Counterion Diffusion Coefficients Research Articles

Electrostatic binding and release: incorporation of IrCl63− into polypyrrole containing viologen groups

Abstract The coupled diffusion coefficient of electrons and counterions in poly[ N , N ′-bis(3-pyrrol-1-ylpropyl)-4,4′-bipyridinium]chloride films was evaluated as (1.0±0.2)×10 −10 cm 2 s −1 and the standard heterogeneous rate constant at the metal ∣ film interface as (2.2±0.2)×10 −5 cm s −1 . The width of the Warburg region measured by impedance spectroscopy showed a distinct minimum at the formal potential, suggesting that the transference number of counterions was considerably larger than that of electrons. Thus charge transport in the polymeric film is probably dominated by the rate of electron self-exchange between neighboring redox sites. Because of strong electrostatic binding, IrCl 6 3− was highly concentrated in the polycationic film from its very dilute solution: the partition coefficient amounted to as much as ∼10 4 . The resulting shift in the half-wave potential of viologen groups indicated a weak ion-pairing interaction between the dicationic viologens and the anionic complex. The incorporated metal complex was released from the polymeric film in a controlled quantity in response to negative potential steps.

Macrokinetics of polyaniline based electrode: effects of porous structure, microkinetics, diffusion, and electrical double layer

The standard porosimetry method (SPM) was used to study in situ real porous structures of poly(aniline) (PAn) swollen in electrolytes containing γ-butyrolactone (GBL). The effects of swelling, the degree of doping, the nature of counterions, and type the of polymerization (chemical or electrochemical) on porous PAn structure were studied. All the PAn forms impregnated with GBL had high porosities of several dozen per cent, high specific surface areas of 80–400 m 2 cm −3, pore radii of 1–100 nm, and average fibril radii of 2–10 nm. Electrochemically synthesized PAn showed better electrochemical characteristics than chemically synthesized PAn. The model of the intercalated porous electrode was used to characterize the discharge curves. Comparison of calculated and experimental curves enabled determination of essential microscopic characteristics: specific exchange current density ( i 0) of real PAn/electrolyte interphase doping–dedoping, specific capacity ( C S) of electrical double layer (EDL) of this interface, and diffusion coefficient ( D) of counterions in the polymer. These characteristics depend upon the nature of counterions and the method of polymerization (chemical or electrochemical). Small D values of 8×10 −19–1×10 −17 cm 2 s −1 result from the solid-phase nature of diffusion; i 0=1×10 −15–1×10 −12 A cm −2, and C S=0.6–5.0 μF cm −2. Very low D, i 0 and C S are compensated by very high S resulting in better electrochemical characteristics. Thin electrodes (<1 mm) showed very small ohmic losses, while the rate of electrochemical doping–dedoping was usually limited by solid-phase diffusion and discharge. The effects of structure, mode, and microscopic parameters on discharge curves were analyzed.

Effect of counterion species on the dynamics of polystyrenesulfonate in aqueous solution as studied by dynamic light scattering

The diffusion behavior of macroions in aqueous solutions especially at low salt concentrations has been interesting and also mysterious problem since Schurr et al. found slow mode in 1978. By the systematic investigations on the structure and dynamics of charged particles and macromolecules in solution, it has been suggested that some novel factor(s) should be taken into account for understanding of interesting phenomena in these systems. In this study, the dynamic character, i.e., diffusion behavior of polystyrenesulfonate (PSS) in aqueous solution has been studied by dynamic light scattering (DLS) as a function of salt concentration in various salt forms. Both fast and slow modes were clearly detected. With increasing salt concentration, the fast mode became dominant and its decay rate became slower. On the other hand, the slow mode was not so sensitive to salt concentration but its contribution markedly decreased with increasing salt concentration and then became almost negligible at higher salt concentrations. The fast mode of LiPSS, NaPSS, and CsPSS was in the order of LiPSS≦NaPSS&amp;lt;CsPSS, although the difference was small, and was consistent with the order of diffusion coefficients of counterions. The fast mode of HPSS was much faster than that of other PSS salts. The same tendency was also observed for HPES and NaPES, salts of polyethylenesulfonate. The slow mode also depended on the counterion species, which may predict the important role of counterion dynamics in electric interaction between macroions.

Polyelectrolyte effects on counterion self-diffusion

The self-diffusion coefficient of tetramethylammonium counterion has been measured in aqueous solutions of polymethacrylic acid (PMA) of 100 and 1000 monomers as well as in persistence-length DNA fragment solutions. The concentration ranged from to 1 M (monomolar) and no low-molecular-weight salt was added. The counterion self-diffusion coefficient was found to be independent of the kind of polyion and of molecular weight over a large concentration range. In the low-concentration region the self-diffusion coefficient is a function of polyion length and species. In this concentration region the self-diffusion coefficient is the smallest in solutions of the polyion with the largest persistence length (TMADNA). The self-diffusion coefficients in solutions of the two PMAs start to deviate upon dilution at the crossover concentration from semidilute to dilute for the shorter PMA (100 monomers). In the dilute solutions of the short PMA (100 monomers) the counterion diffusion coefficient is lower than that in semidilute solutions of the higher-molecular-weight polyelectrolyte at the same monomer concentration.

Charge transport processes in electrochemically deposited poly(pyrrole) and poly( N-methylpyrrole) thin films

Poly(pyrrole) (pPy) and poly( N-methylpyrrole) (pNMePy) films that were electrodeposited under similar conditions were compared in terms of electronic conductivities and counterion diffusion coefficients. Films were prepared and compared both in aqueous electrolyte (Cl −, ClO 4 − counterions) and in non-aqueous (propylene carbonate) electrolyte (ClO 4 − counterion). Consistent with the range of values reported in the literature, the electronic conductivities differed by a factor of ca. 5 × 10 3, although this is lower than the often-cited value of 10 5. This smaller difference in the conductivities is more consistent with that expected on the basis of simple steric factors. A.c. impedance measurements were used to determine the counterion diffusion coefficients. That for ClO 4 − was approximately one order of magnitude lower in pNMePy than that in pPy, possibly due either to differences in morphology or to stronger interactions of the counterion with the polymer chains.

The influence of the salt concentration and the diffusion boundary layers on the bi-ionic potential

Measurements of bi-ionic potential (BIP) across three cation-exchange membranes (CEMs) have been carried out for KCl/CEM/NaCl, KCl/CEM/LiCl, and NaCl/CEM/LiCl systems, where CEM is a polystyrene and divinylbenzene sulfonated membrane (CM2, from Tokuyama Soda), a perfluorosulfonic acid membrane (Nafion ® 117, from Du Pont De Nemours) and an heterogenous membrane prepared by inclusion of cation-exchange resin in PVC (CRP, from Rhone Poulenc). The influence of the salt concentration and the diffusion boundary layers (DBLs) on the BIP values has been analysed both theoretically and experimentally. The theoretical model is based on the Nernst-Planck equations, and gives a good description for salt concentrations higher than 5×10 −4 M. For the CM2 membrane, the DBL thickness changes from 20–23 μm in absence of stirring to 3–4 μm for high stirring rates. Also, the ion diffusion coefficients in this membrane have been estimated to be of the order of 10 −6 cm 2/s. It has been observed that the counter-ion diffusion coefficients ratio ( D A / D B ) in the membrane increases significantly when the membrane water content decreases, which suggests the possibility of achieving highly selective ion transport with low water content membranes.

The influence of the porous structure, microkinetics and diffusion properties on the charge-discharge behaviour of conducting polymers

For different samples of poly(anyline) (PAni) and poly(paraphenylene) (PPP) impregnated with electrolyte solutions the real (swelled) structure was measured. The swelled (PAni) and PPP films and powders show an appreciable internal porosity (some tens %) and a high internal surface (250–600 m 2/g). The main range of pore radii is between 1 and 10 2–10 3 nm. The mean radius of single nonporous fibrils is 2–7 nm for PAni and 4–19 nm for PPP. The doping degree, the nature of the counterions and the method of preparation (chemical or electrochemical) have a considerable influence upon the porous structure. On the base of these data a model for the behaviour of electrodes from conducting polymers was established. An investigation of the kinetic behaviour of such electrodes gives the possibility to assess the intrinsic values of some important parameters: diffusion coefficients of counterions in the solid polymer phase, exchange current density of the doping-undoping reactions and the specific capacity of the polymer/electrolyte interface.

Dielectric Dispersion of Dilute Suspensions of Colloid Particles: Practical Applications

The two characteristic relaxation frequencies at which either the Maxwell−Wagner or the double layer polarization mechanism prevails have been defined in terms of characteristic parameters for colloidal suspensions subjected to an oscillating electric field. Both frequencies are found to increase with increasing ion diffusion coefficient, with decreasing particle radius, and with increasing salinity. For both thin and thick double layers, these frequencies appear to be invariant at low zeta potential (ζ) values. Correlations are developed between these characteristic relaxation frequencies and the colloid suspension parameters. The correlations constants appear to be related to the Boltzman constant, temperature, and electrostatic charge. These correlations can be useful for estimating particle size and counterion diffusion coefficient and can be used in developing dielectric dispersion models for colloid particles suspensions and for porous media. A rigorous dispersion model has been inverted to reciprocate simultaneously the average zeta potential (ζ), particle size, and particle volume fraction of the dispersed material from dielectric permittivity data at three distinct frequencies. Relaxation of colloidal suspensions appears to be an adequate alternative for quantifying these parameters as opposed to using intricate measurements of electrophoretic mobility.

Studies on the electrode kinetics of polypyrrole in aqueous solution by a.c. impedance measurement

Electrode kinetics of PPy(Cl −) film in acidic and neutral solutions has been studied by the a.c. impedance method. The values of the charge transfer resistance and diffusion coefficient of counter-ions in the PPy film depend on the pH value of the solution in contact and on the potential applied. The exchange current density i o of the PPy film electrode is 1.15 mA cm −2 and the apparent diffusion coefficient D app of the counter-anion is 1.8 × 10 −9 cm 2s −1, in a pH 3, 0.5 M KCl solution at 0.1 V(SCE). Both i o and DP app decrease with decrease of applied potential. In a neutral solution, two redox processes can be distinguished in the a.c. impedance plots.

The determination of diffusion coefficients of counter-ions in the ion-exchange membrane by means of batchwise Donnan dialytic experiments

A new method, based on the Nernst-Planck equation, has been proposed for determining diffusion coefficients of counter-ions in an ion-exchange membrane for bi-ionic Donnan dialysis. This method involves dialytic experiments in which both the solution concentration and the membrane potential are measured under the condition controlled by diffusion resistance in the membrane. It also involves mathematical optimization treatment of the experimental data. The K +−H + system with a cation-exchange membrane was studied, and the optimum diffusion coefficients of these counter-ions were obtained. The diffusion coefficients were found to vary with the ionic composition of the solution. The theoretical time courses of the concentration and membrane potential calculated by using the optimum diffusion coefficients agreed with the experimental results.

Development of a space‐charge transport model for ion‐exchange membranes

AbstractA two‐dimensional, electrokinetic transport model that incorporates ionic hydration, orientation of solvent molecules by an applied electric field, and solvent dipole‐dipole interactions is developed. The model is used to simulate equilibrium and transport experiments for perfluorosulfonic acid membranes containing aqueous alkali metal sulfate solutions. The membrane is modeled as an array of cylindrical pores. Solution of the mathematical model requires that the membrane porosity, water partition coefficient, coion partition coefficient, water diffusion coefficients, and coion and counterion diffusion coefficients be known. Membrane coion and counterion diffusion coefficients were determined from free solution equivalent conductance data. All other parameters were determined experimentally for a Nafion (of E. I. du Pont de Nemours Inc.) cation‐exchange membrane and five 0.1 M alkali metal sulfate solutions. Experimental radiotracer data for coion absorption as well as for coion and water transport are compared with theoretical predictions to test the accuracy of the model.

Ion transport in pyrrole-based polymer films

Ionic resistivities and counterion diffusion coefficients for polypyrrole, poly-[1-methyl-3-(pyrrol-1-ylmethyl)pyridinium](poly-MPMP+) and pyrrolex-[Ru(2,2′-bipyridine)2(3-(pyrrol-1-ylmethyl) pyridine)Cl]+ copolymer films have been obtained by chronoamperometry using the single-pore model. For poly-MPMP+ both the electronic resistivity and the ionic resistivity can be simultaneously determined. Finite-difference simulations have been used to confirm the validity of the equations used and to extend the applicability of the model.Counterion diffusion coefficients in polypyrrole and poly-MPMP+ have also been determined by rotating-disc voltammetry and d.c. conductivity measurements. Where possible the results have been confirmed by the use of two independent methods. Diffusion coefficients for I–, Cl–, ClO4– and Fe(CN)64– in the above polymers in water and/or acetonitrile are compared and discussed. It is concluded that: (a) polypyrrole and poly-MPMP+ are solvated and swollen to a much greater extent in water than in acetonitrile, (b) permanent cationic sites increase the permeability of polypyrrole in water but not in acetonitrile and (c) the permeability of polypyrrole in acetonitrile can be increased by the incorporation of bulky metal complexes.

Electric and electrokinetic transport properties of homogeneous weak ion exchange membranes

The effect of H + ions on the membrane potential and electrical resistance of synthetic membranes has been investigated theoretically and experimentally for salt solutions of typical pH values. Employing the equations of Schlögl for the membrane potential Δϕ and the specific electrical resistance ϱ, membrane potentials and resistances have been calculated for binary and ternary electrolyte solutions. Moreover, the effect of a dissociation equilibrium of the fixed charges (COOH groups) in the membrane on the membrane potential and resistance have been considered. The ratios of the mobilities of the cations and the anions have been estimated at relatively large external salt concentrations from membrane potential curves measured with LiCl-HCl, HCl, CaCl 2-HCl, Na 2SO 4-H 2SO 4, and MgSO 4-H 2SO 4 using weak cation exchange membranes such as homogeneous cellulose acetate, cuprophane, and carboxy methyl cellulose, as well as strong cation exchange membranes such as ASAHI's CK-1 and a Nation membrane. From measurements of the electrical resistance of homogeneous cellulose acetate membranes at different salt concentrations but prescribed pH values for the systems LiClHCl, MgCl 2HCl, and MgSO 4H 2SO 4, individual ion diffusion coefficients have been estimated. Further, the concentration dependence of the ion diffusion coefficients in the membrane has been demonstrated. The counterion diffusion coefficients exhibit a strong change of their diffusion coefficients ranging from 10 −14 up to 10 −9 cm 2/sec in the concentration range 10 −4 mole/liter < c s < 10 −1 mole/liter, whereas the coion diffusion coefficients and the H +-ion diffusion coefficient vary slightly with the external electrolyte concentration and are of the order of 10 −8 to 10 −7 cm 2/sec and 8 × 10 −7 to about 3 × 10 −6 cm 2/sec, respectively.

Relation Between the Dielectric Constant of Hydrophobic Cation Exchange Membrane and Membrane Permeability to Counterions

Filters made of cellulose acetate-nitrate when saturated with organic solvents and interposed between aqueous solutions form membranes which behave like cation exchangers. The diffusion coefficients of counterions in such membranes are strongly dependent upon the dielectric constant of the saturating solvent. The results obtained suggest that a linear relationship between the log of the cation's diffusion coefficient (or membrane conductance) and the reciprocal value of the dielectric constant of the saturating solvent exists. There is also a good correlation between the relative membrane permeability to organic cations and the solubility of the cations in the pure solvent phase. These studies indicate that there are two routes for cation movement through the membrane: (a) the bulk hydrophobic phase and (b) continuous narrow aqueous channels.

Diffusion of Radiotracer Ions in a Cation‐Exchange Membrane

The tracer diffusion coefficients of Na + , Cs+ , Sr2 + , and Br− in a homogeneous cation‐exchange membrane have been measured in the homoionic counterion states over the external solution concentration range 0.005–1.0 equiv/liter and in the and heteroionic counterion states over the whole equivalent fraction range at 0.02 and 0.10 equiv/liter total external concentration. Steady‐ and transient‐state permeation and diffusion techniques have been used. The results show that the resin material is essentially uniform apart from a small volume of material of low crosslinking which forms a labyrinthine network interpenetrating the main structure. This labyrinthine network is important mainly in the diffusion of Br− at low external concentrations. In concentrations above about 0.02 equiv/liter the diffusion coefficient DBr of Br− does not vary greatly either with concentration or with counterion type. DBr is greatest in the Cs+ state and least in the Na+ state. These observations and the way in which DBr varies with the equivalent fraction of the counterions in the heteroionic states can be explained by considering the expected frictional interactions between Br− coions and the counterions and by the influence of the local variations in electric potential on the movements of the ions.The diffusion coefficients of all the counterions increase as the external concentration is increased. When these diffusion coefficients are compared with the diffusion coefficients in aqueous solutions Na+ is seen to be the least retarded in the membrane and Sr2+ the most retarded. The observed behavior can be understood qualitatively in terms of the relative roles of “chain” and “volume” diffusion as suggested by Jakubovic et al. (20). A quantitative theory of these mechanisms has not been developed, but the relevance of theoretical treatments of the effects of electric potentials on counterion mobilities in polyelectrolyte and micellar solutions is pointed out. When the membrane is in a heteroionic state the diffusion coefficients of both counterions decrease when the equivalent fraction of Na + , the thermodynamically nonpreferred ion in each mixture, is increased. This behavior is consistent with the mechanism of diffusion discussed above and with the expected distribution of the counterions in a heteroionic state of an exchanger which has the structure deduced from the behavior of the Br− ions.

Tracer diffusion and activity coefficients of counterions in aqueous solutions of polyelectrolytes

Tracer diffusion and activity coefficients of counterions in aqueous solutions of polyelectrolytes