Effective charges of polyelectrolytes in a salt-free solution based on counterion chemical potential

The phenomenon of counterion condensation around a flexible polyelectrolyte chain with N monomers is investigated by Monte Carlo simulations in terms of the degree of ionization alpha, which is proportional to the effective charge. It is operationally defined as the ratio of observed to intrinsic counterion concentration, alpha = co/ci. The observed counterion concentration in the dilute polyelectrolyte solution is equivalent to an electrolyte solution of concentration co with the same counterion chemical potential. It can be determined directly by thermodynamic experiments such as ion-selective electrode. With the polyelectrolyte fixed at the center of the spherical Wigner-Seitz cell, the polymer conformation, counterion distribution, and chemical potential can be obtained. Our simulation shows that the degree of ionization rises as the polymer concentration decreases. This behavior is opposite to that calculated from the infinitely long charged rod model, which is often used to study counterion condensation. Moreover, we find that, for a specified line charge density, alpha decreases with an increment in chain length and chain flexibility. In fact, the degree of ionization is found to decline with increasing polymer fractal dimension, which can be tuned by varying bending modulus and solvent quality. Those results can be qualitatively explained by a simple model of two-phase approximation.     

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

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

Monte Carlo simulation and molecular theory of tethered polyelectrolytes

We investigate the structure of end-tethered polyelectrolytes using Monte Carlo simulations and molecular theory. In the Monte Carlo calculations we explicitly take into account counterions and polymer configurations and calculate electrostatic interaction using Ewald summation. Rosenbluth biasing, distance biasing, and the use of a lattice are all used to speed up Monte Carlo calculation, enabling the efficient simulation of the polyelectrolyte layer. The molecular theory explicitly incorporates the chain conformations and the possibility of counterion condensation. Using both Monte Carlo simulation and theory, we examine the effect of grafting density, surface charge density, charge strength, and polymer chain length on the distribution of the polyelectrolyte monomers and counterions. For all grafting densities examined, a sharp decrease in brush height is observed in the strongly charged regime using both Monte Carlo simulation and theory. The decrease in layer thickness is due to counterion condensation within the layer. The height of the polymer layer increases slightly upon charging the grafting surface. The molecular theory describes the structure of the polyelectrolyte layer well in all the different regimes that we have studied.     

Interactions of a sulfonated ionomer with surfactant in nonaqueous media

The viscometric behavior of dilute solutions of the sodium salt of sulfonated polystyrene (0–6 mol % sulfonation level), with and without surfactant, is investigated to determine the extent of interaction as the structure of the solvent surfactant, and polymer concentration is varied. Reduced viscosity measurements confirm that formation of a polymer–surfactant complex in a relatively polar solvent is controlled to a large extent by charge–charge and hydrophobic forces. The magnitude of these specific interactions is dependent upon the relative polarity of the solvent medium. In a polar solvent, such as dimethylsulfoxide, the hydrophobic forces are strong enough to prevent expansion of the polymer chain at all surfactant concentrations studied. However, in a less polar medium (as in dimethylformamide) the hydrophobic forces are weaker and cannot prevent some chain expansion. It is interesting to note that in this solvent the polystyrene–cationic surfactant complex exhibits a polyelectrolyte effect. Finally, in a lower-polarity medium (cyclohexanone) where the hydrophobic forces are weak, solution behavior is dominated by the interaction of the surfactant with the intramolecular sulfonate ion-pair aggregates.     

Electrophoretic evidence for a new type of counterion condensation

A systematic capillary electrophoresis study uncovered how polyelectrolyte effective charge density varies with backbone charge spacing and solvent dielectric constant. The study primarily focused on aliphatic ionenes, a special class of polyelectrolytes, which possess regularly spaced quaternary ammonium groups in the backbone. Complete ionization of functional units and good solvency in water or mixtures of water with lower dielectric constant solvents (methanol, acetonitrile) enabled continuous measurements of ionene effective charge density through the onset of counterion condensation. Ionenes with both uniform and alternating charge spacing were examined. As expected, effective charge density rose linearly with fixed charge density to a critical value, above which effective charge density remained constant. Deviating from expectation, the onset of condensation did not occur at a critical fixed charge density. Instead, condensation initiated at a constant critical Bjerrum length. The same onset condition was found for quaternized poly(vinyl pyridine)s. These experimental results suggest a new form of condensation, one driven by ion-pairing of polyelectrolyte with counterions. In support of this hypothesis, the onset of condensation appeared to correlate with counterion size. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3616–3627, 2004     

强电解质凝胶的溶胀平衡与体积相变

以作者近年来对强电解质凝胶的研究结果为中心,介绍了磺酸基凝胶和丙烯酸基凝胶在纯水,缓冲溶液中溶胀比与电荷密度的关系及其差异,揭示了磺酸基凝胶中的反离子凝聚现象和在有机溶剂中体积相变,还讨论了体积相变的滞后现象及其成因,最后就体积相变的驱动力,统一认识电解质和离聚体以及有关的实验结果阐述了作者的见解。     

Dynamic exchange of counterions of polystyrene sulfonate

Adopting a cationic fluorescent molecule, rhodamine 6G, as the probe of the counterions of the model anionic polyelectrolyte (sodium polystyrene sulfonate, PSSNa), the diffusion of the counterion probes inside the solution of PSSNa was studied by fluorescence correlation spectroscopy. Two species of the counterion probes with different diffusion coefficient were discovered--the freely diffusing probes and the probes bound to the PSS(-) chains. The concentration fraction of these two species was found to change with the concentration and molecular weight of PSSNa. The results show that the counterion binding to the PSS(-) chain is enhanced with the increase of polymer concentration, attributed to the result of the lowered translational entropic penalty at higher polymer concentrations. The counterion binding is also enhanced with the increase of molecular weight, and the origin was attributed to the chain end effect to the counterion distribution. The results indicate the dynamic exchange process between the free counterions and the bound ones, which is further evidenced by the replacement of the bound probes by the elevated salt levels in the solution.     

Molecular dynamics simulations of polyelectrolyte adsorption

We have performed molecular dynamics simulations of polyelectrolyte adsorption at oppositely charged surfaces from dilute polyelectrolyte solutions. In our simulations, polyelectrolytes were modeled by chains of charged Lennard-Jones particles with explicit counterions. We have studied the effects of the surface charge density, surface charge distribution, solvent quality for the polymer backbone, strength of the short-range interactions between polymers and substrates on the polymer surface coverage, and the thickness of the adsorbed layer. The polymer surface coverage monotonically increases with increasing surface charge density for almost all studied systems except for the system of hydrophilic polyelectrolytes adsorbing at hydrophilic surfaces. In this case the polymer surface coverage saturates at high surface charge densities. This is due to additional monomer-monomer repulsion between adsorbed polymer chains, which becomes important in dense polymeric layers. These interactions also preclude surface overcharging by hydrophilic polyelectrolytes at high surface charge densities. The thickness of the adsorbed layer shows monotonic dependence on the surface charge density for the systems of hydrophobic polyelectrolytes for both hydrophobic and hydrophilic surfaces. Thickness is a decreasing function of the surface charge density in the case of hydrophilic surfaces while it increases with the surface charge density for hydrophobic substrates. Qualitatively different behavior is observed for the thickness of the adsorbed layer of hydrophilic polyelectrolytes at hydrophilic surfaces. In this case, thickness first decreases with increasing surface charge density, then it begins to increase.     

高分子动力学的单链模型

高分子单链模型是高分子稀溶液理论研究的基本模型.对其进行深入地分析,不仅有助于解决高分子稀溶液体系中溶液黏度和分子链扩散等基本问题,而且能够增进人们对高分子链结构与溶液性质间关联性的理解.虽然基于经典连续性介质力学的流体动力学理论可以定性,甚至半定量地获得稀溶液的一些重要性质,但是,随着科学技术的发展,人们从分子水平上建立了许多描述高分子稀溶液性质的模型和理论,期望能够定量地描述高分子稀溶液的性质.本文以高分子稀溶液中3个典型的单链模型为例(包括:不含流体力学相互作用的Rouse模型、含二体流体力学相互作用的Zimm模型和含多体流体力学相互作用的部分穿透球模型),综述高分子稀溶液的重要性质,并详细地给出其动力学方程的推导过程及其重要的研究进展.特别是,对于Rouse模型,本文还将其预言结果拓展到了短链高分子流体体系;此外,还介绍了这一领域的关键科学问题、发展前景和研究方向.     

(Vinyl amine)-(vinyl alcohol) copolymers Synthesis,characterization and potentiometric behaviour

Some copolymers of vinyl amine with vinyl alcohol have been synthesized by hydrolysis of copolymers of tert.-butyl vinyl carbamate with vinyl acetate. From reaction kinetics and counterion distribution, it can be concluded that the copolymers are random. The potentiometric titration behaviour indicates that the very marked dependence of the dissociation constant on the charge fraction, even at high ionic strength, for this polyelectrolyte system may result from a very specific solvation process i.e. a strong dependence on the charge state of the interactions between polyion with counterions and solvent molecules.     

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.     

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.     

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     

Counterion condensation on charged spheres, cylinders, and planes

We use the framework of counterion condensation theory, in which deviations from linear electrostatics are ascribed to charge renormalization caused by collapse of counterions from the ion atmosphere, to explore the possibility of condensation on charged spheres, cylinders, and planes immersed in dilute solutions of simple salt. In the limit of zero concentration of salt, we obtain Zimm-Le Bret behavior: a sphere condenses none of its counterions regardless of surface charge density, a cylinder with charge density above a threshold value condenses a fraction of its counterions, and a plane of any charge density condenses all of its counterions. The response in dilute but nonzero salt concentrations is different. Spheres, cylinders, and planes all exhibit critical surface charge densities separating a regime of counterion condensation from states with no condensed counterions. The critical charge densities depend on salt concentration, except for the case of a thin cylinder, which exhibits the invariant criticality familiar from polyelectrolyte theory.     

粘度法研究壳聚糖对外加盐的敏感性

聚电解质的特性粘度对外加盐的响应是反映聚电解质对外加盐敏感性的一个重要特征，通过分别测定壳聚糖在不同小分子强电解质（ＮａＣｌ、ＫＣｌ、ＣａＣｌ２、ＢａＣｌ２）和相同小分子强电解质（ＮａＣｌ）但不同离子强度的稀溶液粘度，得到：（１）壳聚糖特性粘度与外加盐的离子强度的平方根的倒数成正比；（２）不同小分子强电解质中阳离子对壳聚糖特性粘度的影响次序是Ｎａ＋＞Ｋ＋＞Ｂａ２＋＞Ｃａ２＋．同时，测算了壳聚糖在不同外加盐浓度中的Ｍａｒｋ Ｈｏｕｗｉｎｋ方程参数α，发现其值皆大于０５，得到了壳聚糖分子链的僵硬性参数Ｂ的值为００７４，揭示了壳聚糖具有较大的分子链刚性和抗盐性能．     

Theory of competitive counterion adsorption on flexible polyelectrolytes: divalent salts

The counterion distribution around an isolated flexible polyelectrolyte in the presence of a divalent salt is evaluated using the adsorption model [M. Muthukumar, J. Chem. Phys. 120, 9343 (2004)] that considers the Bjerrum length, salt concentration, and local dielectric heterogeneity as physical variables in the system. Self-consistent calculations of effective charge and size of the polymer show that divalent counterions replace condensed monovalent counterions in competitive adsorption. The theory further predicts that at modest physical conditions for a flexible polyelectrolytes such as sodium polystyrene sulfonate in aqueous solutions polymer charge is compensated and reversed with increasing divalent salt. Consequently, the polyelectrolyte shrinks and reswells. Lower temperatures and higher degrees of dielectric heterogeneity between chain backbone and solvent enhance condensation of all species of ions. Complete diagrams of states for the effective charge calculated as functions of the Coulomb strength and salt concentration suggest that (a) overcharging requires a minimum Coulomb strength and (b) progressively higher presence of salt recharges the polymer due to either electrostatic screening (for low Coulomb strengths) or coion condensation (for high Coulomb strengths). Consideration of ion-bridging by divalent counterions leads to a first-order collapse of polyelectrolytes in modest presence of divalent salts and at higher Coulomb strengths. The authors' theoretical predictions are in agreement with the generic results from experiments and simulations.     

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.     

Solution behavior of random copolymers of styrene with sodium-2-acrylamido-2-methylpropane sulfonate

The nonaqueous solution behavior of random copolymers of styrene (ST) with sodium-2-acrylamido-2-methylpropane sulfonate (Na-AMPS) [poly(ST-Na-AMPS)] has been investigated using the transient electric birefringence (TEB) technique. The copolymers with varying high sulfonate contents (about 30–70 mol%), bridging the gap between conventional ionomers and classical polyelectrolytes, were dissolved in the solvent methylformamide (MFA) with a high permittivity ? of ca. 190. The solutions showed a negative birefringence at electric field strength E of the order of kV/cm. A typical Kerr effect was observed at low polymer concentrations C of ca. 10^?3g/mL and electric field strengths of the order of kV/cm. However, the detailed, TEB studies demonstrated different behavior at two concentration regimes in dilute solution. At a low concentration regime (e.g., C ≤ 1 × 10^?3g/mL for the copolymer with a 66.7 mol % sulfonate content) where the reduced viscosity exhibited a pronounced polyelectrolyte effect, the birefringence signal pattern showed a maximum before reaching a steady value. Additionally, during the rise at an applied electric field strength beyond a threshold value, it was observed that the nonexponential field-free decay was slower than the single exponential field-induced rise. The observed anomalous behavior was similar to those of a polyelectrolyte [sodium poly (styrene sulfonate)] in aqueous solution and might be attributed to the perturbation of the molecular shape by the applied electric field. At the higher concentration regime (e.g., C ≥ 4 × 10^?3g/mL for the same copolymer with a 66.7 mol % sulfonate content) where the polyelectrolyte effects started to diminish as indicated by the viscosity study, the birefringence shape showed no variation with an increased electric field strength and the field-free decay turned out to be faster than the single exponential rise. The dissociation of ionic aggregates was tentatively interpreted to be responsible for this observation. It seems that by simply varying the polymer concentration, poly (ST-Na-AMPS) could behave either as a polyelectrolyte or as an ionomer in a single polar organic solvent.     

Molecular dynamics simulation of discontinuous volume phase transitions in highly-charged crosslinked polyelectrolyte networks with explicit counterions in good solvent

The volumetric properties of highly-charged defect-free polyelectrolyte networks with tetrafunctional crosslinks are studied through molecular dynamics simulations in the canonical ensemble. The network backbone monomers, which are monovalent, and the counterions, which are mono-, di-, or trivalent, are modeled explicitly in the simulations, but the solvent is treated implicitly as a dielectric medium of good solvation quality. The osmotic pressure of the network-solvent system is found to depend greatly on the strength of electrostatic interactions. Discontinuous volume phase transitions are observed when the electrostatic interactions are strong, and the onset of these transitions shifts to higher solvent dielectricity as the counterion valency increases. The roles of the various virial contributions to the osmotic pressure are examined. The network elasticity entropy is found to behave nearly classically. As the network contracts and collapses with increasing strength of electrostatic interactions, the loss of counterion entropy leads to increased counterion osmotic pressure contributions via two mechanisms. The reduction in available configurational space increases the counterion translational entropy contribution to the ideal part of the osmotic pressure, and the greater number of counterion-monomer contacts formed due to counterion condensation and confinement increases the counterion excluded-volume entropy contribution to the excess part of the osmotic pressure. These observations contrast the decrease in the single ideal-gas-like counterion translational entropy contribution to the osmotic pressure predicted by the counterion condensation-charge renormalization theory. An accompanying decrease in the total electrostatic energy balances the loss of counterion excluded-volume entropy as the polyelectrolyte networks collapse in low-dielectric solvents. This interplay between the electrostatic energy and the counterion excluded-volume entropy appears to be responsible for the discontinuous volume phase transitions that are observed in polyelectrolyte networks. The structure of the polyelectrolyte network is also found to be affine in the swollen state, with constituent chains nearly fully extended, and nonaffine in the collapsed state, with the chains adopting a Gaussian conformation.