Linear polyelectrolytes in tetravalent salt solutions

The effect of adding tetravalent salt of different sizes to a solution of linear and flexible polyelectrolytes is investigated by molecular dynamics simulations. Upon the addition of salt, a chain reexpansion takes place, following a well-known collapsed conformation. The degrees of collapse and reexpansion increase with ion size. In the solution, tetravalent counterions replace monovalent ones and condense onto the chains. The condensation for small ions displays a profile different from that for large ones. In a high-salt region, ions can form layering orders around a polyelectrolyte and locally overcompensate the charge inside. Consequently, the integrated charge distribution reveals an oscillatory behavior away from a chain. By studying the radial distribution function between monomers on different polyelectrolytes, like-charge attraction between chains is demonstrated. This attraction is a prerequisite to chain aggregation or precipitation. The results show a strong dependence of salt concentration and ion size on the properties of polyelectrolyte solutions.     

Chain stiffness, salt valency, and concentration influences on titration curves of polyelectrolytes: Monte Carlo simulations

Monte Carlo simulations have been used to study two different models of a weak linear polyelectrolyte surrounded by explicit counterions and salt particles: (i) a rigid rod and (ii) a flexible chain. We focused on the influence of the pH, chain stiffness, salt concentration, and valency on the polyelectrolyte titration process and conformational properties. It is shown that chain acid-base properties and conformational properties are strongly modified when multivalent salt concentration variation ranges below the charge equivalence. Increasing chain stiffness allows to minimize intramolecular electrostatic monomer interactions hence improving the deprotonation process. The presence of di and trivalent salt cations clearly promotes the chain degree of ionization but has only a limited effect at very low salt concentration ranges. Moreover, folded structures of fully charged chains are only observed when multivalent salt at a concentration equal or above charge equivalence is considered. Long-range electrostatic potential is found to influence the distribution of charges along and around the polyelectrolyte backbones hence resulting in a higher degree of ionization and a lower attraction of counterions and salt particles at the chain extremities.     

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.     

Solution properties of ion-containing polymers in polar solvents

The placement of ionic groups within the molecular structure of a polymer produces marked modification in physical properties. A large number of studies have been performed on these ion-containing polymers, but few have focused on the effects of anion–cation interactions (i.e., counterion binding or ionization) on hydrodynamic volume, especially as the molecular structure of the solvent and nature of counterion are varied. In this study changes in hydrodynamic volume are followed through reduced viscosity measurements as a function of the abovementioned molecular parameters. The dilute solution properties of various polyelectrolytes that contain sulfonate and carboxylate groups were investigated as a function of the counterion structure, charge density, molecular weight, and solvent structure. The polymeric materials were selected because of their specific chemical structure and physical properties. In the first instance a (2-acrylamide-2 methylpropanesulfonic acid)-acrylamide-sodium vinyl sulfonate terpolymer was synthesized and subsequently neutralized with a series of bases. Viscometric measurements on these materials indicate that the nature of the cation affects the ability of the polyelectrolyte to expand its hydrodynamic volume at low polymer levels. The magnitude of the molecular expansion is shown to be due in part to the ability of the counterion to dissociate from the backbone chain, which, in turn, is directly related to the solvent structure. The changes in solution behaviour of these inomers lend support for the existence of ion pairs (i.e., site binding) and ionized moieties on the polymer chains. Measurements performed in a variety of solvent systems further confirm this interpretation. In addition, and acrylamide-sodium vinyl sulfonate copolymer was partially hydrolyzed with sodium hydroxide to study the effect of varying the charge density at a constant degree of polymerization and counterion structure. The results show that the charge density has a significant effect on the magnitude of the reduced viscosity and dilute solution behaviour. These observations, made in aqueous and nonaqueous solvents, are related to the interrelation of hydrodynamic volume, counterion concentration, and site binding. Again the controlling factor is the degree of site binding of the counterion onto the polymer backbone. Finally, we observe that the increased hydrodynamic volume affects viscosity behavior beyond the polyelectrolyte effect regime. If the average charge density on the macromolecule is relative high and/or the molecular weight is large (≥ 10⁶) sufficient intermolecular interactions will occur to produce rapid changes in reduced viscosity.     

Polyampholyte terpolymers of amphoteric,amino acid‐based monomers with acrylamide and (3‐acrylamidopropyl)trimethyl ammonium chloride

Low‐charge‐density amphoteric copolymers and terpolymers composed of acrylamide, (3‐acrylamidopropyl)trimethyl ammonium chloride, and the amino acid derived monomers (e.g., N‐acryloyl valine, N‐acryloyl alanine, and N‐acryloyl aspartate) were prepared via free‐radical polymerization in aqueous media to yield terpolymers with random charge distributions and homogeneous compositions. Sodium formate (NaOOCH) was employed as a chain transfer agent during the polymerization to suppress gel effects and broadening of the molecular weight distribution. Terpolymer compositions were determined by ¹³C and ¹H NMR spectroscopy. Terpolymer molecular weights and polydispersity indices were obtained via size exclusion chromatography/multi‐angle laser light scattering, and hydrodynamic diameter values were obtained via dynamic light scattering. The solution properties of low‐charge‐density amphoteric copolymers and terpolymers have been studied as a function of solution pH, ionic strength, and polymer concentration. The low‐charge‐density terpolymers display excellent solubility in deionized (DI) water with no phase separation. The charge‐balanced terpolymers exhibit antipolyelectrolyte behavior at pH values ≥(6.5 ± 0.2). As solution pH is decreased, these charge‐balanced terpolymers become increasingly cationic because of the protonation of the anionic repeat units. Charge‐imbalanced terpolymers generally demonstrate polyelectrolyte behavior, although the effects of intramolecular electrostatic interactions (e.g., polyampholyte effects) on the hydrodynamic volume are evident at certain values of solution pH and salt concentration. The aqueous solution behavior (i.e., globule‐to‐coil transition at the isoelectric point in the presence of salt and globule elongation with increasing charge asymmetry) of the terpolymers in the dilute regime correlates well with that predicted by the polyampholyte solution theories of Dobrynin and Rubinstein as well as Kantor and Kardar. Examination of comonomer charge density, hydrogen‐bonding ability, and spacer group (e.g., the moiety separating the ionic group from the polymer chain) indicates that conformational restrictions of the amino acid comonomers result in increased chain stiffness and higher solution viscosities in DI water and brine solutions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4479–4493, 2006     

Effect of a low-molecular-weight salt on colloidal dispersions of interpolyelectrolyte complexes

Colloidal dispersions of an interpolyelectrolyte complex were prepared by mixing dilute aqueous solutions of poly(dimethyldiallylammonium chloride) and the sodium salt of the alternating copolymer of maleic acid propene in amounts providing about a threefold excess of the charged groups of the cationic polyelectrolyte over those of the anionic polyelectrolyte. These dispersions were examined by means of analytical sedimentation, quasielastic light scattering, and laser Doppler microelectrophoresis. The experimental results obtained suggest that the particles of the interpolyelectrolyte complex are multicomplex aggregates bearing cationic charge. Such aggregates were assumed to consist of a hydrophobic core formed by coupled oppositely charged macromolecules and a hydrophilic shell formed by cationic macromolecules. Hydrodynamic and electrophoretic properties of these aggregates were found to be rather sensitive to variations in the ionic strength of the surrounding medium: with rising salt concentration, their sedimentation coefficient and hydrodynamic size increase, these increases becoming more strongly pronounced at higher salt concentrations, whereas their electrophoretic mobility gradually decreases. The salt effects revealed suggest that the aggregation level of the particles of the interpolyelectrolyte complex rises in response to an increase in the ionic strength of the surrounding medium. This phenomenon was associated with the salt-induced decrease of the stabilizing effect of the hydrophilic shells that protect such particles from progressive aggregation. Received: 15 May 1998 Accepted in revised form: 28 August 1998     

On the theory of polyelectrolyte adsorption : The effect on adsorption behavior of the electrostatic contribution to the adsorption free energy

A theory has been developed for the adsorption of polyelectrolytes on charged interfaces from an aqueous salt solution. This adsorption is determined by the electrical charge density of the polyelectrolyte, the adsorption energy, the salt concentration, the molecular weight, solubility, flexibility, and concentration of polymer. The theory relates these parameters to the properties of the adsorbed polymer layer, i.e., the amount of polymer adsorbed, the fraction of the adsorbent interface covered, the fraction of the segments actually adsorbed on the interface versus the fraction of the segments in the dangling loops, the final surface charge density, and the thickness of the adsorbed layer. As polyelectrolyte adsorption should resemble nonionic polymer adsorption at high ionic strength of the solution or low charge density on the polymer, this work is an extension of the nonionic polymer adsorption theory to polyelectrolyte adsorption. The following effects are taken into account: (a) the conformational change upon adsorption of a coil in solution into a sequence of adsorbed trains interconnected by loops dangling in solution; (b) the interactions of the adsorbed trains with the interface and with each other; (c) the interaction of the dangling loops with the solvent; (d) the change in surface charge density of the adsorbent due to adsorption of charged trains and the accompanying changes in the electrical double layer which contains “small” ions as well as charged loops; (e) the (induced) dipole interaction of the adsorbed trains with the charged adsorbent interface. The theory is worked out for low potentials (Debye—Hückel approximation); in Appendix B an outline of a more complete treatment is given. The predicted adsorption isotherms have the experimentally observed high-affinity character. A relation between the adsorption energy, the surface charge density on the adsorbent, the degree of dissociation of the polymer, and the salt concentration predicts the conditions under which no adsorption will occur. For adsorbent and polymer carrying the same type of charge (both positive or both negative) the adsorption is predicted to decrease with increased charge density on polymer or adsorbent and to increase with salt concentration. If adsorbent and polymer carry different type charges, the adsorption as a function of the degree of dissociation, α, goes through a maximum at a relatively low value of α and, depending on the adsorption energy, an increase in the salt concentration can then increase or decrease the adsorption. At finite polymer concentration in solution the number of adsorbed segments and the fraction of the interface covered practically do not change with an increase in polymer concentration, whereas the total number of polymer molecules adsorbed increases slightly, as does the average fraction of segments in loops. The experimental results for polyelectrolyte adsorption have been reviewed in general and, as far as data are available, the predictions of the theory seem to follow the experimentally observed trends quite closely, except for the thickness of the adsorbed layer. This thickness is systematically overestimated by the theory and two reasons for this are given. The theoretical model implies a not too low ionic strength of the solution. Extrapolation of results to solutions of very low ionic strength is not warranted.     

Hydrodynamic size and charge of polyelectrolyte complexes

Polyelectrolyte complexes have a wide range of applications for surface modification and flocculation and sorption of organic molecules from solutions. As an example, complexes between poly(diallyl dimethyl ammonium chloride) and poly(styrene sulfonate) have been investigated by diffusion and electrophoresis NMR. The formation of primary or soluble complexes is monitored. The hydrodynamic size is characterized by the hydrodynamic radius, calculated from the diffusion coefficient determined by pulsed field gradient NMR. In the combination with electrophoresis NMR, the effective charge of the molecules and complexes is determined. The hydrodynamic size of the primary complex is smaller than that of the pure polyelectrolyte of the larger molecular weight, in the present case poly(styrene sulfonate), in solution, since charges are compensated by the oppositely charged polyelectrolyte and hence the repelling forces diminish. The effective charge of the complexes is drastically reduced.     

Concentration of potassium cations in the permeate solution in the presence of N,N-dimethyl-N-2-propenyl-2-propen-1-aminium chloride homopolymer using dead-end nano-or ultrafiltration

The investigation is based on the nano-or ultrafiltration of inorganic salts in the presence of a polyelectrolyte in the feed solution. Cellulose acetate membranes are selected with a pore size of 10–20 nm. The membranes are imaged using atomic force microscope. The membrane is completely impermeable to the polyelectrolyte. Polyelectrolyte concentrations are taken in the range of 0.5–1 g/l to avoid a gel layer formation over the membrane. It is discovered that, at such low polyelectrolyte concentration, inorganic salt concentration in the permeate is higher than in the feed solution. This process therefore deviates from conventional membrane separation processes, where the permeate salt concentration is lower or equal to the salt concentration in the feed solution. It is shown that during the nano-or ultrafiltration of inorganic salts in the presence of polyelectrolyte, the ratio of salt concentration in the permeate to feed increases when the initial salt concentration in the feed solution is low. Concentration polarization has a negative impact on this concentrating effect. In the case of this investigation, KCl, KNO₃, K₂SO₄ are taken as inorganic salts, N,N-dimethyl-N-2-propenyl-2-propen-1-aminium chloride homopolymer is selected as a polyelectrolyte. The text was submitted by the authors in English.     

Electrophoresis of soft particles with charged rigid core coated with pH-regulated polyelectrolyte layer

We present a theoretical study on the electrophoresis of a soft particle with a dielectric charged rigid core grafted with a charge-regulated polyelectrolyte layer. The polyelectrolyte layer possesses either an acidic or a basic functional group and the charge dissociation depends on the local pH and ionic concentration of the electrolyte. The dielectric rigid core is considered to possess a uniform volumetric charge density. The electric potential distribution is determined by computing the Poisson-Boltzmann equation outside the core coupled with a Poisson equation inside the impermeable core along with suitable matching conditions at the core-shell interface. The computed electric field is used to determine the mobility of the particle through an existing analytic expression based on the Debye-Huckel approximation. Our results are found to be in good agreement with the existing solutions for the limiting cases. The influence of the core charge density, ionic concentration, and pH of the electrolyte on the particle mobility is studied for different choice of hydrodynamic penetration length of the polyelectrolyte and dissociation constant of the functional group. The critical value of the pH required to achieve zero mobility is estimated. We find that in a monovalent electrolyte solution, the soft particle with a net negative (positive) charge can have positive (negative) mobility.     

Diffusiophoresis of a polyelectrolyte in a salt concentration gradient

The diffusiophoresis of a polyelectrolyte subject to an applied salt concentration gradient is modeled theoretically. The entirely porous type of particle is capable of simulating entities such as DNA, protein, and synthetic polymeric particles. The dependence of the diffusiophoretic behavior of the polyelectrolyte on its physical properties, and the types of ionic species and their bulk concentrations are discussed in detail. We show that in addition to the effects coming from the polarization of double layer and the difference in the ionic diffusivities, the polarization of the condensed counterions inside the polyelectrolyte might also be significant. The last effect, which has not been reported previously, reduces both the electric force and the hydrodynamic force acting on the polyelectrolyte. Both the direction and the magnitude of the diffusiophoretic velocity of the polyelectrolyte are found to highly depend upon its physical properties. These results provide valuable references for applications such as DNA sequencing and catalytic nano- or micromotors.     

Effective charge of polyelectrolytes as a function of the dielectric constant of a solution

The combination of diffusion and electrophoresis NMR is applied to determine the effective charge of poly(styrene sulfonate) in solution. While electrophoresis NMR yields the electrophoretic mobility of the molecules in solution, the hydrodynamic friction is determined from diffusion NMR. From the force balance between electrostatic force and hydrodynamic friction, the effective charge of the molecule is determined free of any model. In the present study poly(styrene sulfonate) has been investigated in mixtures of water and methanol of varying composition. The lower dielectric constant in the mixtures with high methanol content results in a drastically reduced effective charge of the polyelectrolytes. The reduced effective charge along the polymer chain is the reason for a much more compact conformation of the polyelectrolyte, which is seen in a smaller hydrodynamic size of the molecule.     

pH‐responsive ampholytic terpolymers of acrylamide,sodium 3‐acrylamido‐3‐methylbutanoate,and (3‐acrylamidopropyl)trimethylammonium chloride. II. Solution properties

The solution properties of low‐charge‐density ampholytic terpolymers of acrylamide, sodium 3‐acrylamido‐3‐methylbutanoate, and (3‐acrylamidopropyl)trimethylammonium chloride were studied as functions of the solution pH, ionic strength, and polymer concentration. Terpolymers with low charge densities, large charge asymmetries, or both exhibited excellent solubility in deionized (DI) water, and higher charge density terpolymers were readily dispersible in DI water; however, the higher charge density terpolymer solutions separated into polymer‐rich and polymer‐poor phases upon standing over time. Charge‐balanced terpolymers exhibited antipolyelectrolyte behavior at pH values greater than or equal to the ambient pH (6.5 ± 0.2); the same terpolymers behaved increasingly as cationic polyelectrolytes with decreasing solution pH because of the protonation of the 3‐acrylamido‐3‐methylbutanoate (AMB) repeat units. Unbalanced terpolymers generally exhibited polyelectrolyte behavior, although the effects of intramolecular electrostatic attractions (i.e., polyampholyte effects) on the hydrodynamic volume of the unbalanced terpolymer coils were evident at certain values of the solution pH and salt concentration. The dilute‐solution behavior of the terpolymers correlated well with the behavior predicted by several polyampholyte solution theories. In the semidilute regime, solution viscosities increased with increasing terpolymer charge density, and this indicated a significant enhancement of the solution viscosity by intermolecular electrostatic associations. Upon the addition of NaCl, semidilute‐solution viscosities tended to decrease because of the disruption of the intermolecular electrostatic associations. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3252–3270, 2004     

Swelling and Collapse of Swiss‐Cheese Polyelectrolyte Gels in Salt Solutions

A simple theory of swelling of microporous Swiss‐cheese polyelectrolyte gels (i. e., polyelectrolyte gels containing water voids) in the solution of 1–1 low‐molecular‐weight salt is developed. Due to the Donnan effect the overall concentration of salt within porous Swiss‐cheese gel can be significantly higher than that within the corresponding homogeneous gel due to the effective absorption of salt by the embedded voids. The degree of this absorption increases with the increase of average size of the voids and of their concentration. In the case of relatively large water voids with radii of about few μm the salt concentration within the water voids is approximately equal to that in the external solution, while the salt concentration in the polymer matrix can be much lower. It is thought that polyelectrolyte Swiss‐cheese gels are promising for use as suitable media for microreactors for nanotechnology.     

Lattice Monte Carlo simulations of a charged polymer chain: effect of valence and concentration of the added salt

The configurational properties of a single polyelectrolyte chain accompanied by counterions and added salt are simulated using the cooperative motion algorithm on the face-centered cubic lattice. In particular, a greater emphasis is put on the effect of valence z(s) and concentration of the added positive (negative) salt ions n(s) on the polymer behavior. This is achieved by inspecting two families of systems with widely varying numbers n(s) of monovalent (z(s)=1) or multivalent (z(s)=4) salt ions at two fixed reduced temperatures T*=0.5, 1. The calculations indicate that especially at the lower temperature the addition of some amount of multivalent salt has a tremendous impact on chain conformations compared to the situation with monovalent salt. Even for relatively low concentrations of the former, the mean radius of gyration (1/2) and the mean end-to-end distance (1/2) decrease sharply, i.e., the polymer exists in strongly collapsed forms. This reduction of polymer size is also accompanied by a drop in the system inner energy e* and the effective mean charge per monomer q*. The analysis of various pair-correlation functions g(ab)(r) indicates that the latter effect-caused by condensation of ions onto the chain-is dominated by the multivalent ones. Furthermore, it is found that for z(s)=4, the uncondensed salt ions tend to group themselves into small clusters.     

Explicit ions condensation around strongly charged polyelectrolytes and spherical macroions: the influence of salt concentration and chain linear charge density. Monte Carlo simulations

The condensation of monovalent counterions and trivalent salt particles around strong rigid and flexible polyelectrolyte chains as well as spherical macroions is investigated by Monte Carlo simulations. The results are compared with the condensation theory proposed by Manning. Considering flexible polyelectrolyte chains, the presence of trivalent salt is found to play an important role by promoting chain collapse. The attraction of counterions and salt particles near the polyelectrolyte chains is found to be strongly dependent on the chain linear charge density with a more important condensation at high values. When trivalent salt is added in a solution containing monovalent salt, the trivalent cations progressively replace the monovalent counterions. Ion condensation around flexible chains is also found to be more efficient compared with rigid rods due to monomer rearrangement around counterions and salt cations. In the case of spherical macroions, it is found that a fraction of their bare charge is neutralized by counterions and salt cations. The decrease of the Debye length, and thus the increase of salt concentration, promotes the attraction of counterions and salt particles at the macroion surface. Excluded volume effects are also found to significantly influence the condensation process, which is found to be more important by decreasing the ion size.     

Adsorption kinetics of cationic polyelectrolytes studied with stagnation point adsorption reflectometry and quartz crystal microgravimetry

The effects of charge density, pH, and salt concentration on polyelectrolyte adsorption onto the oxidized surface of silicon wafers were studied using stagnation point adsorption reflectometry and quartz crystal microgravimetry. Five different polyelectrolytescationic polyacrylamides of four charge densities and one cationic dextranwere examined. The adsorption kinetics was characterized using each technique, and the adsorption kinetics observed was in line with the impinging jet theory and the theory for one-dimensional diffusion, respectively. The polyelectrolyte adsorption increased with pH as an effect of the increased silica surface charge. A maximum in the saturation adsorption for both types of polyelectrolytes was found at 10 mM NaCl concentration. A significant adsorption also occurred at 1 M NaCl, which indicated a significant nonionic contribution to the adsorption mechanism. The fraction of solvent in the adsorbed layer was determined to be 70-80% by combining the two analysis techniques. This indicated a loose structure of the adsorbed layer and an extended conformation at the surface, favoring loops and tails. However, considering the solution structure with a hydrodynamic diameter larger than 100 nm for the CPAM and a thickness of the adsorbed layer on the order of 10 nm, the results showed that the adsorption is accompanied by a drastic change in polymer conformation. Furthermore, this conformation change takes place on a time scale far shorter than seconds.     

Influence of cetyltrimethylammonium bromide on physicochemical properties and microstructures of chitosan-TPP nanoparticles in aqueous solutions

The nanoparticles of chitosan (CS) were prepared using pentasodium triphosphate (TPP) as a crosslinking agent and the influences of cetyltrimethylammonium bromide (CTAB) on the physicochemical properties of the CS-TPP nanoparticles were first studied by laser light scattering, zeta potential, and transmission electron microscopy (TEM). The concentration played a significant role in controlling the particle size of CS and the overlap concentration c(*) was testified to be about 1.0 mg/mL. The combination of static light scattering (SLS) and dynamic light scattering (DLS) allowed us to obtain more information about the CS-TPP nanoparticles in the presence of surfactant molecules. The addition of CTAB could reduce the hydrodynamic diameter of nanoparticles effectively in the salt solutions and simultaneously increase the zeta potential of the nanoparticles. The effect of CTAB concentration on the size of CS-TPP nanoparticle was also examined. The critical micelle concentration (CMC) of CTAB was used to interpret the complicated complex formed by the polyelectrolyte and the surfactant. Finally, TEM was used to observe the CS-TPP nanoparticles, which were affected by CTAB, to verify the results obtained by light scattering.