Mineral SurfacesMinerals which are precipitated can also interact with other molecules and ions at the surfaceAttraction between a particular mineral surface and an ion or molecule due to:Electrostatic interaction (unlike charges attract)Hydrophobic/hydrophilic interactionsSpecific bonding reactions at the surface

Charged SurfacesMineral 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+H+OHOHOHOHH+OH2OHOH

GOUY-CHAPMAN DOUBLE-LAYERMODELSTERN-GRAHAME TRIPLE-LAYERMODEL

Surface reaction vs. transport control vs. diffusion control3 possibilities for controlling overall rate of mineral dissolution:Surface reaction chemical process at the mineral surface with a reactantDiffusion control physical process of dissolved component(s) diffusing into the bulk solutionTransport control physical process of dissolved component(s) being advectively carried from the mineral surface

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-1Many 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 RatesDiffusion, 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.

Mineral diffusion ratesFor diffusion controlled rates:Rd=DrA(Cs-C)/rWhere 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 crystalsDiffusion rates are generally the slowest rate that controls overall dissolution

Transport controlled ratesFor systems where water is flowing:

Where R is the surface-controlled rate of dissolution (R=k+[Cs-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

Zero-order mineral dissolution kineticsMost 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

Rate and equilibriumpH 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 < 0.05, simplifies toR=k+[H+]n

Ligand-assisted dissolutionThought 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)

Mineral precipitation kineticsHow do minerals form?

Ion-ion interaction cluster aggregation nanocrystal formation crystal growth (ionic aggregation, ostwald ripening, topotactic alignment)

What controls the overall rate?

Nuclei formationClassical view of precipitation start with the formation of a critical nuclei, which requires a large degree of supersaturationEnergy to form a nuclei: DGj=DGbulk-DGsurfRate 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

Nucleation rateWhere B is a shape factor equal to 16/3 for a sphere and 32 for a cube, is the interfacial free energy, 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/(^5/3) )

* This slide compares two different models of a mineral surface in contact with aqueous solutions. The Gouy-Chapman double-layer model is essentially the model we considered in slide 12. The Stern-Grahame triple-layer model applies to situations where the surface potential is so strong (owing to high surface charge) that, in addition to the diffuse ion layer, a compact layer of cations exists immediately adjacent to the mineral surface. The ions in this compact layer are held tightly by electrostatic forces and are not free to move like the ions in the diffuse layer.