Sorption behaviour of Pu⁴⁺ and PuO₂²⁺ on amido amine-functionalized carbon nanotubes: experimental and computational study

Abstract

Amido amine-functionalized multi-walled carbon nanotubes (MWCNT-AA) were used for efficient and selective solid phase separation of plutonium(IV) and plutonium(VI). Langmuir, Freundlich, Dubinin–Radushkevich (D–R), and Tempkin isotherms were employed for understanding the sorption mechanism and Lagergren first order kinetics, an intra-particle diffusion model, and pseudo second order kinetics were applied to understand the sorption kinetics. The sorption proceeded through monolayer coverage of MWCNT-AA with capacities of 91.2 mg g⁻¹ and 89.4 mg g⁻¹ for Pu⁴⁺ and PuO₂²⁺, respectively following a Langmuir isotherm while the sorption kinetics followed a pseudo second order reaction with rate constants of 3.86 × 10⁻⁵ and 3.19 × 10⁻⁵ g mg⁻¹ min⁻¹ for Pu⁴⁺ and PuO₂²⁺ respectively. This MWCNT-AA showed high radiolytic stability and a method was developed for almost quantitative back extraction of plutonium in both the oxidation states from MWCNT-AA. Finally, the sorbent MWCNT-AA was employed for processing synthetic high level waste solution obtained from a research reactor origin. Moreover, density functional theory calculation was performed to examine the coordination and interaction behaviour of Pu⁴⁺ and PuO₂²⁺ ions towards MWCNT-AA. The present DFT study reveals that Pu is deca-coordinated (two from each of four nitrates and one AA) in the case of Pu⁴⁺ and octa-coordinated (two from each of two nitrates and one AA, and one from each of two oxo groups) in PuO₂²⁺. The calculated free energy of complexation was found to be almost three times higher for Pu⁴⁺ than PuO₂²⁺ both in the gas and aqueous phase, which thus confirms the experimentally observed higher sorption of Pu⁴⁺ compared to PuO₂²⁺ by MWCNT-AA.

---

Introduction

Heavy radioactive elements like ²³⁹Pu generated from nuclear industries have a great effect on the environment. Fuel reprocessing also generates large amounts of radioactive wastes in aqueous nitric acid medium. Removal of these toxic elements from the environment and solution is of importance for safety and from ecological angles.

Extensive work has been carried out using sorption of such toxic elements. Plutonium is the second pillar of India’s three-stage nuclear program. Utilization of a mixed oxide (MOX) fuel in the fast breeder reactors (FBRs), made from plutonium-239, recovered by reprocessing spent fuel from the first stage is the prime concept of the second stage of this visionary program.¹

Various technologies exist for the removal of plutonium, which include filtration, solvent extraction, ion exchange, and adsorption. Adsorption is considered one of the most attractive processes for Pu removal from solution, since adsorbents are generally easy to handle in the case of radioactive metals and can be used for various situations.² In sorption techniques, a minimum amount of solvent is used and due to this it is eco-friendly. Many materials such as bentonite,³ activated carbon,⁴ clay minerals,^5–9 mesoporous silica,¹⁰ graphene oxide,^11,12 biomass,^13–15 and natural and modified zeolites^16,17 are used as adsorbents.

Carbon nanotubes (CNTs),¹⁸ a new form of carbon, have come under intense multidisciplinary study because of their unique physical and chemical properties. There are two main types of carbon nanotubes that can have high structural perfection. Single-walled nanotubes (SWNTs) consist of a single graphite sheet seamlessly wrapped into a cylindrical tube. Multi-walled nanotubes (MWNTs) comprise an array of such nanotubes that are concentrically nested like rings of a tree trunk.¹⁹ CNTs have a highly porous and hollow structure, large specific surface area, light mass density, and strong interaction between carbon and hydrogen molecules. These properties led to interest in their potential application as quantum nanowires, heterogeneous catalysts,^20,21 solar cells,²² microelectronics,^23,24 chemical sensors,^25,26 and sorbents for hydrogen and other gas storage.^27–30 CNTs have been considered as the most preferred solid phase sorbent material for the removal of organic pollutants^31–33 and heavy metals^34–38 from aqueous medium and for pre-concentration of lanthanides^39,40 and actinides^41–43 from acidic aqueous medium. Additionally density functional theory (DFT) calculation has been performed to study the nature of the coordination and interaction of Pu⁴⁺ and PuO₂²⁺ ions towards MWCNT-AA. Theoretical studies on the adsorption of actinides involving functionalized ligands have started coming recently.⁴⁴ Therefore, DFT calculation was carried out to find the coordination mode of the functionalized ligand with an endeavour to know the complexation of Pu⁴⁺ and PuO₂²⁺ with MWCNT-AA.

Experimental

Reagents

Supra-pure HNO₃ (E-Merck, Darmstadt, Germany) and quartz double-distilled water were used throughout the experiment. ²³⁹Pu was used in the present investigation. Pu stock solution was prepared by dissolving spectra-pure PuO₂ in conc. HNO₃ + 0.05 M HF. To prevent interference from fluoride ions, it was removed by repeated evaporation to dryness. Furthermore, the acidity was adjusted using 1 M HNO₃. Stock solutions of Pu(IV) and Pu(VI) were prepared by the following techniques. Pu(IV) was prepared by adding NaNO₂ in aliquots of stock solution and extracting with 0.5 M thenoyl-trifluoro-acetone (HTTA) in xylene followed by stripping it with 8 M HNO₃ making it suitable for further use. Pu(VI) was prepared by adding AgO in aliquots of stock solution and was used for all experiment purposes. Oxalic acid and Na₂CO₃, used for stripping experiments, were procured from Thomas Baker Chemical limited, India and Qualigens fine Chemicals, Mumbai, India, respectively. Analytical grade ethylenediamine (EDA), N,N′-dicyclohexylcarbodiimide (DCC), nitric acid, and sulphuric acid, all purchased form SDFine Chemical, India, were used for functionalization of the MWCNTs. Ethylene diamine tetra acetic acid (EDTA) was purchased from Sisco Research Laboratories Pvt. ltd., India. The precession of the measurements was assured (RSD = less than 5%) by five replicate measurements.

Preparation of MWCNT-AA

The catalytic CVD method followed by hydrochloric acid and heating treatment for purification was used to synthesize MWCNTs with a purity greater than 98.5%, an outside diameter (OD) of 15–25 nm, an inside diameter (ID) of 5–8 nm, a length ∼200 μm, and a specific surface area (SSA) of more than 150 m² g⁻¹.⁴⁵ The purified MWCNTs were oxidized by a 3 : 1 (v/v) mixture of concentrated sulfuric and nitric acid to introduce carboxylic groups. The carboxyl MWCNTs were treated with EDA in the presence of DCC at 90 °C producing MWCNT-AA. FTIR analysis: ν (cm⁻¹): 3420 (N–H str.), 2371, 2308 (–CH str.), 1650 (C=O str.), 1542, 1520 (N–H bend., C=C str.). XRD analysis: 2θ = 26.08° and 43.08° for (0, 0, 2) and (1, 1, 0) planes of MWCNTs.

Instruments

ICP-AES. The analysis of the raffinate obtained after processing simulated high level waste (SHLW) solution was carried out using inductively coupled plasma atomic emission spectroscopy (ICP-AES) with a charged couple device (CCD) as a detector. The optimized operating conditions and instrument specifications for the present investigation are summarized in Table 1.

Table 1 Specifications and operating conditions of ICP-AES

Instrument specification
Optical design	Paschen-Runge mounting, circular design
Focal length	750 mm
Grating	Holographic
Groove density	1800 grooves per mm (1), 3600 grooves per mm (2)
Wavelength range	130–800 nm
Entrance slit width	15 microns
Resolution (FWHM)	0.01 nm from 130–450 nm, 0.02 nm from 450–800 nm
Thermal regulation	Controlled to 30 ± 1 °C
Frequency	27.12 MHz
Pump	Dual channel peristaltic pump
Detector	Linear arrays of CCD (3648 pixels per array)
Nebulizer	Concentric nebulizer with cyclonic spray chamber
ICP-torch	Demountable, radial viewing
Operating conditions
Coolant flow	15 L min^−1
Auxiliary flow	0.5 L min^−1
Total time of measurement	28 s
Pump speed	30 rpm
RF power output	1.2 kW
Input power	230 V AC

---

Sorption process

For establishing the extraction profiles for Pu⁴⁺ and PuO₂²⁺ using amido amine-functionalized multi-walled carbon nanotubes (MWCNT-AA), a suitable amount of MWCNT-AA was allowed to equilibrate for two hours with the aqueous phase having acidity in the range 0.01 M HNO₃ to 6 M HNO₃ containing Pu⁶⁺ and Pu⁴⁺ tracer. After two hours of equilibration, it was centrifuged for complete phase separation. Then suitable aliquots from the aqueous phase were taken for radiometric analysis using the 60 keV peak of Pu.

For sorption isotherm experiments, a similar protocol was adopted from 3 M HNO₃ at 300 K using various amounts of MWCNT-AA. The K_d value was calculated using the expression below:

where C₀ is the initial concentration of the metal ion (mg⁻¹), C_e is the concentration of the metal ion (mg⁻¹) after equilibrium, v is the volume of the aqueous phase (mL), and w is the weight (mg) of the CNTs taken for the experiment. The K_d value is indicative of the sorption efficiency. A greater K_d value indicates that more of the metal ion will be adsorbed on the MWCNT-AA. Since the amount of sorbent used in the extraction process and the total volume of aqueous solution containing metal ion have an influence on the quantity of the metal ion adsorbed on the sorbent, both of these factors have been included in the K_d values for normalization. Generally a K_d value greater than or equal to 10³ is taken as good sorption.

For sorption kinetics experiments, a suitable amount of MWCNT-AA was allowed to equilibrate in an aqueous phase containing Pu⁴⁺ and PuO₂²⁺ at 3 M HNO₃. After each specified time interval, suitable aliquots of the aqueous phase were collected for radiometric analysis.

To investigate the radiolytic stability, MWCNT-AA was exposed to various gamma exposure up to 1500 kGy. With the irradiated MWCNT materials, the sorption experiments were carried out with 3 M HNO₃ aqueous feed, 2 hours equilibration, and at 300 K.

The composition of the SHLW is summarized in Table 3. 10 mL of SHLW solution was processed using MWCNT-AA material. After processing the raffinate was fed into plasma for ICP-AES analysis.

The stripping experiments were done in two steps. In the first step Pu⁴⁺ and PuO₂²⁺ were loaded on MWCNT-AA from the 3 M HNO₃ feed while in the second stage, aqueous complexing agents like Na₂CO₃, EDTA, and oxalic acid were tried for stripping of the loaded Pu⁴⁺ and PuO₂²⁺ from the MWCNT phase.

Computational methodology

DFT calculation was conducted for the electronic structures, geometry, energy, and thermochemistry related to the sorption of Pu⁴⁺ and PuO₂²⁺ by CNT-AA with the Turbomole program suite.⁴⁶ An (8, 0) zigzag single-walled CNT (SWNT) with four unit cells with a tubular length of 5.78 Å and width of 6.40 Å was considered for the calculation. An amido amine (AA) unit was attached to the open end of the CNT owing to the higher reactivity of the open end dangling carbon atoms.⁴⁷ The geometrical structures of the SWNT-AA and its complexes with Pu⁴⁺ and PuO₂²⁺ were made (using MOLDEN⁴⁸ molecular and electronic structure processing software), and optimized with the B3LYP functional, a hybrid Hartree–Fock/DFT method that includes Becke’s three-parameter functional (B3) with the Lee, Yang and Parr (LYP) correlation functional^49,50 in conjunction with the def-SVP⁵¹ basis set, which contains C(7s4p1d)/[3s2p1d], N(7s4p1d)/[3s2p1d], O(7s4p1d)/[3s2p1d], H(4s1p)/[2s1p], and Pu(14s13p10d8f1g)/[10s9p5d4f1g]. Orbital population analysis on the optimized structures was performed using natural population analysis (NPA).⁵² The charge transfer (ΔN)⁵³ between the Pu metal centre and AA donor of SWNT-AA was evaluated using the absolute electronegativity (χ) and absolute hardness (η) of the metal ion and sorbent. Using Koopmans’ theorem,⁵⁴ χ and η can be calculated from the energy of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of the metal and sorbent, which are inputs from the DFT calculation. The vibrational frequency and single point energy of each optimized geometry were calculated using B3LYP theory in conjunction with triple-zeta def-TZVP⁵⁵ basis sets which contain C(11s6p1d)/[5s3p1d], N(11s6p1d)/[5s3p1d], O(11s6p1d)/[5s3p1d], H(5s1p)/[3s1p], and Pu(14s13p10d8f1g)/[10s9p5d4f1g]. The relativistic effective core potential (RECP)⁵⁶ which includes 60 electrons in the core was used for Pu, whereas the polarized all electron basis sets were used for the light atoms C, H, O, and N. Four unpaired electrons for Pu⁴⁺ and two for PuO₂²⁺ were used for consideration of the spin state of Pu. Gibbs free energies (ΔG) were calculated with the zero point energy (ZPE) calculation and thermal energy correction in the gas phase (T = 298.15 K, P = 0.1 MPa). The aqueous phase energies were attained by introducing bulk solvent effects using the COSMO⁵⁷ continuum solvent model with ionic radii at the B3LYP/def-TZVP level of theory.

Results and discussion

Effect of aqueous feed acidity on the K_d values of Pu⁴⁺ and PuO₂²⁺

For the extraction profile of Pu⁴⁺ and PuO₂²⁺, K_d values as a function of feed acidity were taken into consideration and it was observed that for both the metal ions the K_d values were found to increase with an increase in the HNO₃ concentration. The increase in the K_d values with aqueous feed acidity might be due to the participation of NO₃⁻ anions on complexation.

Pu_(aq)⁴⁺ + AA-MWCNT + 4NO₃⁻_(aq) = Pu(NO₃)₄·AA-MWCNT (2)

PuO₂²⁺_(aq) + AA-MWCNT + 2NO₃⁻_(aq) = PuO₂(NO₃)₂·AA-MWCNT (3)

Fig. 1 represents the variation of K_d values for Pu⁴⁺ and PuO₂²⁺ on AA-MWCNT as a function of aqueous feed acidity.

Fig. 1 Effect of feed acidity on the K_d values of Pu⁴⁺ and PuO₂²⁺.

Understanding the sorption mechanism through isotherms

To understand the sorption mechanism involved, different sorption isotherms are explored as empirical models which are obtain from the regression analysis of experimental data. The present investigation deals with the fitting of the sorption isotherm data for Pu⁴⁺ and PuO₂²⁺ in the four most widely accepted sorption isotherm models: the Langmuir, Dubinin–Radushkevich (D–R), Freundlich, and Tempkin isotherms (Fig. 2). The main objective behind this is to understand the sorption mechanism based on the best linear regression.

Fig. 2 Langmuir, D–R, Freundlich, and Tempkin isotherms for Pu⁴⁺ and PuO₂²⁺ on MWCNT-AA.

Langmuir isotherm

This describes the monolayer formation in between the adsorbate and the outer surface of the adsorbent, and after that no further adsorption takes place. The Langmuir isotherm represents the equilibrium distribution of metal ions between the solid and liquid phases.⁵⁸ This isotherm is valid only for monolayer adsorption onto a surface containing a finite number of identical sites. In this model there is no transmigration of adsorbate in the plane of the surface. Based upon these assumptions, the Langmuir isotherm is represented by the following equation:where C_e is the equilibrium concentration of the plutonium ion, q_e is the amount of metal ion adsorbed on the MWCNTs at equilibrium, q_o is the sorption capacity of MWCNT-AA for Pu⁴⁺ and PuO₂²⁺, and b is the sorption energy. The sorption capacity of PuO₂²⁺ (89.4 mg g⁻¹) was found to be lower than that of Pu⁴⁺ (91.2 mg g⁻¹). The sorption energy values also follow the same trend. The linear regression coefficients for the Langmuir isotherm were found to be 1.00003 and 1.00005 for Pu⁴⁺ and PuO₂²⁺ on MWCNT-AA respectively, as shown in Table 2.

Table 2 Different constants obtained from the Langmuir, D–R, Freundlich, and Tempkin isotherms

Langmuir isotherm
	qe (mg g^−1)	b (L mol^−1)	χ^2
Pu^4+	91.2	0.016	1.00003
PuO2^2+	89.4	0.009	1.00005

---

Dubinin–Radushkevich isotherm
	Xm (mg g^−1)	E (kJ mol^−1)	R
Pu^4+	91.6	12.41	0.99885
PuO2^2+	90.0	10.59	0.99882

---

Freundlich isotherm
	kf (mg g^−1)	n	R
Pu^4+	102.1	16.11	0.99978
PuO2^2+	90.2	15.19	0.99968

---

Tempkin isotherm
	AT (L mg^−1)	b	R
Pu^4+	64.0	42.6	0.99988
PuO2^2+	14.4	40.3	0.99989

---

Table 3 Sorption kinetics for Pu⁴⁺ and PuO₂²⁺ on MWCNT-AA

Lagergren first order kinetics
	qe	kads	R
Pu^4+	1454.5	0.042	0.86728
PuO2^2+	1414.2	0.032	0.80590

---

Intra-particle diffusion model
	kp	C	R
Pu^4+	26.1	26 115.6	0.82965
PuO2^2+	30.8	27 445.0	0.91974

---

Pseudo second order
	qe	k2	R
Pu^4+	26 617.6	3.8 × 10^−5	0.99995
PuO2^2+	28 049.3	3.1 × 10^−5	0.99994

---

The Langmuir adsorption does not explain the surface roughness and inhomogeneity of the adsorbent. It also neglects multiple site sorption and the influence of neighbouring sorption sites. In view of this, it was tried to analyze the experimental data by other isotherm models.

Dubinin–Radushkevich (D–R) isotherm

The Dubinin–Radushkevich isotherm, an empirical model initially conceived for subcritical vapors onto micropore solids by the pore filling mechanism, is used to express the sorption mechanism with a Gaussian energy distribution onto a heterogeneous surface. This isotherm is mainly used for distinguishing physisorption and chemisorption.⁵⁹ It can be expressed as follows:

ln q_e = ln X_m − βε² (5)

where q_e is the amount of metal ion adsorbed on the MWCNTs at equilibrium, X_m is the maximum sorption capacity, β is the activity coefficient, and ε is:

ε = RT ln(1 + 1/C_e) (6)

where C_e is the equilibrium concentration of thorium in the aqueous phase, R is 8.314 kJ mol⁻¹, and T is the absolute temperature in K. The energy (E) can be evaluated from the activity coefficient β:

E = 1/(−2β)^1/2 (7)

The energy values for Pu⁴⁺ and PuO₂²⁺ were found to be 12.41 and 10.59 kJ mol⁻¹, respectively, showing the chemical interaction between the amido amine group and plutonium ion in both the oxidation states. Moreover, this interaction was found to be greater in the case of Pu⁴⁺ compared to that of PuO₂²⁺. A similar observation was also noticed in the case of the K_d values for plutonium. The linear regression coefficients for this model were found to be 0.99885 and 0.99882, respectively for Pu⁴⁺ and PuO₂²⁺. These linear regression coefficient values were inferior compared to those from the Langmuir model.

Freundlich isotherm

This is commonly used to describe the adsorption characteristics for a heterogeneous surface. It describes the relation between the adsorbate concentration on the surface and the adsorbate concentration in a liquid. This isotherm can be applied to multilayer adsorption. This is expressed by the following equation:⁶⁰where k_f is the Freundlich isotherm constant (mg g⁻¹), n is the sorption intensity, C_e is the equilibrium concentration of plutonium (mg L⁻¹), and Q_e is the amount of plutonium ions adsorbed per gram of MWCNT-AA at equilibrium conditions (mg g⁻¹). The Freundlich isotherm constant, k_f, gives an approximate estimation of the adsorption capacity of Pu⁴⁺ and PuO₂²⁺ on the MWCNTs. n is an indication of the strength of sorption. If n = 1 then the partition of the metal ion between the solid and liquid phases is independent of the concentration of the metal ion. An n value above one indicates normal sorption whereas that below one indicates cooperative adsorption. In the present investigation the n values for Pu⁴⁺ as well as PuO₂²⁺ were found to be well above 1. The higher k_f value for Pu⁴⁺ revealed its higher sorption capacity over PuO₂²⁺ on MWCNT-AA. This was in good agreement with that obtained by the Langmuir isotherm. The regression coefficients for Pu⁴⁺ and PuO₂²⁺ for the Freundlich isotherm were evaluated as 0.99978 and 0.99968 for tetra and hexavalent plutonium, respectively.

Tempkin isotherm

The Tempkin isotherm model is based on the fact that the heat of adsorption of all molecules in the layer decreases linearly (not with a logarithmic nature) with a uniform distribution of binding energies.⁶¹ The model can be quantitatively expressed as:

q_e = B ln A_T + B ln C_e (12)

where A_T is the Tempkin isotherm equilibrium binding constant (L g⁻¹), b is the Tempkin isotherm constant, R is the universal gas constant (8.314 J mol⁻¹ K⁻¹), B is a constant related to the heat of sorption (J mol⁻¹), and T is 300 K. For the present experiment it was observed that the A_T value for Pu⁴⁺ was ∼4.5 times greater than that for PuO₂²⁺. But the regression coefficients for Pu⁴⁺ and PuO₂²⁺ on the MWCNT-AA isotherms were found to be 0.99988 and 0.99989, respectively.

Based on the linear regression analysis, the sorption process was found to follow the Langmuir isotherm, i.e. through a monolayer, without interaction of the neighbouring sorbent sites and by considering all the binding sites to be equivalent.

Kinetics study

Kinetics is one of the important sections of a sorption study that should be looked into. If C_t and C_te are the metal ion concentrations on MWCNT-AA at time t and at equilibrium, then the fractional attainment of the equilibrium (F) can be expressed as:⁶²

A plot of 1 − F as a function of time (Fig. 3) reveals that with an increase in time the 1 − F values decrease drastically up to 45 min followed by a gradual decrease. This study primarily revealed that 45 minutes is essential for attaining the equilibrium. To get into the details of sorption kinetics, the experimental data were fitted on different models: Lagergren first order, the intra-particle diffusion model, and finally a pseudo second order reaction.

Fig. 3 Sorption kinetics of Pu⁴⁺ and PuO₂²⁺ on MWCNT-AA.

Lagergren equation/pseudo first order

The pseudo first order rate equation of Lagergren has been widely applied to describe the kinetic process of liquid–solid phase adsorption.⁶³ This is expressed by the following equation:where q and q_e are the amount of metal ion adsorbed on MWCNT-AA at time t and at equilibrium conditions. The rate constant, k_ads, can be calculated from the slope of the curve of log(q_e − q) vs. t. The rate constant k_ads for Pu⁴⁺ was found to be greater compared to that for PuO₂²⁺, while the linear regression coefficients were evaluated as 0.8672 and 0.8059 for Pu⁴⁺ and PuO₂²⁺, respectively (Table 4). The linear regression coefficients were found to be poor in the present model.

Table 4 The analytical results obtained by ICP-AES after processing the SHLW with MWCNT-AA

	Analytical line (nm)	RR
		Initial (mg L^−1)	Final (mg L^−1)	Kd
Al	396.152	250	245 ± 16	0.20
Ba	455.404	100	94 ± 4	0.60
Ca	396.847	400	388 ± 19	0.30
Cd	361.051	300	292 ± 11	0.26
Cr	284.984	400	366 ± 15	0.85
Fe	244.451	1500	1476 ± 20	0.16
Mg	280.270	300	273 ± 14	0.90
Mn	257.611	500	499 ± 15	0.02
Na	588.995	500	497 ± 10	0.06
Ni	227.021	300	288 ± 17	0.40
Sr	407.771	50	46 ± 3	0.80
Ce	413.380	100	0.95 ± 4	9.50
La	379.478	100	0.96 ± 4	9.60
Ru	245.644	7.5	7.1 ± 0.3	0.53
Mo	281.615	30	28 ± 3	0.66

---

Intra-particle diffusion model. The intra-particle diffusion model has been used to describe the sorption process occurring on a porous sorbent. A process is diffusion-controlled if its rate depends on the rate at which the components diffuse towards each other. Based on the intra-particle diffusion model, the rate constant can be expressed by the following equation:⁶⁴

q = k_pt^0.5 + C (15)

where k_p is the intra-particle diffusion rate constant obtained from the slope of a q_t vs. t^0.5 linear plot, while C (mg g⁻¹), evaluated from the intercept, is proportional to the boundary layer thickness. The linear relationship between q_t and t^0.5 revealed that the sorption process is controlled by intra-particle diffusion only.

However, multi-linear graphs indicate that two or more steps influence the sorption process. The intra-particle diffusion rate constant for PuO₂²⁺ and Pu⁴⁺ is found to be almost similar. The C values were found to be almost similar suggesting the same boundary layer thickness for the sorption. The linear regression coefficients for the above analysis were also found to be poor as with those obtained by the Lagergren pseudo first order kinetics.

Pseudo second order model. The sorption kinetics data were also analyzed using pseudo second order kinetics,⁶⁵ expressed as follows:where k₂ (g mg⁻¹ min⁻¹) is the pseudo second order rate constant. A plot of t/q vs. t gives straight lines for both the dendrimers with high linear regression coefficients. The slope of this plot gives the q_e value while the intercept gives the pseudo second order rate constant. The rate constant for Pu⁴⁺ was found to be almost 1.2 times that for PuO₂²⁺. The overall analyses of the sorption kinetics also revealed that sorption of plutonium on MWCNT-AA takes place through pseudo second order rate kinetics.

Back extraction of Pu from MWCNT-AA

During processing of radiotoxic metal ions, it is imperative that a method should be developed for back extraction of both the oxidation states of plutonium from loaded MWCNT-AA. This is very important on the basis of accounting for precious metal and also for its further processing either in a nuclear reactor or as waste for disposal. In view of this, several agents were used to serve the purpose. Out of them only 0.01 M oxalic acid, 0.01 M sodium carbonate, and 0.01 M EDTA were found to be successful for achieving at least more than or equal to 70% elution of the metal ion in both the oxidation states (Fig. 4). It was also observed that for tetravalent plutonium, 0.01 M oxalic acid was the best for almost quantitative (more than 99%) recovery of plutonium. In the case of hexavalent plutonium, 0.01 M sodium carbonate showed the most promising results of ∼99% stripping from loaded MWCNT-AA.

Fig. 4 Elution behaviour of Pu⁴⁺ and PuO₂²⁺ from MWCNT-AA.

Radiolytic degradation

During processing of the radiotoxic metal ion, alpha, beta and other particles along with high energy gamma rays deposit energy on the medium. As a result, the weakest bond of the sorbent will break. This may lead to the degradation of the performance of the sorbent either by reducing the sorbent efficiency or by decreasing the selectivity. A sorbent with maximum radiation resistance is always desirable. In this context, the MWCNT-AA was exposed to a variety of radiation doses up to 1500 kGy and with the irradiated MWCNT-AA, the sorption efficiency for tetra and hexavalent plutonium was determined. The results are shown in Fig. 5. With 500 kGy, 1000 kGy, and 1500 kGy of gamma irradiation, the sorption efficiency for Pu⁴⁺ was found to become ∼94.9%, 90.7%, and 86.5%, respectively, whereas that for PuO₂²⁺ became 93.6%, 88.4%, and 84.1%, respectively. This study revealed that MWCNT-AA had high radiation stability towards gamma irradiation.

Fig. 5 The radiolytic stability of MWCNT-AA.

Selectivity of MWCNT-AA

The success of the sorbent lies in the efficient and selective separation of the targeted metal ion from the actual waste composition. In this regard, simulated high level waste of research reactor origin was processed using MWCNT-AA. The sorption of most of the metal ions present in the nuclear waste i.e. Al, Ba, Ca, Cd, Cr, Fe, Mg, Mn, Na, Ni, Sr, Ru, and Mo was found to be negligibly small while Ce and La were found to be extracted on the solid phase. Table 4 summarizes the analytical results obtained after processing the SHLW by MWCNT-AA followed by feeding the aqueous phase directly into the plasma.

Computational results

The optimized geometrical structures of SWNT-AA and its complexes with Pu⁴⁺ and PuO₂²⁺ with nitrate anions are shown in Fig. 6. The Pu–O and Pu–N bond distances involved in the complexation reaction are shown in Table 5. The AA and all the nitrate anions are coordinated to the Pu metal centre in a bidentate mode for both the Pu⁴⁺ and PuO₂²⁺ complexes. Thus Pu is deca-coordinated (two from each of four nitrates and one AA) in the former complex, and octa-coordinated (two from each of two nitrates and one AA, and one from each of two oxo groups) in the latter.

Fig. 6 The optimized geometric structures at the B3LYP/SVP level of theory for the Pu⁴⁺ (a) and PuO₂²⁺ (b) complexes with SWNT-AA in the presence of nitrate anions.

Table 5 Characteristic Pu–O and Pu–N bond distances in the optimized geometries

Molecular system	Pu–O(C=O)	Pu–N(NH2)	Pu–O(NO3)
Pu(NO3)4(SWNT-AA)	2.24	2.60	2.45
PuO2(NO3)2(SWNT-AA)	2.42	2.67	2.47

---

The Pu–O(C=O) bond distance is shorter (2.24 Å) for the Pu⁴⁺ complex compared to that of PuO₂²⁺ (2.42 Å), whereas the Pu–N and Pu–O(NO₃–) bonds are of a nearly similar strength for both complexes. This implies the formation of a more stable complex by Pu⁴⁺ than that of PuO₂²⁺ with SWNT-AA. For further insight of the binding in these two complexes, the calculated natural population analysis (NPA) results of the optimized complex and bare ions are summarized in Table 6. The f shell of both complexes is populated by a greater number of electrons compared to that of their free corresponding tetravalent and hexavalent oxo plutonium cations.

Table 6 Calculated f orbital population and natural charges on the Pu atoms

Species	Gas phase			Aqueous phase
	f pop	Q	ΔQ*	f pop	Q	ΔQ
Pu(NO3)4(SWNT-AA)	5.15	1.45	2.55	5.43	1.29	2.71
Pu^4+	4.0	4.0		4.0	4.0
PuO2(NO3)2(SWNT-AA)	5.19	1.43	1.03	5.49	1.25	1.40
PuO2^2+	4.88	2.46		4.78	2.65

---

This population enhancement in the f shell is greater in the aqueous phase compared to that in the gas phase (e.g. for the Pu⁴⁺ complex, 4.0 increases to 5.15 in the gas phase, whereas 4.0 increases to 5.43 in the aqueous phase) signifying the involvement of water in the complexation. The natural charge (Q) on the Pu atom in the gas phase changes from 4.0 and 2.46 in the free metal ion to 1.45 and 1.43 in the complex structures of Pu⁴⁺ and PuO₂²⁺, respectively. This also reveals the greater interaction by Pu⁴⁺ than PuO₂²⁺, as cationic charge neutralization occurs more in the former (2.25) case than in the latter (1.03). The same observations are seen in the aqueous phase, only the charge neutralization on the Pu metal is more (2.27/1.40) due to the participation of water molecules in the coordination. The quantum mechanical descriptors for the Pu acceptor and SWNT-AA donor were calculated from the energy of the HOMO and LUMO using Koopmans’ theorem and are summarized in Table 7. The higher HOMO–LUMO gap, electronegativity, and hardness of Pu⁴⁺ (4.96, 43.89, and 2.50 eV, respectively) compared to those of PuO₂²⁺ (4.81 eV, 21.52, and 2.40 eV, respectively) signify the better acceptor property of the former.

Table 7 Calculated various molecular descriptors at the B3LYP/TZVP level of theory

	EHOMO (eV)	ELUMO (eV)	Gap (EHOMO–LUMO (eV))	χ (eV)	η (eV)	ΔN
Pu^4+	−46.39	−41.39	4.96	43.89	2.50	7.60
PuO2^2+	−23.93	−19.11	4.81	21.52	2.40	3.48
SWNT-AA	−3.93	−3.66	0.27	3.79	0.13

---

On the other hand, with lower values of the HOMO–LUMO gap, electronegativity, and hardness (0.27, 3.79, and 0.13 eV, respectively), SWNT-AA has a strong donor capacity. Thus the amount of charge transfer (ΔN) is higher in Pu⁴⁺ (7.60) than in PuO₂²⁺ (3.48) leading to stronger complexation for the former case.

In order to estimate the stability of the Pu amido amine bonds in the two complexes, the free energy of complexation of Pu⁴⁺ and PuO₂²⁺ with SWNT-AA in the presence of nitrate ions is calculated in the gas phase and aqueous solution. As shown in Table 8, the free energy of complexation is almost three times higher for Pu⁴⁺ than for PuO₂²⁺ both in the gas and aqueous phase. The decrease in the aqueous phase energy values is due to extra solvent–metal ion interaction. This confirms the higher sorption of Pu⁴⁺ compared to PuO₂²⁺ by SWNT-AA.

Table 8 Calculated free energy of complexation (kcal mol⁻¹) of Pu⁴⁺ and PuO₂²⁺ with SWNT-AA at the B3LYP/TZVP level

Complexation reaction	ΔGg	ΔGaq
Pu^4+ + SWNT-AA + 4NO3^− → Pu(NO3)4(SWNT-AA)	−1751.36	−326.60
PuO2^2+ + SWNT-AA + 2NO3^− → PuO2(NO3)2(SWNT-AA)	−512.59	−110.93

---

Conclusions

MWCNT-AA is demonstrated as a highly selective and efficient sorbent for tetra and hexavalent plutonium. Different isotherm analysis revealed that the Langmuir isotherm is predominantly operative through a monolayer without mutual interaction of the neighbouring complexation sites. The sorption was also found to be chemisorption. Based on linear regression analysis the sorption process was found to proceed via a pseudo second order reaction. The sorbent was also found to show high radiolytic stability even up to gamma exposure of 1500 kGy. Density functional theory reveals that MWCNT-AA and all the nitrate anions are coordinated to the Pu metal centre in bidentate mode for both the Pu⁴⁺ and PuO₂²⁺ complexes. The present calculated free energy of complexation from DFT is shown to be almost three times higher for Pu⁴⁺ than for PuO₂²⁺ both in the gas and aqueous phase. The theoretical results confirm that MWCNT-AA binds Pu⁴⁺ more strongly than PuO₂²⁺ which is also corroborated from the sorption experiment.

Acknowledgements

The authors wish to acknowledge Dr R. M. Kadam, Head, Actinide Spectroscopy, Section and Dr P.·K. Pujari, Head, radiochemistry Division, and Shri K. T. Shenoy, Head, Chemical Engineering Division, Bhabha Atomic Research centre for their constant support.

References

1. R. Chidambaram and C. Ganguly, Curr. Sci., 1996, 70(1), 21.
2. A. Dabrowski, Adv. Colloid Interface Sci., 2001, 93, 135.
3. Y. Chen, B. Zhu, D. Wu, Q. Wang, Y. Yang, W. Ye and J. Guo, Chem. Eng. J., 2012, 387, 181.
4. M. Sekar, V. Sakthi and S. Rengaraj, J. Colloid Interface Sci., 2004, 279, 307.
5. A. Meleshyn, M. Azeroual, T. Reeck, G. Houben, B. Riebe and C. Bunnenberg, Environ. Sci. Technol., 2009, 43, 4896.
6. H. Marcussen, P. E. Holm, B. W. Strobel and H. C. B. Hansen, Environ. Sci. Technol., 2009, 43, 1122.
7. A. A. Rouff, E. J. Elzinga and R. J. Reeder, Environ. Sci. Technol., 2006, 401, 792.
8. Y. J. Wang, D. A. Jia, R. J. Sun, H. W. Zhu and D. M. Zhou, Environ. Sci. Technol., 2008, 42, 3254.
9. S. B. Wang, T. Terdkiatburana and M. O. Tade, Sep. Purif. Technol., 2008, 62, 64.
10. X. Feng, G. E. Fryxell, L. Q. Wang, A. Y. Kim, J. Liu and K. M. Kemner, Science, 1997, 276, 923.
11. R. Sitko, E. Turek, B. Zawisza, E. Malicka, E. Talik, J. Heimann, A. Gagor, B. Feista and R. Wrzalik, Dalton Trans., 2013, 42, 5682.
12. R. B. Gujar and P. K. Mohapatra, RSC Adv., 2015, 5, 24705.
13. Z. Reddad, C. Gerente, Y. Andres and P. Le Cloirec, Environ. Sci. Technol., 2002, 36, 2067.
14. J. G. Parsons, K. J. Tiemann, J. R. Peralta-Videa and J. L. Gardea-Torresdey, Environ. Sci. Technol., 2006, 40, 4181.
15. S. Deng and Y. P. Ting, Environ. Sci. Technol., 2005, 398, 490.
16. L. M. Camacho, R. R. Parra and S. Deng, J. Hazard. Mater., 2011, 189, 286.
17. K. Payne and T. Abdel-Fattah, J. Environ. Sci. Health, Part A: Toxic/Hazard. Subst. Environ. Eng., 2005, 40, 723.
18. S. Iijima, Nature, 1991, 354, 56.
19. R. H. Baughman, A. A. Zakhidov and W. A. de Heer, Science, 2002, 297, 787.
20. P. Serp, M. Corrias and P. Kalck, Appl. Catal., A, 2003, 253(2), 337–358.
21. J. M. Planeix, N. Coustel, B. Coq, V. Brotons, P. S. Kumbhar, R. Dutartre, P. Geneste, P. Bernier and P. M. Ajayan, J. Am. Chem. Soc., 1994, 116(17), 7935.
22. J. We, Y. Jia, Q. Shu, Z. Gu, K. Wang, D. Zhuang, G. Zhang, Z. Wang, J. Luo, A. Cao and D. Wu, Nano Lett., 2007, 7(8), 2317.
23. A. Bachtold, P. Hadley, T. Nakanishi and C. Dekker, Science, 2001, 294(5545), 1317.
24. W. Hoenlein, F. Kreupl, G. S. Duesberg, A. P. Graham, M. Liebau, R. V. Seidel and E. Unger, IEEE Trans. Compon. Packag. Technol., 2004, 27(4), 629.
25. A. Merkoçi, M. Pumera, X. Llopis, B. Pérez, M. del Valle and S. Alegret, TrAC, Trends Anal. Chem., 2005, 24(9), 826.
26. Q. Zhao, Z. Gan and Q. Zhuang, Electroanalysis, 2002, 14(23), 1609.
27. R. Ma, Y. Bando, H. Zhu, T. Sato, C. Xu and D. Wu, J. Am. Chem. Soc., 2002, 124, 7672.
28. C. Kim, Y. S. Choi, S. M. Lee, J. T. Park, B. Kim and Y. H. Lee, J. Am. Chem. Soc., 2002, 124, 9906.
29. L. Schlapbach and A. Züttel, Nature, 2001, 414, 353.
30. J. Hilding, E. A. Grulke, S. B. Sinnott, D. Qian, R. Andrews and M. Jagtoyen, Langmuir, 2001, 17, 7540.
31. K. L. Salipira, B. B. Mamba, R. W. Krause, T. J. Malefetse and S. H. Durbach, Environ. Chem. Lett., 2007, 5(1), 13.
32. L. Hanchao, F. Suping, D. Xiaolin, Z. Nannan and L. Yongli, Energy Procedia, 2011, 5, 985.
33. K. Pyrzynska, Sep. Purif. Technol., 2008, 37, 372.
34. C. S. Lu, H. S. Chiu and C. Liu, Ind. Eng. Chem. Res., 2006, 45(8), 2850.
35. G. P. Rao, C. Lu and F. S. Su, Sep. Purif. Technol., 2007, 58(1), 224.
36. Y. H. Li, J. Ding, Z. Luan, Z. Di, Y. Zhu, C. Xu, D. Wu and B. Wei, Carbon, 2003, 41(14), 2787.
37. C. Chen and X. Wang, Ind. Eng. Chem. Res., 2006, 45(26), 9144.
38. M. Tuzen, K. O. Saygi and M. Soylak, J. Hazard. Mater., 2008, 152(2), 632.
39. C. L. Chen, X. K. Wang and M. Nagatsu, Environ. Sci. Technol., 2009, 43(7), 2362.
40. X. L. Tan, D. Xu, C. L. Chen, X. K. Wang and W. P. Hu, Radiochim. Acta, 2008, 96(1), 23.
41. S. A. Perevalov and N. P. Molochnikova, J. Radioanal. Nucl. Chem., 2009, 281, 603.
42. A. Sengupta, S. Jayabun, A. Boda and S. M. Ali, RSC Adv., 2016, 6, 39553.
43. X. Wang, C. Chen, W. Hu, A. Ding, D. Xu and X. Zhou, Environ. Sci. Technol., 2005, 39(8), 2856.
44. (a) S. Pahan, S. Anil Boda and S. Musharaf Ali, Theor. Chem. Acc., 2015, 134, 1; (b) A. K. Singha Deb, A. Bhattacharyya, S. Musharaf Ali, K. T. Shenoy and S. K. Ghosh, Mol. Simul., 2015, 41, 490; (c) A. K. Singha Deb, S. Musharaf Ali and K. T. Shenoy, RSC Adv., 2015, 5, 80076; (d) S. Musharaf Ali, S. Pahan, A. Bhattacharyya and P. K. Mohapatra, Phys. Chem. Chem. Phys., 2016, 18, 9816.
45. K. Dasgupta, J. B. Joshi, H. Singh and S. Banerjee, AIChE J., 2014, 60, 2882.
46. R. Ahlrichs, M. Bar, M. Haser, H. Horn and C. Kolmel, Chem. Phys. Lett., 1989, 162, 165–169.
47. T. Lin, V. Bajpai, T. Ji and L. Dai, Aust. J. Chem., 2003, 56, 635.
48. G. Schaftenaar and J. M. Noordik, J. Comput.-Aided Mater. Des., 2000, 14, 123.
49. A. D. Becke, J. Chem. Phys., 1993, 98, 5648.
50. C. Lee, W. Wang and R. G. Parr, Phys. Rev. B: Condens. Matter, 1988, 37, 785.
51. A. Schaefer, H. Horn and R. J. Ahlrichs, J. Chem. Phys., 1992, 97, 2751.
52. A. E. Reed, R. B. Weinstock and F. Weinhold, J. Chem. Phys., 1985, 83, 735.
53. A. Szabo and N. S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory, Dover Publications, 1996.
54. T. Koopmans, Über die Zuordnung von Wellen funktionenund Eigenwertenzu den einzelnen Elektroneneines Atoms, Physica, 1933, 1, 104.
55. R. Ahlrichs, M. Bar, M. Haser, H. Horn and C. Kolmel, Chem. Phys. Lett., 1989, 162, 165.
56. W. Kuchle, M. Dolg, H. Stoll and H. Preuss, J. Chem. Phys., 1994, 100, 7535.
57. A. Klamt, J. Phys. Chem., 1995, 99, 2224.
58. T. H. Vermeulan, K. R. Vermeulan and L. C. Hall, Ind. Eng. Chem. Fundam., 1966, 5, 212.
59. (a) M. B. Ibrahim and S. Sani, Open J. Phys. Chem., 2014, 4, 139; (b) N. D. Hutson and R. T. Yang, Adsorption, 1997, 3(3), 189; (c) K. Y. Foo and B. H. Hameed, Chem. Eng. J., 2010, 156, 2.
60. A. Sengupta, S. Jayabun, I. C. Pius and S. K. Thulasidas, J. Radioanal. Nucl. Chem., 2016, 309(2), 841.
61. (a) M. I. Tempkin and V. Pyzhev, Acta Physicochim. URSS, 1940, 12, 327–356; (b) C. Aharoni and M. Ungarish, J. Chem. Soc., Faraday Trans., 1977, 73, 456; (c) A. O. Dada, A. P. Olalekan, A. M. Olatunya and O. Dada, J. Appl. Chem., 2012, 3(1), 38.
62. R. Chiarizia, E. P. Horwitz and S. D. Alexandratos, Solvent Extr. Ion Exch., 1994, 12, 211.
63. D. B. Singh, G. Prasad, D. C. Rupainwar and V. N. Singh, Water, Air, Soil Pollut., 1988, 42, 373.
64. (a) G. D. Sheng, S. T. Yang, Y. M. Li, X. Gao, Y. Y. Huang, J. Hu and X. K. Wang, Radiochim. Acta, 2014, 102(1–2), 155; (b) G. Sheng, Y. Li, X. Yang, X. Ren, S. Yang, J. Hu and X. Wang, RSC Adv., 2012, 2, 12400.
65. (a) G. Sheng, Y. Li, H. Dong and D. Shao, J. Radioanal. Nucl. Chem., 2012, 293, 797; (b) Y. Li, G. Sheng and J. Sheng, J. Mol. Liq., 2014, 199, 474.

---