The Formation and Salt Induced Melting of a Highly Viscoelastic Mixture of Two Oppositely Charged Polyelectrolytes

A quick and convenient route to prepare a highly viscoelastic mixture of two oppositely charged polyelectrolytes is presented. The investigation was essentially performed at a fixed total polyelectrolyte concentration. The phase behaviour was studied at varying ratios between the two oppositely charged polyions. The mixtures phase separated associatively at mixing ratios in the vicinity of overall charge neutrality, while by screening the attractive forces with NaCl the precipitate could be dissolved. At certain mixing ratios off charge neutrality the mixtures were highly viscoelastic single-phase solutions in the absence of screening electrolyte. When NaCl was added to such a solution the viscoelasticity decreased strongly since the attractive forces between the oppositely charged polyions were screened. Therefore, by contacting an initially salt free mixture of polyions with a brine solution of known concentration, the diffusion of salt into the polyion matrices could be monitored by following the rheology of the mixture as a function of the contact time. It is shown that the transport of NaCl inside the polyion matrices was diffusion controlled.     

Polyion interchange reactions of interpolyelectrolyte complexes in aqueous solutions and gels

Cooperative coupling reaction between two opposite charged polyelectrolytes results in formation of polyelectrolyte complexes (IPEC). This reaction is very fast and diffusion controlled. Whether IPECs formed by linear polyions are soluble or limitary swellable in aqueous media is decided by their composition, namely, by a ratio of oppositely charged polyions as well as by a water phase composition (the nature and the concentration of a simple salt, pH, the presence and the concentration of organic additives etc.). The most important intrinsic property of IPECs is their ability to participate in interchange (exchange and substitution) reactions with competing polyions. The kinetics and the position of equilibria in these reactions are controlled by the low molecular salt concentration, the nature of small counterions, DP of interaction polyelectrolytes, as well as by their linear charge density. IPECs can be formed also by interacting linear and opposite charged networks. It is shown that linear polyelectrolytes dissolved in aqueous solution can penetrate unexpectedly fast into oppositely charged cross-linked polyelectrolyte gels to form “snake-in-cage” composites representing IPECs of corresponding polyion segments. It is proved that the mechanism consists in “relay-race” transfer of linear polyion segments from one segment of the polyelectrolyte network to the other via interpolyelectrolyte exchange reaction. The driving force for the fast transport of linear polyions into the gel is produced by coupling reaction between two polyelectrolytes proceeding on solution/gel interface.     

On the phase diagram of reentrant condensation in polyelectrolyte-liposome complexation

Complexation of polyions with oppositely charged spherical liposomes has been investigated by means of dynamic light scattering measurements and a well-defined reentrant condensation has been observed. The phase diagram of charge inversion, recently derived [T. T. Nguyen and B. I. Shklovskii, J. Chem. Phys. 115, 7298 (2001)] for the complexation of DNA with charged spherical macroions, has been employed in order to define the boundaries of the region where polyion-liposome complexes begin to condense, forming larger aggregates, and where aggregates dissolve again, towards isolated polyion-coated-liposome complexes. A reasonable good agreement is observed in the case of complexes formed by negatively charged polyacrylate sodium salt polyions and liposomes built up by cationic lipids (dioleoyltrimethylammoniumpropane), in an extended liposome concentration range.     

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.     

A theory of electrolyte friction on translating polyelectrolytes

Enormous increases in friction factors of isolated polyelectrolytes have been observed when the concentration of added monovalent salt is decreased below 10^?2M. Electrolyte friction on translating polyions, analogous to dielectric friction on translating small ions, is postulated to account for this effect. A quantitative theory of this electrolyte friction is developed, based on the fluctuating force formulation of Kirkwood and Previous development of the author for the dynamics of smallion concentration fluctuations. By modelling the flexible linear polyelectrolyte as a charged gel sphere of constant radius equal to the measured hydrodynamic radius in 1.0 M NaBr, where electrolyte friction is negligible, and employing the theory of Harris and Rice to determine the net charge on the sphere, remarkably good agreement with the data is obtained using no adjustable parameters. Polyion expansion of only a few percent would make the agreement perfect. Diffusion of polyions at finite concentration is discussed in the light of the present work, and it is suggested that an appropriate reinterpretation of parameters in the existing theories can account for the observed dependence of the measured diffusion coefficients on salt and polyion concentration in the linear range.     

Charged Semi-Permeable Shell with Encapsulated Polyions: Concentration Profile,Surface Potential,and Electrostatic Pressure

Summary: We study theoretically the electrostatic equilibrium for a charged shell filled with a suspension of polyions (e.g., colloids, polyelectrolytes, etc.) and immersed in an infinite salt-free reservoir. The shell is impermeable for polyions, but allows free diffusion of counterions. From the solution of the linearized Poisson-Boltzmann equation we obtain the distribution of the potential and concentration profiles for polyions. We then derive explicit formulas for the electrostatic pressure exerted by the shell. If the overall charge of the filled shell has the same sign as the surface alone the pressure on the shell increases with increase of the surface charge density. Otherwise the surface charge density suppresses the electro-osmotic pressure due to the electrostatic attraction between the oppositely charged polyions and shell.     

Rod-like polyelectrolyte adsorption onto charged surfaces in monovalent and divalent salt solutions

We analyze the adsorption of strongly charged polyelectrolytes onto weakly charged surfaces in divalent salt solutions. We include short-range attractions between the monomers and the surface and between condensed ions and monomers, as well correlations among the condensed ions. Our results are compared with the adsorption in monovalent salt solutions. Different surface charge densities (σ), and divalent (m) and monovalent (s) salt concentrations are considered. When the Wigner-Seitz cells diameter (2R) is larger than the length of the rod, the maximum amount of adsorption scales like n_max ∼ σ^4/3 in both monovalent and divalent solutions. For homogeneously charged surfaces, the maximum adsorption occurs at s* ∼ σ² when s* > ϕ, where ϕ is the monomer concentration, the counterpart for divalent salt solution, m* roughly scales as σ^2.2 when m* > ϕ. The effective surface charge density has a maximum absolute value at m′ < m*. A discrete surface charge distribution and short-range attractions between monomers and surface charge groups can greatly enhance surface charge inversion especially for high salt concentration. The critical salt concentration for adsorption in divalent salt solution roughly scales as m_c ∼ bσ^1.9, where b is the distance between two neighboring charged monomers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3642–3653, 2004     

Phase behaviour of oppositely charged protein and surfactant mixtures: DOTAC-BLG-Water

The interactions between the negatively charged protein, β-lactoglobulin (BLG) and the cationic surfactant dodecyltrimethylammonium chloride (DOTAC) in water have been investigated by determining the phase equilibria of the ternary system within the concentration range of 20 wt.% of both protein and surfactant. Three main regions are formed—an isotropic solution phase, a white precipitation region and a blueish, isotropic, highly viscous gel phase. The protein solution can solubilize 1 mole surfactant, [DOTAC] per mole protein, [BLG] prior to precipitation. The protein-surfactant precipitate complex is neutral and consists of 8 [DOTAC]/[BLG]. The net charge of the protein in water at aqueous pH is −7 and this agrees with the determined composition. The pH is, however, decreased on addition of DOTAC, but this does not seem to affect the composition of the precipitate significantly. The amount of precipitate reaches a maximum at about 8 [DOTAC]/[BLG] and thereafter a plateau region occurs where no more precipitate seems to be formed. On further increasing the surfactant concentration the precipitate redissolves either into a solution phase directly or into a solution phase via a gel phase depending on the protein concentration. On decreasing salt concentration the ternary system shows similar phase behaviour, but the stability of the regions are different. It is also observed that oppositely charged protein-surfactant systems show similar phase behaviour irrespective of nature of the net charge on the protein.     

Stoichiometric polyelectrolyte complexes of ionic block copolymers and oppositely charged polyions

Micellization in dilute solutions of diblock copolymers with a polyelectrolyte and a hydrophilic nonionic blocks and oppositely charged polyions is studied using mean-field theory. In aqueous solutions the micelle core consists of the polyelectrolyte complex (PEC) while the corona is formed by hydrophilic blocks of the block copolymers. Describing PEC as a globule in the framework of the Lifshitz [Zh. Eksp. Teor. Fiz. 55, 2408 (1968)] globule theory we calculate the surface tension of the micellar core/solvent interface as a function of the polyion degree of ionization, solvent quality, and concentration of low-molecular-mass salt. The equilibrium aggregation number of starlike micelles formed by block copolymers and homopolymers of opposite charge at stoichiometric mixture compositions is found as a function of the system parameters. It is shown that micelles disintegrate upon addition of salt.     

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.     

Confinement free energy of flexible polyelectrolytes in spherical cavities

A weakly charged flexible polyelectrolyte chain in a neutral spherical cavity is analyzed by using self-consistent field theory within an explicit solvent model. Assuming the radial symmetry for the system, it is found that the confinement of the chain leads to creation of a charge density wave along with the development of a potential difference across the center of cavity and the surface. We show that the solvent entropy plays an important role in the free energy of the confined system. 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 when chain lengths are small. However, with the increase in chain length, chain conformational entropy and polymer-solvent interaction energy also become important. Our calculations reveal that energy due to electrostatic interactions plays a minor role in the free energy. Furthermore, we show that the total free energy under spherical confinement is not extensive in the number of monomers. Results for the osmotic pressure and mean activity coefficient for monovalent salt are presented. We demonstrate that fluctuations at one-loop level lower the free energy and corrections to the osmotic pressure and mean activity coefficient of the salt are discussed. Finite size corrections are shown to widen the range of validity of the fluctuation analysis.     

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)].     

Density functional theory for planar electric double layers: closing the gap between simple and polyelectrolytes

We report a nonlocal density functional theory (NLDFT) for polyelectrolyte solutions within the primitive model; i.e., the solvent is represented by a continuous dielectric medium, and the small ions and polyions by single and tangentially connected charged hard spheres, respectively. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for hard-sphere repulsion, an extended first-order thermodynamic perturbation theory for chain connectivity, and a quadratic functional Taylor expansion for electrostatic correlations. With the direct and cavity correlation functions of the corresponding monomeric systems as inputs, the NLDFT predicts the segment-level microscopic structures and adsorption isotherms of polyelectrolytes at oppositely charged surfaces in good agreement with molecular simulations. In particular, it faithfully reproduces the layering structures of polyions, charge inversion, and overcharging that cannot be captured by alternative methods including the polyelectrolyte Poisson-Boltzmann equation and an earlier version of DFT. The NLDFT has also been used to investigate the influences of the small ion valence, polyion chain length, and size disparity between polyion segments and counterions on the microscopic structure, mean electrostatic potential, and overcharging in planar electric double layers containing polyelectrolytes.     

Coarse-grained modeling of proline rich protein 1 (PRP-1) in bulk solution and adsorbed to a negatively charged surface

Structural properties of the acidic proline rich protein PRP-1 of salivary origin in bulk solution and adsorbed onto a negatively charged surface have been studied by Monte Carlo simulations. A simple model system with focus on electrostatic interactions and short-ranged attractions among the uncharged amino acids has been used. In addition to PRP-1, some mutants were considered to assess the role of the interactions in the systems. Contrary to polyelectrolytes, the protein has a compact structure in salt-free bulk solutions, whereas at high salt concentration the protein becomes more extended. The protein adsorbs to a negatively charged surface, although its net charge is negative. The adsorbed protein displays an extended structure, which becomes more compact upon addition of salt. Hence, the conformational response upon salt addition in the adsorbed state is the opposite as compared to that in bulk solution. The conformational behavior of PRP-1 in bulk solution and at charged surfaces as well as its propensity to adsorb to surfaces with the same net charge are rationalized by the block polyampholytic character of the protein. The presence of a triad of positively charged amino acids in the C-terminal was found to be important for the adsorption of the protein.     

Loose complexation of weakly charged microemulsion droplets and a polyelectrolyte

The effect of polyelectrolyte addition on the properties of an oil-in-water (O/W) microemulsion of weakly charged spherical micelles is studied. The 81 A radius O/W droplets in this system can be charged by the partial substitution of the nonionic surfactant by a cationic surfactant. The effect of the addition of poly(acrylic acid) (PAA), which is a charged pH-dependent polyelectrolyte, on the interactions between charged or noncharged droplets has been investigated using SANS. We have characterized the phase behavior of this pH-smart system as a function of the microemulsion and the polyelectrolyte concentration and the number of charges per droplet at three pH values: pH = 2, 4.5, and 12. In particular, an associative phase separation due to the bridging of the droplets by the neutral PAA chains through H-bonds is observed with extremely low PAA addition at low pH. At the opposite, an addition of PAA at pH = 4.5 generates a strong repulsive contribution between neutral droplets. Electrostatic bonds between charged droplets and PAA, controlled by the number of charges per droplet, are responsible for a pH drift and then for an associative phase separation similar to that observed at low pH. Finally, at high pH, the creation of electrostatic bonds between fully charged PAA and charged droplets liberates sufficiently counterions in solution at high droplet charge density to screen the electrostatic interactions and to allow an associative phase separation.     

On the phase behavior and structural properties of polyelectrolyte solutions

Correlations between structural properties and phase behavior of polyelectrolyte solutions were discussed along the line of the work reported by Châtellier and Joanny [Joanny JF, Châtellier X. J Phys France II 1996;6:1669]. A multicomponent system made of polyions, salt ions and counterions was considered under poor solvent conditions. Unlike this reference, partial structure factors were derived from the celebrated Zimm’s formula written in the matrix form including the effects of finite chain length. These effects were found to generate significant shifts in phase diagrams and qualitative changes in structural properties. The presence of a charged solid surface was briefly discussed. Here also, the phase diagram was found to shift with an increasing amount as the polyion chain length decreased.     

Zwitterionic stationary phase with covalently bonded phosphorylcholine type polymer grafts and its applicability to separation of peptides in the hydrophilic interaction liquid chromatography mode

A novel phosphorylcholine type zwitterionic stationary phase was synthesized by graft polymerization of 2-methacryloyloxyethyl phosphorylcholine onto the surface of porous silica particles. The resulting material possesses both negatively charged phosphoric acid and positively charged quaternary ammonium groups, which renders it a low net charge over a wide pH range. The composition of the surface grafts were determined by elemental analysis and solid state NMR, and the surface charge (zeta-potential) in different buffer solutions were measured using photon correlation spectroscopy. Separation of several peptides was investigated on packed columns in the hydrophilic interaction liquid chromatography (HILIC) separation mode. It was shown that small peptides can be separated based on hydrophilic interaction and ionic interaction between the stationary phase and analyte. The organic solvent composition, the pH and the salt concentration of the eluent have strong effects on the retention time. Compared to native silica before grafting, the newly synthesized zwitterionic material gave more stable retention times for basic peptides over pH range 3-7 due to elimination of the dissociation of silanol groups.     

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.     

Complex coacervation: a field theoretic simulation study of polyelectrolyte complexation

Using the complex Langevin sampling strategy, field theoretic simulations are performed to study the equilibrium phase behavior and structure of symmetric polycation-polyanion mixtures without salt in good solvents. Static structure factors for the segment density and charge density are calculated and used to study the role of fluctuations in the electrostatic and chemical potential fields beyond the random phase approximation. We specifically focus on the role of charge density and molecular weight on the structure and complexation behavior of polycation-polyanion solutions. A demixing phase transition to form a "complex coacervate" is observed in strongly charged systems, and the corresponding spinodal and binodal boundaries of the phase diagram are investigated.