Study of the diffusion of metals and metals-EDTA complexes in water by capillary method

EDTA can complex with radionuclides (RNs) to form negatively charged complexes, making it difficult for clay minerals to retard the diffusion of RNs waste. The diffusion coefficient of RNs in water (Dw) is an important parameter for the safety assessment of the repository. In this study, the effectsof EDTA on the diffusion of metal ions (Cu2+, Sm3+, Nd3+, Lu3+ and Zn2+) were investigated by a capillary method. The experimental results showed that [Cu-EDTA]2-, [Sm-EDTA]-and [La-EDTA]-have higher Dw thanthe Mn+. Whereas, [Nd-EDTA]-and [Zn-EDTA]2- have lower Dw than Nd3+ and Zn2+ cations. The Dw is consistent with the literatures, indicating the validity of the capillary method to determine the diffusion coefficients. According to Stokes-Einstein relation, the ionic radius and ionic potential of the ion are in disproportional to the Dw value. Cu-, Sm-and La-EDTA complexes have smaller molecular size than the uncomplexed metal ions, indicating that the Mn+ ions might be associated with many water molecules to form hydrated ions with larger ionic radius. Whereas the [Nd-EDTA]-and [Zn-EDTA]2- have larger molecular size than Nd3+ and Zn2+ cations.


Introduction
Ethylenediaminetetraacetate (EDTA) is often used as a chelate for agricultural and industrial applications, resulting in an increase of EDTA concentrations in various water sources. It may complex with free heavy metal ions to form solublecomplexation, thus enhancing the transportation of M-EDTA (Z-4)+ complexes in water and clays barrier systems [1][2][3] . The effect of EDTA on the transportation of metal ions has been attracted a lot of attention, such as 85 Sr-EDTA 2in sediments 4 , Cd/Co-EDTA 2in saprolite 5 , and Eu-EDTAin hard clay rock 6 . EDTA can decrease the adsorption of metal ions on minerals and enhance their transportation not only due to the formation of negatively charge complexes 7,8 , but also due to the reducing of the clay specific surface area 9 . For example, equimolar EDTA inhibited the sorption of U(VI) on montmorillonite due to the formation of negatively charged UO 2 HEDTA -, (UO 2 ) 2 OHEDTAand (UO 2 ) 2 EDTA 2 4-7 . The transportation of Th 4+ through sands was enhanced by EDTA due to the formation of Th(OH)(EDTA) 2 2and Th(OH)(EDTA) -2 .
In order to retard the transportation of radionuclidewaste, it often uses porous materials with low permeability such as clay rock and compacted bentonite as backfill material for the repository. Diffusion is the predominant behavior of radionulide ions. Diffusion coefficient of RNs in water (D w ) is one of the most important parameters to predict the diffusion behavior of RNs in backfill material and the surrounding rock. The diffusion cell method is often used in determining the diffusion coefficient of RNs in water 1, 10 and in minerals 6,11 . EDTA can alter diffusion of RNs by complexaion reaction or by the modification of the properties of minerals. Due to the large molceular size of EDTA, the diffusion coefficient of M-EDTA (Z-4)+ complexes in water was found to be similar among various metal ions 1 . Descostes et al. (2017) reported that EDTA increase the diffusion of RNs in clays due to the formation of negatively charged complexes. Anionic exclusion of [Eu-EDTA]was found in the rock clay. However, to the best of our knowledge, only a few studies related to the effect of EDTA on the diffusion of RNs were reported due to the long experimental period 1,6,9 Tri-valent lanthanides were often used as the surrogates of tri-valent actinides to avoid the operation of radioactivity experiments. In this study, the effect of EDTA on metals ions (Cu 2+ , Sm 3+ , Nd 3+ , Lu 3+ and Zn 2+ ) were investigated by a capillary method. The aim is to verifiy this method to the classis conductivity method and diffusion cell method. Some new diffusion coefficients of ions were also provided. We wish to have more knowledge of the diffusion properties of M-EDTA (Z-4)+ complexes before the diffusion experiment in clay starts.
The aqueous chemical speciation of M-EDTA (Z-4)+ complexes were calculated by using HySS (Hyperquad Simulation and Speciation) computer program. The stablity constants from literature were used for calculations 12 . All M n+ cations was mainly formed with EDTA as soluable M-EDTA (Z-4)+ complexes with almost 100% in 0.5 M NaCl solution due to the large stability constantes of M-EDTA (Z-4)+ complexes.

Diffusion experiment
The diffusion behavior of M n+ and M-EDTA (Z-4)+ complexes in water will be investigated by a capillary method with single element solution (Fig.1). A working solution of Cu 2+ was prepared by dissolving solid metal chlorides in 0.5 M NaCl solution. 0.1 mol/L of Cu 2+ stock solution was prepared by adding some Cu 2+ working solution in 0.5 mol/L of NaCl solution. The pH was adjusted to 7.0  0.2 by adding minor HCl or NaOH. The 5.0 ml vials were filled with 4.0 ml of tracer free NaCl solution. After a capillary was fit into an opening in the cap of the vial, the glass open-ended capillary (diameter ca. 0.85 mm) was filled with 25 L Cu 2+ at a length of ca. 4.7 cm, and then a parafilm membrane sealed the upper end of the capillary. The bottom end of the capillary immerged into 0.5 mol/L of NaCl solution (Fig. 1A). The out-diffusion of Cu 2+ from the capillary into the solution started. After a certain time interval, the capillary was removed from the solution. The concentration of copper in vials was measured by an inductively coupled plasma-optical emission spectrometer (ICP-OES, Perkin Elmer, Optima 7000 DV). The same experimental procedures were conducted for the other metal ions (Sm 3+ , La 3+ , Nd 3+ , Zn 3+ and Lu 3+ ) and M-EDTA (Z-4)+ complexes.

Determination of the diffusion coefficients of free metal ions
The diffusion coefficient (D w ) for a metal ion in NaCl solution was obtained by fitting the concentration of the metal ion in vials as a function of time by the following equation 13 : where D w,Na+ is 1.33  10 -9 m 2 /s 14 .

Calculation of ionic radius of M n+ and M-EDTA (Z-4)+ complexes
The ionic radius of the diffusing species (r, Å) is calculated by the classic Stokes-Einstein relation as follows: where k (1.380649 × 10 -23 Pam 3 /K) is the Boltzmann constant, T (K) is the temperature and η (Pas) is the viscosity of the medium, which is 0.9365 × 10 -3 Pas in 0.5 mol/L of NaCl solution 15 .
The ionic potential (I p ) is defined as: where z is the charge of ion and r is the ionic radius (Å).  The diffusion coefficients, the ionic radii and the ionic potentials (I p ) of M n+ and M-EDTA (Z-4)+ complexes were summerized in Table 1. The results were compared with the D w measuremed by diffusion cell method and the limiting molar ionic conductivites using the Nernst-Einstein equation 1,10,14,16 . The diffusion coefficient was obtained by fitting the experimental data as shown in Fig.1 by Eq.(1). The ionic radius was calculated by Eq.(3) in this work and for the literatures. I p was calculated by Eq.(4). The I p from literatures are listed in the round bracket in Table  1. The diffusion coefficients of M n+ ions in diluted water are calculated by Eq. (2), which are consistent with the D w from literatures, indicating the validity of the capillary method to determine the diffusion coefficients. However, the D w of M-EDTA (Z-4)+ complexes were higher in this work than in literature. Since multi-element solution was employed to determine the diffusion coefficient by diffusion cell method as reported by Furukawa et al. (2007), the descrepancy could be explained by the cocomplexation reaction of ions and EDTA.

Results & Discussion
According to Stokes-Einstein relation as shown in Eq.(1), the diffusion coefficient of ion is in dispropotional to the ionic radius. For Cu 2+ , Sm 3+ and La 3+ , the ionic radius of M-EDTA (Z-4)+ complexes are smaller than that of M n+ , indicating that the M n+ ions might be associated with many water molecules to form hydrated ions with larger ionic radius. Whereas, the ionic radius of [Nd-EDTA]and [Zn-EDTA]are larger than that of Nd 3+ and Zn 2+ . The D w of [Nd-EDTA]and [Zn-EDTA]are in good agreement with that of Furukawa, et al. (2008), who reported that the D w of Ln-EDTA (Z-4)+ complexes were in the range of 5.43  10 -10 -5.76  10 -10 m 2 /s, which is close to that of H 2 EDTA 2-. Since the molceular size of EDTA is much larger tha thato fo metal ions, the diffusion of metal ions lose their characteristics by the complexation. However, the diffusion coefficient of [Cu-EDTA] 2-, [Sm-EDTA]and [La-EDTA]were higher. More experiments will be conducted to clarifed the descrepancy of the diffusion coefficient due to the multi-element solution and single element solution.    It is defined as z/r, where z is the charge of ion and r is the ionic radius (Å). It shows a linear relationsip between the diffusion coefficients and ionic potentials. The intercepts decrease with increasing the charge of ions. The ionic potentials of are lower than 1.2, which is inaccordance with the anions reported by Li and Gergory (1974). However, cations have the lower ionic potentials in this work than in literatures 1, 10, 16 . It can be explained that the ionic radii of M n+ ions are larger due to the formation with water molecules to form hydrated ions in this work. The I p is in proprtional to the D w when combined Eq.(2) and Eq. (3), indicating that the ions with high ionic potentials diffuse faster in the water.

4.Conclusions
The results of this work indicate that EDTA can alter the diffusion behavior of the metal ions. The diffusion coefficients of ions is in disappropotional to the molecular size and ionic potential of metal ions. The