• 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

OH
OH
OH
2
H +
OH
OH
• Mineral surface has exposed ions that have an unsatisfied bond  in water, they bond to
H
2
O, many of which rearrange and shed a H +
• ≡S- + H
2
O  ≡S—H
2
O  ≡S-
OH + H +
OH
OH
H +

GOUY-CHAPMAN
DOUBLE-LAYER
MODEL
STERN-GRAHAME
TRIPLE-LAYER
MODEL

• 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

• General rate law for minerals: d [ mineral ]
  kA [ reactant ] dt
• 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!

• Diffusion, Fickian:
– First law (steady state):
J
 
D

C
 x
– Second Law (change w/time):

C
 t

D
 2
C
 x
2
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.

• For diffusion controlled rates:
R d
=D r
A(C s
-C)/r
Where R d is the diffusion rate (mass volume -1 time -1 ), D is the diffusion coefficient (cm
2
/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

• For systems where water is flowing: dC

R
 k f
C dt
• Where R is the surface-controlled rate of dissolution (R=k
+
[C s
-C]), kf is the flushing frequency (rate of flow/volume), C s 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

• Most silicate minerals (feldspars, quartz polymorphs, pyroxenes, amphiboles) are observed to follow zero-order kinetics:
R=Ak
+ 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 pH

• pH dependence of silicate mineral dissolution, suggests activated surface complex for dissolution:
R
 k

[ H

] n
[ 1

Q
K eq
] where n is a constant, p is the average stoichiometric coefficient, Q is the activity quotient, and Q/K eq is the saturation index (how far from equilibrium the mineral is)
• Far from equilibrium, Q/K eq
< 0.05, simplifies to
R=k
+
[H + ] n

• 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)

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

• Classical view of precipitation – start with the formation of a ‘critical’ nuclei, which requires a large degree of supersaturation
• Energy to form a nuclei: D
G j
=
D
G bulk
-
D
G surf
• 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

J
   exp


 k
3
T
B

3
(ln
2  2
S )
2


Where B is a shape factor equal to 16 π/3 for a sphere and
32 for a cube,
 is the interfacial free energy, Ω is the molecular volume, k is Boltzmann’s constant (1.38x10
-23
J/K), T is temperature (K), S is the supersaturation ratio
(C/C s
), and Г is a pre-exponential factor (around 10 33 ±3 cm -3 sec -1 and approximated by ( Г = D/(Ω^5/3) )