.. _example-phreeqc-manual-08:

08 - Surface Complexation
=========================

Zinc sorbing onto hydrous ferric oxide, as a function of pH, computed twice
at concentrations a thousand-fold apart.

Running it twice is what makes the example. Sorption onto a surface with more
than one kind of site behaves differently depending on how much metal there
is to sorb, and the two figures show that directly.


Strong sites and weak sites
---------------------------

.. raw:: html
   :file: study_08 - Surface Complexation.html

The surface is the Dzombak and Morel hydrous ferric oxide model, which has
two site types:

* a small number of **strong** sites, which bind tightly;
* many more **weak** sites, which bind less tightly.

That is not a fitting convenience. A real oxide surface has a range of
binding environments -- edges, defects, faces -- and two site types is the
smallest model that captures the consequence, which is that the *average*
binding strength depends on how much of the surface is occupied.


The results
-----------

.. figure:: TotalZn=1e_minus_7.svg
   :alt: Zinc on strong sites, weak sites and in solution against pH, at total Zn of 1e-7
   :align: center

   Total zinc 10⁻⁷ mol/kgw. There is far less zinc than there are strong
   sites, so essentially all of it goes to the strong sites and the weak
   sites are irrelevant. Sorption is strong and begins at low pH.

.. figure:: TotalZn=1e_minus_4.svg
   :alt: The same at total Zn of 1e-4, where the strong sites saturate and the weak sites take over
   :align: center

   Total zinc 10⁻⁴ mol/kgw, a thousand times more. The strong sites fill and
   then stop -- their curve flattens, because there are no more of them --
   and the remaining zinc goes to the **weak** sites. The edge moves to
   higher pH, because weaker sites need more favourable conditions to hold
   the metal.

   This is why a distribution coefficient measured at one concentration
   cannot be used at another. The ratio of sorbed to dissolved is not a
   constant of the system; it depends on loading, and the dependence is not
   small.

The ``Charge Balance`` curve on both figures is the surface charge. It is
worth watching alongside the sorption: the surface becomes more negative as
pH rises, which is part of why the metal sorbs more at high pH, and the
sorbed metal in turn changes the charge.


What it shows
-------------

That surface complexation is chemistry, not a partition coefficient, and that
it predicts the concentration dependence a coefficient has to be re-measured
for.

:ref:`example-phreeqc-manual-19` compares this kind of model directly with
the empirical isotherms it replaces.


Source
------

* Parkhurst, D. L. and Appelo, C. A. J. (2013). *Description of input and
  examples for PHREEQC version 3.* U.S. Geological Survey Techniques and
  Methods, book 6, chapter A43. This is Example 8 of that manual.
* Dzombak, D. A. and Morel, F. M. M. (1990). *Surface Complexation Modeling:
  Hydrous Ferric Oxide.* Wiley, New York. The two-site model, its site
  densities and its constants are theirs.