Methods for Determining the Intrinsic and Effective Charges on Spherical Macroions

Colloidal electro-phoresis in the presence of symmetric and asymmetric electro-osmotic flow

We characterize the electro-phoretic motion of charged sphere suspensions in the presence of substantial electro-osmotic flow using a recently introduced small angle super-heterodyne dynamic light scattering instrument (ISASH-LDV). Operation in integral mode gives access to the particle velocity distribution over the complete cell cross-section. Obtained Doppler spectra are evaluated for electro-phoretic mobility, wall electro-osmotic mobility and particle diffusion coefficient. Simultaneous measurements of differing electro-osmotic mobilities leading to asymmetric solvent flow are demonstrated in a custom made electro-kinetic cell fitting standard microscopy slides as exchangeable sidewalls. The scope and range of our approach are discussed demonstrating the possibility of an internal calibration standard and using the simultaneously measured electro-kinetic mobilities in the interpretation of a microfluidic pumping experiment involving an inhomogeneous electric field and a complex solvent flow pattern.

Quantifying the thickness of the electrical double layer neutralizing a planar electrode: the capacitive compactness

The spatial extension of the ionic cloud neutralizing a charged colloid or an electrode is usually characterized by the Debye length associated with the supporting charged fluid in the bulk. This spatial length arises naturally in the linear Poisson-Boltzmann theory of point charges, which is the cornerstone of the widely used Derjaguin-Landau-Verwey-Overbeek formalism describing the colloidal stability of electrified macroparticles. By definition, the Debye length is independent of important physical features of charged solutions such as the colloidal charge, electrostatic ion correlations, ionic excluded volume effects, or specific short-range interactions, just to mention a few. In order to include consistently these features to describe more accurately the thickness of the electrical double layer of an inhomogeneous charged fluid in planar geometry, we propose here the use of the capacitive compactness concept as a generalization of the compactness of the spherical electrical double layer around a small macroion (González-Tovar et al., J. Chem. Phys. 2004, 120, 9782). To exemplify the usefulness of the capacitive compactness to characterize strongly coupled charged fluids in external electric fields, we use integral equations theory and Monte Carlo simulations to analyze the electrical properties of a model molten salt near a planar electrode. In particular, we study the electrode's charge neutralization, and the maximum inversion of the net charge per unit area of the electrode-molten salt system as a function of the ionic concentration, and the electrode's charge. The behaviour of the associated capacitive compactness is interpreted in terms of the charge neutralization capacity of the highly correlated charged fluid, which evidences a shrinking/expansion of the electrical double layer at a microscopic level. The capacitive compactness and its first two derivatives are expressed in terms of experimentally measurable macroscopic properties such as the differential and integral capacity, the electrode's surface charge density, and the mean electrostatic potential at the electrode's surface.

Osmotic Bulk Modulus of Charged Colloids Measured by Ensemble Optical Trapping

The optical-bottle technique is used to measure osmotic bulk moduli of colloid suspensions. The bulk modulus is determined by optically trapping an ensemble of nanoparticles and invoking a steady-state force balance between confining optical-gradient forces and repulsive osmotic-pressure forces. Osmotic bulk moduli are reported for aqueous suspensions of charged polystyrene particles in NaCl solutions as a function of particle concentration and ionic strength, and are compared to those determined by turbidity measurements under the same conditions. Effective particle charges are calculated from the bulk moduli and are found to increase as a function of ionic strength, consistent with previously reported results.

Solvation behavior of short-chain polystyrene sulfonate in aqueous electrolyte solutions: a molecular dynamics study

We analyze the solvation behavior of short-chain polystyrene sulfonate (PSS) in aqueous electrolyte solutions by isothermal-isochoric molecular dynamics simulation to determine the solvation effects on the structure and conformation of the polyelectrolyte as a function of the aqueous environment. To that end, we study these aqueous systems including the explicit atomistic description of water, the PSS chain, and their interactions with all species in solution. In addition, we investigate the effect of the degree of sulfonation and its distribution along the PSS chain on the resulting conformation as well as solvation structure. Moreover, we assess the impact of added salts on the net charge of the PSS backbone, placing emphasis on the valence of the counterion and the extent of the ion-pair formation between the sulfonate group and the counterions. Finally, we present evidence for the so-called like-charge attraction between sulfonate groups through the formation of counterion-mediated interchain sulfonate-sulfonate and water-mediated intrachain sulfonate-sulfonate bridges, as well as between unlike counterion-counterion interactions.

Effects of multivalent salt addition on effective charge of dilute colloidal solutions

The effective charge Z* is often invoked to account for the accumulation of counterions near the colloid with intrinsic charge Z. Although the ion concentrations c(i) are not uniform in the solution due to the presence of the charged particle, their chemical potentials are uniform everywhere. Thus, on the basis of ion chemical potential, effective ion concentrations c(i)*, which can be experimentally measured by potentiometry, are defined with the pure salt solution as the reference state. The effective charge associated with the charged particle can then be determined by the global electroneutrality condition. Monte Carlo simulations are performed in a spherical Wigner-Seitz cell to obtain the effective charge of the colloid. In terms of the charge ratio alpha=Z*/Z, the effects of added salt concentration, counterion valency, and particle charge are examined. The effective charge declines with increasing salt concentration and the multivalent salt is much more efficient in reducing the effective charge of the colloidal solution. Moreover, the extent of effective charge reduction is decreased with increasing intrinsic charge for a given concentration of added salt. Those results are qualitatively consistent with experimental observations by electrophoresis.

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.

Role of the secondary minimum on the flocculation rate of nondeformable droplets

The kinetic stability of suspensions is usually associated with a decrease in the flux of flocculating particles due to the action of a repulsive potential. However, previous calculations on bitumen drops suggest the possible occurrence of relatively fast aggregation rates in systems with large electrostatic barriers for primary minimum flocculation. This indicates a strong effect of the secondary minimum in the process of aggregation. Here, emulsion stability simulations (ESS) are used to study the aggregation behavior of 11 systems showing different depths of the secondary minimum and three particle sizes. Micron size drops (as those of Bitumen emulsions) usually exhibit deep secondary minima, which rarely occur between nanometer size particles. At high surfactant concentrations, these drops do not coalesce but can still show fast aggregation rates caused by irreversible secondary-minimum flocculation. On the other hand, the extent of coalescence in nanometer-size systems markedly depends on the height of the repulsive barrier. Furthermore, the secondary minimum of these smaller particles is usually shallow, causing reversible aggregation or no aggregation at all. In this article, the consequences of the referred behaviors on the magnitude of the stability ratio are discussed.

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 charged spheres based on thermodynamic properties

At strong electrostatic coupling, counterions are accumulated in the vicinity of the surface of the charged particle with intrinsic charge Z. In order to explain the behavior of highly charged particles, effective charge Z(*) is therefore invoked in the models based on Debye-Huckel approximation, such as the Derjaguin-Landau-Verwey-Overbeek potential. For a salt-free colloidal suspension, we perform Monte Carlo simulations to obtain various thermodynamic properties omega in a spherical Wigner-Seitz cell. The effect of dielectric discontinuity is examined. We show that at the same particle volume fraction, counterions around a highly charged sphere with Z may display the same value of omega as those around a weakly charged sphere with Z(*), i.e., omega(Z)=omega(Z(*)). There exists a maximally attainable value of omega at which Z=Z(*). Defining Z(*) as the effective charge, we find that the effective charge passes through a maximum and declines again due to ion-ion correlation as the number of counterions is increased. The effective charge is even smaller if one adopts the Debye-Huckel expression omega(DH). Our results suggest that charge renormalization can be performed by chemical potential, which may be observed in osmotic pressure measurements.

Simultaneous determination of the size and surface charge of individual nanoparticles using a carbon nanotube-based Coulter counter

A resistive-pulse Coulter counter based on a membrane containing a single multiwall carbon nanotube (MWNT) channel was used to simultaneously determine the size and surface charge of carboxy-terminated polystyrene nanoparticles. The membrane was prepared from an epoxy section containing a MWNT channel mounted on a poly(dimethylsiloxane) (PDMS) support structure. The PDMS support reduced the background noise level by a factor of > 20 compared to the Si/Si3N4 support structure used in our previous study. The lower noise level makes it possible to accurately measure the height and width of resistive-pulse signals resulting from transport of individual particles through the MWNT channel. Particle sizes, calculated from current pulse heights, were comparable to those determined by transmission electron microscope (TEM). The width of the current pulses is a measure of the nanoparticle transport time, and it permits calculation of the electrokinetic surface charge. Different types of polystyrene nanoparticles having nearly the same size, but different electrokinetic surface charge, could be resolved on the basis of the difference in their transport time.

Fibronectin fibrillogenesis on sulfonated polystyrene surfaces

Extracellular matrix (ECM) protein adsorption and organization serves as a critical first step in the development and organization of tissues. Advances in tissue engineering, therefore, will depend on the ability to control the rate and pattern of ECM formation. Fibronectin is a prominent component of the ECM, which undergoes fibrillogenesis in the presence of cells. Using sulfonated polysyrene surfaces, we showed that fibronectin undergoes a transition from monolayer to multilayer adsorption at calculated surface charge densities above 0.03 Coulombs (C)/m(2). At charge densities above approximately 0.08 C/m(2), distinct fibronectin fibrillar networks are observed to form with a fibril morphology similar to those observed to form in situ on cell surfaces. This self-organization process is time dependent, with the fibrils achieving dimensions of 30-40 microm in length and 1 microm in height after 72 h of incubation. We suggest that the polarization of charge domains on the polyampholytic fibronectin molecules near high charge density surfaces is sufficient to initiate the multilayer adsorption and the organization of these fibrillar structures. These results suggest that the nonlinear dependence of adsorption on surface charge density may play an important role in the self-organization of many matrix components.

Interaction potentials, structural ordering and effective charges in dispersions of charged colloidal particles

As colloidal dispersions of charged particles exhibit a wide variety of commercial, technological and scientific applications, a considerable theoretical effort has been devoted to finding an effective interaction potential from primitive models. The forces derived from this potential should justify the spatial ordering experimentally observed under certain conditions. This paper reviews the advances in these theoretical studies as well as some experiments (based on the mentioned order) that try to corroborate them. Special attention has been paid to the Derjaguin-Landau-Verwey-Overbeek (DLVO) potential. Nowadays, many of these theoretical investigations suggest that it could be applied if some of its parameters are renormalized. Nevertheless, to achieve a renormalization procedure in a strict way (from a primitive model) is a difficult task as a result of the size and charge asymmetries between small ions and macroions. Thus, several procedures for computing renormalized charges in a simple way have been developed. However, the notion of effective charge has also been widely used (as a adjustable parameter) in order to justify results found for several kinds of colloids (like solid particle dispersions or micellar systems) by means of quite different experimental techniques. Renormalization (as well as ion condensation) approaches, experiments and the controversial relationship between theoretical and phenomenological effective charges are also reviewed in this work.

An Experimental Test of the Ion Condensation Theory for Spherical Colloidal Particles

This paper deals with the notion of ion condensation for spherical colloids and, more specifically, with a recent model developed to predict effective charges (Y. Levin, M. C. Barbosa, and M. N. Tamashiro, Europhys. Lett. 41, 123, 1998). Electrophoretic mobility measurements (carried out for a set of well-characterized latexes) were used to find out to what extent this theory is able to accounts for: (i) the insensitivity of mobility to surface charge, and (ii) the small values of electrokinetic charge found at low ionic strength. As the Levin theory was developed assuming no added salt, a previous discussion about the effect of additional electrolyte was needed. Contrary to what other authors have reported, our results do not support the above-mentioned theory. Copyright 2001 Academic Press.

Ionic condensation theories and the liquidlike structures observed in colloidal dispersions

Though the notion of effective charge has been widely used to fit experimental data, the possibility of predicting this adjustable parameter through a model remains unclear. A likely reason for this is the complexity involved in the theoretical approaches in the case of fluids with large asymmetries between their components. This paper deals with several condensation theories for spherical colloids, developed to provide effective charge values from simple models. Liquidlike structures are formed in colloidal dispersions for a set of latexes with different properties (charge, size, and polymeric composition). Effective charges are determined from experimental structure factors using a Derjaguin-Landau-Verwey-Overbeek potential and an Ornstein-Zernike scheme. The numerical coincidence between effective and post-condensation charges is fairly acceptable only for latexes with small size and charge. A simple approach based on the Manning condensation theory for linear polyelectrolytes is also discussed.