5: Surface Charge of Colloidal Particles

the process in which cations in pure solids are replaced by atoms with lower valence; the number of substituting species is small, resulting in an unchanged crystalline structure but a fixed, permanent negative charge

isomorphic substitution happens at the time of particle formation and growth and cannot be changed by the external medium of the soil

the preferred quantity on fundamental grounds is the fixed or permanent surface charge density $\sigma_f$ (C/m^2); since the surface area is difficult to determine, the practical quantity is the fixed or permanent specific particle charge $\vartheta_f$ (C/kg), usually also expressed as mole of charge (equivalent) per unit of mass (mol/kg)

the net charge of surface groups of a soil particle resulting from the medium pH; charge density given by $\sigma_H=F(\Gamma_H-\Gamma_O)$ where $\Gamma_H$ and $\Gamma_O$ are the surface concentrations of positively and negatively charged sites (protonated and ionized groups), respectively; net proton particle charge is $q_H=A_p \sigma_H$, where $A_p$ is the particle area; net proton-specific charge is $\vartheta_H=z_{\text{H}^+}Q_H+z_{\text{OH}^-}Q_O$ where $Q_H$ and $Q_O$ are the specific amounts of positively and negatively charged groups, the corresponding z being their charges, +1 and -1 respectively

the sum of fixed and protonic charges: $\sigma_{in}=\sigma_f+\sigma_H$ and similarly for $q_{in}$ and $\vartheta_{in}$

the charge added to the soil particle due to inner and outer sphere bound ions; denoted as inner/outer sphere particle charge, charge density and specific charge: $q_I$, $\sigma_I$, $\vartheta_I$ or $q_O$, $\sigma_O$, $\vartheta_O$ respectively

the sum of intrinsic and inner and outer sphere particle charges: $\sigma_p=\sigma_{in}+\sigma_I+\sigma_O$, similarly for $q_{p}$ and $\vartheta_{p}$

$\sigma_d$

the sum of total adsorbed cation surface charge and total adsorbed anion surface charge: $\sigma_{ad}=\sigma_+-\sigma_-=\sigma_I+\sigma_O+\sigma_d$

the sum of particle charge and diffuse layer charge, or the intrinsic charge and net adsorbed ion charge, which is set to zero due to electrostatic equilibrium: $\sigma_p+\sigma_d \equiv \sigma_f+\sigma_H+\sigma_I+\sigma_O+\sigma_d \equiv \sigma_{in}+\sigma_{ad}=0$

some phyllosilicates, such as micas or smectites

most soil colloids develop protonic charge (i.e., show a pH-dependent intrinsic charge), but this contribution is more important for oxides and organic matter than for clay minerals

constant charge soils and variable charge soils; evidently both types contain components with both fixed and variable charges, so there is no clear distinction between them

found mainly in temperate regions, this soil is dominated by clay minerals having an important amount of permanent charge (approximately constant charge in certain pH range, usually low pHs)

found mainly in tropical or subtropical regions, this soil is dominated by oxides and organic matter or clay minerals with low fixed charge such as kaolinite

specific adsorption, being a chemical reaction, can cause a reversal of the surface charge sign, whereas nonspecific adsorption, being essentially driven by electrostatic forces, cannot overturn the intrinsic charge

the proton, because the surface potential value arises from the acid-base reactions

the replacement of sorbed ions by others with charge of the same sign

$S^- \text{Na}^++ \text{K}^+(aq) \rightleftharpoons S^- \text{K}^++\text{Na}^+(aq)$
$S^+\text{Cl}^-+\text{NO}^-_3(aq) \rightleftharpoons S^+ \text{NO}^-_3+ \text{Cl}^-(aq)$
where $S^-$ and $S^+$ represent exchanger phases

a positively or negatively charged site at the solid particle

the maximum amount of monovalent ions (i.e., equivalents of charge) of a given sign that can be retained

(mol/kg) moles of charge (equivalents) per unit of exchanger mass

$\vartheta_{CE}$ or CEC (mol/kg)

$\vartheta_{AE}$ or AEC (mol/kg)

1. saturate the soil colloid (or a whole soil sample) with a salt of a given ion (the index ion, typically Ba2+)
2. treat the sample with MgSO4
3. BaSO4 precipitates and forces the exchange of Ba2+ with Mg2+
4. the amount of Mg2+ consumed in the process gives $\vartheta_{CE}$

$K_{ex}= \frac{ \left( a^W_A \right) ^v \left( a^S_B \right) ^u}{ \left( a^S_A \right) ^v \left( a^W_B \right) ^u}$
the superscripts W and S refer to the solution (water) and solid (exchanger) phases, respectively
$vS_uA+uB^{\text{v}+} \rightleftharpoons uS_vB+vA^{\text{u}+}$
where $A^{\text{u}+}$ and $B^{\text{v}+}$ are cations, S represents sites with single negative charge, u and v are the stoichiometric coefficients resulting from electroneutrality

$a_i=\frac{m_i \gamma^m_i}{m^0}$
where $m_i$ is the solute molality, $\gamma^m_i$ is the solute activity coefficient in molality scale, $m^0$ is the standard molality, where the standard molality is usually 1 mol/kg

$a^S_i=x_i \gamma^R_i$
where $x_i$ is the mole fraction and $\gamma^R_i$ is the Raoult activity coefficient

a conditional constant used in lieu of the thermodynamic exchange equilibrium constant, in effect bypassing the inability to calculate activity coefficients for the exchanger phase predictively

$y_i=\frac{z_in_i}{\sum_jz_jn_j}=\frac{z_ic_i}{\sum_jz_jc_j}=\frac{z_ix_i}{\sum_jz_jx_j}$
where the sum is carried by all ions of the same sign as ion i; note that this is the fraction of the total charge (either positive or negative) carried by ions of species i; also note that for a solution composed of all univalent ions, $y_i=x_i$

exchange between ions of different charge, e.g., Na+ with Ca2+

saturation of a sample with a single ion, either by repeatedly placing the sample in contact with fresh solutions of the ion of interest or by column leaching with an appropriate solution of such ion

the (equivalent) fraction of a given cation in the exchanger phase is plotted as a function of the corresponding (mole) fraction of the same or another cation in the solution phase

a plot in the exchange isotherm obtained assuming that:
$K_{ex}=1$
$\gamma^R_i/\gamma^R_{i+1}=1$ and $\gamma^m_i/\gamma^m_{i+1}=1$;
ions plotting over this have preference over ions plotting below

the process by which water, from either rain or irrigation, pouring through into deeper soil levels, carries unbound solutes, making them unavailable to plants

technically any bound ion is subject to exchange; however, inner sphere bound ions are assumed not to exchange whereas the diffuse layer and outer sphere will

hydration
polarization
Lewis acidity
ion pair formation
counterion adsorption

for two ions with the same valence, the cation with the smaller hydrated radius, or least negative heat of hydration, is preferred (e.g., K+ over Na+)

given two cations with different valence (e.g., Na+ and Ca2+), the cation with the higher valence (Ca2+) is preferred because of its greater polarization capability. For the case of anions, the opposite is true, larger anions show greater polarizability than smaller anions. Thus, larger anions would be preferred by a positively charged surface

comparing two cations with the same valence but one being a stronger Lewis acid than the other (e.g., Cu2+ vs. Ca2+), the cation with the stronger Lewis acidity would be preferred if the surface behaves as a relatively strong Lewis base. A similar statement can be formulated for anions (Lewis bases) and a positive (Lewis acid) surface

for a given cation in the presence of two different anions, the anion with the highest potential to form neutral ion pairs with the cation controls the cation adsorption potential, assuming that the anions do not react with the surface, and vice versa. For example, Ca2+ in the presence of Cl- exhibits greater adsorption potential than Ca2+ in the presence of SO4 2- because of the latter's greater preference to form neutral CaSO4 pairs

for a metal cation in the presence of two different anions, the anion with the highest potential to form surface complexes controls the metal's adsorption potential. E.g., Ni2+ in the presence of Ca(NO3)2 exhibits greater adsorption potential than Ni2+ in the presence of CaSO4 because of the sulfate's potential to react with the surface and produce sites with higher specificity for Ca2+

different adsorption modes
surface electric potential
pH influence
conformational flexibility
surfaces acidity

a surface capable to form inner sphere complexes with certain cations (e.g., K+ or NH4+) shows stronger preference for these over any other cation (e.g., some layered clay minerals such as vermiculite show strong preference for K+ over Na+ or Ca2+)

a surface that does not have the potential to form inner sphere complexes prefers cations with higher valence. This preference depends on the magnitude of the surface electrical potential--the higher the surface electrical potential, the higher the preference for divalent cation (such as Ca2+) over monovalent cations (e.g., Na+)

surfaces that exhibit pH-dependent electrical potential show variable selectivity for a given cation. For example, kaolinite at high pH (where the surface has a high negative charge and so a high negative surface electrical potential) shows increasing preference for divalent cations over monovalent cations, while at low pH (low negative electrical potential), kaolinite or kaolinitic soils show increasing preference for monovalent cations rather than divalent cations

exchangers having the potential to undergo conformational changes (e.g., humic acids) prefer higher valence cations (such as Ca2+) to lower valence cations (such as K+)

exchangers exhibiting weaker acid behavior (high pK_a) show stronger preference for heavy metals than for hard metals in comparison to surfaces with stronger acid behavior (low pK_a)

the movement of charged particles under an electric field

electric field
viscous force
electric force
velocity

often, it is assumed that the shear plane is coincident with, or near to, the OHP, i.e., inside the diffuse layer

the pH at which colloidal particles do not move under an electric field