Environmental Engineering Reference
In-Depth Information
understand how the different metal ion species in a solution behave but also to quantify them. Thus, the theory of metal binding
in colloidal systems and the available instrumental techniques capable of quantifying the speciation will be reviewed.
32.2.2.1 Understanding Trace Metal Ion Speciation in Colloidal Dispersions
Understanding dynamic speciation requires
not only the knowledge of metal-binding equilibrium parameters but also the diffusion and/or kinetic fluxes of the various metal
species in a solution, both depending on the timescale considered. lability is a concept used to define the input of metal species
into an overall flux toward a consuming interface constructed upon the magnitudes of the diffusive mass transport and metal
complex dissociation fluxes [31]. Two limiting cases apply: (1) complex species do not have the time to dissociate/associate in
the diffusion layer and will not contribute to the total flux (static system, inert complexes); and (2) the rates of metal complex
association/dissociation are high enough so that the kinetic flux arising from the dissociation of the complex in the diffusion
layer is greater than the diffusion-limited flux (dynamic system). For a static system, only the free metal contributes to the
overall flux, while for a dynamic system, two situations are possible: (1) the kinetic flux is much larger than the diffusive one
so that the free metal ion will be in equilibrium with its complex forms all along the diffusion layer, and all the metal present
will contribute (labile complexes); and (2) the kinetic and diffusive fluxes are of the same order of magnitude, thus the free
metal and part of the bound metal will contribute to the overall flux (nonlabile complexes).
Besides the kinetic rate parameter, the
D
of the complex species in the diffusion layer also affects the flux in dynamic
systems. The presence of NMs or macromolecular ligands such as humic matter slows down the flux of dynamic metal ions due
to lower
D
of those ligands, resulting in a significant impact on the metal availability toward the consuming interface. For labile
complexes, a mean
D
, taking into account all the diffusing species, should be considered [32].
These are the essential features of dynamic trace metal speciation, and understanding them is important in order to under-
stand why the biouptake equilibrium models (like the free ion activity model (FIAM) [33] and the biotic ligand model (BlM)
[34]) might fail to describe the metal toxicity [35]. Nevertheless, we will focus mostly on the equilibrium situation for the sake
of simplicity. More information on the dynamic aspects of trace metal speciation can be found by Mota et al. [36].
The equilibrium-binding modeling in charged colloidal systems needs to consider two contributions: (1) the electrostatic
binding due to the charges and (2) the chemical intrinsic binding due to the specific interactions between the metal ions and the
binding groups in the colloidal particle. The electrostatic contribution is usually described using a Boltzmann equation or more
commonly in colloidal or biocolloidal systems using Donnan potentials [37]. For example, Donnan potentials have been used to
model the binding of metal ions to the cell walls of bacteria [38] and metal ion interaction with different types of biomass in bio-
sorption studies [39]. For colloidal and/or particulate systems, it is common that more than one chemical ligand is present in the
system (chemical heterogeneity). In this case, a discrete-site model with a large number of binding sites (e.g., Windermere Humic
Aqueous Model computer code (WHAMC) [40] or a continuous model described by a continuous probability distribution of binding
energies such as the nonideal competitive adsorption ((NICA)-Donnan [41]) model is better at modeling the metal binding.
32.2.2.2 The Interaction of Metal Ions with the Stabilizing Soft Shell Layer
The charged polymer layer that stabi-
lizes the NM is effectively a soft shell that possesses a different physicochemical environment compared to the bulk,
namely, an overall negative potential. Depending on the polymer's nature and cross-linking, this layer can behave more
like a gel or even a polymer brush; either way, it will react strongly to ionic strength changes by shrinking or swelling.
Cations can be bound by this layer by electrostatic interactions or even covalent binding, depending on the nature of the
charged group and the metal in question. The ratio between bound and total metal in the stabilizing layer and bulk phase
will depend on the respective layer and matrix composition, especially the amount of metal-binding ligands present.
Nonetheless, the free metal ion concentration will be larger in the soft shell layer than in the bulk. This effect is well
known in gels where the enrichment in free metal ion concentration in the gel regarding the bulk solution is given by a
Boltzmann equation of the following type:
(
)
M
z
+
zF
RT
gel
=
exp
−
ψ
(32.1)
(
)
D
z
+
M
sol
where M
z
+
is a metal ion with charge
z
,
ψ
D
is the Donnan potential resulting from the fixed charged groups in the gel phase,
F
is
the Faraday constant,
R
is the gas constant, and
T
is the absolute temperature. Since the potential in the gel is directly related
with the ionic strength in the solution, this effect is correspondingly larger for lower ionic strengths and negligible at high ionic
strengths. Due to the ion charge dependence, this effect is significantly larger for divalent and trivalent ions than for monovalent
ones. As an example, Davis et al. [42] reported an increase of free cadmium of 3.2× and 5.8× in 0.2 and 0.5% acrylamide gels
