Sorption behavior of hydroselenide (HSe⁻) onto iron-containing minerals

Abstract

The sorption behavior of selenium onto iron-containing minerals such as goethite, ferrous oxide, magnetite, and biotite under reducing conditions were investigated by batch sorption experiments. Selenium was spiked as HSe⁻ and Se₄²⁻ in the experimental solutions and reducing conditions were maintained throughout the sorption periods. The sorption behaviors of HSe⁻ were analyzed by the triple-layer surface complexation model with the Visual Minteq computer program. The sorption data and the model calculations suggested that the dominant sorption mechanisms of HSe⁻ were inner-sphere surface complexation for goethite and ferrous oxide but outer-sphere surface complexation for magnetite and biotite. The intrinsic equilibrium constant of the inner-sphere surface complexation reaction of HSe⁻ with goethite, logK^int_HSe = 6.0, was determined by the fitting to the experimental results. The value of the equilibrium constant for outer-sphere complexation for magnetite and biotite was estimated to be around 12.

Keywords:

• selenium
• sorption
• reducing condition
• distribution coefficient
• surface complex
• triple-layer model
• iron

1. Introduction

Retardation of radionuclide migration by sorption onto a host rock in natural barrier systems is one of the important factors that influence the performance of a radioactive waste disposal system. Performance assessment calculations for hypothetical high-level radioactive waste (HLW) repositories [1] show that ⁷⁹Se is one of the radionuclides that dominate the long-term radiological hazard. The oxidation state of Se varies from selenide [Se(−II)] to selenite [Se(IV)] and selenate [Se(VI)], depending on the redox conditions of the groundwater [2]. Selenium is likely to be stable as Se(−II) under reducing conditions in deep subsurface environments, and hydroselenide, HSe⁻, is considered to be dominant species in groundwater [1,2].

Iron-containing minerals are important sorbents of Se in rocks and soils [3–10]. A considerable amount of sorption data of Se(IV) and Se(VI) onto iron-containing minerals such as goethite [3,4,6,11–20], hematite [5,6,13,19,21], magnetite [21–27], ferric oxides/oxyhydroxides [12,18,28,29], pyrite [3], biotite [3], and chlorite [3,13] has been obtained. Both Se(IV) and Se(VI) are sorbed onto iron-containing minerals, but the sorbability of Se(IV) is generally higher than that of Se(VI). This is due to differences in the nature of their respective surface complexes. Extended X-ray absorption fine-structure (EXAFS) studies [4,30,31] showed that Se(IV) formed a strongly bonded inner-sphere complex, whereas Se(VI) formed a mixture of outer- and inner-sphere surface complexes on ferric oxyhydroxides.

The sorption behaviors of Se(IV) and Se(VI) species onto iron-containing minerals have been analyzed by surface complexation models [32–34] such as the diffuse-layer model (DLM) [34–36], the constant-capacitance model (CCM) [37–42], and the triple-layer model (TLM) [12,28,30,43–48]. Hayes et al. [12] investigated the sorption behaviors of Se(IV) and Se(VI) onto goethite and hydrous ferric oxide (HFO) in sodium nitrate solutions by using the TLM. They found that the sorption behavior of Se(IV) was independent of the ionic strength and could be explained by inner-sphere complexation with a ferrol site (≡FeSeO₃⁻ and ≡FeSeO₃⁻₋Na⁺). On the other hand, the sorption of Se(VI) depending on ionic strength was explained as outer-sphere complexation (≡FeOH₂⁺₋SeO₄²⁻ and ≡FeOH₂⁺₋HSeO₄⁻). Zhang and Sparks [14] analyzed the sorption phenomena of Se(IV) and Se(VI) onto goethite by using the TLM. The sorption of Se(IV) was explained as inner-sphere complexation (≡FeHSeO₃⁰ and ≡FeSeO₃⁻) and Se(VI) was explained as outer-sphere complexation (≡FeOH₂⁺₋SeO₄²⁻). Using the sorption data from Hayes et al. [12] and Zhang and Sparks [14], Goldberg [49] evaluated the ability of the TLM to describe the adsorption of Se(IV) and Se(VI) onto goethite, and the adsorption was found to be sensitively dependent on the surface site densities. Duc et al. [5] investigated the sorption of Se(IV) onto goethite and hematite by the CCM. It was reported that goethite and hematite, which have different acid–base properties, exhibit very similar sorption properties for Se(IV). The monodentate complexes ≡FeOSe(O)OH and ≡FeOSe(O)O⁻ were assumed in the CCM analysis. Duc et al. [6] assumed a bidentate complex (≡FeO)₂SeO for the CCM calculation for the sorption of Se(IV) onto hematite. Fukushi and Sverjensky [50] demonstrated the applicability of an extended TLM, which took into account the effect the electrostatics of water dipole desorption had on the measurements reported for the sorption of Se(VI) onto goethite by Rietra et al. [16,17] and Hayes et al. [12]. The sorption behaviors of Se(VI) were explained by a mixture of outer- and inner-sphere surface complexes [≡FeOH₂⁺₋SeO₄²⁻, (≡FeOH₂⁺)₂₋SeO₄²⁻, and ≡FeOSeO₃⁻]. Shibutani et al. [3] obtained sorption data of Se(IV) onto goethite and biotite and analyzed them using the DLM. By assuming the surface site of biotite to be ≡FeOH, the model calculations showed good agreement with experimental results. Martinez et al. [22] modeled the variation of the sorption of Se(IV) and Se(VI) onto magnetite as a function of pH by the TLM. The best fitting was obtained for Se(IV) by assuming two inner-sphere complexes (≡FeOHSeO₃²⁻ and ≡FeHSeO₃⁰), while assuming an outer-sphere complex (≡FeOH₂⁺₋SeO₄²⁻) for Se(VI). Missana et al. [25], Jordan et al. [26], and Kim et al. [27] investigated the sorption of Se(IV) onto magnetite by the diffuse double-layer model (DDLM). They supposed that Se(IV) sorbed onto magnetite by forming an inner-sphere monodentate species such as ≡FeOSeO₂⁻. Goldberg [51] investigated the adsorption behavior of Se(IV) on amorphous Fe oxides using the TLM. The dominant surface species predicted by the TLM were an inner-sphere complex (≡FeHSeO₃⁰) at pH < 9 and an outer-sphere complex (≡FeOH₂⁺₋SeO₃²⁻) at pH > 10.

In contrast to Se(IV) and Se(VI), the data of Se(−II) are scarce [9,13,52] and the sorption mechanisms of Se(−II) are poorly understood. Although the exact speciation of selenium in the vitrified HLW waste is unclear, it is estimated as Se(IV) or Se(VI) because selenium is exposed to oxidizing conditions during the reprocessing of spent fuel, and SeO₃²⁻ and SeO₄²⁻ can substitute trigonal borate or tetrahedral silicate entities, respectively, in the glass network [53–56]. Selenium had been considered to migrate as soluble SeO₃²⁻/SeO₄²⁻ because of its slow reduction kinetics [53–56], in spite of thermodynamic stability of Se(−II) under reducing disposal conditions. Recent works have demonstrated the abiotic reduction of Se(IV) and Se(VI) to Se(0) by several Fe(II)-bearing minerals [24,55–62] and to Se(−II) by Fe(0) nanoparticles [63]. Understanding the sorption behavior of Se(−II) species is important; however, the sorption data of Se(−II) are scarce because of the experimental difficulties of maintaining the reducing state of Se. In the long term, the sorption behavior of Se(−II) would change because the composition of groundwater is likely to be changed by intrusion of saline groundwater for coastal repositories and alkaline groundwater induced by cementitious materials. For a long-term evaluation of the sorption of Se(−II), it is necessary to understand the sorption mechanisms, such as inner-sphere surface complexation and outer-sphere surface complexation.

In the present study, sorption data of Se(−II) onto iron-containing minerals, magnetite, goethite, ferrous oxide, and biotite were obtained by batch sorption experiments under reducing conditions. The sorption behaviors of Se(−II) were analyzed by the TLM with the Visual Minteq computer program. Sorption experiments for Se(IV) were also carried out under anaerobic conditions and the sorption behaviors were reproduced by the TLM to confirm the validity of this experimental method and surface parameters of the employed iron-containing minerals.

2. Materials

2.1. Iron-containing minerals

Goethite (α–Fe^(III)OOH) and magnetite (Fe^{(II, III)}₃O₄) samples were purchased from Rare Metallic Co. Ltd. Ferrous oxide (Fe^(II)O) and biotite [K(Mg, Fe^(II))₃(Al, Fe^(III))Si₃O₁₀(OH, F)₂] were purchased from Nichika Inc. and Soekawa Chemical Co. Ltd., respectively. All of the mineral samples were in granulated form and used without pretreatment. For a determination of specific surface area of granulated samples, the air-permeability method and the gas adsorption method are generally used [64]. The gas adsorption method is used more widely and can determine the total surface area including cracks and micro pores [65]. By the reasons, the specific surface areas of employed minerals were measured by the Brunauer–Emmett–Teller gas adsorption method [66] which is widely used and useful [34]. The measured specific surface areas were 17.6 m² g⁻¹ (goethite), 1.6 m² g⁻¹ (magnetite), 0.2 m² g⁻¹ (ferrous oxide), and 4.6 m² g⁻¹ (biotite).

2.2. Selenium stock solution

A Se(−II) stock solution was prepared in a controlled-atmosphere glove box under Ar (O₂ < 1 ppm) by the following procedure. A solution of ⁷⁵Se (4 MBq cm⁻³, carrier: 100 μg cm⁻³ Na₂SeO₃) was purchased from GE Healthcare Limited. A 0.5 cm³ volume of a 98% aqueous solution of hydrazine monohydrate (N₂H₄·H₂O) was mixed with a 0.5 cm³ volume of the ⁷⁵Se solution in a polypropylene test tube and the mixture was stored for seven days to reduce Se(IV) to Se(−II) [9]. The mixture was the diluted with distilled deionized water to 10 cm³. The solution was filtered through a 10,000 nominal molecular weight limit (NMWL) ultrafilter (USY–1, Toyo Roshi Kaisha Ltd.) to remove the precipitated fraction of Se. The filtrate was sampled to analyze the aqueous Se species by UV-vis spectrometry, which confirmed that Se was dissolved as a stable species (HSe⁻ and Se₄²⁻) under reducing conditions [9].

A Se(IV) stock solution was prepared by diluting 0.5 cm³ volume of the ⁷⁵Se solution to 10 cm³ with distilled deionized water.

3. Sorption experiments

The experimental runs were made following the procedure of the “Measurement Method of the Distribution Coefficient on the Sorption Process” compiled by the Atomic Energy Society of Japan [67]. Batch sorption experiments for Se(−II) were performed in a controlled-atmosphere glove box under Ar at 25°C ± 1°C. A 0.5 cm³ volume of 98% N₂H₄·H₂O solution was added to a 1000 cm³ volume of 0.01, 0.1, and 1 mol dm⁻³ sodium chloride (NaCl) solution. The concentration of N₂H₄·H₂O was 0.01 mol dm⁻³. A 0.2 cm³ volume of Se(−II) stock solution was spiked into the NaCl solution. By filtering this solution through a 0.45 μm filter, experimental Se(−II) solutions (Se: 1.3 × 10⁻⁸ mol dm⁻³) were prepared. A 1 cm³ aliquot was sampled and the radioactivity of the solution was measured by γ-spectrometry (LOAX-51370/20-P, SEIKO EG&G) with a peak at 0.136 MeV to determine the initial concentration of Se.

Prior to the sorption runs, blank tests were carried out to check for precipitation of Se(−II). A 10 cm³ volume of the Se(−II) solution was poured into a polypropylene test tube. A 2 cm³ aliquot was sampled and filtered through a 10,000 NMWL ultrafilter preconditioned with a small amount of the sample solution. The filtrate was sampled (1 cm³) and its radioactivity was measured by γ-spectrometry. The Se concentration decreased from the initial concentration at pH < 7 but it did not decrease at pH > 7.

A mineral sample (1 g) was immersed in a 10 cm³ volume of the Se(−II) solution in a polypropylene test tube. For goethite, which has a large surface area, sorption runs using 0.1 g of the solid phase were added. The pH of the sample suspension was adjusted to 7–13 with sodium hydroxide (NaOH) solution or hydrochloric acid (HCl). The sample suspensions were agitated once a day. After two weeks, the pH, redox potential (Eh), and radioactivity of the solutions were measured. The pH was measured with a Sure-Flow combination glass electrode (ROSS 8172BNWP, Thermo Fisher Scientific Inc.), which is suitable for the measurement of high-ionic-strength and high-pH samples. The electrode was calibrated with standard pH buffer solutions of 7.00, 10.01, and 12.46. Because of the difference in activity coefficients between the standard buffers and the high-ionic-strength solutions, the observed pH value (pH_obs) can shift from actual pH (−log a_H+). The difference between pH_obs and −log a_H+ was determined by measuring the pH_obs of NaCl/HCl and NaCl/NaOH solutions of known H⁺ and OH⁻ concentrations [68]. The Eh was determined against NHE using a platinum electrode combined with an Ag/AgCl reference electrode (ROSS 9180BNMD, Thermo Fisher Scientific Inc.) after checking its accuracy with saturated quinhydrone solutions. A 2 cm³ aliquot was sampled and filtered through a 10,000 NMWL ultrafilter preconditioned with a small amount of the sample solution. The filtrate was sampled (1 cm³) and the radioactivity of the solution was measured by γ-spectrometry to determine the equilibrated concentration of Se.

Batch sorption experiments for Se(IV) were also performed in the controlled-atmosphere glove box under Ar. The starting solution was prepared by adding a 0.2 cm³ volume of the Se(IV) stock solution to a 1000 cm³ volume of the NaCl solution, so the concentration of Se(IV) was 1.3 × 10⁻⁸ mol dm⁻³. Batch sorption runs for Se(IV) were performed in the same manner as those for Se(−II). The Eh of the Se(IV) solution without a redox buffer was not measured.

4. Results and discussion

4.1. Experimental results

4.1.1. Sorption behavior of Se(IV)

The sorption ratio, R_s (%), and the distribution coefficient, K_d (m³ kg⁻¹), were calculated using the following equations, respectively: (1) (2) where c_ini is the initial concentration of Se (mol dm⁻³), c_eq the equilibrated concentration of Se (mol dm⁻³), V_ini the initial volume of the solution (m³), and M the weight of the solid phase (kg). The obtained pH, R_s, and K_d values are listed in Tables 1–4. The dominant Se(IV) species under the experimental conditions are HSeO₃⁻ or SeO₃²⁻ (Figure 2) dependent on pH: (3)

Table 1. Experimental variables and data for Se(IV) sorption on goethite.

NaCl
0.01 mol dm^−3			0.1 mol dm^−3			1 mol dm^−3
pH	Rs (%)	Kd (m^3 kg^−1)	pH	Rs (%)	Kd (m^3 kg^−1)	pH	Rs (%)	Kd (m^3 kg^−1)
7.13	99	(1.6 ± 1.4) × 10^0	7.28	99	(1.6 ± 1.3) × 10^0	7.12	98	(6.4 ± 0.1) × 10^−1
7.46	99	(1.4 ± 1.0) × 10^0	8.02	99	(1.4 ± 1.1) × 10^0	8.00	97	(3.3 ± 0.1) × 10^−1
8.27	96	(2.7 ± 0.7) × 10^−1	9.45	96	(2.6 ± 0.1) × 10^−1	8.33	98	(4.6 ± 1.6) × 10^−1
9.08	95	(1.8 ± 0.4) × 10^−1	9.54	96	(2.3 ± 0.6) × 10^−1	8.47	98	(4.1 ± 1.2) × 10^−1
9.23	96	(2.5 ± 0.1) × 10^−1	10.33	92	(1.1 ± 0.2) × 10^−1	10.23	88	(7.2 ± 1.2) × 10^−2
10.27	90	(9.3 ± 0.2) × 10^−2	10.72	77	(3.3 ± 0.4) × 10^−2	10.55	78	(3.5 ± 0.5) × 10^−2
10.62	85	(5.6 ± 0.8) × 10^−2	11.23	40	(6.6 ± 1.2) × 10^−3	11.36	21	(2.6 ± 1.0) × 10^−3
11.46	22	(2.9 ± 1.0) × 10^−3	11.62	16	(1.9 ± 0.9) × 10^−3	11.47	15	(1.7 ± 1.0) × 10^−3
12.05	6	<1.4 × 10^−3	12.17	10	(1.1 ± 0.8) × 10^−3	11.51	17	(2.0 ± 1.0) × 10^−3
12.50	11	(1.3 ± 0.9) × 10^−3	12.53	4	<1.0 × 10^−3	11.66	13	(1.6 ± 1.0) × 10^−3
						11.73	14	(1.6 ± 1.0) × 10^−3
						11.75	18	(2.1 ± 1.0) × 10^−3
						12.18	10	(1.1 ± 0.8) × 10^−3
						12.41	7	<1.5 × 10^−3
						12.59	1	<7.5 × 10^−4

Table 2. Experimental variables and data for Se(IV) sorption on ferrous oxide.

NaCl
0.01 mol dm^−3			0.1 mol dm^−3			1 mol dm^−3
pH	Rs (%)	Kd (m^3 kg^−1)	pH	Rs (%)	Kd (m^3 kg^−1)	pH	Rs (%)	Kd (m^3 kg^−1)
8.53	100	(3.0 ± 2.7) × 10^0	8.42	100	>3.4 × 10^0	9.14	99	(1.5 ± 0.6) × 10^0
9.44	100	>3.3 × 10^0	9.24	99	(1.5 ± 1.2) × 10^0	9.79	99	>1.5 × 10^0
9.55	100	(3.5 ± 1.0) × 10^0	9.47	100	>2.1 × 10^0	10.53	38	(6.2 ± 1.6) × 10^−3
9.88	100	(2.7 ± 2.1) × 10^0	9.57	100	(2.6 ± 2.1) × 10^0	10.72	18	(2.2 ± 1.4) × 10^−3
9.94	97	(3.7 ± 1.3) × 10^−1	10.72	11	<2.3 × 10^−3	10.81	8	<1.9 × 10^−3
11.04	8	<1.9 × 10^−3	10.87	6	<1.7 × 10^−3	10.86	9	<2.1 × 10^−3
11.04	5	<1.5 × 10^−3	10.98	2	<1.2 × 10^−3	11.13	5	<1.6 × 10^−3
11.10	3	(2.7 ± 2.0) × 10^−4	11.39	2	<1.2 × 10^−3	11.32	3	<1.4 × 10^−3
12.03	3	(2.7 ± 2.0) × 10^−4	12.03	7	<1.8 × 10^−3	11.83	5	<1.6 × 10^−3
12.55	6	(6.0 ± 2.0) × 10^−4	12.61	10	<2.2 ×10^−3	12.46	7	<1.8 × 10^−3

Table 3. Experimental variables and data for Se(IV) sorption on magnetite.

NaCl
0.01 mol dm^−3			0.1 mol dm^−3			1 mol dm^−3
pH	Rs (%)	Kd (m^3 kg^−1)	pH	Rs (%)	Kd (m^3 kg^−1)	pH	Rs (%)	Kd (m^3 kg^−1)
7.10	99	(1.0 ± 0.4) × 10^0	7.02	99	(6.7 ± 1.6) × 10^−1	7.10	98	(5.8 ± 1.9) × 10^−1
7.21	99	(1.0 ± 0.4) × 10^0	7.08	99	(1.2 ± 0.5) × 10^0	7.22	98	(4.2 ± 0.6) × 10^−1
7.41	100	>4.5 × 10^0	7.10	99	(8.3 ± 2.4) × 10^−1	7.40	99	(8.3 ± 2.5) × 10^−1
7.43	98	(6.2 ± 2.0) × 10^−1	7.50	98	(6.4 ± 2.3) × 10^−1	7.45	98	(5.6 ± 1.8) × 10^−1
7.49	99	(1.2 ± 0.5) × 10^0	7.80	98	(6.0 ± 1.9) × 10^−1	8.10	98	(4.9 ± 1.4) × 10^−1
7.56	99	(1.0 ± 0.5) × 10^0	7.80	99	(8.0 ± 3.3) × 10^−1	8.20	98	(4.2 ± 1.1) × 10^−1
7.80	99	(6.6 ± 2.4) × 10^−1	8.10	99	(7.7 ± 3.2) × 10^−1	8.24	99	(8.5 ± 1.1) × 10^−1
7.90	99	(6.7 ± 2.4) × 10^−1	8.15	98	(4.7 ± 1.3) × 10^−1	8.31	99	(8.4 ± 4.3) × 10^−1
8.40	99	(1.7 ± 1.5) × 10^0	8.19	97	(3.1 ± 0.9) × 10^−1	8.83	94	(1.5 ± 0.2) × 10^−1
8.45	99	(1.2 ± 0.7) × 10^0	8.24	96	(2.5 ± 0.6) × 10^−1	9.24	98	(4.4 ± 0.3) × 10^−1
8.50	99	(7.8 ± 3.4) × 10^−1	8.50	98	(6.2 ± 2.2) × 10^−1	9.25	78	(3.6 ± 0.2) × 10^−2
8.59	99	(9.1 ± 1.2) × 10^−1	8.50	100	>4.6 × 10^0	9.41	71	(2.5 ± 0.1) × 10^−2
8.61	100	(3.5 ± 0.6) × 10^0	8.53	100	(2.6 ± 0.4) × 10^0	9.48	73	(2.7 ± 0.1) × 10^−2
8.64	95	(1.8 ± 0.3)×10^−1	8.89	99	(9.0 ± 1.2) × 10^−1	9.55	67	(2.0 ± 0.8) × 10^−2
8.75	99	(7.0 ± 0.8) × 10^−1	8.94	100	(4.2 ± 0.7) × 10^0	9.80	54	(1.2 ± 0.1) × 10^−2
8.90	98	(6.1 ± 0.7) × 10^−1	9.05	99	(9.0 ± 1.1) × 10^−1	9.95	17	(2.1 ± 0.3) × 10^−3
9.36	87	(6.8 ± 5.0) × 10^−2	9.25	98	(4.1 ± 0.3) × 10^−1	10.19	24	(3.2 ± 0.1) × 10^−3
9.89	50	(1.0 ± 0.4) × 10^−2	10.19	32	(4.8 ± 1.2) × 10^−3	10.25	21	(2.7 ± 1.0) × 10^−3
10.32	13	(1.5 ± 0.3) × 10^−3	10.31	20	(2.5 ± 0.4) × 10^−3	10.26	13	(1.4 ± 0.3) × 10^−3
10.51	6	(6.8 ± 3.3) × 10^−4	10.47	8	(8.1 ± 3.2) × 10^−4	10.56	7	<1.5 × 10^−3
10.58	23	(2.9 ± 1.0) × 10^−3	10.67	17	(2.0 ± 0.9) × 10^−3	10.83	11	(1.3 ± 0.3) × 10^−3
10.97	0	<3.8 × 10^−4	10.68	24	(3.2 ± 1.0) × 10^−3	11.05	4	<1.1 × 10^−3
11.23	3	<1.0 × 10^−3	10.95	4	(4.1 ± 3.2) × 10^−4	11.13	5	<1.2 × 10^−3
12.06	0	<3.3 × 10^−4	12.02	2	<5.1 × 10^−4	11.93	6	(6.9 ± 2.9) × 10^−4
12.30	0	<3.3 × 10^−4	12.30	2	<4.8 × 10^−4	12.19	6	(6.0 ± 2.9)× 10^−4

Table 4. Experimental variables and data for Se(IV) sorption on biotite.

NaCl
0.01 mol dm^−3			0.1 mol dm^−3			1 mol dm^−3
pH	Rs (%)	Kd (m^3 kg^−1)	pH	Rs (%)	Kd (m^3 kg^−1)	pH	Rs (%)	Kd (m^3 kg^−1)
7.06	95	(1.8 ± 0.6) × 10^−1	7.14	94	(1.7 ± 0.6) × 10^−1	7.11	96	(2.5 ± 1.3) × 10^−1
7.12	96	(2.2 ± 0.9) × 10^−1	7.20	94	(1.6 ± 0.5) × 10^−1	7.37	97	(3.3 ± 2.2) × 10^−1
7.56	95	(1.8 ± 0.6) × 10^−1	8.06	86	(6.3 ± 0.4) × 10^−2	7.48	95	(2.0 ± 0.8) × 10^−1
8.04	89	(8.0 ± 0.7) × 10^−2	8.52	67	(2.1 ± 0.1) × 10^−2	7.79	92	(1.1 ± 0.1) × 10^−1
8.26	84	(5.2 ± 0.6) × 10^−2	8.56	60	(1.5 ± 0.1) × 10^−2	7.85	89	(8.1 ± 0.7) × 10^−2
8.38	74	(2.8 ± 0.1) × 10^−2	8.79	57	(1.3 ± 0.2) × 10^−2	8.29	86	(6.0 ± 0.4) × 10^−2
8.47	66	(1.9 ± 0.1) × 10^−2	9.05	31	(4.4 ± 1.9) × 10^−3	8.45	65	(1.8 ± 0.3) × 10^−2
8.57	73	(2.7 ± 0.4) × 10^−2	9.05	30	(4.3 ± 1.9) × 10^−3	8.49	54	(1.2 ± 0.2) × 10^−2
8.64	76	(3.2 ± 0.4) × 10^−2	9.14	43	(7.6 ± 2.0) × 10^−3	8.55	65	(1.9 ± 0.3) × 10^−2
8.92	48	(9.3 ± 2.1) × 10^−3	9.31	29	(4.0 ± 1.9) × 10^−3	8.60	63	(1.7 ± 0.3) × 10^−2
9.23	45	(8.3 ± 2.1) × 10^−3	9.42	18	(2.2 ± 1.8) × 10^−3	8.62	52	(1.1 ± 0.2) × 10^−2
9.25	21	(2.7 ± 1.9) × 10^−3	9.68	15	<3.2 × 10^−3	8.63	48	(9.4 ± 2.1) × 10^−3
10.02	3	<1.7 × 10^−3	9.76	8	(8.6 ± 1.8) × 10^−4	8.64	50	(1.0 ± 0.2) × 10^−2
10.16	4	<1.9 × 10^−3	11.46	3	<1.7 × 10^−3	8.68	61	(1.5 ± 0.3) × 10^−2
12.30	1	<1.5 × 10^−3	11.89	3	<1.8 × 10^−3	8.72	34	(5.2 ± 1.9) × 10^−3
						8.81	52	(1.1 ± 0.1) × 10^−2
						8.81	42	(7.2 ± 2.0) × 10^−3
						8.93	50	(1.0 ± 0.1) × 10^−2
						8.98	28	(3.9 ± 1.9) × 10^−3
						9.01	41	(7.0 ± 0.3) × 10^−3
						9.07	27	(3.6 ± 1.9) × 10^−3
						11.05	8	<2.3 × 10^−3
						11.23	6	<2.1 × 10^−3
						11.57	2	<1.7 × 10^−3
						11.71	2	<1.6 × 10^−3

Figure 1. Comparison of K_d values for Se(IV) obtained in this study (open marks) and previously reported ones (closed marks) for (a) goethite [3,12,13,15], (b) ferrous oxide, (c) magnetite [21,27], and (d) biotite [3]. “0.01 M” represents the 0.01 mol dm⁻³ NaCl concentration. The previous data for ferrous oxide are not available.

Figure 2. Experimental conditions of equilibrated solutions in a pH–Eh diagram for the H–O–Se system under standard conditions. The total concentration of Se is 10⁻⁸ mol dm⁻³. The circles, squares, triangles, and asterisks represent the conditions for the sorption experiments using goethite, ferrous oxide, magnetite, and biotite, respectively.

The uncertainty of K_d was often larger than the most probable value under the conditions that the R_s was higher than 99% or lower than about 10%. For such data, the maximum or minimum values were shown in the tables.

The R_s values for goethite were almost 100% at pH < 10 and decreased to a few percent at around pH 12 (Table 1). In Figure 1(a), the obtained and previously reported [3,12,13,15] K_d values for goethite are plotted versus pH; the obtained K_d values agree with the previous ones. The K_d values show negative dependences on pH and are independent of the NaCl concentration. The sorption tendency was also in agreement with the previous one [12]. The dominant sorption mechanism of Se(IV) onto goethite has been reported to be inner-sphere surface complexation [12,52,69]. The results of the current study can also be explained by inner-sphere surface complexation.

The R_s values for ferrous oxide were almost 100% at pH < 10 and decreased to a few percent at around pH 11 (Table 2). The obtained K_d values for ferrous oxide are plotted in Figure 1(b). It was found that the K_d values were independent of the ionic strength. Although previous sorption data for ferrous oxide cannot be found, the pH dependences of K_d values for ferrous oxide show the same tendency as those for goethite. The dominant sorption mechanism of Se(IV) onto ferrous oxide can be estimated to be inner-sphere surface complexation from similarities of pH and ionic strength dependence of K_d to those for goethite. The difference in the sorption properties between Fe(II) and Fe(III) oxides was not significant in this experiment.

The R_s values for magnetite were almost 100% at pH < 9 and decreased to a few percent around pH 11(Table 3). The obtained and previously reported [21,27] K_d values for magnetite are plotted versus pH in Figure 1(c). The K_d values were independent of the ionic strength. The obtained data were in agreement with those from Kim et al. [27] obtained in Ar-filled glove box. On the other hand, the data from Fujikawa and Fukui [21] are more than one order of magnitude lower than the data obtained in this study. The lower K_d values are due to the oxidation of Se(IV) to low adsorbable Se(VI) in their experiments conducted under the atmospheric conditions [21]. The dominant sorption mechanism of Se(IV) onto magnetite has been reported to be inner-sphere surface complexation [22,27]. The results of the current study can also be explained by inner-sphere surface complexation.

The R_s values for biotite were almost 100% at pH 7 and decreased to a few percent at around pH 10 (Table 4). The obtained and previously reported [3] K_d values for biotite are plotted versus pH in Figure 1(d). The K_d values were independent of the ionic strength. The pH dependences of the K_d values for biotite are similar to those obtained by Shibutani et al. [3]. Although the sorption mechanism of Se(IV) onto biotite has not been reported, it can be estimated to be inner-sphere surface complexation from the similarities of pH and the ionic strength dependence of K_d to those for goethite and magnetite.

4.1.2. Sorption behavior of Se (−II)

Experimental data from the sorption experiments are summarized in Tables 5–9. The experimental conditions for Se(−II) are plotted on a pH−Eh diagram for the system H−O−Se [2] and shown in Figure 2. Based on the pH and Eh of the equilibrated experimental solutions in all of the experimental runs, the dominant Se(−II) species in the experimental solution was estimated to be HSe⁻.

Table 5. Experimental variables and data for Se(−II) sorption on goethite (using 0.1 g of the solid phase).

NaCl
0.01 mol dm^−3				0.1 mol dm^−3				1 mol dm^−3
pH	Eh (mV)	Rs (%)	Kd (m^3 kg^−1)	pH	Eh (mV)	Rs (%)	Kd (m^3 kg^−1)	pH	Eh (mV)	Rs (%)	Kd (m^3 kg^−1)
7.17	−220	99	(1.0 ± 0.8) × 10^1	7.90	−467	100	(3.2 ± 2.4)×10^1	7.28	−353	99	(1.9 ± 1.0)×10^1
7.98	−312	99	>1.1 × 10^1	8.08	−425	100	(3.3 ± 2.7)×10^1	7.59	−360	100	(3.1 ± 2.7)×10^1
8.02	−446	99	(1.6 ± 0.5) × 10^1	8.10	−287	98	(5.2 ± 1.5)×10^0	7.63	−329	100	>6.8 ×10^1
8.05	−287	98	(6.5 ± 3.8) × 10^0	8.29	−382	100	>8.0 × 10^1	7.89	−384	100	(2.4 ± 1.8) × 10^1
8.11	−285	98	(6.5 ± 3.8) × 10^0	8.39	−365	99	>1.5 × 10^1	7.90	−338	100	(3.8 ± 3.4) × 10^1
8.40	−362	98	(4.7 ± 0.6) × 10^0	8.42	−278	98	(5.8 ± 1.9) × 10^0	7.92	−333	99	(1.8 ± 0.9) × 10^1
8.41	−289	99	>1.3 × 10^1	8.43	−389	100	>2.3 × 10^1	8.13	−344	99	(7.6 ± 1.8) × 10^0
8.64	−399	95	(1.7 ± 0.1) × 10^0	8.57	−428	100	>9.0 × 10^1	8.15	−371	98	(4.4 ± 1.3) × 10^0
8.65	−301	99	(7.0 ± 5.0) × 10^0	8.57	−401	97	(3.4 ± 1.4) × 10^0	8.25	−416	97	(3.0 ± 0.4) × 10^0
8.65	−300	96	(2.7 ± 1.1) × 10^0	8.63	−368	98	(4.6 ± 1.9) × 10^0	8.39	−386	95	(1.8 ± 0.3) × 10^0
8.76	−302	97	(3.0 ± 1.0) × 10^0	8.70	−396	99	(9.6 ± 9.3) × 10^0	8.40	−368	99	>1.9 × 10^1
8.87	−314	98	(4.9 ± 2.5) × 10^0	8.76	−300	98	(6.1 ± 4.0) × 10^0	8.92	−340	94	(1.5 ± 0.1) × 10^0
9.01	−383	94	(1.5 ± 0.1) × 10^0	8.76	−321	99	(6.6 ± 2.4) × 10^0	8.97	−369	96	(2.1 ± 0.6) × 10^0
9.41	−326	98	(5.8 ± 3.5) × 10^0	8.86	−327	97	(3.8 ± 0.8) × 10^0	8.98	−405	93	(1.4 ± 0.3) × 10^0
10.05	−365	95	(1.8 ± 0.5) × 10^0	8.97	−312	96	(2.7 ± 1.3) × 10^0	9.50	−427	93	(1.3 ± 0.1) × 10^0
10.38	−316	90	(9.5 ± 1.3) × 10−^1	9.00	−339	96	(2.8 ± 0.4) × 10^0	9.83	−411	94	(1.6 ± 0.4) × 10^0
10.45	−338	96	(2.7 ± 0.9) × 10^0	9.53	−311	95	(1.9 ± 0.4) × 10^0	9.84	−436	91	(9.9 ± 0.2) × 10^−1
10.61	−367	92	(1.1 ± 0.2) × 10^0	9.70	−368	93	(1.4 ± 0.2) × 10^0	10.42	−462	83	(4.8 ± 0.6) × 10^−1
10.83	−369	93	(1.2 ± 0.3) × 10^0	9.89	−401	99	>1.7 × 10^1	10.55	−403	86	(6.3 ± 1.0) × 10^−1
10.95	−368	82	(4.5 ± 0.4) × 10^−1	9.98	−520	97	(2.8 ± 0.3) × 10^0	10.57	−395	96	(2.2 ± 0.5) × 10^0
11.05	−385	74	(2.8 ± 0.3) × 10^−1	10.14	−468	97	(3.4 ± 1.9) × 10^0	10.58	−388	92	(1.2 ± 0.2) × 10^0
11.16	−403	93	(1.4 ± 0.4) × 10^0	10.47	−470	97	(2.9 ± 0.9) × 10^0	10.68	−537	93	(1.3 ± 0.1) × 10^0
11.27	−411	87	(6.7 ± 1.0) × 10^−1	10.72	−481	87	(6.5 ± 0.9) × 10^−1	10.68	−324	79	(3.9 ± 0.2) × 10^−1
11.36	−435	83	(5.0 ± 0.6) × 10^−1	10.80	−469	91	(1.0 ± 0.2) × 10^0	10.89	−349	76	(3.1 ± 0.1) × 10^−1
11.49	−434	65	(1.8 ± 0.2) × 10^−1	11.12	−501	86	(6.0 ± 0.8) × 10^−1	10.89	−405	90	(9.3 ± 1.5) × 10^−1
11.50	−422	78	(3.6 ± 0.4) × 10^−1	11.23	−487	83	(5.0 ± 0.6) × 10^−1	10.96	−384	83	(4.7 ± 0.6) × 10^−1
11.51	−562	66	(1.9 ± 0.1) × 10^−1	11.28	−468	71	(2.5 ± 0.2) × 10^−1	11.00	−336	74	(2.8 ± 0.1) × 10^−1
11.61	−496	52	(1.1 ± 0.1) × 10^−1	11.31	−478	85	(5.6 ± 0.8) × 10^−1	11.07	−396	71	(2.5 ± 0.2) × 10^−1
11.64	−532	63	(1.7 ± 0.1) × 10^−1	11.51	−465	68	(2.1 ± 0.2) × 10^−1	11.09	−357	67	(2.0 ± 0.1) × 10^−1
11.68	−592	62	(1.6 ± 0.1) × 10^−1	11.57	−495	74	(2.9 ± 0.2) × 10^−1	11.16	−407	76	(3.1 ± 0.3) × 10^−1
11.70	−521	51	(1.1 ± 0.1) × 10^−1	11.58	−482	80	(4.0 ± 0.4) × 10^−1	11.30	−395	67	(2.0 ± 0.2) × 10^−1
11.72	−501	68	(2.1 ± 0.2) × 10^−1	11.59	−479	78	(3.6 ± 0.3) × 10^−1	11.34	−408	66	(1.9 ± 0.2) × 10^−1
11.72	−533	51	(1.0 ± 0.1) × 10^−1	11.63	−492	74	(2.8 ± 0.2) × 10^−1	11.36	−452	74	(2.9 ± 0.3) × 10^−1
11.77	−489	53	(1.1 ± 0.1) × 10^−1	11.65	−506	74	(2.9 ± 0.3) × 10^−1	11.39	−409	74	(2.9 ± 0.2) × 10^−1
11.87	−503	53	(1.1 ± 0.1) × 10^−1	11.67	−511	73	(2.8 ± 0.2) × 10^−1	11.40	−473	71	(2.4 ± 0.2) × 10^−1
12.01	−497	43	(7.5 ± 0.8) × 10^−2	11.70	−483	72	(2.6 ± 0.2) × 10^−1	11.47	−421	70	(2.3 ± 0.2) × 10^−1
12.14	−481	26	(3.5 ± 0.5) × 10^−2	12.03	−381	45	(8.3 ± 0.3) × 10^−2	11.52	−483	68	(2.1 ± 0.2) × 10^−1
12.28	−465	31	(4.5 ± 0.5) × 10^−2	12.07	−424	42	(7.3 ± 0.3) × 10^−2	11.91	−382	39	(6.4 ± 0.3) × 10^−2
12.55	−487	17	(2.1 ± 0.4) × 10^−2	12.43	−441	31	(4.4 ± 0.2) × 10^−2	11.92	−431	50	(9.9 ± 0.1) × 10^−2
12.66	−483	31	(4.5 ± 0.5) × 10^−2	12.46	−396	35	(5.4 ± 0.2) × 10^−2	12.33	−401	28	(3.9 ± 0.2) × 10^−2

Table 6. Experimental variables and data for Se(−II) sorption on goethite (using 1 g of the solid phase).

NaCl
0.01 mol dm^−3				0.1 mol dm^−3				1 mol dm^−3
pH	Eh (mV)	Rs (%)	Kd (m^3 kg^−1)	pH	Eh (mV)	Rs (%)	Kd (m^3 kg^−1)	pH	Eh (mV)	Rs (%)	Kd (m^3 kg^−1)
8.71	−361	100	(2.8 ± 1.7) × 10^0	8.58	−431	100	(4.6 ± 4.2) × 10^0	8.47	−441	100	(3.9 ± 3.4) × 10^0
8.72	−333	100	(2.8 ± 1.6) × 10^0	8.59	−362	100	(3.1 ± 1.9) × 10^0	8.54	−441	100	(3.9 ± 3.6) × 10^0
8.74	−316	100	(4.4 ± 4.0) × 10^0	8.60	−337	100	(2.5 ± 1.3) × 10^0	8.56	−411	100	(2.4 ± 1.3) × 10^0
8.75	−325	100	(2.5 ± 1.4) × 10^0	8.60	−335	100	(3.1 ± 1.9) × 10^0	8.63	−381	100	(2.4 ± 1.3) × 10^0
8.86	−421	98	(5.4 ± 0.7) × 10^−1	8.66	−326	100	(4.6 ± 4.2) × 10^0	8.69	−349	100	(3.3 ± 2.7) × 10^0
9.42	−336	100	(2.9 ± 2.3) × 10^0	9.03	−321	100	(4.6 ± 4.2) × 10^0	8.97	−361	100	(3.6 ± 3.1) × 10^0
9.48	−299	100	(4.0 ± 3.4) × 10^0	9.24	−311	100	>4.1 × 10^0	9.05	−366	100	(2.8 ± 1.8) × 10^0
9.97	−307	100	(2.9 ± 1.8) × 10^0	10.07	−311	100	(3.7 ± 2.8) × 10^0	9.40	−363	100	(3.9 ± 3.5) × 10^0
11.23	−494	95	(1.9 ± 0.1) × 10^−1	11.24	−421	96	(2.1 ± 0.1) × 10^−1	9.42	−336	100	>3.5 × 10^0
11.94	−463	94	(1.5 ± 0.1) × 10^−1	11.99	−465	92	(1.1 ± 0.0) × 10^−1	10.86	−355	96	(2.6 ± 0.2) × 10^−1
12.04	−483	90	(9.3 ± 0.3) × 10^−2	12.02	−472	92	(1.1 ± 0.0) × 10^−1	11.75	−432	87	(6.6 ± 0.2) × 10^−2
12.07	−497	88	(7.3 ± 0.2) × 10^−2	12.03	−478	87	(6.8 ± 0.2) × 10^−2	11.81	−443	93	(1.4 ± 0.1) × 10^−1
12.68	−485	72	(2.6 ± 0.1) × 10^−2	12.65	−496	68	(2.1 ± 0.0) × 10^−2	12.38	−486	66	(2.0 ± 0.1) × 10^−2

Table 7. Experimental variables and data for Se(−II) sorption on ferrous oxide.

NaCl
0.01 mol dm^−3				0.1 mol dm^−3				1 mol dm^−3
pH	Eh (mV)	Rs (%)	Kd (m^3 kg^−1)	pH	Eh (mV)	Rs (%)	Kd (m^3 kg^−1)	pH	Eh (mV)	Rs (%)	Kd (m^3 kg^−1)
7.79	−478	99	(1.1 ± 1.1) × 10^0	8.68	−453	98	(5.2 ± 3.1) × 10^−1	8.85	−398	99	(6.7 ± 6.1) × 10^−1
8.67	−460	99	>1.9 × 10^0	8.68	−468	97	(3.0 ± 0.9) × 10^−1	8.88	−516	99	>1.3 × 10^0
8.89	−298	94	(1.5 ± 0.3) × 10^−1	8.72	−537	99	(8.1 ± 6.3) × 10^−1	8.97	−423	99	>1.9 × 10^0
8.90	−352	99	(7.0 ± 4.2) × 10^−1	8.89	−491	99	>1.5 × 10^0	9.07	−400	97	(3.3 ± 1.6) × 10^−1
8.95	−396	100	>2.9 × 10^0	8.91	−488	99	>1.9 × 10^0	9.20	−421	99	>7.9 × 10^−1
8.95	−490	99	>1.9 × 10^0	8.92	−475	99	>9.4 × 10^−1	9.23	−549	99	>1.4 × 10^0
8.98	−426	96	(2.6 ± 0.6) × 10^−1	9.18	−501	99	>1.7 × 10^0	9.51	−567	85	(5.6 ± 0.5) × 10^−2
9.02	−497	99	>1.2 × 10^0	9.34	−511	97	(3.0 ± 1.0) × 10^−1	9.54	−523	94	(1.6 ± 0.3) × 10^−1
9.17	−485	98	(4.0 ± 1.4) × 10^−1	9.43	−566	99	>1.3 × 10^0	9.67	−425	98	(5.0 ± 3.3) × 10^−1
9.27	−488	99	(6.8 ± 4.6) × 10^−1	9.43	−486	99	>1.6 × 10^0	9.81	−506	98	(6.2 ± 5.1) × 10^−1
9.38	−472	100	>3.4 × 10^0	9.44	−509	99	(7.1 ± 4.3) × 10^−1	9.83	−529	71	(2.4 ± 0.2) × 10^−2
9.48	−486	99	(7.8 ± 6.1) × 10^−1	9.51	−471	99	>1.1 × 10^0	9.91	−456	74	(2.9 ± 0.3) × 10^−2
9.84	−539	99	(7.3 ± 5.2) × 10^−1	9.59	−468	99	(8.8 ± 8.7) × 10^−1	9.98	−417	90	(8.6 ± 1.4) × 10^−2
10.09	−436	99	>7.7 × 10^−1	9.66	−517	93	(1.3 ± 0.2) × 10^−1	10.06	−506	63	(1.7 ± 0.1) × 10^−2
10.24	−457	95	(2.0 ± 0.4) × 10^−1	9.78	−495	82	(4.5 ± 0.4) × 10^−2	10.45	−546	63	(1.7 ± 0.1) × 10^−2
10.52	−465	51	(1.1 ± 0.1) × 10^−2	10.18	−520	62	(1.6 ± 0.1) × 10^−2	10.62	−538	57	(1.3 ± 0.1) × 10^−2
10.57	−482	53	(1.1 ± 0.1) × 10^−2	10.61	−516	58	(1.4 ± 0.1) × 10^−2	10.69	−607	14	(1.7 ± 0.5) × 10^−3
10.83	−469	34	(5.1 ± 0.6) × 10^−3	10.73	−547	52	(1.1 ± 0.1) × 10^−2	10.72	−430	14	(1.6 ± 0.6) × 10^−3
10.93	−472	46	(8.4 ± 0.8) × 10^−3	10.75	−550	62	(1.6 ± 0.1) × 10^−2	10.94	−424	7	(7.4 ± 4.4) × 10^−4
11.19	−412	49	(9.6 ± 0.9) × 10^−3	10.87	−632	57	(1.3 ± 0.1) × 10^−2	10.97	−621	53	(1.1 ± 0.1) × 10^−2
11.53	−507	43	(7.6 ± 0.8) × 10^−3	11.23	−562	8	(9.2 ± 4.7) × 10^−4	11.04	−569	12	(1.4 ± 0.6) × 10^−3
11.58	−631	9	(1.0 ± 0.4) × 10^−3	11.24	−576	13	(1.5 ± 0.5) × 10^−3	11.25	−572	56	(1.3 ± 0.1) × 10^−2
12.15	−552	5	(5.4 ± 3.6) × 10^−4	11.38	−625	45	(8.0 ± 0.8) × 10^−3	11.84	−533	10	(1.1 ± 0.5) × 10^−3
12.32	−631	8	(8.2 ± 4.1) × 10^−4	11.42	−643	62	(1.7 ± 0.1) × 10^−2	11.93	−531	7	(7.4 ± 5.3) × 10^−4
12.49	−525	10	(1.1 ± 0.4) × 10^−3	12.03	−643	3	<6.8 × 10^−4	12.30	−581	4	<9.6 × 10^−4

Table 8. Experimental variables and data for Se(−II) sorption on magnetite.

NaCl
0.01 mol dm^−3				0.1 mol dm^−3				1 mol dm^−3
pH	Eh (mV)	Rs (%)	Kd (m^3 kg^−1)	pH	Eh (mV)	Rs (%)	Kd (m^3 kg^−1)	pH	Eh (mV)	Rs (%)	Kd (m^3 kg^−1)
7.61	−271	75	(2.9 ± 0.2) × 10^−2	7.11	−211	76	(3.1 ± 0.3) × 10^−2	7.32	−234	66	(2.0 ± 0.1) × 10^−2
7.77	−240	85	(5.6 ± 0.6) × 10^−2	7.34	−301	78	(3.5 ± 0.4) × 10^−2	7.41	−227	61	(1.5 ± 0.4) × 10^−2
7.81	−256	69	(2.3 ± 0.1) × 10^−2	7.46	−253	78	(3.5 ± 0.2) × 10^−2	7.57	−268	68	(2.2 ± 0.1) × 10^−2
7.87	−236	80	(4.1 ± 0.4) × 10^−2	7.48	−263	78	(3.4 ± 0.3) × 10^−2	7.66	−291	63	(1.7 ± 0.1) × 10^−2
7.91	−295	74	(2.8 ± 0.5) × 10^−2	7.51	−275	74	(2.8 ± 0.1) × 10^−2	7.81	−244	70	(2.4 ± 0.1) × 10^−2
7.93	−256	69	(2.2 ± 0.1) × 10^−2	7.82	−256	74	(2.8 ± 0.5) × 10^−2	7.87	−226	69	(2.2 ± 0.1) × 10^−2
8.00	−274	73	(2.7 ± 0.2) × 10^−2	7.83	−256	74	(2.9 ± 0.7) × 10^−2	8.02	−281	74	(2.9 ± 0.1) × 10^−2
8.12	−256	75	(3.0 ± 0.3) × 10^−2	7.84	−284	71	(2.5 ± 0.5) × 10^−2	8.05	−304	58	(1.4 ± 0.1) × 10^−2
8.15	−238	75	(3.1 ± 0.3) × 10^−2	7.88	−241	74	(2.8 ± 0.2) × 10^−2	8.19	−267	63	(1.7 ± 0.1) × 10^−2
8.20	−300	82	(4.6 ± 0.5) × 10^−2	7.89	−256	73	(2.7 ± 0.3) × 10^−2	8.24	−245	57	(1.3 ± 0.1) × 10^−2
8.35	−286	77	(3.4 ± 0.4) × 10^−2	7.90	−241	68	(2.1 ± 0.1) × 10^−2	8.35	−321	75	(3.0 ± 0.3) × 10^−2
8.37	−267	84	(5.3 ± 0.5) × 10^−2	8.00	−312	84	(5.2 ± 0.6) × 10^−2	8.46	−264	67	(2.0 ± 0.5) × 10^−2
8.49	−284	66	(1.9 ± 0.1) × 10^−2	8.02	−296	66	(2.0 ± 0.1) × 10^−2	8.49	−241	77	(3.3 ± 0.3) × 10^−2
8.50	−284	66	(1.9 ± 0.1) × 10^−2	8.09	−258	82	(4.7 ± 0.5) × 10^−2	8.51	−287	65	(1.9 ± 0.1) × 10^−2
8.51	−250	68	(2.2 ± 0.4) × 10^−2	8.21	−345	77	(3.4 ± 0.4) × 10^−2	8.52	−287	68	(2.2 ± 0.1) × 10^−2
8.55	−250	63	(1.7 ± 0.3) × 10^−2	8.22	−329	71	(2.4 ± 0.1) × 10^−2	8.60	−333	75	(3.0 ± 0.3) × 10^−2
8.57	−279	69	(2.2 ± 0.1) × 10^−2	8.49	−251	74	(2.8 ± 0.2) × 10^−2	8.64	−251	65	(1.8 ± 0.1) × 10^−2
8.68	−303	61	(1.6 ± 0.1) × 10^−2	8.50	−251	66	(2.0 ± 0.1) × 10^−2	8.69	−355	58	(1.4 ± 0.1) × 10^−2
8.74	−303	54	(1.2 ± 0.1) × 10^−2	8.51	−303	74	(2.8 ± 0.6) × 10^−2	8.72	−280	57	(1.3 ± 0.3) × 10^−2
8.77	−289	55	(1.2 ± 0.2) × 10^−2	8.60	−333	76	(3.1 ± 0.3) × 10^−2	8.74	−346	63	(1.7 ± 0.1) × 10^−2
8.77	−293	81	(4.2 ± 0.4) × 10^−2	8.60	−298	74	(2.8 ± 0.3) × 10^−2	8.79	−303	60	(1.5 ± 0.1) × 10^−2
8.77	−271	68	(2.1 ± 0.1) × 10^−2	8.63	−315	78	(3.6 ± 0.3) × 10^−2	9.00	−366	54	(1.2 ± 0.1) × 10^−2
8.79	−289	62	(1.6 ± 0.3) × 10^−2	8.67	−361	68	(2.1 ± 0.1) × 10^−2	9.02	−363	58	(1.4 ± 0.1) × 10^−2
8.86	−301	70	(2.4 ± 0.2) × 10^−2	8.69	−294	62	(1.6 ± 0.1) × 10^−2	9.04	−313	52	(1.1 ± 0.3) × 10^−2
8.97	−252	67	(2.0 ± 0.1) × 10^−2	8.71	−292	68	(2.1 ± 0.4) × 10^−2	9.06	−312	62	(1.6 ± 0.1) × 10^−2
9.04	−299	52	(1.1 ± 0.2) × 10^−2	8.72	−305	77	(3.4 ± 0.3) × 10^−2	9.06	−369	48	(9.4 ± 0.4) × 10^−3
9.05	−307	63	(1.7 ± 0.1) × 10^−2	8.74	−294	65	(1.9 ± 0.1) × 10^−2	9.09	−312	59	(1.4 ± 0.1) × 10^−2
9.06	−307	58	(1.4 ± 0.1) × 10^−2	8.92	−284	77	(3.4 ± 0.3) × 10^−2	9.12	−281	60	(1.5 ± 0.1) × 10^−2
9.37	−320	52	(1.1 ± 0.2) × 10^−2	9.00	−351	73	(2.7 ± 0.2) × 10^−2	9.54	−358	49	(9.7 ± 2.2) × 10^−3
9.38	−320	43	(7.7 ± 1.6) × 10^−3	9.05	−311	59	(1.5 ± 0.1) × 10^−2	9.56	−358	54	(1.2 ± 0.4) × 10^−2
9.41	−348	54	(1.2 ± 0.1) × 10^−2	9.05	−335	56	(1.3 ± 0.2) × 10^−2	9.58	−332	62	(1.6 ± 0.1) × 10^−2
9.42	−348	65	(1.9 ± 0.1) × 10^−2	9.05	−335	61	(1.5 ± 0.3) × 10^−2	9.69	−332	52	(1.1 ± 0.1) × 10^−2
9.62	−330	64	(1.8 ± 0.2) × 10^−2	9.19	−367	77	(3.3 ± 0.3) × 10^−2	9.69	−321	39	(6.4 ± 0.6) × 10^−3
9.91	−329	49	(9.8 ± 0.7) × 10^−3	9.23	−394	67	(2.0 ± 0.1) × 10^−2	9.69	−321	43	(7.6 ± 0.7) × 10^−3
10.12	−369	42	(7.1 ± 0.5) × 10^−3	9.30	−342	70	(2.4 ± 0.2) × 10^−2	9.74	−419	50	(9.8 ± 0.4) × 10^−3
10.21	−391	42	(7.1 ± 0.5) × 10^−3	9.34	−373	66	(1.9 ± 0.1) × 10^−2	10.03	−385	59	(1.5 ± 0.1) × 10^−2
10.24	−417	45	(8.1 ± 1.4) × 10^−3	9.39	−388	72	(2.6 ± 0.2) × 10^−2	10.10	−341	28	(3.9 ± 0.5) × 10^−3
10.24	−391	48	(9.3 ± 0.6) × 10^−3	9.42	−339	58	(1.4 ± 0.1) × 10^−2	10.10	−341	44	(7.9 ± 0.7) × 10^−3
10.26	−417	42	(7.3 ± 1.6) × 10^−3	9.44	−339	51	(1.0 ± 0.1) × 10^−2	10.14	−421	45	(8.1 ± 2.3) × 10^−3
10.36	−351	35	(5.4 ± 0.5) × 10^−3	9.66	−372	54	(1.2 ± 0.3) × 10^−2	10.15	−385	46	(8.4 ± 0.6) × 10^−3
10.42	−356	41	(6.9 ± 0.7) × 10^−3	9.68	−372	50	(1.0 ± 0.2) × 10^−2	10.20	−439	36	(5.6 ± 0.3) × 10^−3
10.51	−399	33	(4.9 ± 0.5) × 10^−3	10.19	−392	51	(1.0 ± 0.1) × 10^−2	10.28	−461	29	(4.1 ± 0.3) × 10^−3
10.72	−431	18	(2.2 ± 0.4) × 10^−3	10.39	−325	42	(7.3 ± 0.7) × 10^−3	10.29	−450	37	(5.9 ± 0.6) × 10^−3
10.82	−425	37	(6.0 ± 0.6) × 10^−3	10.46	−403	49	(9.6 ± 0.9) × 10^−3	10.34	−478	21	(2.7 ± 0.3) × 10^−3
10.83	−398	54	(1.2 ± 1.0) × 10^−2	10.63	−451	60	(1.5 ± 0.1) × 10^−2	10.43	−371	35	(5.5 ± 0.5) × 10^−3
11.01	−460	27	(3.7 ± 1.1) × 10^−3	10.70	−428	61	(1.6 ± 0.1) × 10^−2	10.56	−398	24	(3.1 ± 0.5) × 10^−3
11.06	−460	32	(4.6 ± 1.3) × 10^−3	10.76	−459	32	(4.7 ± 1.7) × 10^−3	10.63	−435	53	(1.1 ± 1.0) × 10^−2
11.06	−441	18	(2.3 ± 0.4) × 10^−3	10.81	−418	59	(1.4 ± 0.1) × 10^−2	10.73	−419	38	(6.1 ± 0.8) × 10^−3
11.11	−441	18	(2.2 ± 0.3) × 10^−3	10.93	−481	57	(1.3 ± 0.1) × 10^−2	10.87	−471	25	(3.4 ± 1.5) × 10^−3
11.16	−457	10	(1.1 ± 0.4) × 10^−3	10.95	−455	27	(3.8 ± 0.5) × 10^−3	10.91	−427	40	(6.6 ± 0.8) × 10^−3
11.22	−471	31	(4.5 ± 0.6) × 10^−3	11.12	−473	56	(1.2 ± 0.1) × 10^−2	10.92	−471	30	(4.2 ± 2.0) × 10^−3
11.29	−451	11	(1.2 ± 0.4) × 10^−3	11.17	−464	25	(3.3 ± 0.5) × 10^−3	10.95	−467	47	(8.8 ± 0.9) × 10^−3
11.39	−491	18	(2.2 ± 0.4) × 10^−3	11.20	−489	24	(3.2 ± 1.3) × 10^−3	11.18	−491	16	(1.9 ± 0.4) × 10^−3
11.41	−491	19	(2.4 ± 0.3) × 10^−3	11.27	−489	27	(3.7 ± 1.6) × 10^−3	11.24	−491	22	(2.9 ± 0.8) × 10^−3
11.53	−468	36	(5.6 ± 0.6) × 10^−3	11.28	−554	29	(4.2 ± 0.6) × 10^−3	11.25	−497	25	(3.3 ± 1.6) × 10^−3
11.57	−501	19	(2.3 ± 0.9) × 10^−3	11.33	−498	38	(6.1 ± 0.7) × 10^−3	11.58	−531	18	(2.1 ± 0.4) × 10^−3
11.62	−501	25	(3.4 ± 1.3) × 10^−3	11.57	−504	52	(1.1 ± 0.1) × 10^−2	11.60	−484	34	(5.2 ± 0.8) × 10^−3
11.79	−531	13	(1.5 ± 0.4) × 10^−3	11.77	−532	15	(1.7 ± 0.3) × 10^−3	11.68	−536	23	(2.9 ± 1.6) × 10^−3
11.84	−511	6	(6.8 ± 3.9) × 10^−4	11.87	−550	16	(1.8 ± 1.2) × 10^−3	11.68	−531	15	(1.8 ± 0.4) × 10^−3
11.86	−533	19	(2.3 ± 0.9) × 10^−3	12.59	−534	29	(4.1 ± 0.6) × 10^−3	11.93	−583	8	(8.5 ± 0.2) × 10^−4

Table 9. Experimental variables and data for Se(−II) sorption on biotite.

NaCl
0.01 mol dm^−3				0.1 mol dm^−3				1 mol dm^−3
pH	Eh (mV)	Rs (%)	Kd (m^3 kg^−1)	pH	Eh (mV)	Rs (%)	Kd (m^3 kg^−1)	pH	Eh (mV)	Rs (%)	Kd (m^3 kg^−1)
7.46	−288	86	(6.0 ± 0.6) × 10^−2	8.15	−333	81	(4.3 ± 0.4) × 10^−2	7.94	−263	82	(4.6 ± 0.5) × 10^−2
7.46	−332	93	(1.3 ± 0.3) × 10^−1	8.59	−325	89	(7.8 ± 1.0) × 10^−2	8.42	−310	80	(4.1 ± 0.4) × 10^−2
8.12	−296	80	(3.9 ± 0.3) × 10^−2	8.62	−295	83	(4.8 ± 0.5) × 10^−2	8.46	−328	87	(6.9 ± 1.0) × 10^−2
8.20	−321	85	(5.6 ± 0.6) × 10^−2	8.75	−268	80	(4.0 ± 0.4) × 10^−2	8.47	−333	82	(4.5 ± 0.5) × 10^−2
8.57	−375	84	(5.2 ± 0.5) × 10^−2	8.91	−337	90	(8.8 ± 1.3) × 10^−2	8.48	−293	82	(4.7 ± 0.5) × 10^−2
8.60	−372	85	(5.5 ± 0.6) × 10^−2	9.09	−301	81	(4.3 ± 0.4) × 10^−2	8.73	−331	89	(8.0 ± 1.2) × 10^−2
8.70	−300	77	(3.3 ± 0.3) × 10^−2	9.29	−344	90	(8.7 ± 1.2) × 10^−2	8.91	−351	78	(3.6 ± 0.3) × 10^−2
8.72	−314	88	(7.5 ± 1.0) × 10^−2	9.31	−400	81	(4.2 ± 0.3) × 10^−2	9.01	−306	74	(2.8 ± 0.3) × 10^−2
8.78	−298	86	(6.3 ± 0.7) × 10^−2	9.39	−348	90	(9.1 ± 1.3) × 10^−2	9.01	−333	86	(6.0 ± 0.7) × 10^−2
8.82	−351	87	(6.4 ± 0.7) × 10^−2	9.54	−407	82	(4.4 ± 0.4) × 10^−2	9.11	−336	86	(6.4 ± 0.8) × 10^−2
8.95	−382	84	(5.1 ± 0.5) × 10^−2	9.79	−414	81	(4.3 ± 0.4) × 10^−2	9.17	−387	87	(6.8 ± 0.7) × 10^−2
9.02	−393	79	(3.9 ± 0.4) × 10^−2	9.81	−398	78	(3.7 ± 0.3) × 10^−2	9.19	−339	88	(7.4 ± 1.1) × 10^−2
9.09	−402	77	(3.3 ± 0.3) × 10^−2	9.89	−419	88	(7.6 ± 1.0) × 10^−2	9.35	−392	86	(6.0 ± 0.6) × 10^−2
9.23	−387	84	(5.4 ± 0.5) × 10^−2	9.93	−363	89	(7.9 ± 1.0) × 10^−2	9.36	−345	88	(7.7 ± 1.2) × 10^−2
9.27	−378	87	(6.8 ± 0.8) × 10^−2	9.93	−402	75	(3.0 ± 0.2) × 10^−2	9.53	−396	88	(7.7 ± 0.9) × 10^−2
9.35	−389	84	(5.1 ± 0.5) × 10^−2	9.96	−430	85	(5.5 ± 0.6) × 10^−2	9.57	−382	75	(3.0 ± 0.3) × 10^−2
9.44	−401	80	(4.1 ± 0.5) × 10^−2	10.27	−433	93	(1.3 ± 0.3) × 10^−1	9.61	−406	83	(4.9 ± 0.4) × 10^−2
9.45	−351	84	(5.2 ± 0.5) × 10^−2	10.36	−378	83	(5.0 ± 0.5) × 10^−2	9.67	−400	84	(5.3 ± 0.5) × 10^−2
9.67	−403	79	(3.8 ± 0.4) × 10^−2	10.41	−368	72	(2.6 ± 0.2) × 10^−2	10.08	−362	86	(6.3 ± 0.8) × 10^−2
9.88	−452	77	(3.3 ± 0.2) × 10^−2	10.46	−438	90	(9.3 ± 1.3) × 10^−2	10.09	−415	87	(6.9 ± 0.7) × 10^−2
9.92	−410	58	(1.4 ± 0.1) × 10^−2	10.49	−382	79	(3.8 ± 0.3) × 10^−2	10.53	−421	71	(2.4 ± 0.2) × 10^−2
10.21	−399	71	(2.4 ± 0.2) × 10^−2	10.66	−443	85	(5.7 ± 0.5) × 10^−2	10.66	−453	70	(2.3 ± 0.2) × 10^−2
10.41	−423	56	(1.3 ± 0.1) × 10^−2	10.93	−425	62	(1.6 ± 0.1) × 10^−2	10.88	−389	54	(1.2 ± 0.1) × 10^−2
10.46	−443	68	(2.2 ± 0.1) × 10^−2	11.14	−413	58	(1.4 ± 0.1) × 10^−2	10.99	−433	55	(1.2 ± 0.1) × 10^−2
10.57	−452	52	(1.1 ± 0.1) × 10^−2	11.17	−395	60	(1.5 ± 0.1) × 10^−2	11.26	−426	42	(7.4 ± 0.9) × 10^−3
10.72	−411	62	(1.6 ± 0.1) × 10^−2	11.18	−452	67	(2.0 ± 0.1) × 10^−2	11.43	−472	55	(1.2 ± 0.1) × 10^−2
10.82	−413	66	(2.0 ± 0.2) × 10^−2	11.24	−412	69	(2.2 ± 0.2) × 10^−2	11.85	−493	44	(8.0 ± 0.8) × 10^−3
10.90	−406	67	(2.1 ± 0.1) × 10^−2	11.62	−472	70	(2.3 ± 0.2) × 10^−2	11.89	−507	45	(8.2 ± 1.0) × 10^−3
11.13	−501	61	(1.5 ± 0.1) × 10^−2	12.06	−503	31	(4.6 ± 0.5) × 10^−3	12.33	−470	30	(4.3 ± 0.6) × 10^−3
11.15	−457	44	(7.9 ± 0.7) × 10^−3	12.50	−530	35	(5.5 ± 0.5) × 10^−3	12.33	−532	33	(4.9 ± 0.6) × 10^−3
11.28	−436	49	(9.7 ± 0.9) × 10^−3
11.33	−472	43	(7.5 ± 0.8) × 10^−3
11.36	−468	45	(8.1 ± 0.7) × 10^−3
11.38	−520	52	(1.1 ± 0.1) × 10^−2
11.76	−412	50	(9.9 ± 0.9) × 10^−3
12.09	−465	24	(3.2 ± 0.5) × 10^−3
12.22	−461	21	(2.7 ± 0.5) × 10^−3
12.26	−462	44	(7.8 ± 0.7) × 10^−3
12.51	−491	37	(6.0 ± 0.6) × 10^−3
12.63	−491	27	(3.7 ± 0.5) × 10^−3

The R_s values for goethite were almost 100% at pH < 10 and decreased to 30% at pH 12.5 in the experimental runs using 0.1 g of the solid phase (Table 5). The R_s values were almost 100% at pH < 11 and decreased to 70% at pH 12.5 in the experimental runs using 1 g of the solid phase (Table 6). The obtained K_d values for goethite – from 2.0 × 10⁻² to 38 m³ kg⁻¹ – are plotted versus pH in Figure 3(a). The K_d values obtained from the experiments using 1 g of the solid phase were consistent with those obtained using 0.1 g of the solid phase.

The R_s values for ferrous oxide were almost 100% at pH < 9.5 and decreased to a few percent at pH 12 (Table 7). The obtained K_d values for ferrous oxide, 5.4 × 10⁻⁴ to 1.1 m³ kg⁻¹, are plotted versus pH in Figure 3(b). The influence of the NaCl concentration on the sorption was not significant. The K_d values for ferrous oxide were approximately 2 orders of magnitude lower than those for goethite. The difference in K_d is likely to be due to the difference in the specific surface areas (17.6 m² g⁻¹ for goethite and 0.2 m² g⁻¹ for ferrous oxide). The pH dependences of K_d values for ferrous oxide show the same tendencies as those for goethite.

The R_s values for magnetite were almost 80% at pH 7 and gradually decreased to 10% at pH 12 (Table 8). The obtained K_d values for magnetite are plotted versus pH in Figure 3(c). The variation in K_d was not systematically related to the ionic strength. The K_d values of Se(−II) for magnetite, 6.8 × 10⁻⁴ to 5.6 × 10⁻² m³ kg⁻¹, are 1–3 orders of magnitude lower than those for goethite, and the pH dependences of the K_d values for magnetite are also lower than those for goethite.

The R_s values for biotite were almost 90% at pH 8 and gradually decreased to 30% at pH 12.5 (Table 9). The obtained K_d values for biotite, 2.7 × 10⁻³ to 1.3 × 10⁻¹ m³ kg⁻¹, versus pH are plotted in Figure 3(d). The pH dependences of the K_d values of Se(−II) for biotite show the same tendencies as those for magnetite.

4.2. Analysis of the sorption behavior by the TLM

4.2.1. Sorption behavior of Se (IV)

The sorption behaviors of Se(IV) were analyzed by the TLM. Figure 4 shows a schematic representation of the TLM. The protonation and deprotonation reactions of ≡FeOH can be expressed by (4) (5)

Figure 3. The K_d values for Se(−II) obtained in this study: (a) goethite, (b) ferrous oxide, (c) magnetite, and (d) biotite. Open marks and closed marks represent the data obtained using 1 g and 0.1 g of the solid phase, respectively.

Figure 4. Schematic drawing of the triple-layer model.

Figure 5. Comparison of R_s values of Se(IV) predicted using the TLM (lines) with experimentally measured ones (marks): (a) goethite, (b) ferrous oxide, (c) magnetite, (d) biotite (calculated with K^int_SeO3 = 10^15.1), and (e) biotite (calculated with K^int_SeO3 = 10^16.1).

Figure 6. Comparison of R_s values of Se(−II) predicted using the TLM (lines) with experimentally measured ones (marks): (a) goethite (using 0.1 g of the solid phase; assuming inner-sphere complexation), (b) goethite (0.1 g of the solid phase; outer-sphere complexation), (c) goethite (1 g of the solid phase; inner-sphere complexation), (d) goethite (1 g of the solid phase; outer-sphere complexation), (e) ferrous oxide (inner-sphere complexation), and (f) ferrous oxide (outer-sphere complexation).

Figure 7. Comparison of R_s values of Se(−II) predicted using the TLM (lines) with experimentally measured ones (marks): (a) magnetite (assuming inner-sphere complexation), (b) magnetite (outer-sphere complexation), (c) biotite (inner-sphere complexation), and (d) biotite (outer-sphere complexation).

In this model, the activity of protons at any location {H⁺}_i is related to the bulk activity {H⁺}_b by the Boltzmann distribution: (6) where F is the Faraday constant (96,485 C mol⁻¹), ψ_i the electric potential (V) at any given location, R the gas constant (8.3145 J K⁻¹ mol⁻¹), and T the temperature (298.15 K). The intrinsic surface acidity constants of ≡FeOH are given by using the surface potential ψ₀ as an electrostatic correction factor: (7) (8) where the square brackets represent concentrations (mol dm⁻³) and the curly brackets represent activities (the activity coefficients for the surface species are assumed to be equal [34]). The sorption of the electrolyte ions, Na⁺ and Cl⁻, can be described as outer-sphere surface complexation [12,70]: (9) (10) (11) (12) where ψ_β is the surface potential at the β plane. The sorption of Se(IV) onto ≡FeOH sites can be described as inner-sphere surface complexation [12,22,27,52,69]. Biotite includes aluminol (≡AlOH) and silanol (≡SiOH) sites on the edge surfaces, in addition to ≡FeOH sites [3]. In this study, the sorption of Se(IV) onto biotite was analyzed by assuming inner-sphere surface complexation with ≡FeOH sites, as reported by Shibutani et al. [3]. The inner-sphere surface complexation of Se(IV) with ≡FeOH sites can be described by assuming a simple monodentate surface complex (≡FeSeO₃⁻) [12,27] as (13) (14)

Considering all the species in equilibrium, the surface site density Ns (C m⁻²) and the surface charge density σ (C m⁻²) at the 0, β, and d planes are written as [32,71] (15) (16) (17) (18) where S is the specific surface area (m² g⁻¹), V the volume of the solution (dm³), W the weight of the solid sample (g), I_c the ionic strength (mol dm⁻³), ψ the electric potential (V), ϵ the relative dielectric constant of water (78.5 at 25°C [32]), ϵ₀ the permittivity of free space (8.854 × 10⁻¹² C V⁻¹ m⁻¹), and z the ionic charge (valid for a symmetrical electrolyte). Considering the electrostatics of the layers, the following equations are obtained: (19) (20) (21) where C₁ is the inner-layer capacitance (F m⁻²) and C₂ is the outer-layer capacitance (F m⁻²). The values of R_s and K_d were calculated as (22) (23)

The TLM was calculated by the Visual Minteq computer program with the Davies equation for activity correction [32].

For the TLM parameters on the sorption of Se(IV) onto goethite, the values reported by Hayes et al. [12] were used in this calculation. The K^int_Clvalue, which was not reported by Hayes et al. [12] is in the range of 6.4–9.0 in the literatures [3,52,70,72–74]; the intermediate value of 8.0 reported by Fukushi and Sverjensky [50] was adopted. The model parameters are summarized in Table 10. Figure 5(a) shows the comparison of the R_s values of Se(IV) for goethite calculated using TLM with the experimentally measured values and there is good agreement between the two.

Table 10. Model parameters and equilibrium constants for the TLM calculation.

			Goethite	Ferrous oxide	Magnetite	Biotite
Surface area	S	m^2 g^−1	17.6^a	0.2^a	1.6^a	4.6^a
Site density	ns	sites nm^−2	7.0^b	7.0	2.5^e	2.5
capacitance	C1	F m^−2	1.1^b	1.1	1.2^f	1.2
	C2	F m^−2	0.2^b	0.2	0.2^f	0.2
Equilibrium
constant			5.8^b	5.8	5.1^e	4.6^i
			–11.1^b	−11.1	–9.1^e	–6.4^i
	log K^intNa		–8.8^b	−8.8	–6.8^g	–6.8
	log K^intCl		8.0^c	8.0	8.0	8.0
			15.1^b	15.1	16.1^e	15.1
	log K^intHSe		6.0^d	6.0	−	−
	log K′^intHSe		−	−	12^h	12^h

Notes: The parameters for ferrous oxide were same as for goethite. The logK^int_Cl value for magnetite was same as that for goethite. The site density, capacitance, logK^int_Na, and logK^int_Clvalues for biotite were the same as those for magnetite. The logvalue for biotite was same as that for goethite.

^aObtained by Brunauer–Emmett–Teller method.

^bFrom Hayes et al. [12].

^cFrom Fukushi and Sverjensky [50].

^dDetermined by the least-squares fitting to the experimental data.

^eFrom Kim et al. [27].

^fFrom Sahai and Sverjensky [72].

^gFrom Criscenti and Sverjensky [75].

^hProvisional value estimated from the experimental data.

ⁱFrom Chakraborty et al. [76].

The TLM parameters for ferrous oxide are not available. Instead, the parameters for goethite were used to analyze the sorption onto ferrous oxide based on the similarities of pH dependence of K_d for ferrous oxide to that for goethite (Figure 1). Figure 5(b) shows the comparison of the predicted R_s values for ferrous oxide with the experimentally measured values and there is good agreement between the two.

The sorption behavior of Se(IV) onto magnetite has been analyzed using DDLM by Kim et al. [27]. The surface site density (n_s = 2.5 sites nm⁻²), surface acidity constants (log = 5.1 and log = −9.1), and the surface complexation constant (24) (25) reported by Kim et al. [27] were adopted in this calculation. The value for magnetite was calculated to be 10^16.1 from Equations (3) and (25), which was 1 order of magnitude higher than that for goethite (10^15.1). For the values of capacitances and the surface complexation constants for Na⁺ and Cl⁻, which were not reported by Kim et al., the values C₁ = 1.2 F m⁻² [72], C₂ = 0.2 F m⁻² [72], logK^int_Na = −6.8 [75], and logK^int_Cl = −8.0 (the same as for goethite) were adopted. Figure 5(c) shows the comparison of R_s values of Se(IV) for magnetite calculated, using TLM with the experimentally measured values and there is good agreement between the two.

The surface acidity constants of biotite were reported by Chakraborty et al. [76] (log = 4.6 and log = −6.4); however, other parameters are not available. The TLM parameters for magnetite were used for the analysis of sorption behavior onto biotite. For , the value for goethite (10^15.1) was more suitable than that for magnetite (10^16.1) (Figures 5(d) and 5(e)). The calculated values show good agreement with the experimentally measured values.

From the calculation results, the validity of surface parameters for employed iron-containing minerals was confirmed.

4.2.2. Sorption behavior of Se (−II)

The sorption behaviors of Se(−II) were also analyzed by the TLM. The chemical properties of selenium are known to be similar to those of sulfur which is chalcogen congener (the group 16 elements of the periodic table) [54,77]. The stokes radii, conductivity and softness of HSe⁻ are 110 pm, 70.4 cm² Ω⁻¹ mol⁻¹ and 0.44, respectively, and these values are similar to those of hydrosulfide ion (HS⁻), 110 pm, 65 cm² Ω⁻¹ mol⁻¹ and 0.65, respectively [78]. In addition, the incorporation of selenide into iron sulfides, such as pyrite (FeS₂) and mackinawite (FeS), can be seen [54–56,77]. Therefore, the sorption behavior of HSe⁻ onto iron-containing minerals is expected to be similar to that of HS⁻. Although the inner-sphere surface complexation reaction of HSe⁻ with ≡FeOH sites has not been reported, it can be estimated from its chemical similarity to HS⁻ as [79–81] (26) (27)

The outer-sphere surface complexation of HSe⁻ can be described as (28) (29)

The values of R_s and K_d were calculated as (30) (31)

The TLM parameters for the surface characteristics of the minerals were the same as those used for Se(IV) (Table 10).

The obtained R_s values for goethite using 0.1 g of the solid phase versus pH are plotted with the results of the TLM calculation by assuming inner-sphere surface complexation (Figure 6(a)) and outer-sphere surface complexation (Figure 6(b)). The sorption tendency for goethite can be well explained by inner-sphere surface complexation but not by outer-sphere surface complexation (logK′^int_HSe = 12). The inner-sphere surface complexation constant for goethite,K^int_HSe, was determined by a least-squares fitting of the model calculations to the experimental R_s data using 0.1 g of the solid phase (Figure 6(a)). The obtained value, logK^int_HSe = 6.0, was slightly higher than the value for HS⁻, (32) which is derived from the equilibrium constants of the reactions (33) and (34)

The experimental R_s data using 1 g of the solid phase were reproduced by assuming inner-sphere surface complexation with logK^int_HSe = 6.0 (Figure 6(c)) but not by outer-sphere surface complexation (logK′^int_HSe = 12) (Figure 6(d)). In addition, the experimental R_s data for ferrous oxide were also successfully reproduced by the TLM calculation by assuming inner-sphere surface complexation with the K^int_HSevalue for goethite (logK^int_HSe = 6.0) (Figure 6(e)) but not by outer-sphere surface complexation (logK′^int_HSe = 13) [Figure 6(f)].

The K_d values of Se(−II) for magnetite showed different tendencies from those of goethite and ferrous oxide (Figure 3). The obtained R_s values for magnetite are plotted versus pH with the results of the TLM calculation by assuming inner-sphere surface complexation (logK^int_HSe = 6.0) in Figure 7(a). The sorption tendency for magnetite cannot be explained by inner-sphere surface complexation. The data plot show vertical dispersion and the dependences of the data of Se(−II) on pH and ionic strength are unclear as compared to those of Se(IV). The large variation in the sorption data of Se(−II) may have been caused by polymerization of the HSe⁻ species. The dominant species of Se(−II) were estimated to be HSe⁻ under the experimental pH–Eh conditions, but HSe⁻ can partially polymerize to a lower adsorbable divalent anion species, such as Se₃²⁻ and Se₄²⁻, depending on the redox potentials (Figure 2): (35) (36)

The variation of several tens of percent in the R_s data could be induced by the uncertainty of the Eh measurements at the boundary area (Figure 2). Figure 7(b) shows the results of the model calculation by assuming an outer-sphere surface complexation with logK′^int_HSe = 11.7 as compared with the experimentally obtained R_s data. The model calculation predicted the R_s values of Se(−II) for magnetite reasonably well. Although the variation in data is too large to obtain the exact value of logK′^int_HSe, it can be estimated to be around 12. The value of logK′^int_HSe = 12 is comparable with the previously reported values for the outer-sphere complexation of Se(IV) and Se(VI) [12]: log for goethite (13.4) and HFO (12.8) and logfor goethite (14.0) and HFO (12.8), described as (37) (38)

The obtained R_s values of Se(−II) for biotite are plotted as a function of pH in Figures 7(c) and 7(d). The pH dependences of the R_s values for biotite show the same tendencies as those for magnetite and cannot be explained by inner-sphere surface complexation (logK^int_HSe = 8) (Figure 7(c)). Figure 7(d) shows the results of the model calculation by assuming outer-sphere surface complexation with logK′^int_HSe = 11.8 as compared with the experimental R_s data. Although the variation in data is significant, logK′^int_HSecan be estimated to be around 12. The sorption behavior of Se(−II) onto biotite can thus be explained by assuming outer-sphere surface complexation.

5. Conclusion

The sorption data of Se(−II) and Se(IV) onto the iron-containing minerals, goethite, ferrous oxide, magnetite, and biotite were obtained by batch sorption experiments. The obtained K_d values of Se(IV) agree with previously reported values and were successfully reproduced by the TLM calculations by assuming inner-sphere complexation, the validity of this experimental method and surface parameters used for the TLM calculations were confirmed.

The K_d values of Se(−II) were obtained in a range of 2.0 × 10⁻² to 38 m³ kg⁻¹ for goethite, 5.4 × 10⁻⁴ to 1.1 m³ kg⁻¹ for ferrous oxide, 6.8 × 10⁻⁴ to 5.6 × 10⁻² m³ kg⁻¹ for magnetite, and 2.7 × 10⁻³ to 1.3 × 10⁻¹ m³ kg⁻¹ for biotite at pH 7–13. The sorption data and the TLM calculations suggest that the dominant sorption mechanisms of Se(−II) were inner-sphere complexation (≡FeSe⁻) for goethite and ferrous oxide but outer-sphere complexation (≡FeOH₂⁺₋HSe⁻) for magnetite and biotite. The equilibrium constant for inner-sphere complexation (logK^int_HSe) was determined to be 6.0 and that for outer-sphere complexation (logK′^int_HSe) was estimated to be approximately 12.

Acknowledgements

The authors acknowledge Mr. M. Kamoshida for experimental measurements.

Additional information

Funding

Part of this research is funded by the Secretariat of Nuclear Regulation Authority (NRA), NRA, Japan (formerly the Nuclear and Industrial Safety Agency, Ministry of Economy, Trade and Industry, Japan).