Mineral Surfaces

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Mineral Surfaces

• Minerals which are precipitated can also interact
  with other molecules and ions at the surface
• Attraction between a particular mineral surface
  and an ion or molecule due to
• Electrostatic interaction (unlike charges
  attract)
• Hydrophobic/hydrophilic interactions
• Specific bonding reactions at the surface

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Charged Surfaces

• Mineral surface has exposed ions that have an
  unsatisfied bond ? in water, they bond to H2O,
  many of which rearrange and shed a H
• S- H2O ? SH2O ? S-OH H

OH
OH
OH2
H
OH
OH
OH
H
OH
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GOUY-CHAPMAN DOUBLE-LAYER MODEL
STERN-GRAHAME TRIPLE-LAYER MODEL
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Surface reaction vs. transport control vs.
diffusion control

• 3 possibilities for controlling overall rate of
  mineral dissolution
• Surface reaction chemical process at the
  mineral surface with a reactant
• Diffusion control physical process of dissolved
  component(s) diffusing into the bulk solution
• Transport control physical process of dissolved
  component(s) being advectively carried from the
  mineral surface

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General mineral dissolution rates (surface
reaction)

• General rate law for minerals
• Where k is in something similar to units of mol-1
  sec-1 to give a rate, R, in terms of mol cm-3
  sec-1
• Many ways to write the rate constant units
  depending on the rate law (which is almost never
  an elementary rxn for minerals), but dissolution
  rate for minerals is normalized to surface area
  as the primary control on overall rates!

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Diffusion Rates

• Diffusion, Fickian
• First law (steady state)
• Second Law (change w/time)
• Where J is the flux (concentration area-1
  time-1), D is the diffusion coefficient (area-1
  time-1), C is concentration and t is time.

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Mineral diffusion rates

• For diffusion controlled rates
• RdDrA(Cs-C)/r
• Where Rd is the diffusion rate (mass volume-1
  time-1), D is the diffusion coefficient
  (cm2/sec), r is porosity, A is the surface area
  of the dissolving crystals per volume solution,
  Cs is the equilibrium concentration of ion in
  question, C is concentration, and r is spherical
  radius of dissolving crystals
• Diffusion rates are generally the slowest rate
  that controls overall dissolution

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Transport controlled rates

• For systems where water is flowing
• Where R is the surface-controlled rate of
  dissolution (RkCs-C), kf is the flushing
  frequency (rate of flow/volume), Cs is the
  saturation concentration, and C is conc.
• SO at high flow rate dissolution is surface
  reaction controlled, at low flow rate it is
  diffusion controlled

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Zero-order mineral dissolution kinetics

• Most silicate minerals (feldspars, quartz
  polymorphs, pyroxenes, amphiboles) are observed
  to follow zero-order kinetics
• RAk
• where A is the surface area and k is the rate
  constant (mol cm-3 sec-1) for rate, R, of an ion
  dissolving from a mineral

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Rate and equilibrium

• pH dependence of silicate mineral dissolution,
  suggests activated surface complex for
  dissolution
• where n is a constant, p is the average
  stoichiometric coefficient, Q is the activity
  quotient, and Q/Keq is the saturation index (how
  far from equilibrium the mineral is)
• Far from equilibrium, Q/Keq lt 0.05, simplifies to
• RkHn

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Ligand-assisted dissolution

• Thought to be minor for many aluminosilicates,
  but key for many other minerals (ex. FeOOH
  minerals)
• Similar to surface-complex control, ligands
  strongly binding with surface groups on the
  mineral surface can greatly increase rate (and
  solubility of the ion in solution, changing the
  SI)

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Mineral precipitation kinetics

• How do minerals form?
• Ion-ion interaction ? cluster aggregation ?
  nanocrystal formation ? crystal growth (ionic
  aggregation, ostwald ripening, topotactic
  alignment)
• What controls the overall rate?

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Nuclei formation

• Classical view of precipitation start with the
  formation of a critical nuclei, which requires
  a large degree of supersaturation
• Energy to form a nuclei DGjDGbulk-DGsurf
• Rate of nuclei formation is then related to the
  energy to form the particle, the size of the
  critical nuclei, collisional efficiency of ions
  involved, the degree of supersaturation, and
  temperature

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Nucleation rate

• Where B is a shape factor equal to 16p/3 for a
  sphere and 32 for a cube, ? is the interfacial
  free energy, O is the molecular volume, k is
  Boltzmanns constant (1.38x10-23 J/K), T is
  temperature (K), S is the supersaturation ratio
  (C/Cs), and ? is a pre-exponential factor (around
  10333 cm-3 sec-1 and approximated by (?
  D/(O5/3) )