normalization of binding site constants in PhreeqC at different site densities

[SlippinJimmy]

I am having trouble reconciling the Sverjensky-Kulik normalization procedure (e.g. http://bit.ly/2cRmtQi) for surface protonation reactions as it is applicable to forward modelling in PhreeqC and I'm hoping someone might be able to clarify this for me...

For a monodentate surface complexation reaction, between say a metal cation and a surface binding site, it is straightforward to demonstrate that altering the site density necessitates adjustment of the Kint binding constant to obtain the same Rd value for a given mass and surface area of sorbent in a forward calculation (Since Kint values are always calibrated against an assumed, or measured site density when fitting to macroscopic sorption data).

Applying the corresponding correction to surface site protolysis constants (pKa's), however, implies an altered delta_pKa (although unaltered pHpzc) for the surface site which gives completely different surface charging characteristics in PhreeqC. This makes it impossible to match up the sorption edge with the original data when using normalized reaction constants for a different assumed reference site density. The only way to obtain a match with the original sorption edge seems to be to normalize the metal binding reactions and leave the protolysis constants as they are irrespective of binding site density used in the calculation (see attached pdf files for a simplified example involving trace Ni(II) sorption and a single site NEM. I use an NEM here because electrostatics makes the surface charging curve more difficult to interpret).

I'm not sure whether this is because PhreeqC uses mole fractions for surface species (other codes seem to use molarities or molalities), or whether I have misunderstood something fundamental with the theory underpinning normalization. Sverjensky and Sahai's paper (1996) and Sverjenksy's (2003) paper on standard states, (http://dx.doi.org/10.1016/0016-7037(96)00207-4 & http://dx.doi.org/10.1016/S0016-7037(02)01074-8) indicate pretty clearly that there is no universally valid delta_pKa that can be given without invoking a reference site density, thus my confusion here.

[dlparkhurst]

I don't think I can help you very much. Seems like it is not so much a question of how PHREEQC does calculations, as how to normalize empirical data. I am not familiar with the normalization theory.

Note that activities in the DDL of PHREEQC are equivalent fractions, so they range from 0 to 1.

I do argue that molarity (or molality) is not the correct activity for surface species when considering bidentate or multidentate surface species.

Here is a thought experiment.

2SurfOH + Ba+2 = Surf2O2Ba + 2H+

k = ([Surf2O2Ba][H+]^2)/([SurfOH]^2[Ba+2])*exp(...)

where [] indicates activity. If activity is molarity, consider a surface in equilbrium with 1 L of solution. Now if you add a second liter of the same exact composition, the activities of H+ and Ba+2 do not change, but the molalities of the surface species do change by a factor of 0.5, and the ratio of [Surf2O2Ba]/[SurfOH]^2 changes by a factor 0.5/0.5^2 = 2. So the composition of the surface will need to adjust to a new equilibrium. It does not make sense that the surface should change just because you increased the volume of solution without changing its composition.

By using equivalent fraction, the activities of the surface species do not change under the same thought experiment.

[SlippinJimmy]

Thank-you Dr Parkhurst for your prompt reply. I tend to agree with you that equivalent fractions make more sense mathematically. I may need to get in touch with Kulik or Brendler to sort this out; I just thought that someone here may have encountered this issue before since it seems quite fundamental to the use of literature data for describing surface charging in generic SCMs. Previously, I have skirted around the issue by using exactly the same parameters as in the literature sources for a particular model system.