1.1.1. Linear K_d Model

The partition (or distribution) coefficient, K_d, is a measure of sorption of contaminants to geomedia, and is defined as the ratio of the quantity of the adsorbate adsorbed per unit mass of solid to the amount of the adsorbate remaining in solution at equilibrium. K_d values are thermodynamically determined at stated equilibrium conditions as opposed to distribution ratios such as R_d which are not thermodynamically determined. In this work R_d is preferred to K_d. Values for K_d not only vary greatly between contaminants, but also vary as a function of aqueous and solid phase chemistry ([3]). Some adsorption studies are conducted in a systematic fashion to evaluate the effects of various parameters (such as pH, and ionic strength) on K_d. The results of a suite of experiments evaluating the effect of contaminant concentration on adsorption, while temperature is held constant, are called an “adsorption isotherm.” Among all phenomena governing the mobility of substances in aqueous porous media and aquatic environments, the transfer of substances from a mobile phase (liquid or gaseous) to a solid phase is a universal phenomenon. That is the reason why the “isotherm”, a curve describing the retention of a substance on a solid at various concentrations, is a major tool to describe and predict the mobility of this substance in the environment ([13]) This isotherm often cannot of itself provide information about the type of reaction involved. For example, the retention can be either due to surface retention without creating three-dimensional structure or to precipitation of a new solid phase ([19]; [23]). However, isotherms give a general view of the distribution of radionuclides between the solid-liquid phases.

Isotherm models are used to describe the case where sorption relationships deviate from linearity. For many short-lived radionuclides, the mass present never reaches quantities large enough to start loading surface adsorption sites to the point that the linear K_d relationship is not applicable. However, long-lived radionuclides and stable elements can be found in leachates and groundwaters near waste sources at concentrations large enough to affect the saturation of surface adsorption sites.

The partition (or distribution) coefficient, K_d, is expressed mathematically as shown below, as the ratio of the quantity of the adsorbate adsorbed per unit mass of solid (Q) to the amount of the adsorbate remaining in solution at equilibrium (C).

Most of the time, the concentration of the compound retained on the solid Q is calculated by difference between the initial solute concentration C_a0 and the final solute concentration C. In the case of retention stage, the solid concentration at equilibrium Q (mol·g⁻¹) is given by Equation (2) with V being the volume of solution (dm³), M is the solid mass (g) and Q_a0 (mol·g⁻¹) is the concentration of the compound initially retained by the solid, which must be measured or shown to be negligible ([13]).

The use of a distribution coefficient in describing nuclide migration requires some assumptions:

1) The sorption process during migration is reversible.

2) The ratio of solute concentration between the solid and solution phases also remains constant ([5]).

A more realistic approach to the concept of K_d, which is a thermodynamically determined value, is the R_d (Distribution ratio) of the solute between the solid and liquid phases, at the stated experimental conditions and it is not thermodynamically determined.

1.1.2. The Freundlich Isotherm

For rocks and minerals, contaminant adsorption can sometimes deviate from the linear relationship established by the distribution coefficient. In some circumstances, the amount of contaminant in solution contacting the solid will reach such a concentration that all adsorption sites would become saturated and the linear relationship between contaminant adsorbed to contaminant in solution would no longer hold.

Long-lived radionuclides and stable elements can be found in leachates and groundwaters near waste sources at concentrations large enough to affect the saturation of surface adsorption sites. The Freundlich equation; Equation (3), ([1]; [4]) is one of the various models that have been employed for the study of metal adsorption. It expresses relation between the adsorbed quantity Q and the remained solute concentration.

The equation is expressed in the linear form as:

where Q is the concentration of metal sorbed (mol·g⁻¹), C is the concentration of metal in the equilibrium solution (mol·dm⁻³), K (dm³·g⁻¹) and n (dimensionless) is a parameter that describes the heterogeneity of the sorption sites. A graph with log C as x-axis versus log Q as y-axis provides a line of slope 1/n and intercepts the y-axis at log K. According to the Freundlich equation, the isotherm does not reach a plateau as C increases. As 1/n tends to unity the surface becomes more uniform. Intact and crystalline minerals have higher 1/n values than pulverised and non-crystalline minerals. The constants are usually derived from a plot of sorbed concentration (Q) against concentration in solution (C). The Freundlich equation assumes that the surface of the solid is covered with a monolayer of sorbed species. The monolayer is not covered by any other layer. The Freundlich model does not account for finite adsorption capacity at high concentrations of solute ([16]).

1.1.3. Langmuir Isotherm

Sorption by the Langmuir isotherm assumes the solid has a limited adsorption capacity Q_max.

Adsorption occurs up to the extent of one monolayer. All adsorption sites are identical. Occupation of a site is independent of the occupation of neighbouring site(s). The temperature is constant. The surface is uniform and homogeneous. The process is reversible. Each site retains one molecule of the given compound and All sites are energetically and sterically independent of the adsorbed quantity ([12]).

The reversibility/irreversibility of the sorption process is of fundamental importance for the understanding of the fate of radionuclides in the geological systems. If the process is reversible, the same isotherm should be valid for sorption and desorption under the same experimental conditions ([6]). The Langmuir Model equation takes the form as shown in Equation (5) ([18]):

The linearised form of the equation is represented as

where bis the maximum adsorption capacity of the substrate (mol·g⁻¹) and K is a constant representing the strength with which the solute is bound to the substrate (dm³·meq⁻¹). Values of band K can be determined by plotting the linearised Equation (6) ([11]).

The Freundlich and the Langmuir models have been used in describing results that showed deviations from a linear distribution. Empirical models like those mentioned are mathematical descriptions of the experimental data without any particular theoretical basis ([22]).

The Langmuir model assumes that not all the adsorption sites are equally active; all adsorbing molecules do not exert an influence on their neighbourhood. Large molecules may occupy more than one adsorption site, and assuming that the adsorbed layer will be only one molecule thick is not valid. However, the Langmuir model gives us a basis for modelling adsorption by fitting data sets.

¹⁵²Eu, ¹⁵⁴Eu, and ¹⁵⁵Eu are produced primarily as fission products from fissile nuclides such as ²³⁵U, ¹⁵²Eu can also be produced by neutron activation of nuclear reactor control rods.

¹⁵¹Eu + 1n → ¹⁵²Eu neutron capture process

¹⁵¹Eu is a naturally occurring isotope and used in the control of fission reactions, due to its ability to accommodate neutrons. The associated gamma energies (in keV) and yields for ¹⁵²Eu are 121.78 (0.284), 244.7 (0.07), 344.28 (0.266), 778.91 (0.1296), 964.13 (0.143), 1085.8 (0.10), 1112.12 (0.1355), 1408.0 (0.2087).

Trace amounts of ¹⁵²Eu, ¹⁵⁴Eu, and ¹⁵⁵Eu are present in soil around the globe from radioactive fallout. They can also be present at certain nuclear facilities, such as reactors and spent fuel reprocessing plants. Europium is generally one of the more immobile radioactive metals in the environment. It preferentially adheres fairly strongly to soil (80). The importance of ¹⁵²Eu and ¹⁵⁴Eu is due to their relatively long half-lives for fission products, of 13.5 and 8.8 years, respectively. Due to behavioural similarities of the 4f-orbital lanthanides with some of the 5f-orbital actinides, Eu is often used as an analogue for the studies of trivalent actinides such as Am³⁺, Cm³⁺ ([20]).

The results of quantitative powder XRD analyses are summarised in Table 1. Powder X-ray diffraction analysis indicated that the five granites had approximately similar mineralogies and were predominantly composed of quartz (mean ca.33%), plagioclase feldspar (mean ca.31%) and K-feldspar (mean ca.31%) together with small/trace amounts of “mica” (undifferentiated mica species possibly including muscovite, biotite, illite, illite/smectite etc.). Small amounts of amphibole were also identified in the samples “Biotite granite” and “Rapakivi granite”. Traces of chlorite, kaolinite and smectite were also identified in some of the samples.

Further elemental characterisation and identification of the granite samples were carried out using energy dispersive spectroscopy. The elemental composition of elements present confirmed samples to be granites.

Table 1. Summary of quantitative whole-rock XRD analysis.

nd = not detected, “mica” = undifferentiated mica species including muscovite, biotite, illite and illite/smectite etc ([24]).

Eu is one of the 14 elements in the Lanthanide series used as analogues for the trivalent actinides and exhibits a strong sorption on mineral surfaces ([10]; [14]) Fitting the results to different sorption models, showed that sorption was different from one granitic rock to another. Best fit models showed that sorption was best described by the Langmuir model for GG, Linear K_d model for GA, BG and GrG, and by the Freundlich model for RG. Sorption parameters are shown in Table 2. The difference in sorption models is reflected in the R_d values calculated. R_d values for GA, BG and GrG obtained from the linear sorption isotherms were in the range 20 to 50 cm³·g⁻¹ for the granitic rocks. Allard et al., and Erdal et al., ([2]; [8]) obtained K_d value of 8 - 32 m³·kg⁻¹ and values of around 0.24 and 0.55 m³·kg⁻¹ for Eu sorption to Finnsjön granite respectively. Taking into consideration the effect of surface area per gram of solid, results showed that the most sorbing among the granitic rocks was GrG while the least sorbing was RG. Based on the calculated R_d, sorption to the different granitic rocks studied can be ranked in the order; GrG > GG > GA > BG > RG.

Figure 1. Variation of R_d with metal loading for different granitic rocks used in sorption experiments.

Figure 1 shows the sorption isotherms for the different granitic rocks. From this, it is evident that sorption occurred linearly for all the samples up to about 1 × 10⁻⁷ mol·dm⁻³ of Eu loading. Above this concentration range, sorption deviated from linearity as a result of saturation/modification of sorption sites. The deviation from linearity is highlighted in Figure 1. According to [9], deviation from linearity occurs in adsorption where, individual solute molecules bound to the solid interact with each other. This increases the strength of the individual solute bonds to the solid surface when the solid has low contaminant loading. Thus, for a brief period during adsorption, the first bound molecules enhance adsorption of the next molecules that bind to the solid. From Figure 1, deviation from linearity is evident from the decrease in R_d with increasing, metal concentration in solution.

Values of N close to unity RG implied that all sorption sites were energetically identical, and sorption occurred by a single mechanism. When N is close to 1, the Linear K_d sorption model and the Freundlich models are equivalent, as such deviation from linearity does not occur. Table 2 shows the different sorption parameters studied and the best fit models that are used in describing the sorption process.

Table 2. Sorption parameters for Eu sorption to granitic rocks and minerals. Data in table determined by fitting experimental to the linearised Freundlich isotherm, linearised Langmuir and the Linear model. Only best fit models are shown on the table, *R_d is the arithmetic mean of the R_ds derived from individual points. R_d* is the mean R_d corrected for surface area per gram effect. N is a dimensionless factor related to the heterogeneity of the sorption sites.

Graphic Granite GG, Biotite Granite BG, Granite Adamellite GA, Rapakivi Granite RG, Grey Granite GrG. BF= Best fit model, B = Maximum sorbable amount for the Langmuir model, K = Langmuir parameter, relates to the binding strength, *R_d = mean R_d, L, F, Li, stand for Langmuir, Freundlich, Linear and models respectively. BM = Best fit model, N = The Freundlich parameter, relates to the heterogeneity of the sorption sites, indicative to the presence of different sorption mechanisms.

Sorption verification studies of Eu on granitic bulk sample was conducted with the help of FIE QUANTA 600 Environmental scanning electron microscope, coupled with Oxford Instrument-INCA450 a solid state 2 diode type detector, operating at environmental pressure of <1 torr at the British Geological Survey. The micrographs and elemental spectra of the samples in EuCl₃ and DI water showed that adsorption of Eu occurred at the different mineral phases of the granite sample with most of the sorption taking place at the mica phase Figure 5. The attribution of higher sorption capacity to mica solely based on the microanalysis is not fully justified. While mica might be a significant sorption site, the contribution of other minerals cannot be ruled out. Attribution of high sorption values to mica have also been highlighted by work done by [7] in which they studied how ⁶³Ni sorbed to different granitic components.

Figure 2. Energy dispersive X-ray, microanalysis of blank granite sample in DI, using a wavelength of 700 nm, a solid state 2 diode type detector for the back scatter electrons in a low-pressure mode (0.98 torr of water vapour), and a specimen current of 0.98 nA. Figure shows the elemental composition of granite, with high concentrations of Si and O.

Figure 3. Energy dispersive X-ray Micrograph of granite sample doped with Eu, showing sorption of Eu (White spots on different areas of the granite sample).

Figure 4. Energy dispersive X-ray, microanalysis of feldspar showing Eu peaks.

Figure 5. Energy dispersive X-ray, microanalysis of mica showing Eu peaks.

Figure 6. Energy dispersive X-ray, microanalysis map, showing elemental mapping of Eu on the granite surface. Micrograph shows high concentration of Eu on the mica surface.