Salt-free Suspensions Research Articles

Electrophoretic Mobility and Electric Conductivity of Salt-Free Suspensions of Charged Soft Particles

A unit cell model is employed to analyze the electrophoresis and electric conduction in a concentrated suspension of spherical charged soft particles (each is a hard core coated with a porous polyelectrolyte layer) in a salt-free medium. The linearized Poisson–Boltzmann equation applicable to a unit cell is solved for the equilibrium electrostatic potential distribution in the liquid solution containing the counterions only surrounding a soft particle. The counterionic continuity equation and modified Stokes/Brinkman equations are solved for the ionic electrochemical potential energy and fluid velocity distributions, respectively. Closed-form formulas for the electrophoretic mobility of the soft particles and effective electric conductivity of the suspension are derived, and the effect of particle interactions on these transport characteristics is interesting and significant. Same as the case in a suspension containing added electrolytes under the Debye–Hückel approximation, the scaled electrophoretic mobility in a salt-free suspension is an increasing function of the fixed charge density of the soft particles and decreases with increases in the core-to-particle radius ratio, ratio of the particle radius to the permeation length in the porous layer, and particle volume fraction, keeping the other parameters unchanged. The normalized effective electric conductivity of the salt-free suspension also increases with an increase in the fixed charge density and with a decrease in the core-to-particle radius ratio, but is not a monotonic function of the particle volume fraction.

Electrokinetic detection of the salt-free condition in colloids. Application to polystyrene latexes

Because of their singular phenomenology, the so-called salt-free colloids constitute a special family of dispersed systems. Their main characteristic is that the dispersion medium ideally contains only the solvent and the ions compensating exactly the surface charge of the particles. These ions (often called released counterions) come into the solution when the surface groups responsible for the particles charge get ionized. An increasing effort is nowadays dedicated to rigorously compare theoretical model predictions for ideal salt-free suspensions, where only the released counterions are supposed to be present in solution, with appropriately devised experiments dealing with colloids as close as possible to the ideal salt-free ones. Of course, if the supporting solution is aqueous, the presence of atmospheric contamination and any other charged species different from the released counterions in the solution must be avoided. Because this is not an easy task, the presence of dissolved atmospheric CO2 and of H+ and OH− from water dissociation cannot be fully discarded in aqueous salt-free solutions (often denominated realistic in such case). Ultimately, at some point, the role of the released counterions will be comparable or even larger in highly charged concentrated colloids than that of added salts. These topics are covered in the present contribution. The model results are compared with experimental data on the dynamic mobility and dielectric dispersion of polystyrene spheres of various charges and sizes. As a rule, it is found that the model correctly predicts the significance of alpha and Maxwell-Wagner-O'Konski relaxations. Positions and amplitudes of such relaxations are well predicted, although it is necessary to assume that the released counterions are potassium or sodium instead of protons, otherwise the frequency spectra of experimental mobility and permittivity differ very significantly from those theoretically calculated. The proposed electrokinetic evaluation is an ideal tool for detecting in situ the possible contamination (or incomplete ion exchange of the latexes). A satisfactory agreement is found when potassium counterions are assumed to be in solution, mostly if one considers that the comparison is carried out without using any adjustable parameters.

Electrophoresis and electric conduction in a salt-free suspension of charged particles.

The electrophoresis and electric conduction of a suspension of charged spherical particles in a salt-free solution are analyzed by using a unit cell model. The linearized Poisson-Boltzmann equation (valid for the cases of relatively low surface charge density or high volume fraction of the particles) and Laplace equation are solved for the equilibrium electric potential profile and its perturbation caused by the imposed electric field, respectively, in the fluid containing the counterions only around the particle, and the ionic continuity equation and modified Stokes equations are solved for the electrochemical potential energy and fluid flow fields, respectively. Explicit analytical formulas for the electrophoretic mobility of the particles and effective electric conductivity of the suspension are obtained, and the particle interaction effects on these transport properties are significant and interesting. The scaled zeta potential, electrophoretic mobility, and effective electric conductivity increase monotonically with an increase in the scaled surface charge density of the particles and in general decrease with an increase in the particle volume fraction, keeping each other parameter unchanged. Under the Debye-Hückel approximation, the dependence of the electrophoretic mobility normalized with the surface charge density on the ratio of the particle radius to the Debye screening length and particle volume fraction in a salt-free suspension is same as that in a salt-containing suspension, but the variation of the effective electric conductivity with the particle volume fraction in a salt-free suspension is found to be quite different from that in a suspension containing added electrolyte.

Relaxation dynamics of two interacting electrical double-layers in a 1D Coulomb system

We consider an out-of-equilibrium one-dimensional model for two electrical double-layers. With a combination of exact calculations and Brownian dynamics simulations, we compute the relaxation time (τ) for an electroneutral salt-free suspension, made up of two fixed colloids, with N neutralizing mobile counterions. For N odd, the two double-layers never decouple, irrespective of their separation L; this is the regime of like-charge attraction, where τ exhibits a diffusive scaling in L 2 for large L. On the other hand, for even N, L no longer is the relevant length scale for setting the relaxation time; this role is played by the Bjerrum length. This leads to distinctly different dynamics: for N even, thermal effects are detrimental to relaxation, increasing τ, while they accelerate relaxation for N odd. Finally, we also show that the mean-field theory is recovered for large N and moreover, that it remains an operational treatment down to relatively small values of N (N > 3).

One-dimensional colloidal model with dielectric inhomogeneity.

We consider a one-dimensional model allowing analytical derivation of the effective interactions between two charged colloids. We evaluate exactly the partition function for an electroneutral salt-free suspension with dielectric jumps at the colloids' position. We derive a contact relation with the pressure that shows there is like-charge attraction, whether or not the counterions are confined between the colloids. In contrast to the homogeneous dielectric case, there is the possibility for the colloids to attract despite the number of counterions (N) being even. The results are shown to recover the mean-field prediction in the limit N→∞.

Non-monotonic concentration dependence of the electro-phoretic mobility of charged spheres in realistic salt free suspensions.

Using super-heterodyne Doppler velocimetry with multiple scattering correction, we extend the optically accessible range of concentrations in experiments on colloidal electro-kinetics. Here, we measured the electro-phoretic mobility and the DC conductivity of aqueous charged sphere suspensions covering about three orders of magnitude in particle concentrations and transmissions as low as 40%. The extended concentration range for the first time allows the demonstration of a non-monotonic concentration dependence of the mobility for a single particle species. Our observations reconcile previous experimental observations made on other species over restricted concentration ranges. We compare our results to the state-of-the-art theoretical calculations using a constant particle charge and the carefully determined experimental boundary conditions as input. In particular, we consider the so-called realistic salt free conditions, i.e., we respect the release of counterions by the particles, the solvent hydrolysis, and the formation of carbonic acid from dissolved neutral CO2. We also compare our results to previous results obtained under similarly well-defined conditions. This allows identification of three distinct regions of differing density dependence. There is an ascent during the build-up of double layer overlap, which is not expected by theory, an extended plateau region in quantitative agreement with theoretical expectation based on a constant effective charge and a sudden decrease, which occurs way before the expected gradual decrease. Our observations suggest a relation of the non-monotonic behavior to a decrease in particle charge, and we tentatively discuss possibly underlying mechanisms.

Rheological inversion of the universal aging dynamics of hectorite clay suspensions

Abstract Aging of salt-free suspensions of hectorite clay was investigated with rheology of multi-wave small amplitude oscillatory shear. The frequency-dependent storage and loss moduli at different waiting times and temperatures were scaled into a master curve, conforming the time-temperature-aging time superposition. In other words, thermorheological simplicity was maintained during aging. While the relaxation time of the system grew monotonically with increasing waiting time, and showed non-monotonic dependence on temperature, consistent with our previous results. The relaxation spectra converted from the master curves of different clay concentrations were described by a power-law distribution with a stretched exponential cutoff. The dynamics were slower for high clay concentration. A rheological inverse from gel-like to glass-like distribution was observed with the increase in clay concentration.

A zeta potential value determines the aggregate's size of penta-substituted [60]fullerene derivatives in aqueous suspension whereas positive charge is required for toxicity against bacterial cells.

BackgroundThe cause–effect relationships between physicochemical properties of amphiphilic [60]fullerene derivatives and their toxicity against bacterial cells have not yet been clarified. In this study, we report how the differences in the chemical structure of organic addends in 10 originally synthesized penta-substituted [60]fullerene derivatives modulate their zeta potential and aggregate’s size in salt-free and salt-added aqueous suspensions as well as how these physicochemical characteristics affect the bioenergetics of freshwater Escherichia coli and marine Photobacterium phosphoreum bacteria. Dynamic light scattering, laser Doppler micro-electrophoresis, agarose gel electrophoresis, atomic force microscopy, and bioluminescence inhibition assay were used to characterize the fullerene aggregation behavior in aqueous solution and their interaction with the bacterial cell surface, following zeta potential changes and toxic effects.ResultsDynamic light scattering results indicated the formation of self-assembled [60]fullerene aggregates in aqueous suspensions. The measurement of the zeta potential of the particles revealed that they have different surface charges. The relationship between these physicochemical characteristics was presented as an exponential regression that correctly described the dependence of the aggregate’s size of penta-substituted [60]fullerene derivatives in salt-free aqueous suspension from zeta potential value. The prevalence of DLVO-related effects was shown in salt-added aqueous suspension that decreased zeta potential values and affected the aggregation of [60]fullerene derivatives expressed differently for individual compounds. A bioluminescence inhibition assay demonstrated that the toxic effect of [60]fullerene derivatives against E. coli cells was strictly determined by their positive zeta potential charge value being weakened against P. phosphoreum cells in an aquatic system of high salinity. Atomic force microscopy data suggested that the activity of positively charged [60]fullerene derivatives against bacterial cells required their direct interaction. The following zeta potential inversion on the bacterial cells surface was observed as an early stage of toxicity mechanism that violates the membrane-associated energetic functions.ConclusionsThe novel data about interrelations between physicochemical parameters and toxic properties of amphiphilic [60]fullerene derivatives make possible predicting their behavior in aquatic environment and their activity against bacterial cells.

Spontaneous evolution of self-assembled phases from anisotropic colloidal dispersions

We demonstrate spontaneous evolution of various self-assembled phases from a homogeneous aqueous dispersion of high aspect ratio Montmorillonite (MMT, platelet diameter ~250 nm and thickness 1 nm) nanoclay platelets based on the observations made over a period of 4 years. The phase diagram for this system in salt-free suspensions in normal pH conditions using rheology, light scattering, and dilution experiments was established, and we have noticed that these suspensions do undergo nontrivial phase evolution yielding formation of equilibrium fluids and gels and aging dynamics. This observation showed that the yield stress dependence on the concentration of clay followed a power-law behavior similar to low aspect ratio Laponite nanoclay dispersions. During the initial period, all dispersions formed stable sols, and with aging network-like structures were found to form via two routes not reported hitherto: one for below gelation concentration by phase separation and another for above the same, through equilibrium gelation resembling the Laponite nanoclay system, where existence of patchy colloids, equilibrium gels, and empty liquids was observed experimentally.

Temperature dependence of aging kinetics of hectorite clay suspensions

The aging of salt-free hectorite suspensions with different concentrations (cL=2.9, 3.2 and 3.5wt%) stored for 2days or 4days was studied by rheology at different temperatures. The evolution of storage and loss moduli G′ and G″ during aging followed aging time–temperature superposition. The temperature dependence of the shift factor aT, which reflected the aging kinetics, was interpreted by the reaction-limited colloidal aggregation (RLCA) mechanism with counterion condensation in calculating the double-layer interaction of the charged clay particles. Temperature dependence of the plateau modulus and yield stress of the suspension aged for 800s was modeled with the soft glassy rheology (SGR) theory. The estimated noise temperature x indicated that the sample aged at higher temperature corresponded to a deeper quench in the nonergodic state. Under larger amplitude of oscillatory shear, the suspension exhibited a strain rate-frequency superposition (SRFS). The shearing eliminated the effects of aging and heating.

DC electrophoresis and viscosity of realistic salt-free concentrated suspensions: Non-equilibrium dissociation–association processes

Most of the suspensions usually found in industrial applications are concentrated, aqueous and in contact with the atmospheric CO2. The case of suspensions with a high concentration of added salt is relatively well understood and has been considered in many studies. In this work we are concerned with the case of concentrated suspensions that have no ions different than: (1) those stemming from the charged colloidal particles (the added counterions, that counterbalance their surface charge); (2) the H+ and OH− ions from water dissociation, and (3) the ions generated by the atmospheric CO2 contamination. We call this kind of systems “realistic salt-free suspensions”. We show some theoretical results about the electrophoretic mobility of a colloidal particle and the electroviscous effect of realistic salt-free concentrated suspensions. The theoretical framework is based on a cell model that accounts for particle–particle interactions in concentrated suspensions, which has been successfully applied to many different phenomena in concentrated suspensions. On the other hand, the water dissociation and CO2 contamination can be described following two different levels of approximation: (a) by local equilibrium mass-action equations, because it is supposed that the reactions are so fast that chemical equilibrium is attained everywhere in the suspension, or (b) by non-equilibrium dissociation–association kinetic equations, because it is considered that some reactions are not rapid enough to ensure local chemical equilibrium. Both approaches give rise to different results in the range from dilute to semidilute suspensions, causing possible discrepancies when comparing standard theories and experiments concerning transport properties of realistic salt-free suspensions.

Slow dynamics, hydration and heterogeneity in Laponite dispersions

Age dependent hydration, heterogeneity and network rigidity of aqueous Laponite dispersions in their sol, gel and glass phases have been studied systematically in the clay concentration range c = 0.3–3.5 % (w/v) which revealed the following interesting features: (i) both in the sol and gel regime (c < 1.8% (w/v)), the intensity of light scattered I(q,c) scaled with concentration c as, I(q,c) ∼ cα with α = 0.95 at t = 0, and 0.63 after t = 6 months implying that this temporal growth resulted from the formation of a colloidal gel; (ii) in the glass phase (c ≥ 2% (w/v)), scattered intensity from samples remained constant (α = 0), meaning that there was disorder in the system at higher solid contents, and the clay particles were randomly arranged, and this intensity profile did not change with the aging; (iii) the dynamic structure factor data showed low concentration dispersions (gels) having a single mode relaxation time (fast mode) which shifted to longer relaxation time with aging. In the glass phase, in addition to the fast mode that remained invariant of aging, a slow mode which shifted to longer relaxation time with aging was noticed; (iv) rigidity modulus (G′) and yield stress (σ) measurements showed that there are two universal power-law relations governing their behavior as a function of clay concentration; G′, σ ∼ cδ with δ = 2.3 for gels and 2.8 for glass. Both these parameters revealed similar logarithmic time dependence with aging as σ, G′ = βln(tw/tm), where β is a constant and tm is the characteristic time scale for the development of micro structures; (v) Raman spectroscopy data revealed three distinct OH bands characteristic of the structure of water which revealed change in the structured water content with the aging, and the heterogeneity of the samples was established using a Cole–Cole plot. We have proposed a time-dependent phase diagram for the salt free suspensions of Laponite clay using the abovementioned results.

Ion size effects on the electrokinetics of salt-free concentrated suspensions in ac fields

We analyze the influence of finite ion size effects in the response of a salt-free concentrated suspension of spherical particles to an oscillating electric field. Salt-free suspensions are just composed of charged colloidal particles and the added counterions released by the particles to the solution that counterbalance their surface charge. In the frequency domain, we study the dynamic electrophoretic mobility of the particles and the dielectric response of the suspension. We find that the Maxwell–Wagner–O’Konski process associated with the counterions condensation layer is enhanced for moderate to high particle charges, yielding an increment of the mobility for such frequencies. We also find that the increment of the mobility grows with ion size and particle charge. All these facts show the importance of including ion size effects in any extension attempting to improve standard electrokinetic models.

Ion size effects on the electric double layer of a spherical particle in a realistic salt-free concentrated suspension

A new modified Poisson-Boltzmann equation accounting for the finite size of the ions valid for realistic salt-free concentrated suspensions has been derived, extending the formalism developed for pure salt-free suspensions [Roa et al., Phys. Chem. Chem. Phys., 2011, 13, 3960-3968] to real experimental conditions. These realistic suspensions include water dissociation ions and those generated by atmospheric carbon dioxide contamination, in addition to the added counterions released by the particles to the solution. The electric potential at the particle surface will be calculated for different ion sizes and compared with classical Poisson-Boltzmann predictions for point-like ions, as a function of particle charge and volume fraction. The realistic predictions turn out to be essential to achieve a closer picture of real salt-free suspensions, and even more important when ionic size effects are incorporated to the electric double layer description. We think that both corrections have to be taken into account when developing new realistic electrokinetic models, and surely will help in the comparison with experiments for low-salt or realistic salt-free systems.

Electric double layer for spherical particles in salt-free concentrated suspensions including ion size effects

The equilibrium electric double layer (EDL) that surrounds colloidal particles is essential for the response of a suspension under a variety of static or alternating external fields. An ideal salt-free suspension is composed of charged colloidal particles and ionic countercharges released by the charging mechanism. Existing macroscopic theoretical models can be improved by incorporating different ionic effects usually neglected in previous mean-field approaches, which are based on the Poisson-Boltzmann equation (PB). The influence of the finite size of the ions seems to be quite promising because it has been shown to predict phenomena like charge reversal, which has been out of the scope of classical PB approximations. In this work we numerically obtain the surface electric potential and the counterion concentration profiles around a charged particle in a concentrated salt-free suspension corrected by the finite size of the counterions. The results show the high importance of such corrections for moderate to high particle charges at every particle volume fraction, especially when a region of closest approach of the counterions to the particle surface is considered. We conclude that finite ion size considerations are obeyed for the development of new theoretical models to study non-equilibrium properties in concentrated colloidal suspensions, particularly salt-free ones with small and highly charged particles.

Dc electrokinetics for spherical particles in salt-free concentrated suspensions including ion size effects

We study the electrophoretic mobility of spherical particles and the electrical conductivity in salt-free concentrated suspensions including finite ion size effects. An ideal salt-free suspension is composed of just charged colloidal particles and the added counterions that counterbalance their surface charge. In a very recent paper [Roa et al., Phys. Chem. Chem. Phys., 2011, 13, 3960-3968] we presented a model for the equilibrium electric double layer for this kind of suspensions considering the size of the counterions, and now we extend this work to analyze the response of the suspension under a static external electric field. The numerical results show the high importance of such corrections for moderate to high particle charges, especially when a region of closest approach of the counterions to the particle surface is considered. The present work sets the basis for further theoretical models with finite ion size corrections, concerning particularly the ac electrokinetics and rheology of such systems.

Double layer polarization in “realistic” aqueous salt-free suspensions

The analysis of the frequency dependent electric permittivity of colloidal suspensions as a function of the frequency of the externally applied field is a powerful tool, very sensitive to the particle–solution interface and can provide rich information on the dynamics of electrical double layers. Among the different physical situations that can manifest themselves in the permittivity spectrum, attention will be paid in this paper to the case of concentrated suspensions of spherical colloidal particles in “realistic” salt-free conditions. This means that the ionic species in the liquid phase will be: (1) the “released counterions” coming from the dissociation of surface groups of the particles, (2) the H + and OH − ions from water dissociation, and (3) the ions generated by the environmental CO 2 dissolved in the suspension if it is open to the atmosphere. Theoretical predictions based on the cell model indicate the presence of two relaxations in the permittivity spectrum when the particle charge is large enough. The lowest frequency peak (appearing at frequencies around 10 5 Hz) changes with the overall conductivity of the medium, while the faster relaxation (characteristic frequency in the range 10 7–10 8 Hz) only depends on the surface charge of the particle. This suggests that the first relaxation corresponds to the classical Maxwell–Wagner (MW) relaxation associated to interfacial polarization of the diffuse layer, whereas the second, higher-frequency one, relates to the polarization of a compact layer of counterions developed very close to the particle surface at high particle charges (ionic condensation effect). In order to really prove the physical origin of these dispersions we have compared the results with equivalent salt-added (or low salt) suspensions. These have been built using the same surface charge density values for the particles and an added salt concentration such that the DC conductivities of the salt-free systems are mimicked. Interestingly, it has been found for the first time that a clear alpha-process (observed at the kHz frequency region, and linked to the freezing of the concentration polarization of the double layer) is present together with the above mentioned two MW processes. The alpha relaxation is, however, absent in the case of the realistic salt-free suspensions. In these, the existence of links between the local concentrations of ions due to the weak character of the main electrolyte in solution, carbonic acid, apparently prevents or largely hinders the formation of concentration polarization clouds.

Cationization of field pea starch in salt-free aqueous suspension

Industrial production of cationic starches involves excessive amounts of costly and environmentally toxic salts (∼60%, starch dry weight basis) as swelling inhibitors. The present study investigated the preparation of cationic field pea starch using the reagent, 3-chloro-2-hydroxypropyltrimethylammonium chloride (CHPTAC), substituting a commonly used salt, sodium sulfate, with natural sugars such as sucrose or glucose under alkaline conditions. The effects of sugar type and concentration on the degree of substitution were studied. At a concentration of 20% of the weight of starch solids both sucrose and glucose effectively prevented starch granule swelling. Under reaction conditions similar to those used in industrial processing, cationization of pea starch in the presence of sodium sulfate resulted in a degree of substitution and reaction efficiency approximately twice as high as sucrose and four times as high as glucose. For this reason, sucrose was investigated further as a more suitable alternative to sodium sulfate than glucose in the salt-free preparation of cationic starch. Optimization of reaction conditions such as temperature, pH, swelling inhibitor and cationic reagent concentrations using sucrose as the swelling inhibitor resulted in a cationic starch with a degree of substitution of 0.07, comparable to the 0.06 that was obtained using sodium sulfate. These results indicate that sucrose may be a viable alternative to sodium sulfate in the production of cationic pea starch.

Electroviscous effect of concentrated suspensions in salt-free media: Water dissociation and CO 2 influence

The electroviscous effect of realistic salt-free colloidal suspensions is analyzed theoretically. We study the influence on the electroviscous coefficient of the surface charge density and the particle volume fraction. By realistic salt-free colloidal suspensions we mean aqueous suspensions which have been deionized as far as possible without any electrolyte added during the preparation, in which the only ions present can be (i) the so-called added counterions, coming from the ionization of surface groups and thus counterbalancing the surface charge, (ii) the H + and OH − ions from water dissociation, and (iii) the ions produced by the atmospheric CO 2 contamination. Our model is elaborated in the framework of a classical mean-field theory, using the spherical cell model approach and the appropriate local equilibrium reactions. It is valid for arbitrary surface charge density and particle concentrations. We have also made a new interpretation of the electroviscous coefficient: the electroviscous coefficient p of the suspension is the ratio between the electrohydrodynamic and the pure hydrodynamic contributions to the specific viscosity of the suspension. The numerical results show that it is necessary to consider the water dissociation influence for volume fractions lower than approximately 10 −3, whereas the atmospheric contamination, if the suspensions are open to the atmosphere, is important in the region of volume fractions ϕ < 0.03.

Diffusion and conduction in a salt-free colloidal suspension via molecular dynamics simulations

Molecular dynamics (MD) simulations are used to determine the diffusion coefficients, electrophoretic mobilities and electrical conductivity of a charged colloidal suspension in the salt-free regime as a function of the colloid charge. The behavior of the colloidal particles' diffusion constant can be well understood in terms of two coupled effects: counterion 'condensation' and slowdown due to the relaxation effect. We find that the conductivity exhibits a maximum which approximately separates the regimes of counterion-dominated and colloid-dominated conduction. We analyze the electrophoretic mobilities and the conductivity in terms of commonly employed assumptions about the role of "free" and "condensed" counterions, and discuss different interpretations of this approach.