This article offers a technical overview of common methods used to model heavy metal adsorption onto geologic surfaces.


Metals can enter the environment via many pathways: from natural erosion to anthropogenic release from industry or mining operations. Unlike environmental contaminants such as pesticides or hydrocarbons, metals cannot be degraded or volatilised. The speciation of toxic metals is particularly important when trying to understand their bioavailability and mobility in the environment.

In the September 2012 issue of AWE International, Dr Claire Stone provided an overview of metals in the environment, and defined toxic metals of environmental interest to include arsenic, beryllium, barium, cadmium, chromium, copper, mercury, nickel, lead, selenium, vanadium, and zinc. She rightly pointed out that factors such as pH, soil characteristics (composition) and organic matter influence the complexation of these metals to soils.

Scientists working in the remediation of heavy metals are charged with predicting the ultimate distribution of metals in soils, and because soils and sediments are inherently complex this distribution depends on a large number of variables.

Various environmental interfaces, such as minerals and bacteria, have the ability to adsorb metals and can have a great impact on their cycling. To predict the fate of these metals, scientists develop models to describe how the metal will react in solution and at interfaces under field-relevant conditions.

While it is important to develop a reductionist approach to modelling, it is also important to use enough detail to correctly model the system. This becomes a balancing act to determine what level of detail is required to answer the scientific question at hand, while not over interpreting the available data. Increasing model complexity requires more experimental measurements to determine the reaction parameters used in the model.

Regardless of the modelling approach employed, detailed information about the quantity and reactivity of each component inthe system is necessary to develop models that can predict the fate of metals.

Over the years, many approaches have been developed to model the mobility of metal ions in the environment. These modelling approaches fall into two major categories: empirical and mechanistic models.

Empirical models

Empirical models are often employed to determine the partitioning of metals between solution and environmental interfaces. These models define the fraction of a contaminant metal that is adsorbed to solids versus what remains in solution after the system has equilibrated.

Empirical models are popular because they do not require a detailed understanding of heavy metal complexation or adsorption mechanisms, and as such are less data intensive. Here we discuss three commonly used metal adsorption models: distribution coefficients ( Kd ), Freundlich isotherms ( KF ) and Langmuir isotherms ( KL ).

Distribution coefficient adsorption model The distribution coefficient ( Kd ) approach to modelling metal transport defines the partitioning of a metal between aqueous solution and the bulk geologic solids as a ratio. The adsorption of a metal (M) onto soils or sediments can be expressed by the reaction:

M + EI ↔ EIM      (1)

Where EIM represents the fraction of metal adsorbed onto the environmental interface EI. The distribution coefficient, Kd , is defined as:

Kd = EIM (2) M

The Kd constant is a simple ratio that defines the amount of metal sorbed on solids to the amount of metal remaining in solution. This model is a quick and easy way to describe heavy metal distribution. Kd models, however, do not consider molecular-scale information about binding mechanisms and the Kd constant determined depends on the chemical conditions at which the metal adsorption experiments were conducted.

The Kd model is the most generic because it assumes a linear relationship between the amount of metal adsorbed and remaining in solution, and any change in pH, ionic strength, temperature, metal concentration, or competing adsorbates may render model predictions incorrect. Furthermore, this approach ignores metal saturation of the sorbent at higher metal concentrations, by essentially assuming an infinite number of available surface sites. For this reason Kd models are used only when the metal concentration is low relative to the metal adsorption capacity of the bulk solid sorbent.

Freundlich adsorption model The Freundlich modelling approach expands on the Kd approach by considering decreasing metal adsorption capacity of the solids with increasing saturation of the solids with metal. Using the first equation, the isotherm can be expressed as follows:

KF = EIM (1) Mn

The exponent n is a dimensionless constant with a value between 0 – 1 which, in practise, is normally varied to best fit the experimental data, and KF is the Freundlich constant. When n = 1, the Freundlich isotherm is identical to the Kd linear relationship. When n < 1, the Freundlich model can account for cases where the metal:sorbent ratio is higher; in other words, where saturation of the bulk sorbent (EI) with metal causes the amount of adsorbed species to decrease.

As with Kd models, the approach requires no determination of the total number of metal adsorption sites. The Freundlich model is valid for use for systems with higher concentrations of metals than the Kd approach. As in the Kd approach, the Freundlich adsorption model does not directly consider metal speciation in solution or on the solid sorbent.

Although the Freundlich model may account for factors such as adsorption of monolayers, multilayers or metal precipitation, it is not because the mechanisms of metal behaviour are known a priori .

Langmuir adsorption model The Langmuir modelling approach improves on the Kd and KF approaches because it considers the total number of metal binding sites on the bulk solids. Metal adsorption may be expressed according to the following reaction:

EI, total + M ↔ EIM + EI     (4)

In the above reaction EIM is the amount of metal adsorbed to specific sites, EI is the concentration of surface sites not occupied by metal after the metal M adsorbs, and EI, total is the total concentration of surface sites available for adsorption.

The Langmuir isotherm equation is typically expressed, as with KL, as:

EIM = EI, total KL M (5) 1+KL M The quantification of total surface sites to which the metal can adsorb is a significant improvement from the Kd approach. Since there are a finite number of surface sites, a maximum adsorption can be predicted.

The KL model assumes adsorption sites on the environmental interfaces are homogeneous and equivalent, that the adsorption is nonreversible, that the metal does not interact with other metal atoms bound at adjacent surface sites, and that there is monolayer coverage by the adsorbed metal.

Similar to the Kd and KF approaches, the Langmuir model fits are vulnerable to changes in metal concentration, pH, competing ions, and temperature. Thus all three empirical approaches are difficult to apply in dynamic environmental systems.

Surface complexation modelling

Surface complexation modelling (SCM) is a mechanistic modelling technique, in contrast to the empirical approaches described earlier. This is primarily because the SCM approach considers the binding affinity of individual sorbent-metal reactions at discrete surface sites on the solids in predicting overall metal adsorption behaviour.

SCM also allows for consideration of metal precipitation and dissolution reactions, the electric field around charged mineral to water interfaces, aqueous metal speciation and complexation, and competition of the metal of interest with other dissolved species for adsorption sites on solid surfaces.

Soils and sediments can either be viewed as one bulk, metal adsorbing solid – as with empirical approaches – or be broken into individual components; for example, clays, hydrous ferric oxides (HFO), dissolved metal complexing agents, and biomass. Either way, each solid component considered may have several types of metal adsorbing sites.

The primary advantage of SCM over empirical approaches is that it accounts for changes in pH, ionic strength, and metal speciation, as well as competition of the metal of interest with other metals in solution for adsorption onto the solid surfaces.

In predicting metal fate and transport at contaminated field sites, where chemical conditions or the composition of soils and sediments may change considerably, this flexibility is a considerable advantage.

SCM development The SCM approach uses systems of equations, based on chemical reactions, to predict the equilibrium distribution of metal species between solids and solution.

To develop a model, the following questions must be answered: 1. How many adsorption sites, and of which types, are present on the solid? 2. What is the affinity of protons (H+) for the adsorbing sites, i.e. what is the effect of pH? 3. How much of the contaminant metal is present in the system? 4. What is the affinity of the adsorbing heavy metal for the sites on the solid? 5. What is the speciation of the heavy metal in solution? 6. Under which conditions, if any, will the metal of interest precipitate from solution?

In the process of answering these questions, two constants will be derived for each metal binding surface site. The acidity constant ( Ka ) accounts for system pH – or the H+ binding behaviour onto the site; the second is the metal binding constants ( K1, K2, K3 ). Solubility constants (Ksp) may also be employed in cases where the metal may precipitate from solution to form solids.

To answer the first two questions above, potentiometric titrations of solids are normally performed in the laboratory. These titrations probe the binding behaviour of H+ to a particular solid or mixture of solids across a wide pH range (typically 3 – 10). Approaches for modelling titration data vary, but usually aim at solving for a discrete number of surface site types (often 1 – 4) that allow the proton adsorption behaviour to the solid to be modelled across the experimental pH range. Site constants and concentrations are simultaneously calculated.

Characterisations of the solids, for example by X-ray absorption or infrared spectroscopy, are often employed to further constrain the types and concentrations of the sites.

After the reactivity of a solid to H+ has been modelled and the surface binding sites defined, its ability to complex any number of individual metals can be determined using metal adsorption experiments – addressing questions three and four, to the left.

Metal adsorption is determined experimentally, by mixing together solids with a solution containing a known amount of the metal of interest, and allowing the two to equilibrate. A series of this type of experiment is performed across a wide pH range and/or as a function of metal concentration.

By combining the site acidity constants (Ka) and site concentrations determined in the modelling of the titrations data with these metal adsorption data, the metal binding constant (K1 here) can be solved for in a system of equations. If the metal of interest were, for example, cadmium (Cd2+) adsorbing to a particular site with a -1 charge, in a 1:1 relationship (monodentate binding), the pertinent reactions would be:

Site- + H+ = Site – H0        (6)

Site- + Cd2+ = Site – Cd+        (7)

Site – H0 and Site – Cd+ represent the surface-proton and surface-metal complexes formed after proton or metal adsorption to a specific binding site on the solids. Reactions six and seven are used to express the equilibrium constants Ka and K1 , which are defined as the quotient of the activities – or concentrations, in the case of the surface sites – of the products and the reactants:

Ka = [Site – H0] (8) [Site-]{H+}

K1 = [Site – Cd+] (9) [Site-]{Cd2+}

Herein lies the power of the SCM approach. Equations eight and nine, when solved simultaneously, allow for the prediction of Cd2+ distribution between solution and this site on the solid at any pH – because H+ are competing directly with Cd2+ for adsorption to the same sites at affinities defined by Ka and K1 , respectively.

Figure 2 illustrates generally the sorts of reactions that can be considered in SCM. Other metals can be added to the system of equations. If a field location were simultaneously contaminated with, for example, Cd2+ and lead (Pb2+), a binding constant for Pb2+ could be calculated from metal adsorption experiment data (perhaps K2 here), and the resulting equation could be solved in consort with the Ka and K1 equations. Thus we could predict the distribution of H+, Cd2+, and Pb2+ between solid and solution while all three species compete for adsorption onto the same type of sites.

The speciation of the heavy metal of interest in water, and its potential precipitation to form solid species at certain metal concentrations or pH, is also an important modelling parameter. Fortunately, fairly extensive databases detailing the aqueous speciation or solubility constants of heavy metals are available in scientific literature or as part of commonly used geochemical modelling software. These constants can be included in the system of equations used to solve equilibrium metal speciation in the system.

Comparison of SCM with empirical approaches Figure 3 illustrates a hypothetical case where a positively charged heavy metal is adsorbed to a bulk sorbent such as soil or sediment, at either pH 6 (panel A) or pH 8 (panel B) using series of individual laboratory adsorption experiments (diamonds). Initial metal concentration is varied in these experiments, and as the amount of total metal initially added to solution increases (horizontal axis), so does the amount adsorbed to a fixed amount of solids in the adsorption reactor (vertical axis). We see that as the metal concentration increases, the amount of metal adsorbed to the solids plateaus – indicating that the solids are saturated with metal.

The adsorption data at pH 6 (panel A) are modelled using the four approaches discussed here: Kd, KF, KL , and SCM (models shown as solid lines). Because the solids become saturated with metal, we see that the Kd model, a linear fit, quickly fails to estimate the overall data trend.

The KF and KL models, which have mechanisms to account for metal saturation of the solids, fit the data reasonably well. As discussed above, the SCM approach considers aqueous metal speciation and chemical reactions at each proton-active site on the solids, and the model fits the data well.

Panel B considers adsorption of the same metal to the same solids as discussed in panel A, but the metal adsorption experiments were conducted instead at pH 8. Metal adsorption is enhanced versus the experiments at pH 6, largely because competition of the positively charged metal with H+ for adsorption to binding sites on the solids has declined considerably at the more basic pH 8.

SCM accounts for this change automatically – without the need for further laboratory experiments – because the system of equations solved to predict metal distribution includes proton and metal competition for each binding site. The empirical isotherm models cannot account for changes in pH, and thus do not fit the data. In order for the data at pH 8 to be explained, the new data in panel B would need to be used to calculate completely new empirical constants.

Limitations and advantages of SCM The primary reason that SCM is underused by environmental remediation firms and even in academia, is because it is data intensive and requires a more technical understanding of aqueous geochemistry. Modelling a typical field situation – having perhaps multiple contaminant metals and several potential sorbents – may involve dozens of surface complexation reactions. Each of these reactions must be carefully characterised in laboratory metal adsorption experiments to define a binding constant (K) value for each metal-sorbent pair, or existing constants must be gleaned from scientific literature.

The amount of labour and/or expertise involved in using SCM, and its inherent complexity, may preclude its use in favour of the more simple empirical models in some cases.

In remediating large sites, where reactive transport models are part of the remediation plan, there is a clear advantage to using SCM. Larger projects are more likely to involve experts in geochemistry, may run for a longer duration, and often consider greater environmental risk factors. Using constants derived from empirical models is particularly questionable in predicting the fate of heavy metals at sites were transport of the metal in groundwater is a major consideration. The use of empirical approaches in these situations may result in considerable under or over prediction of metal mobility.


Empirical modelling approaches to metal adsorption are widely employed by scientists working in environmental remediation, due to their simplicity and ease of use. Although appropriate in some cases, we argue here that a greater application of surface complexation modelling, which has a footing in molecular-scale reality, is needed.

The modelling approaches can be likened to the story of the three little pigs. While it may seem cheaper, faster, and easier to build a house of straw, such as in the empirical model, when the winds change it may have been safer to have spent the effort building a house of bricks, or using the SCM approach.

Published: 07th Mar 2013 in AWE International