Effect Of Counterion Condensation Research Articles

Dynamic Electrophoretic Mobility of Spherical Colloidal Particles in Salt-Free Concentrated Suspensions

In this contribution, the dynamic electrophoretic mobility of spherical colloidal particles in a salt-free concentrated suspension subjected to an oscillating electric field is studied theoretically using a cell model approach. Previous calculations focusing the analysis on cases of very low or very high particle surface charge are analyzed and extended to arbitrary conditions regarding particle surface charge, particle radius, volume fraction, counterion properties, and frequency of the applied electric field (sub-GHz range). Because no limit is imposed on the volume fractions of solids considered, the overlap of double layers of adjacent particles is accounted for. Our results display not only the so-called counterion condensation effect for high particle charge, previously described in the literature, but also its relative influence on the dynamic electrophoretic mobility throughout the whole frequency spectrum. Furthermore, we observe a competition between different relaxation processes related to the complex electric dipole moment induced on the particles by the field, as well as the influence of particle inertia at the high-frequency range. In addition, the influences of volume fraction, particle charge, particle radius, and ionic drag coefficient on the dynamic electrophoretic mobility as a function of frequency are extensively analyzed.

Effect of Counterion Condensation on Rigidity of Semiflexible Polyelectrolytes

I have calculated the effect of counterion condensation on the electrostatic persistence length of semiflexible polyelectrolytes. There are two contributions to the electrostatic persistence length. The first contribution is due to neutralization of the ionized groups by condensed ions that changes the effective linear charge density along the polymer backbone, weakening intrachain electrostatic repulsion. In the case of the monovalent counterions this contribution to the chain persistence length is proportional to the Debye screening length, underlining the fact of the exponential screening of electrostatic interactions on the length scales of the order of Debye screening length. The second contribution is due to correlation/fluctuation-induced attractive interactions between condensed counterions that result in a negative contribution to the chain persistence length. In the case of multivalent ions these interactions are assumed to be due to strong lateral correlations between condensed multivalent ions and were accounted for in the framework of the strongly correlated Wigner liquid approximation.

Cell Model of the Direct Current Electrokinetics in Salt-Free Concentrated Suspensions: The Role of Boundary Conditions

In this paper, a general electrokinetic theory for concentrated suspensions in salt-free media is derived. Our model predicts the electrical conductivity and the electrophoretic mobility of spherical particles in salt-free suspensions for arbitrary conditions regarding particle charge, volume fraction, counterion properties, and overlapping of double layers of adjacent particles. For brevity, hydrolysis effects and parasitic effects from dissolved carbon dioxide, which are present to some extent in more "realistic" salt-free suspensions, will not be addressed in this paper. These issues will be analyzed in a forthcoming extension. However, previous models are revised, and different sets of boundary conditions, frequently found in the literature, are extensively analyzed. Our results confirm the so-called counterion condensation effect and clearly display its influence on electrokinetic properties such as electrical conductivity and electrophoretic mobility for different theoretical conditions. We show that the electrophoretic mobility increases as particle charge increases for a given particle volume fraction until the charge region where counterion condensation takes place is attained, for the above-mentioned sets of boundary conditions. However, it decreases as particle volume fraction increases for a given particle charge. Instead, the electrical conductivity always increases with either particle charge for fixed particle volume fraction or volume fraction for fixed particle charge, whatever the set of boundary conditions previously referred. In addition, the influence of the electric permittivity of the particles on their electrokinetic properties in salt-free media is examined for those frames of boundary conditions.

Stabilization of PCC dispersions prepared directly in the mother-liquid after synthesis through the carbonation of (hydrated) lime

Various CaCO 3-based products are often used in the form of concentrated aqueous dispersions. This study investigates the stabilization of PCC dispersions prepared directly in the mother-liquid after the carbonation of (hydrated) lime through the adsorption of a commercial sodium polyacrylate dispersant. The results demonstrate that the composition of the mother-liquid, particularly the Ca 2 + activity, profoundly influences virtually all processes pertinent to dispersion stabilization—from the initial charging of the CaCO 3 surface in base PCC dispersions, to the surface charge regulation and dispersion stabilization efficiency of the polyacrylate dispersing agent. Rising prominence of the counterion condensation effects in Ca 2 + rich solutions limits the conditions conducive to the surface charge regulation through dispersant adsorption to an optimum pH range of about 8–11. Furthermore, dispersion stability analysis, based on the classical DLVO theory of colloid stability, and corroborated by experimental evidence in the form of particle size distribution analyses, also indicates that optimum stability conditions for such PCC dispersions are established with small dispersant doses (0.25–0.5% per dry weight) in the pH range of about 9–11.

Voltammetric Detection of Heparin at Polarized Blood Plasma/1,2-Dichloroethane Interfaces

Heparin, a highly negatively charged polysaccharide, which has been used widely as an anticoagulant and antithrombotic, was detected by ion-transfer voltammetry at the interface between 1,2-dichloroethane and an aqueous buffer solution or undiluted blood plasma. Quaternary ammoniums with different numbers of methyl and long alkyl groups were examined as positively charged heparin ionophores using pipet electrodes filled with the organic electrolyte solutions of their tetrakis(4-chlorophenyl)borate salts. It was shown that octadecyltrimethylammonium most selectively facilitates interfacial heparin adsorption without interference from potential-dependent ionophore transfer into the aqueous phase. Water-filled pipet electrodes were also used to study the stoichiometry of the interfacial complex between a heparin molecule and multiple ionophore molecules, which is discussed as a counterion condensation effect. Stripping voltammetry based on facilitated heparin adsorption and desorption gives a detection limit of 0.012 unit/mL in 0.12 M NaCl buffered at pH 7.2, which is 1 order of magnitude lower than therapeutic heparin concentrations (>0.2 unit/mL) and is comparable to a detection limit of the most sensitive heparin sensor reported so far. The biomedical utility of ion-transfer voltammetry was demonstrated for the first time in an undiluted blood sample. Despite interferences by Na+, Cl-, and plasma proteins such as serum albumin, a detection limit of 0.13 unit/mL was obtained in sheep blood plasma with the stripping method.

Effect of Thiocyanate Counterion Condensation on Poly(allylamine hydrochloride) Chains on the Buildup and Permeability of Polystyrenesulfonate/Polyallylamine Polyelectrolyte Multilayers

In this study, we investigate the buildup of PEI-(PSS-PAH)(n) polyelectrolyte multilayers at pH 7.4 in the presence of either NaCl or NaSCN as a supporting electrolyte. It appears that in the presence of increasing thiocyanate concentrations (from 0.1 to 0.5 M), the thickness increment, obtained from optical waveguide lightmode spectroscopy experiments, increases whereas it stays practically constant for increasing sodium chloride concentrations (between 0.1 and 0.5 M). The hydration of the films differs also markedly between both electrolyte solutions. The differences in the construction of the polyelectrolyte multilayers in the presence of both supporting electrolytes are rationalized in terms of strong SCN(-) condensation on the PAH chains. The occurrence of this ion condensation is indirectly demonstrated by means of zeta potential measurements and directly demonstrated by means of attenuated total internal reflection infrared spectroscopy on the multilayer films. Moreover when the films are built up in the presence of SCN(-), these ions are only slowly exchanged by the Cl(-) ions introduced in the bulk. Conversely the thick films obtained from 0.5 M NaSCN solutions do not deswell when the buffer solution is replaced by a 0.5 M NaCl containing buffer. The permeability of the films constructed in the presence of both sodium salts is also studied by means of cyclic voltametry and is found to be markedly different in the case of films made from five bilayers at 0.5 M salt concentration. This difference is due to the different morphology and porosity of the films constructed in the presence of 0.5 M NaCl and 0.5 M NaSCN.

Electroosmotic velocity in an array of parallel soft cylinders in a salt-free medium

A theory of electroosmosis in an array of parallel soft cylinders (i.e. polyelectrolyte-coated cylinders) in a salt-free medium is presented. It is shown that there is a certain critical value of the particle charge and that if the particle charge is greater than the critical value, then the electroosmotic velocity becomes constant independent of the particle charge due to the counterion condensation effects, as in the case of other electrokinetic phenomena in salt-free media.

Association behavior of poly(methyl methacrylate-b-methacrylic acid-b-methyl methacrylate) in aqueous medium

Abstract ABA type triblock amphiphilic polyelectrolyte consisting of poly(methyl methacrylate- block -methacrylic acid- block -methyl methacrylate) (P(MMA- b -MAA- b -MMA)) was synthesized by atom transfer radical polymerization technique and the self-assembly behavior of the polymers in aqueous solution was studied over the course of neutralization. Combination of potentiometric and conductometric titrations along with dynamic light scattering techniques were used to investigate the size and shape of aggregates at various degrees of neutralization. The effect of hydrophobic–hydrophilic (MMA–MAA) ratio and polymer chain length on the aggregation behavior during neutralization was studied. P(MMA- b -MAA- b -MMA) with longer MMA segment self-assembles via the closed association mechanism through stronger self-entanglement of MMA chains, whereas P(MMA- b -MAA- b -MMA) with shorter MMA chain self-assembles via the open association mechanism, as confirmed by transmission electron microscopy. Conductometric titration was used to determine the counterion condensation during the course of neutralization. When the charge density of micelle approaches a critical value as neutralization progresses, counterion condensation of Na + ions on the polymer chains occurs. The effect of counterion condensation on the aggregation behavior during neutralization was elucidated.

FTIR-ATR measurements of the ionization extent of acrylic acid within copolymerized methacrylated dextran/acrylic acid networks and its relation with pH/salt concentration-induced equilibrium swelling

In this study, dextran hydrogels were obtained by free radical copolymerization of methacrylated dextran with acrylic acid (AAc) in aqueous solution. The fractions of dissociation of AAc units within hydrogel in response to changes in pH and ionic strength of external aqueous solution were determined by FTIR-ATR spectroscopy. The influence of small ion concentration within hydrogel on the dissociation constant of AAc follows the Debye–Hückel behavior. Based on the results from the FTIR-ATR measurements, the total ion concentration difference inside and outside the hydrogel was determined according to the Donnan equilibrium theory, taking account of the counterion condensation effect quantitatively. The swelling response of hydrogels to changes in external pH and ionic strength was governed mainly by the ionic osmotic pressure due to the accumulation of diffusible ions within hydrogels. The energy balance between the osmotic and elastic retractile responses indicates the non-Gaussian behavior of elastically effective subchains with increasing swelling.

Electrophoretic mobility of a soft particle in a salt-free medium

A theory is presented for the electrophoretic mobility μ of dilute spherical soft particles (i.e., polyelectrolyte-coated particles) in salt-free media containing only counterions. As in the case of other types of particles (rigid particles and liquid drops) in salt-free media, there is a certain critical value of the particle charge separating two cases, the low-surface-charge case and the high-surface-charge case. For the low-charge case, the mobility is proportional to the particle charge and coincides with that of a soft particle in an electrolyte solution in the limit of very low electrolyte concentrations κ→0 (Hückel's limit), where κ is the Debye–Hückel parameter. For the high-charge case, however, μ becomes essentially constant, independent of the particle charge, due to the counterion condensation effect.

Dynamic electrophoretic mobility of spherical colloidal particles in a salt-free medium

A theory is proposed for the dynamic electrophoretic mobility μ( ω) of spherical colloidal particles in a salt-free medium containing only counterions in an oscillating electric field of frequency ω. The dynamic mobility depends on the frequency ω of the applied electric field and on the particle volume fraction as well as on the particle surface charge. It is found that as in the case of the static electrophoretic mobility μ(0) in salt-free media, there is a certain critical value of the particle surface charge separating two cases, that is, the low-surface-charge case and the high-surface-charge case (in the latter case the counterion condensation takes place near the particle surface). For the low-surface-charge case, the dynamic mobility agrees with that of a sphere in an electrolyte solution in the limit of very low electrolyte concentrations κa→0 (Hückel's limit), where κ is the Debye–Hückel parameter and a is the particle radius. For the high-surface-charge case, however, the dynamic mobility becomes constant independent of the particle surface charge, because of the counterion condensation effects. A simple expression for the ratio μ( ω)/ μ(0) applicable for all cases is given.

Polyelectrolytes in Electric Fields

We investigate the effect of an electric field on a highly charged polyelectrolyte (PE) chain by Brownian-dynamics simulation methods and a combination of different scaling arguments. In the simulation we take the counterions explicitly into account and therefore include the effects of counterion condensation and PE collapse as the coupling parameter (proportional to counterion valency) is increased. For highly charged PEs in the collapsed phase, a nonequilibrium unfolding transition occurs at sufficiently high electric fields where the PE aligns parallel to the external field. The critical field strength E* is determined from scaling results for the polarizability of a PE globule and exhibits a dependence on the chain length N, E* ∼ N-1/2, which might be useful for electrophoretic separation of charged, collapsed biopolymers. For noncollapsed PEs this unfolding transition is less pronounced: the critical field depends on the swelling exponent ν and scales as E* ∼ N-3ν/2. The electrophoretic mobility of PE monomers and counterions is determined. For large fields, counterions bound to the PE contribute significantly to the total conduction, since they can glide along the PE. This is an important factor in understanding experimental conduction experiments. The electrophoretic mobility of the bound counterions is determined by the electrostatic friction with the PE backbone and an activation barrier for decondensing from the PE; it in fact changes sign as the field strength is increased.

Electrokinetic phenomena in a dilute suspension of spherical colloidal particles in a salt-free medium

Electrokinetic phenomena are considered in a dilute suspension of spherical colloidal particles in a salt-free medium containing counter-ions only. Simple derivation is given for the electrophoretic mobility of the particles. Expressions for the electrical conductivity and the sedimentation potential are also obtained. An Onsager relation is found to hold between electrophoretic mobility and sedimentation potential. It is shown that if the particle charge Q is lower than a certain critical value, then the electrophoretic mobility and the electrical conductivity due to counter-ions increase linearly with increasing Q. If Q is higher than the critical value, then these quantities become constant independent of Q because of counter-ion condensation effects. The sedimentation potential, however, is not subject to the counter-ion condensation effects, since these effects upon the electrical conductivity and the concentration of the counter-ions cancel out with each other.

Numerical calculation of the electrophoretic mobility of a spherical particle in a salt-free medium

By extending an approximate theory of the electrophoretic mobility of dilute spherical colloidal particles in a salt-free medium containing only counterions (H. Ohshima, J. Colloid Interface Sci. 248 (2002) 499–503), a systematic numerical method is given for the calculation of the electrophoretic mobility, which is based on an iteration method. We assume that each sphere is surrounded by a spherical free volume, within which counterions are distributed so that electroneutrality is satisfied. The electrophoretic mobility is found to be determined mainly by the pressure due to the counterions at the outer surface of the free volume. It is shown how the mobility values deviate from those expected from Hückel's formula for high particle charges or zeta potentials because of the counterion condensation effect.

Electrophoretic Mobility of a Cylindrical Colloidal Particle in a Salt-Free Medium

Approximate expressions are derived for the electrophoretic mobility of dilute cylindrical colloidal particles in a salt-free medium containing only counterions. The cylinder is assumed to be infinitely long. It is shown that as in the case of a spherical particle, there is a certain critical value of the particle surface charge separating two cases. When the particle surface charge is lower than the critical value (case 1), the electrophoretic mobility increases with increasing particle surface charge per unit length. When the particle surface charge is higher than the critical value (case 2), the mobility becomes constant (for a cylinder in a transverse field) or the increase in the electrophoretic mobility with the particle surface charge becomes suppressed (for a cylinder in a tangential field). These phenomena are caused by the effect of counterion condensation in the vicinity of the particle surface. The critical value of the particle charge is essentially independent of the particle volume fraction φ for the dilute case, unlike the case of a sphere, in which case the critical charge value is proportional to ln(1/φ).

Effective interactions and phase behaviour for a model clay suspension in anelectrolyte

Since the early observation of nematic phases of disc-like clay colloids byLangmuir in 1938, the phase behaviour of such systems has resisted theoreticalunderstanding. The main reason is that there is no satisfactory generalization forcharged discs of the isotropic DLVO (Derjaguin, Landau, Verwey and Overbeek)potential describing the effective interactions between a pair of spherical colloidsin an electrolyte. In this paper, we show how to construct such a pair potential,incorporating approximately both the non-linear effects of counter-ioncondensation (charge renormalization) and the anisotropy of the chargedplatelets. We discuss the consequences for the phase behaviour of laponitedispersions (thin discs of 30 nm diameter and 1 nm thickness), and we presentan investigation into the mesostructure via Monte Carlo simulations.

Electrophoretic Mobility of a Spherical Colloidal Particle in a Salt-Free Medium

A general expression as well as approximate expressions are derived for the electrophoretic mobility of dilute spherical colloidal particles in a salt-free medium containing only counter ions. It is shown that there is a certain critical value of the particle surface charge. When the particle surface charge is lower than the critical value, the electrophoretic mobility is proportional to the particle surface charge or the particle zeta potential, following Hückel's formula. When the particle surface charge is higher than the critical value, the electrophoretic mobility becomes independent of the particle surface charge. This is due to the effect of counter ion condensation in the vicinity of the particle surface.

Role of counterion condensation in folding of the Tetrahymena ribozyme. I. Equilibrium stabilization by cations

Folding of RNA into an ordered, compact structure requires substantial neutralization of the negatively charged backbone by positively charged counterions. Using a native gel electrophoresis assay, we have examined the effects of counterion condensation upon the equilibrium folding of the Tetrahymena ribozyme. Incubation of the ribozyme in the presence of mono-, di- and trivalent ions induces a conformational state that is capable of rapidly forming the native structure upon brief exposure to Mg 2+. The cation concentration dependence of this transition is directly correlated with the charge of the counterion used to induce folding. Substrate cleavage assays confirm the rapid onset of catalytic activity under these conditions. These results are discussed in terms of classical counterion condensation theory. A model for folding is proposed which predicts effects of charge, ionic radius and temperature on counterion-induced RNA folding transitions.

Polycation comb-type copolymer reduces counterion condensation effect to stabilize DNA duplex and triplex formation

We have previously demonstrated that the polycation comb-type copolymer having abundant grafts of hydrophilic polymer chains significantly stabilizes DNA duplexes and triplexes [Maruyama et al., Bioconjugate Chem., 8 (1997) 3, Ferdous et al., Nucleic Acids Res., 26 (1998) 39]. This study was designed to estimate the mechanisms involved in the copolymer-mediated stabilization of DNA duplexes and triplexes. The melting temperatures, T m, of DNA duplex and triplex increased with increasing salt concentration, as well documented by the Poisson–Boltzmann and counterion condensation theories that were originally proposed by Manning [J. Chem. Phys., 51 (1969) 924] and further elaborated by Manning [Biopolymers 11 (1972) 937, Biopolymers. 15 (1976) 2385] and Record [Biopolymers, 14 (1975) 2137–2158, Biopolymers, 15 (1976) 893]. In the presence of the copolymer, however, the T m values of DNA duplexes and triplexes did not show significant change with salt concentration. It was concluded that the copolymer is capable of reducing the counterion condensation effects to stabilize DNA duplexes and triplexes. Strong but exchangeable interaction between the copolymer and DNA is seemingly involved in the stabilization behavior.

Superabsorbent polymeric material. V. Synthesis and swelling behavior of sodium acrylate and sodium 2-acrylamido-2-methylpropanesulfonate copolymeric gels

A series of xerogels based on sodium acrylate (SA), sodium 2-acrylamido-2-methyl propanesulfonate (NaAMPS), and N,N-methylene-bis-acrylamide (NMBA) are prepared by inverse suspension polymerization. The water absorbency and swelling behavior for these high absorbent polymers in deionized water and transition salt solutions are investigated. Experimental results indicated that the absorbency in deionized water increases with an increase of the NaAMPS content in the copolymeric gels, which is related to the degree of charge density of the network and the strength of hydrophilic group. The extent of crosslinking agent also influenced the swelling capacity because of elastic chain force of the polymer chain. The absorbency in chloride salt solutions decreases with an increase in the ionic strength of salt. But the decrease of absorbency is different in monovalent and multivalent salt solution. This behavior can be accounted for in terms of counterion condensation or screening effect for monovalent cations, as well as complexation for multivalent cations. The swelling rates in various salt solutions for these xerogels are also investigated. At last, SA-NaAMPS copolymeric gels were used for ion adsorption. But the result showed that the adsorptive amount of transition metal ions for SA-NaAMPS copolymeric gels was lower than that for pure poly(SA) gel. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 69: 229–237, 1998