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Caveats – don’t give Kd more power than it deserves • Kp and Kd are partitioning and distribution coefficients that vary with soil properties, solution concentration, sorption sites, etc • Kd or KD is a property not just of the chemical but of the particular soil • Don’t extrapolate beyond experimental values – Kd should be determined using soil or sorbent material from the site • Most Kd values were determined on standard ‘reagent grade’ materials or soil separates, not on soil in situ
Equilibrium-Based Adsorption Models Freundlich eqn: q = KdC1/n log q = log Kd + 1/n log C where, q = moles of sorbate per mass of sorbent C = equilibrium sorptive concentration Kd = distribution coefficient (y-intercept) 1/n = curve-fitting factor (slope) when n = 1, q = KdC and Kd = Kp y = b + mx
Freundlich Model • Empirical (obs’n based, not theory) • No maximum adsorption predicted • Assumes sorption is independent of surface coverage and that surface is homogeneous • Good model to use at low concentrations • Log-log plots give you a straight line (and ‘hide’ a lot of erratic data) • Cannot be used to prove sorption mechanisms or complexation at soil surface
Freundlich eqn, normal and linearlized http://www.mtas.es/insht/images/legislacion/etiAVc2_19.jpg
Langmuir Eqn q = kCb / (1 + kC) or C/q = 1/kb +C/b where q = moles of sorbate per mass of sorbent C = equilibrium sorptive concentration k is a constant related to binding strength b is the maximum amount of adsorptive that can be adsorbed 1/b is the slope 1/kb is the y-intercept
Langmuir model assumptions • The surface of the adsorbent is uniform, that is, all the adsorption sites are equal. • Adsorbed molecules do not interact with each other. • All adsorption occurs through the same mechanism. • At the maximum adsorption, only a monolayer is formed: molecules of adsorbate do not deposit on other, already adsorbed, molecules of adsorbate, only on the free surface of the adsorbent.
Uranium sorption isotherms experimental data and model regression(—) Langmuir model; (---) Freundlich model pH 2.5 pH 3.2 pH 4 http://biosorption.mcgill.ca/publication/jy4spain/Image2.gif
Double-Layer Theory The "double layer" refers to a charged surface and a diffuse "layer", cloud, or distribution of countercharged ions surrounding the surface http://www.silver-colloids.com/Tutorials/Intro/pcs17.html http://microfluidics.stanford.edu/edl.gif
Gouy-Chapman Model • all ions behave as point charges • electrostatic attraction dominates behavior • considers only electrostatic interactions (outer-sphere) • counterions concentrate near the charged surface and decrease exponentially with distance from the surface until anions = cations in bulk solution • double-layer thickness is inversely proportional to (ion concentration) x (valence) of the electrolyte in solution • double-layer thickness is directly proportional to the dielectric constant • use model to predict the effect of electrolyte valence on colloidal stability (i.e. whether your soil is flocculated or dispersed)
Flocculation and Dispersal of soil • mainly determined by the valence of the electrolyte ion: Flocculating power: Al+3 > Ca+2 > Mg+2 > Na+ • Concentration of solution is also important: Higher concentrations are required for monovalent ions than di- or trivalent ions: 25 - 150 mM for NaCl 0.5 - 2.0 mM for CaCl2 0.01 - 0.1 mM for AlCl3
Flocculating power is related to ion radius or charge density - (smaller ionic radii have larger charge density and are more tightly held on charged surfaces): Cs+ > Rb+ > NH4+ > K+ > Na+ > Li+
Stern Theory • considers both inner- and outer-sphere complexes. • Modified Gouy-Chapman model with addition of the "Stern Layer“: • An "uncharged" zone near the solid surface where inner-sphere complexation presumably occurs (thus neutralizing some of the surface charge) • Any remaining surface charge is balanced by the diffuse or Gouy Layer of counterions