Degree Of Counterion Condensation Research Articles

Polymer complexation: Partially ionizable asymmetric polyelectrolytes.

Theories of bulk coacervation of oppositely charged polyelectrolytes (PE) obscure single molecule level thermodynamic details, considered significant for coacervate equilibrium, whereas simulations account for only pairwise Coulomb interaction. Also, studies of effects of asymmetry on PE complexation are rare compared to symmetric PEs. We develop a theoretical model, accounting for all entropic and enthalpic contributions at the molecular level, and the mutual segmental screened Coulomb and excluded volume interactions between two asymmetric PEs, by constructing a Hamiltonian following Edwards and Muthukumar. Assuming maximal ion-pairing in the complex, the system free energy comprising configurational entropy of the polyions and free-ion entropy of the small ions is minimized. The effective charge and size of the complex, larger than sub-Gaussian globules as for symmetric chains, increase with asymmetry in polyion length and charge density. The thermodynamic drive for complexation is found to increase with ionizability of symmetric polyions and with a decrease in asymmetry in length for equally ionizable polyions. The crossover Coulomb strength demarcating the ion-pair enthalpy-driven (low strength) and counterion release entropy-driven (high strength) is marginally dependent on the charge density, because so is the degree of counterion condensation, and strongly dependent on the dielectric environment and salt. The key results match the trends in simulations. The framework may provide a direct way to calculate thermodynamic dependencies of complexation on experimental parameters such as electrostatic strength and salt, thus to better analyze and predict observed phenomena for different sets of polymer pairs.

Effects of dielectric inhomogeneity in polyelectrolyte solutions

We illustrate the effects of dielectric inhomogeneity on the statistical properties of polyelectrolytes in solution, by a lattice Monte Carlo simulation that combines the bond fluctuation model with a local algorithm for computing the electrostatic interactions. Our model accounts for the difference in the dielectric properties between the polymer backbone and the solvent. Taking the coil–globule transition of a single polyelectrolyte chain in solvent as an example, we show that the chain conformation and the degree of counterion condensation are substantially affected by the dielectric contrast.

Comparative study of three structurally related acid polyelectrolytes as carriers of basic drugs: Carbomer, Eudragit L-100 and S-100

A detailed description of equilibrium and drug release properties of aqueous dispersions of complexes of model basic drugs (D) [lidocaine (Ld), atenolol and metoclopramide (Me)] with three structurally related acid polyelectrolytes (PE) is reported. Thus, affinity constants for ionic pair formation (K ip) of dispersions of polymetacrylates, Eudragit L-100 and Eudragit S-100, neutralised with increasing proportions of Ld and Me, were determined and compared with those of Carbomer previously reported. Affinity constants were calculated from the concentration of D condensed with PE (RCOO− DH+) and those of free species (D and DH+). In agreement with the high degree of counterionic condensation observed, the three PE–D complexes placed on Franz-type cells released D at slow rates as water was placed as receptor medium. Rates increased over three times as water was replaced by 0.9% NaCl solution. Similar average of diffusional exponent n (water, 0.61 and NaCl, 0.69) was found in both media. The overall kinetic behaviour suggests that, under the conditions assayed, the dissociation of RCOO− DH+ is the factor that controls releasing rates. Structure-related properties of the PE–D systems were identified in order to expand their potential uses as drug carriers.

Counterion Condensation on a Polyelectrolyte near an Electronically Responsive Cylinder

The existence of a nearby electronically responsive cylinder can affect the counterion condensation (CC) on a polyelectrolyte (PE) embedded in a dilute solution. This is examined by studying a system consisting of two infinitely long cylinders with parallel axes: one representing the PE, and the other is either metallic or dielectric. Using the Debye−Huckel equation coupled with Manning’s theory of CC, analytical expressions are obtained for the electrostatic free energy per unit length of the PE and the degree of CC. It is found that, in the presence of a metallic cylinder, counterions are gradually released from the surface of the PE as the separation between the PE and the metallic cylinder decreases. Near a dielectric cylinder, depending on its dielectric constant relative to that of the solution, the amount of CC can decrease, increase, or remain unchanged as the PE approaches the cylinder.

Counterion condensation and release in micellar solutions

Counterion condensation and release in micellar solutions are investigated by direct measurement of counterion concentration with ion-selective electrode. Monte Carlo simulations based on the cell model are also performed to analyze the experimental results. The degree of counterion condensation is indicated by the concentration ratio of counterions in the bulk to the total ionic surfactant added, alpha< or =1. The ionic surfactant is completely dissociated below the critical micelle concentration (cmc). However, as cmc is exceeded, the free counterion ratio alpha declines with increasing the surfactant concentration and approaches an asymptotic value owing to counterion condensation to the surface of the highly charged micelles. Micelle formation leads to much stronger electrostatic attraction between the counterion and the highly charged sphere in comparison to the attraction of single surfactant ion with its counterion. A simple model is developed to obtain the true degree of ionization, which agrees with our Monte Carlo results. Upon addition of neutral polymer or monovalent salts, some of the surfactant counterions are released to the bulk. The former is due to the decrease of the intrinsic charge (smaller aggregation number) and the degree of ionization is increased. The latter is attributed to competitive counterion condensation, which follows the Hefmeister series. This consequence indicates that the specific ion effect plays an important role next to the electrostatic attraction.

Charge renormalization of cylinders and spheres: Ion size effects

AbstractThe effect of the counterion size on the degree of counterion condensation onto a cylindrical macroion and a spherical one in the absence of salt is studied theoretically within a modified Poisson–Boltzmann approach. We find that excluded volume interactions reduce the degree of condensation. Using a simple variational free energy we show that this reduction can be attributed to an effective increase in the macroion size due to the contribution of the condensed counterions. We also find that for a charged cylinder, the reduction in charge renormalization vanishes at infinite dilution because of the extended nature of the condensed layer. In contrast, excluded volume interactions can reduce the degree of charge renormalization of a sphere even at high dilutions. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3598–3615, 2004

Influence of sodium sulfate or sodium sulfite on the solubilization of benzylalcohol in cationic micellar solutions

The enthalpy of benzylalcohol (BzOH) solution has been determined as a function of alcohol concentration in aqueous trimethyltetradecylammonium bromide (TTAB) solutions in the presence of sodium sulfite or sodium sulfate up to high salt concentration. The electrolytes studied do not seem to induce TTAB sphere-torod transition at least up to 0.6 mol/kg of salt. Comparison with the enthalpic behavior of BzOH in sodium dodecylsulfate solutions and with that of 1-pentanol in both cationic and anionic micellar solutions suggests that the solubilization of BzOH in TTAB solutions is specifically favored by intramolecular interactions between alcohol molecules within the cationic micelles. The replacement of the bromide counterions by the sulfite or sulfate ions has been studied using potentiometry with an ionselective electrode in the case of trimethylhexadecylammonium bromide (CTAB). No difference could be detected between the effects of either divalent anions on the rate of change of the bromide ion-condensation with the salt/surfactant concentration ratioR. The degree of counter-ion condensation on micellar surface depends not only on theR values, but also on the total surfactant concentration.

Reanalysis of the electrostatic component of the persistence length of poly(styrene sulphonate)

The electrostatic component of the persistence length ( L el ) for three molecular-weight preparations of poly(styrene sulphonate) was determined from magnetic birefringence measurements (m.b.m.) by Weill and Maret in 1982. The ratio L el / L a el plotted as a function of the Debye-Huckel screening length (λ DH ) exhibited significant deviations from unity over the range24 ⩽ λ DH (a˚) ⩽ 108, where L a el is the analytical expression for the electrostatic persistence length for finite chain lengths given by Odijk. Weill, Maret and Odijk attempted to explain the discrepancy between theory and experiment by invoking ‘semidilute’ solution conditions for the long-chain results concomitant with a different degree of counterion condensation than used for the short-chain results. It is proposed in the present paper that a ‘three-region’ model for the counterion distribution about the polyion accurately represents the m.b.m. data without having to invoke differential counterion condensation properties of short and long chains, or having to postulate semidilute solution conditions. The three regions are: (1) Manning-type condensation on the surface of the polyion; (2) a counterion sheath in the vicinity of the polyion; and (3) the remaining solution.

The role of the ionic environment in the orientation of nucleic acids in electric fields

The relationship between polyelectrolyte theories based on linear charge density models and the electric-field induced orientation of the polyelectrolytes, poly(A), poly(C) and DNA is examined by varying their ionic environment with respect to ionic strength and acidity. The degree of counterion condensation on the polyelectrolytes predicted by the theories of Manning and Record is shown to be related linearly to the orientation as measured by their dichroism in the field. Micro-structural differences between poly(A) and poly(C) account for the differences in their dependence on the pH of the medium which affects the counterion condensation and thus the polarization in the orienting electric fields. The results consequently support recent treatments of linear polyelectrolytes having a high charge density which model them as smoothly charged linear polyions, but indicate that these models are insufficient to account for some of the effects of microstructural variations.