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.     

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.     

Complexation of semiflexible chains with oppositely charged cylinder

We study the complexation of long thin semiflexible polymer chains with an oppositely charged cylinder. Starting from the linear Poisson-Boltzmann equation, we calculate the electrostatic potential and the energy of such a charge distribution. We find that sufficiently flexible chains prefer to wrap around the cylinder in a helical manner, when their charge density is smaller than that of the cylinder. The optimal value of the helical pitch is found by minimization of the sum of electrostatic and bending energies. The dependence of the pitch on the number of chains, their rigidity, and salt concentration in solution is analyzed. We discuss our results in the light of recent experiments on DNA complexation with cylindrical dendronized polymers.     

Numerical study of the interplay of monomer-surface electrostatic and non-electrostatic interactions in the adsorption of weak polyelectrolytes on oppositely charged surfaces

The adsorption of weak polybase on oppositely charged planar surfaces has been investigated numerically by using the self-consistent field theory (SCFT). Particular attention was paid to the interplay of monomer-surface electrostatic and non-electrostatic interactions in the adsorption behaviors of weak polybase. In this study, the strength of monomer-surface non-electrostatic interactions was set to be no more than the thermal energy k _B T. It was found from the numerical study that in the regime of low surface charge density of the substrate and low pH or high bulk degree of ionization, both the screening-enhanced and screening-reduced salt effects emerge. On the contrary, in the opposite regime, only the screening-reduced salt effect was observed. Moreover, the overall charge neutrality inside the adsorption layer was analyzed. The underlying mechanism governing the adsorption behaviors of weak polybase on oppositely charged surfaces was elucidated.     

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.     

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.     

Fluorescence and ESR studies of the conformational behavior of oppositely charged polyelectrolytes at solid/liquid interfaces

The conformational behavior of oppositely charged polyelectrolytes on alumina in solutions was investigated by means of excimer fluorescence and electron spin resonance spectroscopy using maleic acid-propene copolymer labeled with pyrene or TEMPO. It was found that the ability of the polyanion at the surface for conformational rearrangements is strongly influenced by the constraints of the adsorbed state that restrict its complexation. Polyelectrolyte complexes (PEC) formed by mixing of the oppositely charged polyelectrolytes exhibited extreme coiling due to the screening of the charged groups. The polyelectrolytes undergo spreading during the adsorption process due to the electrostatic attraction. Surface binding can irreversibly limit the flexibility for the reconformation process to a great extent. It is also shown here that a flatter adsorbed state could be reached by sequential adsorption of polyanion and polycation than could be reached by the direct adsorption of the polyelectrolyte complex itself.     

Counter-ion activity and microstructure in polyelectrolyte complexes as determined by osmotic pressure measurements

We have investigated the activity of counter-ions at 60 degrees C through the osmotic coefficient K in solutions of anionic and cationic polyelectrolyte complexes of variable compositions. For excess of polyanion in the complexes (molar fraction of polycation f < 0.5), K increases as the polyanion is neutralized by the polycation (f getting closer to 0.5). By contrast, for an excess of polycation (f > 0.5), K stays constant or even slightly decreases as the polycation is getting neutralized by the polyanion. This asymmetric behavior depending on the charge of the complexes indicates that the globally negatively charged complexes are homogeneous and can be treated as a single polyelectrolyte of reduced linear charge density. On the other hand, the positively charged complexes show a micro-phase separation between neutral fully compensated microdomains and domains where the excess polycation is locally segregated. These two different microstructures are reminiscent of the coacervation and segregation regimes observed at higher concentrations and salinities, and also of polyelectrolyte complexes with oppositely charged surfactants. This interpretation is supported by two simple predictive models.     

Mixed systems of hydrophobically modified polyelectrolytes: controlling rheology by charge and hydrophobe stoichiometry and interaction strength

Rheology and phase separation were investigated for aqueous mixtures of two oppositely charged hydrophobically modified polyelectrolytes. The typical phase separation, normally seen for oppositely charged polymer mixtures, is dramatically reduced by the presence of hydrophobic modification, and phase separation is only detected close to the point of charge neutralization. While the two polyelectrolytes separately can give high viscosities and a gel-like behavior, a pronounced maximum in viscosity and storage modulus with the mixing ratio of the polyelectrolytes is observed; the maximum is located between the points of charge and hydrophobe stoichiometry and reflects a combination of hydrophobic and electrostatic association. Lowering the charge density of the anionic polymer leads to a strengthened association at first, but at lower charge densities there is a weakened association due to the onset of phase separation. The strength of the electrostatic interaction was modified by adding salt. Increased ionic strength can lead to phase separation and to increased or decreased viscosity depending on the polyelectrolyte mixing ratio.     

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.     

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.     

Equilibrium domains on heterogeneously charged surfaces

Recent experiments have shown that salt solutions containing surfaces with two oppositely charged species show stable, possibly equilibrium, structures with finite domain sizes. The short-range interactions between the two species would normally result in phase separation that is driven by the line tension with macroscopically large domains of each species. In this paper, we show that, when at least one of the charged species is mobile, finite domains can occur in equilibrium. The domain size is determined by a competition of the electrostatic free energy that promotes charge mixing and small domains, with the line tension that promotes macroscopic phase separation. We calculate the equilibrium patch size as a function of the surface charge and the concentration of dissolved monovalent salts in the bulk phase. An important finding is the prediction of a first-order transition from finite patches to macroscopic phase separation of the two charge species as the salt concentration is increased.     

Electrostatic self-assembly of neutral and polyelectrolyte block copolymers and oppositely charged surfactant

We investigated the phase behavior and the microscopic structure of the colloidal complexes constituted from neutral/polyelectrolyte diblock copolymers and oppositely charged surfactant by dynamic light scattering (DLS) and small-angle neutron scattering (SANS). The neutral block is poly(N-isopropylacrylamide) (PNIPAM), and the polyelectrolyte block is negatively charged poly(acrylic acid) (PAA). In aqueous solution with neutral pH, PAA behaves as a weak polyelectrolyte, whereas PNIPAM is neutral and in good-solvent condition at ambient temperature, but in poor-solvent condition above approximately 32 degrees C. This block copolymer, PNIPAM-b-PAA with a narrow polydispersity, is studied in aqueous solution with an anionic surfactant, dodecyltrimethylammonium bromide (DTAB). For a low surfactant-to-polymer charge ratio Z lower than the critical value ZC, the colloidal complexes are single DTAB micelles dressed by a few PNIPAM-b-PAA. Above ZC, the colloidal complexes form a core-shell microstructure. The core of the complex consists of densely packed DTA+ micelles, most likely connected between them by PAA blocks. The intermicellar distance of the DTA+ micelles is approximately 39 A, which is independent of the charge ratio Z as well as the temperature. The corona of the complex is constituted from the thermosensitive PNIPAM. At lower temperature the macroscopic phase separation is hindered by the swollen PNIPAM chains. Above the critical temperature TC, the PNIPAM corona collapses leading to hydrophobic aggregates of the colloidal complexes.     

Molecular dynamics simulations of polyelectrolyte multilayering on a charged particle

Molecular dynamics simulations of polyelectrolyte multilayering on a charged spherical particle revealed that the sequential adsorption of oppositely charged flexible polyelectrolytes proceeds with surface charge reversal and highlighted electrostatic interactions as the major driving force of layer deposition. Far from being completely immobilized, multilayers feature a constant surge of chain intermixing during the deposition process, consistent with experimental observations of extensive interlayer mixing in these films. The formation of multilayers as well as the extent of layer intermixing depends on the degree of polymerization of the polyelectrolyte chains and the fraction of charge on its backbone. The presence of ionic pairs between oppositely charged macromolecules forming layers seems to play an important role in stabilizing the multilayer film.     

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.     

Colloidal complexes from poly(vinyl amine) and carboxymethyl cellulose mixtures

The phase behaviors of polyelectrolyte complexes formed from dilute solutions of poly(vinyl amine) (PVAm) and carboxymethyl cellulose (CMC) were determined as a function of overall composition and pH. The phase diagram included regions with soluble complexes, colloidal complexes, and macroscopic precipitates. Colloidal complexes were stable when either polymer was in sufficient excess to give electrosteric stabilization. The polymer mixing ratios giving complexes with an isoelectric point of 7 could be predicted from a simple model using the degree of ionization vs pH data for PVAm and CMC. The model failed at extreme pH values because not all added polymer was incorporated into the complexes. At pH 7, essentially all the added polymer was incorporated into the colloidal complex or precipitate, as long as the mixing ratio was within +/-10% of charge stoichiometry. The interaction of PVAm and CMC at pH 7 was endothermic, supporting the generally accepted viewpoint that the interaction of oppositely charged polyelectrolytes is entropy-driven. Although the colloidal complexes had a broad particle size distribution, the average particle size was rather insensitive to mixing ratio. By contrast, complex size was sensitive to electrolyte concentration with no complex formation when the NaCl concentration was > or =2 M.     

Ionic micelles in solutions of polyelectrolytes and block copolymers with oppositely charged blocks: Computer simulation

Complexation in solutions of strongly charged polyelectrolytes and diblock copolymers composed of oppositely charged and neutral blocks were studied via the molecular dynamics method. Stoichiometric micellar complexes formed in a dilute solution represent cylindrical brushes whose conformation is determined by the linear charge density on the polyelectrolyte and by temperature. As the concentration of macromolecules increases, the orientational ordering of anisotropic ionic micelles takes place. The complexation can induce the stiffening of the polyelectrolyte chain.     

Molecular dynamics simulations of layer-by-layer assembly of polyelectrolytes at charged surfaces: effects of chain degree of polymerization and fraction of charged monomers

We performed molecular dynamics simulations of the electrostatic assembly of multilayers of flexible polyelectrolytes at a charged surface. The multilayer build-up was achieved through sequential adsorption of oppositely charged polymers in a layer-by-layer fashion from dilute polyelectrolyte solutions. The steady-state multilayer growth proceeds through a charge reversal of the adsorbed polymeric film which leads to a linear increase in the polymer surface coverage after completion of the first few deposition steps. Moreover, substantial intermixing between chains adsorbed during different deposition steps is observed. This intermixing is consistent with the observed requirement for several deposition steps to transpire for completion of a single layer. However, despite chain intermixing, there are almost perfect periodic oscillations of the density difference between monomers belonging to positively and negatively charged macromolecules in the adsorbed film. Weakly charged chains show higher polymer surface coverage than strongly charged ones.