Aqueous solutions of ionenes: interactions and counterion specific effects as seen by neutron scattering

Aqueous solutions of ionenes with bromide and fluoride counterions have been investigated using small angle neutron scattering for the first time. Ionenes are a class of cationic polyelectrolytes based on quaternary ammonium atoms and, considering the very low solubility of their uncharged part (hydrocarbon chain), would be formally classified as hydrophobic. Ionenes present important structural differences over previously studied polyelectrolytes: (a) charge is located on the polyelectrolyte backbone, (b) the distance between charges is regular and tunable by synthesis, (c) hydrophobicity comes from methylene groups of the backbone and not from bulky side groups. Results for Br ionenes feature a disappearance of the well-known polyelectrolyte peak beyond a given monomer concentration. Below this concentration, the position of the peak depends on the chain charge density, f(chem), and scales as f(chem)(0.30±0.04). This is an indication of a hydrophilic character of the ionene backbone. In addition, osmotic coefficients of ionene solutions resemble again other hydrophilic polyelectrolytes, featuring no unusual increase in the water activity (or a significant counterion condensation). We conclude that despite the hydrophobicity of the hydrocarbon chain separating charged centers on ionenes, these chains behave as hydrophilic. In contrast to Br ionenes, the polyelectrolyte peak remains at all concentrations studied for the single F ionene investigated. This strong counterion effect is rationalized in terms of the different hydrating properties and ion pairing in the case of bromide and fluoride ions.     

Molecular dynamics and neutron scattering study of the dependence of polyelectrolyte dendrimer conformation on counterion behavior

Atomistic molecular dynamics (MD) simulations and contrast variation small angle neutron scattering (SANS) have been combined to investigate the Generation-5 polyelectrolyte polyamidoamine starburst dendrimer. This work reveals the dendrimer conformational dependence on counterion association at different levels of molecular charge. The accuracy of the simulations is verified through satisfactory comparison between modeled results, such as excess intra-dendrimer scattering length density distribution and hydration level, and their experimental counterparts. While the counterion distributions are not directly measureable with SANS, the spatial distribution of the counterions and their dendrimer association are extracted from the validated MD equilibrium trajectories. It is found that the conformation of the charged dendrimer is strongly dependent on the counterion association. Sensitivity of the distribution of counterions around charged amines to the counterion valency is qualitatively explained by adopting Langmuir adsorption theory. Moreover, via extending the concept of electrical double layer for compact charged colloids, we define an effective radius of a charged dendrimer including the spatial distribution of counterions in its vicinity. Within the same framework, the correlation between the strength of intra-dendrimer electrostatic repulsion and the counterion valency and dynamics is also addressed.     

Simulation Study of the Conformational Properties of Diblock Polyelectrolytes in Salt Solutions

Coarse-grained molecular dynamics simulations are performed to understand the behavior of diblock polyelectrolytes in solutions of divalent salt by studying the conformations of chains over a wide range of salt concentrations. The polymer molecules are modeled as bead spring chains with different charged fractions and the counterions and salt ions are incorporated explicitly. Upon addition of a divalent salt, the salt cations replace the monovalent counterions, and the condensation of divalent salt cations onto the polyelectrolyte increases, and the chains favor to collapse. The condensation of ions changes with the salt concentration and depends on the charged fraction. Also, the degree of collapse at a given salt concentration changes with the increasing valency of the counterion due to the bridging effect. As a quantitative measure of the distribution of counterions around the polyelectrolyte chain, we study the radial distribution function between monomers on different polyelectrolytes and the counterions inside the counterion worm surrounding a polymer chain at different concentrations of the divalent salt. Our simulation results show a strong dependence of salt concentration on the conformational properties of diblock copolymers and indicate that it can tune the self-assembly behaviors of such charged polyelectrolyte block copolymers.     

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.     

Similarities between polyelectrolyte gels and biopolymer solutions

Small angle neutron scattering (SANS) measurements and osmotic swelling pressure measurements are reported for polyelectrolyte gels and solutions under nearly physiological conditions. A synthetic polymer (sodium-polyacrylate) and three biopolymers (DNA, hyaluronic acid, and polyaspartic acid) are studied. The neutron scattering response of these anionic polyelectrolytes is closely similar, indicating that at larger length scales the organization of the polymer molecules is not significantly affected by the fine details of the molecular architecture (e.g., size and chemical structure of the monomer unit, type of polymer backbone). The results suggest that specific interactions between the polyelectrolyte chains and the surrounding monovalent cations are negligible. It is found that the osmotic compression modulus of these biopolymer solutions determined from the analysis of the SANS response decreases with increasing chain persistence length. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3679–3686, 2006     

Structural investigation of PAMAM dendrimers in aqueous solutions using small-angle neutron scattering: effect of generation

We investigate a series of poly(amidoamine) starburst dendrimers (PAMAM) of different generations in acidic, aqueous solutions using small-angle neutron scattering (SANS). While the overall molecular size is found to be practically unaffected by a pD change, a strong generational dependence of counterion association is revealed. Upon increasing the dendrimer generation, the effective charge obtained from our SANS experiments only shows a small increase in contrast to the nearly exponential increase predicted by a recent atomic simulation. We also find that with the same degree of molecular protonation the specific counterion association, which is defined as the ratio of bound chloride anions to positively charged amines in solutions, is larger for higher-generation PAMAM dendrimer. The associated counterion density also increases upon increasing generation number.     

Fluorescence correlation spectroscopy studies of diffusion of a weak polyelectrolyte in aqueous solutions

We apply fluorescent correlation spectroscopy (FCS) to investigate solution dynamics of a synthetic polyelectrolyte, i.e., a weak polycarboxylic acid in aqueous solutions. The technique brings single molecule sensitivity and molecular specificity to dynamic measurements of polyelectrolyte solutions. Translational diffusion of Alexa-labeled poly(methacrylic acid), PMAA*, chains was studied in very dilute, 10(-4) mg/ml, solutions as a function of solution pH and ionic strength. The observed changes in diffusion coefficients were consistent with about twofold expansion of PMAA* coils when pH was changed from 5 to 8, and with chain contraction for alkaline metal ion concentrations from 0.01 to 0.1 M. The dependence of the hydrodynamic size of PMAA* chains on the counterion type followed the sequence: Li(+)>Na(+) approximately equal to Cs(+)>K(+). The dependence of translational diffusion on polyacid concentration was weak at the low concentration limit, but chain motions were significantly slower at higher polymer concentrations when PMAA chains overlapped. Finally, measurements of dynamics of PMAA* chains in "salt-free" solutions showed that self-diffusion of PMAA* chains significantly slowed down when PMAA concentration was increased, probably reflecting the sensitivity of PMAA* translational motions to the onset of interchain domain formation. These results illustrate the utility of the FCS technique for studying hydrodynamic sizes of polyelectrolyte coils in response to variation in solution pH or concentration of salt and polyelectrolytes. They also suggest that FCS will be a promising technique for selective observation of the dynamics of polyelectrolyte components in complex polymer mixtures.     

Counterion adsorption theory of dilute polyelectrolyte solutions: apparent molecular weight, second virial coefficient, and intermolecular structure factor

Polyelectrolyte chains are well known to be strongly correlated even in extremely dilute solutions in the absence of additional strong electrolytes. Such correlations result in severe difficulties in interpreting light scattering measurements in the determination of the molecular weight, radius of gyration, and the second virial coefficient of charged macromolecules at lower ionic strengths from added strong electrolytes. By accounting for charge-regularization of the polyelectrolyte by the counterions, we present a theory of the apparent molecular weight, second virial coefficient, and the intermolecular structure factor in dilute polyelectrolyte solutions in terms of concentrations of the polymer and the added strong electrolyte. The counterion adsorption of the polyelectrolyte chains to differing levels at different concentrations of the strong electrolyte can lead to even an order of magnitude discrepancy in the molecular weight inferred from light scattering measurements. Based on counterion-mediated charge regularization, the second virial coefficient of the polyelectrolyte and the interchain structure factor are derived self-consistently. The effect of the interchain correlations, dominating at lower salt concentrations, on the inference of the radius of gyration and on molecular weight is derived. Conditions for the onset of nonmonotonic scattering wave vector dependence of scattered intensity upon lowering the electrolyte concentration and interpretation of the apparent radius of gyration are derived in terms of the counterion adsorption mechanism.     

Transport properties of some cationic polysaccharides 2. Charge density effect

The charge density effect on the behavior of some cationic polysaccharides in aqueous and nonaqueous (methanol) solutions was studied by viscometric and conductometric measurements. The polyelectrolytes investigated contain quaternary ammonium salt groups, N-alkyl-N,N-dimethyl-2-hydroxypropylene ammonium chloride, attached to a dextran backbone. This new class of polyelectrolytes has various linear charge density parameters, xi, located below and above the critical threshold value of counterions condensation, xi(c)=1(xi=0.25-3.18). The viscometric data revealed that all copolymers exhibit a polyelectrolyte behavior and were plotted in the terms of Rao equation. The conductometric measurements of solutions of these copolymers were presented as a function of polymer concentration and charge density. The results were analyzed within the Manning's theory and lower experimental values of the equivalent conductivity than the theoretical ones were found. Possible reasons of this discrepancy have been discussed. The interaction parameters were evaluated and these were found to depend on both the polymer concentration and the charge density. The conductometric behavior of these cationic polysaccharides has shown that counterion condensation is not a threshold phenomenon, their association to the charged groups of the polyions taking place for xi>1 as well as xi<1.     

Rheological and structural properties of aqueous solutions of a hydrophobically modified polyelectrolyte and its unmodified analogue

Rheological methods and small angle neutron scattering (SANS) were used in the characterization of dilute and semidilute aqueous solutions, both with and without added salt, of anionic poly(vinyl alcohol) (PVA⁻) and its hydrophobically modified analogue (HM-PVA⁻). The rheological measurements showed that the concentration induced viscosification effect and elastic responses are considerably stronger for solutions of HM-PVA⁻ than in solutions of the unmodified polyelectrolyte. Over the considered polymer concentration domain, the solutions of PVA⁻ exhibit virtually Newtonian behavior, whereas strong shear thinning effects are observed in the HM-PVA⁻ solutions. The SANS results for HM-PVA⁻ solutions reveal a pronounced peak in the plot of scattering intensity versus scattering wavevector q at intermediate q values and the position of the maximum scales with polymer concentration as q_max∼c^0.28±0.02. This peak is suppressed in solutions of the unmodified polyelectrolyte and merely a shoulder in the scattering curve appears. Additionally, an “upturn” in the scattered intensity is observed at small q values and the magnitude of this effect depends on polymer concentration, hydrophobicity and salt addition. At large q values, the SANS results from HM-PVA⁻ solutions suggest morphological changes, from rod-like chains to a network of semiflexible chains, as the polyelectrolyte concentration increases.     

Structure and Dynamics of Blends of Diblock Copolymers

The melt state rheological behavior of a series of blends of a lamellae‐forming nearly symmetrical polystyrene‐polyisoprene (PS‐PI) diblock copolymer with a sphere‐forming highly asymmetrical PS‐PI diblock copolymer is correlated to their structure obtained from small‐angle neutron scattering (SANS). The exponential composition dependence of the relaxation of fluctuations associated with the disordered asymmetrical diblock is similar to that observed in solutions of star polymers. Further, the zero‐shear viscosity of the blends in the disordered state exhibits unusually strong composition dependence. These dynamic properties are closely linked with the SANS‐based structural data that suggest strong compositional fluctuations, even in the disordered state.     

Proteins and polyelectrolytes: A charged relationship

We review the interaction of charged polymeric systems with proteins. In solutions of low ionic strength there are many examples of proteins attracted to polyelectrolytes even if both systems carry the same overall charge. This attractive interaction is widespread, having been observed for single polyelectrolyte chains as well as for polyelectrolytes grafted to surfaces (polyelectrolyte brushes) and charged polymeric networks. In all cases, adding salt weakens the interaction considerably. We discuss the suggestion that the attractive force at low salinity originates from the asymmetry of interaction between charged polymer segments and charged patches on the surface of the protein globule. This can be explained if the attractive force is mainly due to a counterion release force, i.e., the polyelectrolyte chains become the multivalent counterions for the patches of opposite charge localized on the surface of the proteins. We review a selection of simple models that lead to semi-quantitative estimates of this force as the function of salt concentration.     

Electrophoresis of a spherical dispersion of polyelectrolytes in a salt-free solution

The electrophoretic behavior of a spherical dispersion of polyelectrolytes of arbitrary concentration is analyzed theoretically under a salt-free condition, that is, the liquid phase contains only counterions which come from the dissociation of the functional groups of polyelectrolytes. We show that, in general, the surface potential of a polyelectrolyte increases nonlinearly with its surface charge. A linear relation exists between them, however, when the latter is sufficiently small; and the more dilute the concentration of polyelectrolytes, the broader the range in which they are linearly correlated. If the amount of surface charge is sufficiently large, counterion condensation occurs, and the rate of increase of surface potential as the amount of surface charge increases declined. Also, it leads to an inverse in the perturbed potential near the surface of a polyelectrolyte, and its mobility decreases accordingly. For a fixed amount of surface charge, the lower the concentration of polyelectrolytes and/or the lower the valence of counterions, the higher the surface potential. The qualitative behavior of the mobility of a polyelectrolyte as the amount of its surface charge varies is similar to that of its surface charge.     

A model for the Gibbs energy of aqueous solutions of polyelectrolytes

A new model for the excess Gibbs energy of aqueous solutions of polyelectrolytes is presented and applied for the correlation of the activity of water in aqueous solutions of polyelectrolytes without as well as with an added (single) salt. The model considers the phenomenon of counterion condensation, i.e., the partial dissociation of highly charged polyelectrolytes in water. Three parameters (a binary interaction parameter between polymer segments, the equilibrium constant of the dissociation reaction and a parameter which accounts for the polymer configuration) were fitted to the experimental results. The model allows for a reliable correlation of experimental results for the osmotic coefficient of aqueous solutions of a single polyelectrolyte (without as well as with an added salt).     

Structure and mechanism formation of polyelectrolyte complex obtained from PSS/PAH system: effect of molar mixing ratio, base–acid conditions, and ionic strength

Colloidal dispersions of polyelectrolyte complexes were prepared in aqueous solutions. We have used mixtures containing the strongly charged anionic polyelectrolyte sodium polystyrene sulfonate (PSS) and the weak cationic polyelectrolyte polyallylamine hydrochloride (PAH). Both polymers have the same molecular weight. The complexes were obtained by adding drop by drop a solution of the anionic polyelectrolyte to excess cationic polyelectrolyte. In these conditions, sodium polystyrene sulfonate and polyallylamine hydrochloride self-assembled in nanometer-range complexes; the self-assembly is driven by electrostatic interactions, as well as by entropy changes due to counterion release. The electrostatic interactions were controlled in several ways: by changing the C _PSS/C _PAH concentration ratio, by modifying the pH (and thus the protonation degree of polyallylamine hydrochloride), and by adding sodium chloride (screened interactions). Dynamic light scattering experiments demonstrated that the hydrodynamics radius of the polyelectrolyte complex increases, changing from soluble to insoluble complex formation, when some physicochemical parameters are increased: the concentration ratio between polyelectrolytes, the sodium chloride concentration, and pH. Zeta potential measurements, as a function of the C _PSS/C _PAH concentration ratio, as well as of pH and ionic strength, allow us to state that the resulting particles have a structure constituted by a neutral core surrounded by a positively charged shell. The polyelectrolyte complexes have globular shapes, as observed by electron microscopy.     

pH-controlled exponential and linear growing modes of layer-by-layer assemblies of star polyelectrolytes

We report the unique layer-by-layer (LbL) assembly behavior of pH-sensitive star-shaped polyelectrolytes with both linear and exponential growth modes controlled by star architecture and assembly conditions. Cationic poly[2-(dimethylamino)ethyl methacrylate] and anionic poly(acrylic acid) stars were synthesized via "core-first" atom-transfer radical polymerization (ATRP) based on multifunctional initiators, in addition to their linear analogues. We demonstrated the LbL growth behavior as a function of deposition pH (ranging from 5 to 7), number of layers (up to 30 bilayers), and the method of assembly (dip- vs spin-assisted LbL). The spin-assisted LbL assembly makes it possible to render smoother and thinner LbL films with parameters controlled by the shear rate and pH conditions. In contrast, for dip-assisted LbL assembly, the pH-dependent exponential growth was observed for both linear and star polyelectrolytes. In the case of linear/linear pair, the exponential buildup was accompanied with a notable surface segregation which resulted in dramatic surface nonuniformity, "wormlike" heterogeneous morphology, and dramatic surface roughening. In contrast, star/linear and star/star LbL films showed very uniform and smooth surface morphology (roughness below 2.0 nm on the scale of 10 μm × 10 μm) with much larger thickness reaching up to 1.0 μm for 30 bilayers and rich optical interference effects. Star polyelectrolytes with partially screened charges and high mobility caused by compact branched architecture appear to facilitate fast diffusion and exponential buildup of LbL films. We suggest that the fast buildup prevents long-range lateral diffusion of polyelectrolyte star components, hinders large-scale microphase separation, and thus leads to unique thick, smooth, uniform, transparent, and colorful LbL films from star polyelectrolytes in contrast to mostly heterogeneous films from traditional linear counterparts.     

Colligative properties of polyelectrolyte solutions

The solution properties of polyelectrolytes are not well understood despite increasing theoretical and experimental effort, particularly during the last 10 years. Some of the current models for polyelectrolyte solutions are valid only at infinite dilution because they account only for long-range interactions. Nagvekar and Danner [M. Nagvekar, R.P. Danner, An Excess Gibbs Free Energy Model for Polyelectrolyte Solutions, Fluid Phase Equilibria 53 (1989) 219.] have developed an excess Gibbs free energy model for polyelectrolyte solutions. The key feature of the model is to express the excess Gibbs free energy as the sum of the contributions from long-range and short-range interactions. The `limiting laws' of Manning [G.S. Manning, Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions. I. Colligative Properties, J. Chem. Phys. 51 (1969a) 924; G.S. Manning, Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions. II. Self-diffusion of Small Ions, J. Chem. Phys. 51 (1969b) 934.] were used to account for the long-range interactions while a local composition model of the Non-Random Two Liquid (NRTL) type was used for short-range interactions. In this work, we present the expressions for counterion activity coefficients and the motic coefficients in polyelectrolyte solutions with and without added salts at finite concentrations. Data for a number of polyelectrolyte systems with univalent and divalent counterions are analyzed using Nagvekar's proposed model. In the low concentration regime, the osmotic coefficient data are practically independent of concentration, and are in reasonable agreement with the Manning model. With increasing polyelectrolyte concentration, the osmotic coefficient data are a strong function of concentration, and the local composition model is shown to successfully represent the data.     

Interaction of cylindrical polymer brushes in dilute and semi-dilute solution

We present a systematic study of flexible cylindrical brush-shaped macromolecules in a good solvent by small-angle neutron scattering (SANS), static light scattering (SLS), and by dynamic light scattering (DLS) in dilute and semi-dilute solution. The SLS and SANS data extrapolated to infinite dilution lead to the shape of the polymer that can be modeled in terms of a worm-like chain with a contour length of 380 nm and a persistence length of 17.5 nm. SANS data taken at higher polymer concentration were evaluated by using the polymer reference interaction site model (PRISM). We find that the persistence length reduce from 17.5 nm at infinite dilution to 5.3 nm at the highest concentration (volume fraction 0.038). This is comparable with the decrease of the persistence length in semi-dilute concentration predicted theoretically for polyelectrolytes. This finding reveals a softening of stiffness of the polymer brushes caused by their mutual interaction.     

The build-up of polyelectrolyte multilayers of microfibrillated cellulose and cationic polyelectrolytes

A new type of nanocellulosic material has been prepared by high-pressure homogenization of carboxymethylated cellulose fibers followed by ultrasonication and centrifugation. This material had a cylindrical cross-section as shown by transmission electron microscopy with a diameter of 5-15 nm and a length of up to 1 microm. Calculations, using the Poisson-Boltzmann equation, showed that the surface potential was between 200 and 250 mV, depending on the pH, the salt concentration, and the size of the fibrils. They also showed that the carboxyl groups on the surface of the nanofibrils are not fully dissociated until the pH has reached pH = approximately 10 in deionized water. Calculations of the interaction between the fibrils using the Derjaguin-Landau-Verwey-Overbeek theory and assuming a cylindrical geometry indicated that there is a large electrostatic repulsion between these fibrils, provided the carboxyl groups are dissociated. If the pH is too low and/or the salt concentration is too high, there will be a large attraction between the fibrils, leading to a rapid aggregation of the fibrils. It is also possible to form polyelectrolyte multilayers (PEMs) by combining different types of polyelectrolytes and microfibrillated cellulose (MFC). In this study, silicon oxide surfaces were first treated with cationic polyelectrolytes before the surfaces were exposed to MFC. The build-up of the layers was monitored with ellipsometry, and they show that it is possible to form very well-defined layers by combinations of MFC and different types of polyelectrolytes and different ionic strengths of the solutions during the adsorption of the polyelectrolyte. A polyelectrolyte with a three-dimensional structure leads to the build-up of thick layers of MFC, whereas the use of a highly charged linear polyelectrolyte leads to the formation of thinner layers of MFC. An increase in the salt concentration during the adsorption of the polyelectrolyte results in the formation of thicker layers of MFC, indicating that the structure of the adsorbed polyelectrolyte has a large influence on the formation of the MFC layer. The films of polyelectrolytes and MFC were so smooth and well-defined that they showed clearly different interference colors, depending on the film thickness. A comparison between the thickness of the films, as measured with ellipsometry, and the thickness estimated from their colors showed good agreement, assuming that the films consisted mainly of solid cellulose with a refractive index of 1.53. Carboxymethylated MFC is thus a new type of nanomaterial that can be combined with oppositely charged polyelectrolytes to form well-defined layers that may be used to form, for example, new types of sensor materials.     

Polyelectrolyte conductivity

Using the de Gennes scaling model for the configuration of a polyelectrolyte chain in semidilute solution, we construct a simple model of AC conductivity for semidilute solutions of strongly charged polyelectrolytes without added salt. We compare the predictions of this model with literature data and new data on two polyelectrolytes with very different affinities for water. The sodium salt of sulfonated polystyrene in water is a hydrophobic polyelectrolyte (the uncharged monomer does not dissolve in water), where the chain is locally collapsed. The sodium salt of poly(2-acrylamido-2-methylpropanesulfonate), is a much more hydrophilic polyelectrolyte, making the chain quite expanded locally. The model describes the conductivity of both cases reasonably for concentrations below 10⁻² M (mol of monomer per liter). Deviations between experiment and theory at higher concentrations lead us to conclude that counterion condensation decreases as concentration is increased. This is qualitatively consistent with the experimental observation that the dielectric constant of the polyelectrolyte solution increases as polyelectrolyte is added. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2951–2960, 1997