i the history how and who cares of surface complexation models ii application of scm s to the mmr
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I. The History, How, and Who Cares of Surface Complexation Models, II. Application of SCM’s to the MMR. GES 166/266 Discussion 5 Feb 2004. Objectives of SCM. To determine the chemical and electrostatic forces involved in ion retention

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i the history how and who cares of surface complexation models ii application of scm s to the mmr

I. The History, How, and Who Cares of Surface Complexation Models, II. Application of SCM’s to the MMR

GES 166/266 Discussion

5 Feb 2004

objectives of scm
Objectives of SCM
  • To determine the chemical and electrostatic forces involved in ion retention
  • To provide a framework that allows such processes to be modeled
  • To improve problem solving
    • Sewage and mining discharges
    • Assessment of radioactive waste repositories
slide3
diffuse layer

Stern layer

surface

development of scm s
Development of SCM’s

1.Used mass law equations to describe reactions at individual surface sites (Kurbatov et al. 1951, Stanton and Maatman 1963, Dugger et al. 1964)

2. Origin and importance of surface charge on oxides (Parks and DeBruyn 1962)

3. Schindler’s group: Constant Capacitance Model and Stumm’s group: Diffuse Layer Model (~1970)

4. Leckie’s group: Triple Layer Model (Davis et al. 1978).

the 2 layer stern and 3 layer models
The 2-layer/Stern and 3-layer models
  • Sorbates considered part of the solid surface (1st layer) -- specific
  • Electrostatic charge balanced by adjacent diffuse layer of ions in solution (2nd layer) – nonspecific
    • Satisfies residual charge
  • Bound water layer added (T-LM) – diffuse layer is farther from solid
  • Surface reactions include H+ exchange, cation binding, and anion binding
    • Need to know surface potentials!
slide6
C1

C2

To get potential, must relate it to charge:

In the Stern layer:

σ = C ψ

σ = charge

C = Capacitance (prop. factor)

ψ = potential

In the diffuse layer:

σB = σD = 2.31 no1/2ψd

σB= charge on outer sphere plane

σD = charge on diffuse plane

no = concentration of counterions

d = distance of interfacial region

σp

distance

the fundamental concepts and assumptions of scm s
The Fundamental Concepts and Assumptions of SCM’s
  • Protons are the dominant potentially determining ions
  • All surfaces have a single site type
  • Each site can undergo two protonation rxns
  • Charges are always expressed as integers
  • Strict distinction between inner- and outer-sphere complexes
reactions responsible for surface charge
Reactions responsible for surface charge

(1) SOH2+ <==> SOHo + H+

Ka1 = [SOHo]{H+} / [SOH2+]

(2) SOHo <==> SO- + H+

Ka2 = [SO-] {H+} / [SOHo]

where {} = mol / Kg, and [] = mol / L

slide9
For a titration…

(CA - [H+]) - (CB - [OH]) =

{(+) surface sites} - {(-) surface sites} = W

where, W is the charge (mol )

C is [ ] of acid or base

Q = charge (mol / Kg) = W / a (amount of sorbent)

σ (C / m2) = Q F / A

where, F is Faraday

A is surface area (m2/kg)

The zero point of charge (ZPC) is: {SO-} = {SOH2+}

k a values must be corrected for electrostatic forces
Ka values must be corrected for electrostatic forces!

Following ∆Gads = ∆Gcoul + ∆Gchem,

Ka = Kintrinsic + (electrostatic)

Ka = Kintrinsic exp (∆ZFψ / RT)

The electrostatic contribution – dependence on potential – that allows SCM’s to describe adsorption as a function of pH

Electrostatic or coulombic correction factor

the actual adsorption rxn becomes
The actual adsorption rxn becomes…

SOHo + Me2+ = SOMe+ + H+

K1c = [SOMe+] {H+} / [SOHo] {Me2+}

K1c = K1int exp (∆ZFψ / RT)

chemical characteristics
Chemical Characteristics
  • Groundwater around sewage plume has highest [DO], pH values of 5.3-5.8, low dissolved salts
  • High NO3- under beds, [DO] decreases with depth
  • Biodegradation of OM and solute transport away from disposal beds
      • decreases [DO] through plume, decreases [NO3-], accumulates dissolved Fe(II) ---- impact pH!
  • Leading edge of Zn contamination = 400 m from source; low Zn until 195 m
assumptions
unsaturated

pond

saturated

Assumptions
  • Simple groundwater flow model
assumptions cont d
Assumptions (cont’d)
  • Mechanical dispersion >>> molecular dispersion
  • Zn adsorption onto sediments is the 1° influence on Zn transport
  • Local equilibrium wrt to adsorption rxns achieved faster than timescale of transport
mass action equations
Mass action equations
  • The one-site SCM

Zn2+ + >SOH = >SOZn+ + H+

sQSOZn = S>SOZnγHCH / CZnS>SOH

  • The two-site SCM

Zn2+ + >SsOH = >SsOZn+ + H+

Zn2+ + >SwOH = >SwOZn+ + H+

sQSOZn = mass action constant

Sx = density of adsorption sites

γH = activity coef of H+

C = conc

what happens when you cut off the source
What happens when you cut off the source?
  • Acidification
  • Transport: head and tail behavior
  • [Zn] in the core

Source: Kent et al. 2000

slide19
4. Used empirical parameters associated with adsorption isotherms
  • Linear isotherms: cs = Kd*c

Cs = concentration in solid phase

Kd = equilibrium distribution coefficient

c = concentration in fluid phase

  • Langmuir or Freundlich isotherms:

Θi = Bai/(1+Bai)

Θi = fraction of adsorption sites occupied by the adsorbate

B = bonding constant

ai = activity of the adsorbate

cs = Kf*cn

Kf = Freundlich adsorption constant

n = Freundlich exponent

slide20
Brusseau and Srivastava (1999) used different Kd values in different geochemical zones to compensate for variable chemistry affecting Li adsorption during transport
  • Kirkner et al. (1985) and Viswanathan et al. (1998) account for variable chemistry by calculating changes in aqueous speciation of adsorbing solutes with changing chemical conditions
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