INTRODUCTION
The term ”electrokinetics” means the combined effects of motion and electrical phenomena. However, the term ”electrokinetic properties” carry a wider connotation including zeta potential (zp), the structure of electrical double layer (EDL), surface potential, and isoelectric point (iep) phenomena. The electrokinetic properties of a substance, inorganic or organic, are used to explain the mechanism of dispersion and agglomeration in a liquid phase and to identify the adsorption mechanisms of ions or molecules at a solid-liquid interface. Therefore they play an important role in a spectrum of applications including ceramics, food, mining, paper, medicine, water and wastewater treatment, emulsions, biochemistry, and detergents. In this paper, the type and significance of electrokinetic properties of mineral nanoparticles, the mechanism of particle-particle interactions in liquid systems, and the applications of electrokinetic phenomena are presented.
DESCRIPTION OF ELECTROKINETIC PROPERTIES OF MINERAL PARTICLES
Origin of Surface Charge
Each mineral particle in a liquid whether colloidal (< 1 mm) or nanoparticle (<100 nm) carries electrokinetic charges depending on the properties of liquid phase such as pH and ionic strength.[1-3] The surface charge of minerals can originate as a result of a number of mechanisms discussed below.
Dissociation of surface groups
In most solid minerals, dissociable functional surface groups such as carboxyl (-COOH) and hydroxyl (-OH) are present. These groups may be ionizable depending on the solution pH; a surface is charged either negatively at high pHs or positively at low pHs.
For metal oxides and hydroxides: (see Eq. (1) below), where M represents a metal cation at the surface.
For coal representing a typical hydrophobic mineral-where R represents a hydrocarbon compound constituting the coal structure (see Eq. (2) below).
Consequently, for simple metal oxides and hydroxides, e.g., SiO2, Al2O3, Fe2O3, and AlOOH, complex metal oxides including clay minerals[4-6] and some hydrophobic minerals, e.g., coal,[7] H+, and OH" ions are considered as the potential determining ions (pdis) (see ”Potential Determining, Indifferent, and Specifically Adsorbed Ions” section).
Preferential dissolution of lattice ions
This type of charging mechanism is generally developed in aqueous solutions with some soluble ionic solids, viz., AgI, CaCO3, BaSO4, and CaF2 as a result of the preferential release of certain constituent lattice ions from the solid into liquid phase as a result of hydration and lattice energies.[8] The concentrations of these ions at equilibrium state are dictated by the solubility product of the solid.[9] For AgI particles, for instance, the amount of Ag+ ions released into water from the particle surface at 25 °C is more than that of I" ions. Therefore the surface of AgI particle remains negatively charged. Thus the constituent lattice ions for these minerals are considered as the pdis.
Preferential adsorption of ions from solution
This mechanism is most commonly observed and results from the differences in the affinity of two phases for some ions. Some specific ions (see ”Potential Determining, Indifferent, and Specifically Adsorbed Ions” section) can strongly adsorb on a solid surface and charge the particle, or, vice versa, a charged particle can become noncharged through such adsorption, e.g., adsorption of H+ and OH" on oxide minerals (Eqs. 3 and 4 in the case of SiO2), Ag+ and I" adsorption on silver iodide particles, and Al3+ and HDTMA+ (hexadecyltrimethylammonium) adsorption on clinoptilolite.[10] It should be noted that especially for H+ and OH" ions, it is difficult to distinguish whether the charging of a particle is generated from the adsorption or dissociation of these ions. (see below).[2]
Isomorphic substitutions
Almost all clay and zeolite minerals that are generally characterized as aluminum silicates exhibit negative charges in water, which results from the substitutions within the crystal lattice of Al3+ for Si4+ or Mg2+ for Al3+.[11-14] Consequently, negative charges are developed in the lattice to compensate the so-called exchangeable cations, i.e., Na+, K+, and Ca2+ entering the crystal structure. When such minerals come in contact with water, some of these cations can easily dissociate, leading to negatively charged surfaces.
Accumulation and transfer of electrons
Besides ion transfer, as explained above, electron transfer is also possible between solid and liquid phases depending on differences in the electron affinities of the two phases. Also, some molecules of dipole character may be oriented at the solid-liquid interface leading to charged surfaces;[2,3] this is mostly observed at the metal-solution interface.
Electrical Double Layer and Double-Layer Models
When a mineral particle is immersed in a liquid, a surface charge will be developed through one of the mechanisms discussed above. Let us imagine a negatively charged solid particle in an electrolyte solution; while the oppositely charged counterions will congregate in the vicinity of the particle, coions having the same sign with that of the particle will be repelled from the surface as a result of electrostatic interactions. Thus a charged surface layer (layer 1) and an ionic layer (layer 2) all the way to the bulk water constitute the electrical double layer with a thickness usually ranging from a few angstroms to a few hundred angstroms. To examine the structure of EDL, different models have been proposed.[3,15] These models are introduced below.
Helmholtz compact layer model
The earliest model of the EDL, in which a rigid layer away from the surface in solution consists of oppositely charged ions, was proposed in 1879 by Helmholtz.[16] Also, the surface charge of particle is equal to that of rigid layer. Because this model ignores the disrupting effect of thermal agitation, it is unreasonable. This model is known as a molecular condenser model owing to its similarity to a parallel plate condenser.[1] Using the law of distribution of EDL, the potential C (V) across the double layer for this capacitor is
where s is the charge density per unit area of a plate (C/m2), e (dimensionless) is the dielectric constant of the medium, and e0 is the permittivity of free space (8.854 x 10"12 C2/J m).
Gouy-Chapman diffuse double-layer model
This is independently known as the Gouy-Chapman model. They expressed that, in addition to the electrostatic attraction of counterions to the charged surface, some of them tend to diffuse toward the bulk solution because of
their thermal motion. Note that the EDL theory can be developed for different solid geometries such as flat plate, sphere, and cylinder. Because most studies for organic and inorganic solids in liquids assume the flat plate geome-try,[17,18] here we also consider the flat plate to simplify the structure of EDL. The theory of Gouy-Chapman is based on the two fundamental equations: Poisson and Boltzmann.[16] The Poisson equation (Eq. 6) for a flat surface given below is related to the potential distribution of an electric charge relative to the distance from the surface in a medium.
where C(x) is the double-layer potential (V) at a point located a distance x from the surface, p(x) is the charge density per unit volume (C/m3) at the same point. The Boltzmann equation is given by
where nt is the number of ions of type i per unit volume near the surface or in diffuse layer, n0 is the number of ions of type i per unit volume in the bulk solution, zi is the valence number of i including its sign, e is the electronic charge (1.602 x 10"19 C), k is the Boltzmann constant (1.381 x 10"23 J/K), and T is the absolute temperature (K). The term zieip signifies the electrostatic (or coulombic) work required to bring the ion, i, from the bulk of the solution (where x n and C0=0) to a position where the potential is C.
The volume charge density near the surface is
Substituting Eq. 8 into Eq. 6 yields the Poisson-Boltz-mann equation (Eq. 9).
Eq. 9 shows a nonlinear differential equation without an explicit general solution but can be analytically solved by the Debye-Huckel approximation provided that zieC < kT, i.e., the potential (C)< 25.7/z, mV throughout the EDL. Thus Eq. 9 is converted to the following form[16]
where k is known as the Debye-Huckel parameter with a unit of reciprocal length (m" 1) and given by where I is the ionic strength (I =V2 ^cizi2) of the solution and ci is the concentration of an ion, i in mol/L, and zi is the valence number of i. Note that the inverse of k, 1/k, is a very important term in the stability of colloidal particles and is called as ”the electrical double-layer thickness.” When the distance from surface reaches the value of 1/k, the double-layer (DL) potential (C) equals C0/e (e=2.7182). Eq. 12 clearly shows that the double-layer thickness is basically dependent on the ion concentration and the valency of the ion. An increase in both parameters results in a decrease in double-layer thickness and potential as shown in Fig. 1.
Fig. 1 Variation of electrical double-layer thickness with electrolyte concentration.
For surface potentials (C0) < 25 mV, the solution of Eq. 10 yields[3]
where x is the distance from surface and k is the Debye-Huckel parameter. For high surface potentials, i.e., z,eC > kT, the exact solution of Eq. 9 is required. The solution given by Gouy (1910) and Chapman (1913), for the case of a symmetrical electrolyte (z, + = — z,— = z, such as
NaCl, CaSO4; and n0+= n°_ = n0) and some mathematical manipulations, becomes [16]
where g=tanh(zeC/4kT) and g0=tanh(zeCo/4kT).
Evidently, although Eq. 14 is relatively more complex than Eq. 13, it has wider applicability. The surface charge density (s0) of a particle in a liquid is given elsewhere.[3]
Stern-Grahame model
The Gouy-Chapman model of EDL includes some unrealistic cases. For example, the ions are assumed as point charges and any specific effects related to the ion size are neglected. Therefore the adsorption densities on the solid surface calculated for moderate surface potentials and ionic strength values are so high that they are physically impossible. Also, the solvent is assumed to have continuous properties everywhere in solution; however, its properties such as the dielectric constant and the viscosity may be different in the EDL and the bulk solution.
Fig. 2 The Stern-Grahame model represented by (a) by low concentration of specifically adsorbed ions and (b) by higher concentration of the specifically adsorbed ions.
Fig. 2
Stern (1924)[19] modified the Gouy-Chapman model with an adsorbed layer of ions of thickness d, which is usually considered as 0.3-0.5 nm. This layer, assumed to be held fixed at the surface, is called the Stern layer. Thus the ion distribution in solution around the charged particle is divided into two parts: the Stern layer, which is the identical form in the Helmholtz model and consists of specifically adsorbed ions, and the diffuse (or Gouy) layer. The double layer in Fig. 2 essentially shows three layers, i.e., the layer of charged solid surface, the Stern layer, and the diffuse layer, but in the literature the commonly used term is ”double layer.” Also, there is a shear plane in the diffuse layer at which the double layer potential (C) is called the zeta (X) potential.
Grahame[19] further divided the Stern layer into two parts: inner Helmholtz plane (IHP) and outer Helmholtz plane (OHP) (Fig. 2a,b). At the b plane, there are specifically adsorbed unhydrated ions known as the IHP, while that of the closest approach to the more weakly adsorbed hydrated ions at d is known as the OHP, the onset of the diffuse layer. This model, known as the Stern-Grahame model, is usually represented with low amounts of specifically adsorbed ions (Fig. 2a) while the modified version (Fig. 2b) incorporates the specifically adsorbed ions. In the former, the sign of particle surface cannot be reversed, but it is possible in the latter. The potential distribution in the diffuse layer for a symmetrical electrolyte (Eq. 14) can be rewritten as;
Note that, in the case of electrolyte concentrations less than 0.1 M, the zeta (X) potential can be used instead of Cd. The composition of the double layer is usually inferred from a comparison between s0 and sd or C0 and Cd, then computed by some model. The following equation has a reasonably wide applicability if the amount of specifically adsorbed ions is low.
where 0=sb/s0 (0 <0 < 1), sb and s0 are charge densities at the IHP and at the surface (in C/cm2), and F stands for the specific adsorption free energy in units of kT and Cb is the potential at the IHP, ci is the bulk concentration of ion i (mol/L). Eq. 16 is an extension of the familiar Langmuir equation.[2]
