of FCS to evaluate local charge transport properties within polyelectrolyte brush systems, and demonstrate that the technique shows promise in the development of novel polyelectrolyte films for charge storage/transport materials.     

Modeling of protein interactions with surface-grafted charged polymers. Correlations between statistical molecular modeling and a mean field approach

Ion exchange media involving charge groups attached to flexible polymers are widely used for protein purification. Such media often provide enhanced target protein purity and yield. Yet, little is understood about protein interaction with such media at the molecular level, or how different media architectures might affect separation performance. To gain a better understanding of such adsorptive systems, statistical mechanical perturbation calculations, utilizing a Debye-Hückel potential, were performed on surface-grafted charged polymers and their interaction with model proteins. The studied systems were weakly charged, and the polymers were linear and relatively short (degree of polymerization is 30). Segment distributions from the surface were also determined. The interaction of spherical model protein particles of 12-30 A radius were investigated with respect to polymer grafting density, distance from matrix surface, protein charge, and ionic strength. The partitioning coefficient of the model proteins was determined for different distances from the surface. An empirical mean field theory that scales the entropy of the protein with the square of the protein radius correlates well to Monte Carlo statistical modeling results. Upon adsorption to the polymer layers, the model proteins exhibit a critical surface charge density that is proportional to the ionic strength, independent of the grafting density, and appears to be a fundamental determinant of protein adsorption. Partitioning of protein-like nanoparticles to the charged polymer surface is only favored above the particle critical charge density.     

Polyelectrolyte complexes of carboxyl-containing polyanions: Stabilization of complexes in neutral and weakly acidic media and factors affecting this phenomenon

The stability of insoluble polyelectrolyte complexes formed by various carboxyl-containing polyanions with a positively charged partner—a linear polycation or protein—has been studied by means of turbidimetric titration. In most cases, acidification of the reaction medium leads to a significant strengthening of complexes against the action of the added salt in neutral or weakly acidic media. The data concerning the effect of the chemical nature of polymer components, the degree of polymerization, the density of charge, and the structure of their chains on the pH-dependent profiles of complex dissociation provide evidence that this effect is related to stabilization of the polyelectrolyte complex through the system of hydrogen bonds formed by carboxyl groups of a partially charged polyanion incorporated into the complex. Owing to a sharp and reversible change in the stability of systems at a pH and ionic strength of solution that are favorable for functioning of biopolymers (proteins, enzymes, antibodies, and nucleic acids), polycarboxylate polyelectrolyte complexes offer promise for solving practically important problems, for example, in biotechnology for separation of biological mixtures.     

Ionizable polyelectrolyte brushes: brush height and electrosteric interaction

Semi-analytical scaling theory is used to describe quenched and annealed (weakly charged, ionizable, charge-regulating) polyelectrolyte brushes in electrolyte solutions of arbitrary salt concentration. An Alexander-De Gennes box model with homogeneous distribution of polymer segments and the free ends located at the edge of the brush is assumed, as is local electroneutrality in the brush. For annealed polyelectrolyte and in the low-salt regime, the theory predicts that for sufficiently dense brushes, the salt concentration has a small influence on brush height, while the brush expands with increasing grafting density, in agreement with experiment. Expressions are presented for the interaction free energy of compressed ionizable and quenched polyelectrolyte brushes (proportional to the force between particles or curved surfaces). In all cases, the required prefactors are explicitly stated. The theory is compared directly with published experiments on the influence of salt concentration, pH, and grafting density on the thickness and interaction force of polystyrene sulfonate (quenched) and poly(meth)acrylic acid (annealed) brushes. In general, trends are well reproduced but significant deviations remain.     

Theory of volume transition in polyelectrolyte gels with charge regularization

We present a theory for polyelectrolyte gels that allow the effective charge of the polymer backbone to self-regulate. Using a variational approach, we obtain an expression for the free energy of gels that accounts for the gel elasticity, free energy of mixing, counterion adsorption, local dielectric constant, electrostatic interaction among polymer segments, electrolyte ion correlations, and self-consistent charge regularization on the polymer strands. This free energy is then minimized to predict the behavior of the system as characterized by the gel volume fraction as a function of external variables such as temperature and salt concentration. We present results for the volume transition of polyelectrolyte gels in salt-free solvents, solvents with monovalent salts, and solvents with divalent salts. The results of our theoretical analysis capture the essential features of existing experimental results and also provide predictions for further experimentation. Our analysis highlights the importance of the self-regularization of the effective charge for the volume transition of gels in particular, and for charged polymer systems in general. Our analysis also enables us to identify the dominant free energy contributions for charged polymer networks and provides a framework for further investigation of specific experimental systems.     

Polyelectrolyte adsorption kinetics under an applied electric potential: Strongly versus weakly charged polymers

Previous work has demonstrated adsorption of weakly basic polycations to a conducting substrate to be continuous, i.e. asymptotically linear in time over hours, under an applied anodic potential [A.P. Ngankam, P.R. Van Tassel, Proc. Natl. Acad. Sci. USA 104 (2007) 1140]. Adsorption without apparent saturation requires an interfacial charge regulation, which is possible for weakly charged polymers via segment deprotonation. We investigate here whether deprotonation is a necessary condition for continuous adsorption by comparing the behavior of a weakly and a strongly charged polyelectrolyte, the latter containing permanently charged segments incapable of deprotonation. We employ optical waveguide lightmode spectroscopy (OWLS) to measure adsorption of poly(N-vinyl imidazole) (PVI), a weakly basic polycation, and quaternized poly(N-vinyl imidazole) (QPVI), a structurally similar polymer with ca. 20% of its monomers containing a permanent positive charge, onto indium tin oxide (ITO). Under open circuit conditions, we observe both PVI and QPVI adsorption to reach a rapid saturation and be essentially irreversible. In contrast, at an ITO potential of 1.5 V (versus hydrogen) in a 0.1 M NaCl solution, we observe adsorption of both PVI and QPVI to be continuous and reversible. In salt free solution, we observe PVI but not QPVI to exhibit continuous adsorption at 1.5 V, and for both polymers to be essentially irreversibly attached. We propose interfacial charge regulation to occur via a deprotonation mechanism for PVI, and via a counterion condensation mechanism for QPVI. Continuous adsorption is therefore possible for a strongly charged polyelectrolyte, via a counterion condensation mechanism; this finding opens the door to nanofilms of controlled polymer content containing permanent charges.     

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.     

Counterion release from adsorbed highly charged polyelectrolyte: an electrooptical study

The adsorption of sodium poly(4-styrene sulfonate) on oppositely charged beta-FeOOH particles is studied by electrooptics. The focus of this paper is on the release of condensed counterions from adsorbed polyelectrolyte upon surface charge overcompensation. The fraction of condensed Na+ counterions on the adsorbed polyion surface is estimated according to the theory of Sens and Joanny and it is compared with the fraction of condensed counterions on nonadsorbed polyelectrolyte. The relaxation frequency of the electrooptical effect from the polymer-coated particle is found to depend on the polyelectrolyte molecular weight. This is attributed to polarization of the layer from condensed counterions on the polyion surface, being responsible for creation of the effect from particles covered with highly charged polyelectrolyte. The number of the adsorbed chains is calculated also assuming counterion condensation on the adsorbed polyelectrolyte and semiquantative agreement is found with the result obtained from the condensed counterion polarizability of the polymer-coated particle. Our findings are in line with theoretical predictions that the fraction of condensed counterions remains unchanged due to the adsorption of highly charged polyelectrolyte onto weakly charged substrate.     

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)].     

Influence of polyelectrolyte and salt on the structure of dispersions containing charged colloidal particles

An integral equation theory has been used as the basis for studying the structure of dispersions containing charged colloidal particles: globular protein molecules with a nonzero dipole moment, a polyelectrolyte and a low-molecular salt. It is demonstrated that there is an effective attraction between charged colloidal particles, which increases in the presence of charged polymer chains. The influence of the length of polyelectrolyte chains and of salt concentration on the partial structure factor of colloidal particles was studied.     

Self-consistent field theory and its applications in polymer systems

This review article addresses the widely used self-consistent field theory (SCFT) in interacting polymer systems. The theoretical framework and numerical method of solving the self-consistent equations are presented. In this paper, different structures of polymer can be considered, such as homopolymer, block copolymer, polydisperse polymer and charged polymer. Several systems, micro/macro phase separation, interface, self-assembly, are presented as examples to demonstrate its applications in details. Besides, the fluctuation effects are considered. The first order is Gaussian fluctuation theory, which can be used to determine the stability of the mean-field solution and predict the kinetics of unstable structure. The derivation and applications of Gaussian fluctuation theory are presented as well.     

Entropy and enthalpy of polyelectrolyte complexation: Langevin dynamics simulations

We report a systematic study by Langevin dynamics simulation on the energetics of complexation between two oppositely charged polyelectrolytes of same charge density in dilute solutions of a good solvent with counterions and salt ions explicitly included. The enthalpy of polyelectrolyte complexation is quantified by comparisons of the Coulomb energy before and after complexation. The entropy of polyelectrolyte complexation is determined directly from simulations and compared with that from a mean-field lattice model explicitly accounting for counterion adsorption. At weak Coulomb interaction strengths, e.g., in solvents of high dielectric constant or with weakly charged polyelectrolytes, complexation is driven by a negative enthalpy due to electrostatic attraction between two oppositely charged chains, with counterion release entropy playing only a subsidiary role. In the strong interaction regime, complexation is driven by a large counterion release entropy and opposed by a positive enthalpy change. The addition of salt reduces the enthalpy of polyelectrolyte complexation by screening electrostatic interaction at all Coulomb interaction strengths. The counterion release entropy also decreases in the presence of salt, but the reduction only becomes significant at higher Coulomb interaction strengths. More significantly, in the range of Coulomb interaction strengths appropriate for highly charged polymers in aqueous solutions, complexation enthalpy depends weakly on salt concentration and counterion release entropy exhibits a large variation as a function of salt concentration. Our study quantitatively establishes that polyelectrolyte complexation in highly charged Coulomb systems is of entropic origin.     

Gelation of "catanionic" vesicles by hydrophobically modified polyelectrolytes

The gelation of mixed cationic/anionic surfactant vesicles of sodium dodecyl sulfate/didodecyldimethylammonium bromide and sodium dodecylbenzenesulfonate/cetyltrimethylammonium tosylate by hydrophobically modified sodium polyacrylate is studied rheologically. When the vesicles are cationically charged, mixtures with this anionic polyelectrolyte form precipitates. When the vesicles are anionically charged, however, these mixtures display a progression from a Maxwell fluid to a critical gel to a solidlike gel with increasing vesicle and/or polyelectrolyte concentration. Consideration of the viscous behavior with increasing vesicle and polymer volume fraction indicates that the gel network is formed by the bridging of the hydrophobically modified polymer between vesicles. The similarity between the gelation results for the two anionic systems suggests the results can be generalized to other similarly charged mixtures.     

One‐Step Microfluidic Fabrication of Polyelectrolyte Microcapsules in Aqueous Conditions for Protein Release

We report a microfluidic approach for one‐step fabrication of polyelectrolyte microcapsules in aqueous conditions. Using two immiscible aqueous polymer solutions, we generate transient water‐in‐water‐in‐water double emulsion droplets and use them as templates to fabricate polyelectrolyte microcapsules. The capsule shell is formed by the complexation of oppositely charged polyelectrolytes at the immiscible interface. We find that attractive electrostatic interactions can significantly prolong the release of charged molecules. Moreover, we demonstrate the application of these microcapsules in encapsulation and release of proteins without impairing their biological activities. Our platform should benefit a wide range of applications that require encapsulation and sustained release of molecules in aqueous environments.