An amide functionalized task specific carbon nanotube for the sorption of tetra and hexa valent actinides: experimental and theoretical insight

Abstract

An amide functionalized multiwalled carbon nanotube (CNT-DHA) was used for efficient and selective solid phase separation of tetravalent (Th⁴⁺) and hexavalent (UO₂²⁺) actinides. Langmuir, Freundlich, Dubinin–Rodushkevich (D–R) and Tempkin isotherms were employed for understanding the sorption mechanism while various models (Lagergren first order kinetics, intra particle diffusion model and pseudo second order kinetics) were applied to understand the sorption kinetics. The sorption proceeded via monolayer coverage of CNT-DHA with capacities of 32 mg g⁻¹ and 47 mg g⁻¹ for UO₂²⁺ and Th⁴⁺, respectively following a Langmuir isotherm while the sorption kinetics followed a pseudo second order reaction with rate constants of 0.044 and 0.095 g mg⁻¹ min⁻¹ for UO₂²⁺ and Th⁴⁺, respectively. The CNT-DHA was found to have high radiolytic stability up to 1000 kGy gamma exposure. The stripping study revealed that oxalic acid can be used for almost quantitative back extraction of Th⁴⁺ and for UO₂²⁺ sodium carbonate can be effectively used. DFT calculations were performed to understand the complexation of Th⁴⁺ and UO₂²⁺ with CNT-DHA. The structural parameters of UO₂²⁺ and Th⁴⁺ ions with CNT-DHA, and the large ion–ligand interaction energy were correlated with the higher selectivity of Th⁴⁺ ions over UO₂²⁺ ions.

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Introduction

In the three-stage nuclear power programme of India, the first stage is the utilization of uranium resources in a Pressurized Heavy Water reactor while the second stage is the utilization of plutonium generated in the first stage while the most important third stage is the use of vast thorium resources which have a self sustaining nuclear power programme based on ²³³U generated from thorium.¹ Therefore, either in the back end or in the front end of the nuclear fuel cycle separation of uranium and thorium is essential for their effective utilization, waste management and other environmental safety aspects.² Mainly solvent extraction and precipitation methods have been adopted for the separation of these actinides for various applications.³ In these regards, tri-n-butyl phosphate (TBP) is used as work horse in nuclear industries for the separation of uranium, plutonium and thorium in various processes including PUREX and ThOREX.⁴ Unfortunately, the radiolytic stability of TBP was found to be poor which not only resulted the reduction in extraction efficiency but selectivity too due to the formation of the degradation products (MBP, DBP etc.).⁵ The main disadvantages of TBP also include the poor separation factor with respect to Zr, Ru; formation of third phase for tetravalent actinides, aqueous phase solubility of TBP and non bio degradability. Moreover, the distribution ratio of thorium was found to be only moderate for its plant scale application. Several research demonstrated that di-n-hexyl octanamide (DHOA) is one of the promising ligands for the extraction of tetra and hexa valent actinides.⁶ Additionally, the plant scale application of the solvent extraction process generates large amount of radioactive organic liquid waste which requires a separate strategy to manage. Therefore, there is a need of development of solid phase separation of uranium and thorium which is efficient, selective and biodegradable.

There are several studies available in the literature where polymer and polymers networks are functionalized with amideoximes and phosphoric, methacrylic, acrylic, succinic, glutamic, iminoacetic and hydroxamic acids were used for the removal of metal ions waste solutions.⁷ A crosslinked polyester resin containing acrylic acid as functional groups was synthesized to study the adsorption behavior of strontium ions using Freundlich, Elovich, pseudo-first order and pseudo-second order kinetic models, Langmuir and Dubinin–Radushkevich isotherms. Radiation induced polyacrylamidoxime were used for separation of U isotopes by difference in the stability constants of their complex. Even sodium methacrylate functionalized cross-linked copolymer has been demonstrated for the removal of Cs⁺ ions from aqueous solutions. The polyethylene adsorbents were prepared by grafting of acrylonitrile, acrylic acid, and their mixture for the chemisorption of uranyl ion from aqueous solution.

Due to the novel structural, electronic, mechanical, and nonlinear optical properties, carbon nano tube (CNT) show promise with a wide range of applications in heterogeneous catalysis, transparent electrodes and capacitors, electrochemical sensors, solar cells, batteries and transistors etc.⁸ The unique physicochemical properties such as highly porous and hollow structure, large specific surface area, light mass density, and strong interaction between carbon and molecules, make carbon nano tube as the preferential solid supports for the extraction of either radio toxic actinides or chemically toxic heavy metal ions from environmental samples or from aqueous media.⁹ Functionalized multiwalled carbon nano tube used for task specific applications, is one of the most important areas of modern research in metal ion separation.¹⁰

In view of these, N,N-dihexyl amide functionalized multi-walled carbon nano tube (CNT-DHA) was applied for the separation of hexavalent uranium and tetra valent thorium from the aqueous acidic waste solution. To throw light on the nature of sorption and sorption kinetics different isotherm and kinetic models were applied. The selectivity, stripping and radiolytic stability of the CNT-DHA have been explored. The theoretical study have been carried out to understand the complexation of Th⁴⁺ and UO₂²⁺ with CNT-DHA and it also explained the higher selectivity of Th⁴⁺ towards CNT-DHA.

Experimental

Reagents and instruments

Th(IV) stock solution was prepared by dissolving spectra pure ThO₂. For dissolution HF–HNO₃ was used primarily. To avoid the interference from fluoride ion, it was removed by repeated evaporation to dryness and finally, the feed was adjusted to the required acidity. The stock solution of uranyl was prepared by dissolving high purity U₃O₈ in conc. HNO₃ followed by its feed adjustment to a particular acidity. Oxalic acid and Na₂CO₃ were produced from Thomas Baker Chemical limited and Qualigens fine Chemicals, Mumbai, India, respectively. CNT-DHA was procured from Global Nanotech, India with purity more than 99% and was used for sorption experiments without further treatment. All the experiments were carried out using Suprapure HNO₃ (E-Merck, Darmstadt, Germany), CertiPUR® solutions of individual elements (E-Merck, Darmstadt, Germany) and quartz double distilled water.

The analyses were carried put using Inductively Coupled Plasma Atomic Emission Spectrometer (ICP-AES) with Charged Coupled Device (CCD) as detector procured from Spectro ARCOS, Germany. The optimized instrumental and experimental parameters were summarized in ESI Table 1.† For irradiation ⁶⁰Co gamma chamber (GB 5000), FTD, BARC, India was used.

Method

For the sorption experiments 20 mg of CNT-DHA was taken in a test tube. Then 10 mg L⁻¹ of the uranyl or thorium solution (10 mL) was added into the CNT-DHA. Then it was allowed to equilibrate for 2 hours. Then after complete phase separation/settlement, the aqueous phase was collected and it was fed into the plasma of ICP-AES for quantitative determination of the metal ion after sorption. The K_d values were calculated as followswhere, C₀ is the initial concentration of the metal ion C_e is the concentration of metal ion after equilibrium, v is the volume of the aqueous phase and w is the weight of the CNT-DHA taken for the experiment.

The stripping experiments were carried out in two steps. In the first step, 20 mg of CNT-DHA was allowed to equilibrate with 10 mL of 10 mg L⁻¹ uranyl and thorium solution at 3 M HNO₃ for 2 hours. Then the loaded CNT-DHA was separated and collected separately. In the second stage, the loaded 10 mg CNT-DHA was allowed to equilibrate with 10 mL of stripping solution (0.05 M oxalic acid, 0.05 M sodium carbonate and 0.01 M HNO₃) for half an hour and then after complete phase separation the aqueous phase was analyzed for metal ion by ICP-AES.

The composition of simulated high level waste solution (SHLW) of research reactor (RR) origin has been summarized in ESI Table 2† in 3 M HNO₃. 10 mL of SHLW was allowed to equilibrate with 50 mg of CNT-DHA for 2 hours. The after complete settlement, the aqueous phase was collected and fed into the plasma for analysis. The K_d values for other analytes were determined using eqn (1). The SHLW solution was prepared by dissolving the equivalent amount of spec pure metal nitrates.

For radiolytic degradation study, 20 mg of CNT-DHA was exposed to gamma irradiation from ⁶⁰Co source for different dose. Then the irradiated CNT-DHA was allowed to equilibrate with 10 mL of 10 mg L⁻¹ thorium and uranyl solution in 3 M HNO₃ for two hours. After complete settlement of these two phase the aqueous phase was analyzed to determine the K_d values.

Computational study

The structure of CNT-DHA(dihexyl amide) and its complexes with UO₂²⁺ and Th⁴⁺ ions in the presence of nitrate ion were optimized using B3LYP functional with split valence plus polarization (SVP) basis set as implemented in Turbomole package.¹¹ Relativistic effective core potential (ECP) was used for U and Th, where 60 electrons are kept in the core of U and Th atom.¹² Scalar relativistic effects were incorporated in the present calculation using relativistic ECP. The single point energies were calculated with hybrid B3LYP functional¹³ using triple zeta valence plus polarization (TZVP) basis set. Due to inclusion of non-local HF contribution in the exchange functional, the B3LYP (Becke's three-parameter non-local hybrid exchange correlation functional, Becke–Lee–Yang–Parr) functional works well in predicting the energetic.¹⁴ The frequency calculations were carried at the same level which is used for the geometry optimization. The gas phase free energy, ΔG_g was computed at T = 298.15 K and P = 1 atm. The solvent effects were considered using conductor like screening model (COSMO)¹⁵ solvation model. The default COSMO radii were used for all the elements. The dielectric constant, ε of water was taken as 80. The gas phase minimum energy structures were used for the calculation of single point energy in COSMO solvent phase. The visualization of various molecular geometry and structural parameters was performed using MOLDEN program.¹⁶

Results and discussion

Effect of feed acidity on the K_d values of U and Th

Extraction profiles for UO₂²⁺ and Th⁴⁺ were established by varying K_d values as a function of aqueous feed acidity. For both the metal ions the K_d values were found to increase with increase in feed acidity upto 3 M HNO₃ followed by plateau. The initial increase in K_d values were attributed to the law of mass action considering the eqn (1). Beyond 3 M HNO₃, since there was sufficient concentration of H⁺ ion, it competed with metal ions (eqn (2)). Consequently, the K_d values remained almost constants. Similar trend in the extraction profiles were observed for the extraction of actinides by using DHOA (N,N-dihexyl octanamide) in molecular diluents like dodecane.¹⁷ At lower feed acidity, the K_d values for uranyl ion was found to be greater compared to the Th⁴⁺. Lower feed acidity led to lower concentration of NO₃⁻, which was insufficient for effective complexation of Th⁴⁺ as Th(NO₃)₄. CNT-DHA but sufficient for UO₂²⁺ as UO₂(NO₃)₂·CNT-DHA. At moderate feed acidity, the NO₃⁻ concentration was found to be sufficient for both the metal ions, and the metal ion with higher ionic potential was expected to form better complex than the other. According to the expectation, there was a cross over in the K_d values near 1 M HNO₃ and beyond this feed acidity, the K_d values for Th⁴⁺ were found to be higher than that of UO₂²⁺ (Fig. 1).

UO₂²⁺ + CNT-DHA + 2NO₃⁻ = UO₂(NO₃)₂·CNT-DHA (2a)

Th⁴⁺ + CNT-DHA + 2NO₃⁻ = Th(NO₃)₄·CNT-DHA (2b)

H⁺ + CNT-DHA + NO₃⁻ = HNO₃·CNT-DHA (3)

Fig. 1 Effect of feed acidity on the K_d values of uranium and thorium.

Sorption isotherm

The sorption isotherm are mostly explored as empirical models which were obtained from the regression analysis of several experimental data. In the present investigation, the sorption isotherm data for uranyl and thorium ion were used for fitting in the four most popularly used sorption isotherm models, Langmuir, Freundlich, Dubinin–Rodushkevich (D–R) and Tempkin isotherms. The main aim of this investigation to understand the sorption mechanism based on the best linear regression.

Langmuir isotherm

The Langmuir isotherm model is the most popularly used model mainly accounting the ideal nature of sorbent–sorbate interaction and is based on the following assumptions (i) the surface having the adsorbing sites is homogeneous; (iii) all sorption sites are equivalent, (iv) sorption occurs only through mono-layer, (v) there are no interactions between adsorbate molecules on neighbouring sites.¹⁸ It can be expressed as

C_e/q_e = 1/q₀b + C_e/q₀ (4)

where, C_e is the equilibrium concentration of the uranyl or thorium ion, q_e is the amount of metal ion adsorbed on CNT-DHA at equilibrium; q₀ is the sorption capacity of CNT-DHA for thorium and uranium; and b is the sorption energy. Sorption capacity for thorium was found to be more than that of uranium while there was only marginal changes in their sorption energy. The linear regression coefficients for Langmuir isotherm were found to be 0.9987 and 0.9995 for U and Th, respectively.

Freundlich isotherm

The Freundlich adsorption isotherm is based on an empirical relation between the concentration of solute on the surface of the sorbent to that in the liquid. Unlike Langmuir isotherm, this accounts for the non-homogeneity and non-ideal nature of the sorbent beyond mono layer.¹⁹ Based on this isotherm

log Q_e = log k_f + 1/n log C_e (5)

where, k_f is Freundlich isotherm constant (mg g⁻¹), n is the sorption intensity; C_e is the equilibrium concentration of uranyl and thorium (mg L⁻¹), Q_e is the amount of uranyl or thorium ions adsorbed per gram of the CNT-DHA at equilibrium condition (mg g⁻¹). The Freundlich isotherm constant, k_f gives an approximate estimation of adsorption capacity of uranyl and thorium on CNT-DHA. The ‘n’ is an indication of the strength of sorption. If n = 1 then the partition of metal ion between the solid and liquid phases are independent of the concentration of metal ion. The n value above one indicates the normal sorption whereas below one indicates cooperative adsorption. In the present investigation the ‘n’ values for uranyl as well as thorium were found to be well above 1. The higher k_f value for Th⁴⁺ revealed the higher sorption capacity of Th⁴⁺ on CNT-DHA compared to UO₂²⁺. This was in good agreement with that obtained by Langmuir isotherm. The regression coefficients for UO₂²⁺ and Th⁴⁺ for Freundlich isotherm were evaluated as 0.9987 and 0.9813, respectively.

Dubinin–Rodushkevich (D–R) isotherm

Dubinin–Radushkevich isotherm, an empirical model initially conceived for the subcritical vapors onto micro pore solids by 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 physi-sorption and chemi-sorption.²⁰ It can be expressed as follows

ln q_e = ln X_m − βε² (6)

where q_e is the amount of uranyl or thorium adsorbed on CNT-DHA at equilibrium condition. X_m is the maximum sorption capacity and β is the activity coefficient. The Polanyi potential, ε can be evaluated as

ε = RT ln(1 + 1/C_e) (7)

where, C_e, R and T represent the equilibrium concentration of metal ion, the universal gas constant (8.314 kJ mol⁻¹) and the absolute temperature, respectively. The energy (E) can be determined from β, slope of the ln q_e vs. ε² plot, as followsE values for uranyl and Th⁴⁺ were found to be 14.6 and 15.1 kJ mol⁻¹, respectively revealing the chemical interaction between the actinides and the CNT-DHA. The X_m values for these metal ions were in good agreement with those obtained from Langmuir and Freundlich isotherms.

Tempkin isotherm

Tempkin isotherm model is based on that the heat of adsorption of all molecules in the layer decrease linearly (not by logarithmic nature) with a uniform distribution of binding energies.²¹ The model can be quantitatively expressed aswhere, A_T is Temkin isotherm equilibrium binding constant (L g⁻¹), b is Temkin isotherm constant. For the present investigation, the A_T value for uranyl was found to be more than that for thorium while the b value followed the reverse trend.

Based on the linear regression for the above four isotherms, the uranyl and thorium sorption on CNT-DHA data [Table 1] were found to be the best fitted in Langmuir isotherm and hence sorption process was homogeneous, no participation of neighbouring sites and occurring through monolayer (Fig. 2).

Table 1 Sorption data for U and Th on CNT-DHA, fitted on Langmuir, D–R, Freundlich and Tempkin isotherms

Langmuir isotherm
Metal ion	q0 (mg g^−1)	b (L mol^−1)	χ^2
UO2^2+	32.5	4.68	0.9987
Th^4+	47.1	4.43	0.9995

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Dubinin–Radushkevich isotherm
Metal ion	Xm (mg g^−1)	E (kJ mol^−1)	χ^2
UO2^2+	38.8	14.6	0.9969
Th^4+	48.8	15.1	0.9915

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Freundlich isotherm
Metal ion	kf (mg g^−1)	n	χ^2
UO2^2+	36.1	17.3	0.9887
Th^4+	49.0	23.2	0.9813

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Tempkin isotherm
Metal ion	AT (L mg^−1)	b	χ^2
UO2^2+	67.66	108	0.9606
Th^4+	60.34	161	0.9786

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Fig. 2 Langmuir, Freundlich, D–R and Tempkin isotherms for uranyl and thorium on CNT-DHA.

Sorption kinetics

The kinetics is one of the important aspects in the sorption process which should be looked into. If C_t and C_te are the metal ion concentration on CNT-DHA at time ‘t’ and at equilibrium, then the fractional attainment of the equilibrium (F) can be expressed as,²²

F = C_t/C_te (11)

The plots of (1 − F) as a function of equilibration time for thorium and uranyl ion were shown in Fig. 3a. Beyond 60 min there was almost no change in the 1 − F values for uranyl while that for thorium was 40 min. This revealed that for completion of the equilibrium thorium required 40 min while uranyl it was 60 min.

Fig. 3 Sorption kinetics of uranyl and thorium on CNT-DHA.

The kinetics data were fitted on different kinetics models to achieve the best fitted model. The kinetics equation for the Lagergren first order rate kinetics can be expressed as²³

where q and q_e are the amount of metal ion adsorbed on CNT-DHA at time ‘t’ and at equilibrium condition. The rate constant, k_ads can be evaluated from the plots of log(q_e − q) vs. ‘t’. The rate constant (k_ads) for Th⁴⁺ was found to be more but the linear regression coefficients were not very impressive (for U = 0.9775, Th = 0.9759).

The kinetics data were also fitted for 'intra particle diffusion' model,²⁴ which can be expressed by the following equation

q = k_pt^0.5 + C (13)

where, k_p is the intra-particle diffusion rate constant obtained from the slope of q vs. t^0.5 linear plot, and C, the intercept of the line (mg g⁻¹), is proportional to the boundary layer thickness. This linear relationship suggested the involvement of intra-particle diffusion in sorption of actinides on CNT-DHA. The positive intercept revealed that intra-particle diffusion was not the only rate determining step. The pore volume diffusion, the surface diffusion or both the process simultaneously might be responsible for intra particle diffusion between liquid–solid equilibrium. Though the intra particle diffusion model was found to be better fitted compared to the Lagergren first order rate kinetics, improvement in fitting was required to understand the kinetics.

In view of this, the experimental data were used to be fitted on pseudo-second-order kinetics²⁵ expressed by the following equation

where k₂ (g mg⁻¹ min⁻¹) is the pseudo-second-order rate constant. A plot of t/q vs. t should give a straight line. The q_e can be evaluated form the slope and which on substitution in the intercept value, the pseudo second order rate constant can be evaluated. The rate constant for thorium was found to be almost two times more than that for uranyl. The above analysis of the kinetics data revealed that the sorption of uranyl and thorium on the CNT-DHA followed the pseudo second order rate kinetics [Table 2].

Table 2 Sorption kinetics for uranyl and thorium on CNT-DHA

Lagergren first order kinetics
Metal ion	qe	kads	χ^2
U	18.07	0.93 × 10^−4	0.9775
Th	19.53	1.50 × 10^−4	0.9759

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Intra particle diffusion model
Metal ion	kp (mg g^−1 min^−1)	C	χ^2
U	0.22	17.4	0.9969
Th	0.05	19.3	0.9924

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Pseudo second order
Metal ion	qe (mg g^−1)	k2 (g mg^−1 min^−1)	χ^2
U	19.58	0.044	0.9999
Th	19.98	0.095	0.9998

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Selectivity of CNT-DHA

The selectivity of CNT-DHA towards other metal ions present in the Simulated High Level Waste solution (SHLW) have been tested by processing the SHLW of research reactor (RR) origin. The analytical results were pictorially depicted in Fig. 4. Almost no sorption (K_d values less than 50) was found for Sr, Y, Rb, Mo, Ag, Na, La, Pr, Nd, Sm, Eu, Gd, Dy, Mn, Fe and Ni. While moderate sorption of Zr, Nb, Ru, Pd, Ba and Cd were observed. Ce was one of the elements showed very high K_d value. Fortunately, the uranyl ion was extracted almost more than 3.5 times than that for Ce whereas for Th, the K_d value was an order of magnitude greater than of Ce. This study revealed that CNT-DHA was highly selective for Th, while moderate selectivity was also observed for uranyl ion.

Fig. 4 The sorption of other metal ion present in SHLW of RR on CNT-DHA.

Stripping of thorium and uranyl ion from CNT-DHA

Back extraction of the metal ion of interest from the loaded sorbent is one of the important aspects which should be looked into. In view of this, 0.1 M HNO₃ was used for the stripping of uranium and thorium from the loaded CNT-DHA. Only 70% and 62% of U and Th were found to be back extracted. To improve the stripping behavior, it was therefore, required to have aqueous complexing agents. The stripping study revealed that, for hexavalent actinides, i.e. uranyl ion, 0.05 M Na₂CO₃ was successful in almost quantitative stripping (∼99%). For tetravalent actinides like Th⁴⁺, 0.05 M oxalic acid can be used for almost 97% elution from CNT-DHA. The stripping behaviour of uranyl and thorium ion were shown in Fig. 5.

Fig. 5 Stripping of metal ion from CNT-DHA.

Radiolytic stability of CNT-DHA

During the processing of radioactive waste solution, the sorbent is expected to be in continuous exposure of high energy particle (alpha, beta) and photons (gamma). Due to high energy deposition, there would be radiolytic degradation of the sorbent. The best sorbent should retain its efficiency and selectivity even after high energy deposition without any performance degradation. In view of these, the CNT-DHA was exposed to different amount of gamma irradiation and with this irradiated CNT-DHA, the extraction efficiency for uranyl and thorium were calculated. It was noticed that there was only marginal decrease (less than 5%) in their K_d values even with CNT-DHA having 1000 kGy gamma exposure. This study revealed that the CNT-DHA had very high radiolytic stability upto 100 kGy. Fig. 6 represents the effect of gamma dose on the sorbent materials on the K_d values for uranyl and thorium ion.

Fig. 6 Performance degradation of CNT-DHA after gamma exposure of different dose.

For the Fig. 4–6 (bar diagrams), the error associated with each data is less than 5%.

Structure and structural parameters for CNT-DHA and its uranyl and thorium complex

The optimized structure of uncomplexed CNT-DHA ligand and the complexes of UO₂²⁺ and Th⁴⁺ ions with nitrate ions are presented in Fig. 7 and the calculated structural parameters are presented in Table 3. The calculated C=O, C–C (terminal CNT carbon) and C–N bond distance in free DHA was found to be 1.230, 1.467 and 1.373 Å respectively. In case of UO₂–CNT-DHA(NO₃)₂ complex, the C=O bond distance was stretched to 1.289 Å and the C–C bond was shortened to 1.423 Å compared to free CNT-DHA ligand. This is due to the interaction of UO₂²⁺ ion with amide O atom. Similarly the U=O distance also elongated from 1.749(free UO₂²⁺ ion) to 1.770 Å. The U–O distance was found to be 2.271 Å. In case of CNT-DHA–Th(NO₃)₄–H₂O complex, the C=O bond distance was further stretched to 1.305 Å compared to UO₂²⁺ ion complex with CNT-DHA indicating stronger interaction compared to UO₂²⁺ ion. The C–C bond was shortened to 1.396 Å compared to free CNT-DHA ligand. The Th–O distance was found to be 2.309 Å. The U–O(amide) distance was computed to be shorter (2.271 Å) in the present case compared to the other literature data obtained from single crystal analysis of uranyl complexes with similar type of mono amides: UO₂(NO₃)₂{ⁱC₃H₇CON(ⁱC₄H₉)₂}₂: 2.349 Å,^26a UO₂(NO₃)(DMF)₂: 2.397 Å,^26b UO₂(NO₃)₂(tetrabutylglutaramide)₂: 2.378 Å,^26c UO₂(NO₃)₂(dibutyldecanamide)₂: 2.37 Å (ref. 26d) and UO₂(NO₃)₂(ⁱC₃H₇)₂NCOCH₂CON(ⁱC₃H₇)₂: 2.40 Å.^26e It revealed the stronger interaction of uranyl ion with the amidic moiety in case of CNT-DHA. The single crystal data revealed that the U=O bond length in UO₂(NO₃)₂{ⁱC₃H₇CON(ⁱC₄H₉)₂}₂ (1.756 Å)^26a is comparable to that obtained by computational study in the present case for U–CNT-DHA (1.770 Å) system.

Fig. 7 Optimized structures of UO₂²⁺ and Th⁴⁺ with CNT-DHA.

Table 3 Structural parameters (in Å) of CNT-DHA and their complexes at B3LYP/SVP level of theory

Chemical species	C=O	C–C	C–N	M=O	M–O (C=O)	M–O (OH2)
CNT-DHA	1.230	1.467	1.373
CNT-DHA–UO2(NO3)2	1.289	1.423	1.379	1.770	2.271
CNT-DHA–Th(NO3)4–H2O	1.305	1.396	1.409		2.309	2.631

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Gas phase binding energy/free energy of complexation

The metal ion–ligand complexation reaction is modeled as the 1 : 1 (M : L) stoichiometric reaction as follows:

UO₂²⁺(H₂O)₅ + 2NO₃⁻ + CNT-DHA = CNT-DHA−UO₂(NO₃)₂ + 5H₂O (15)

Th⁴⁺(H₂O)₈ + 4NO₃⁻ + CNT-DHA = CNT-DHA−Th(NO₃)₄·H₂O + 7H₂O (16)

The selectivity for a particular metal ion over another metal ion for a complexion ligand can be explained using binding energy or free energy. Hence, the gas phase binding energy is computed for the complexation reaction of eqn (17) and (18) as follows

ΔE_g (U) = (E_{CNT-DHA–UO2(NO3)2} + 5E_H2O) − (E_{UO2²⁺(H2O)5} + 2E_NO3⁻ + E_CNT-DHA) (17)

ΔE_g (Th) = (E_{CNT-DHA–Th(NO3)4·H2O} + 7E_H2O) − (E_{Th⁴⁺(H2O)8} + 4E_NO3⁻ + E_CNT-DHA) (18)

The thermal correction to the electronic energy (E_el), enthalpy (H) and free energy (G) of the optimized complexes has been performed following the earlier reported prescription.^27,28

The calculated values of binding energy and free energy in the gas phase were presented in Table 4. It is observed that the binding energy of Th⁴⁺ ion towards CNT-DHA is −927.09 kcal mol⁻¹ which is considerably higher than that of UO₂²⁺ ion i.e. −297.67 kcal mol⁻¹. The higher interaction energy of Th⁴⁺ ion over UO₂²⁺ ion is accredited to the higher ionic charge on Th (+4) over UO₂ (+2). The orbital population analysis was performed using natural population analysis (NPA)^27,28 to explain higher binding energy of Th⁴⁺ ion. The NPA analysis shown that the charge on Th atom is 1.845 which is lower compared to charge on U atom i.e. 1.871 indicating more amount of the charge is transferred to donor atoms which leads to higher binding energy. The gas phase free energy values also followed the similar trend of binding energies. Whereas, the values are smaller than the corresponding binding energy due to the structure making nature of the complexation.

Table 4 Gas and solvent phase energetic values (kcal mol⁻¹) of complexes of UO₂²⁺ and Th⁴⁺ with CNT-DHA at B3LYP/TZVP level of theory

Complexation reaction	Gas phase		Aqueous phase
	ΔEg	ΔGg	ΔEs	ΔGs
UO2^2+(H2O)5 + 2NO3^− + CNT-DHA → CNT-DHA–UO2(NO3)2 + 5H2O	−297.67	−313.53	−27.25	−43.12
Th^4+(H2O)8 + 4NO3^− + CNT-DHA + H2O→ CNT-DHA–Th(NO3)4–H2O + 7H2O	−927.09	−942.67	−68.88	−84.46

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Solvent phase binding energy/free energy of complexation

The metal ions are extracted from the aqueous environment, where it remains in strongly hydrated form. Hence it is essential to compute the solvation energy of the metal ions in aqueous environment for accurate prediction of extraction energy. Although the gas phase binding and free energy values showed the experimental selectivity it is always preferable to calculate selectivity in the solvent phase. In order to account for the aqueous solvent effect, we have considered explicit solvation model, where the hydrated metal ion (first sphere of water coordination) is solvated in the continuum solvent using COSMO solvation model.

The calculated values of binding energy and free energy in the solvent phase were presented in Table 4. It is observed that the free energy of Th⁴⁺ ion towards CNT-DHA is very (−84.46 kcal mol⁻¹) high compared to UO₂²⁺ ion (−43.12 kcal mol⁻¹) which highly indicating the strong selectivity of the CNT-DHA for Th⁴⁺ ion over UO₂²⁺ ion as observed in the batch experiments. The solvent results are found to be similar like gas phase results. Though, the account of solvation effects considerably reduces the magnitude of binding and free energy, the experimental selectivity remains unaffected.

Bonding analysis

Bonding analysis was performed to get an insight into the nature of bonding in the complexes of CNT-DHA with UO₂²⁺ and Th⁴⁺ ions. The atomic orbital population and residual charge on the metal ion in the metal ion complexes was analyzed using natural population analysis (NPA). The calculated values are tabulated in Table 5. There is a significant charge transfer to the CNT-DHA ligand as clear from the residual charge on the metal ion leading to high interaction energy. Further, the transfer of charge is more for Th⁴⁺ ion compared to UO₂²⁺ ion leading to higher interaction in the former compared to later ion. There is an augmentation of electronic population in the s, d and f orbitals of the metal ions after complexation indicating the covalent nature of bonding.

Table 5 Calculated charge and orbital population using NBO analysis in gas phase at B3LYP/TZVP level of theory

System	Charge	s	p	d	f
CNT-DHA–UO2(NO3)2	1.871	4.16	11.76	11.47	2.72
CNT-DHA–Th(NO3)4–H2O	1.845	4.19	11.99	11.08	0.87

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Further, the LUMO–HOMO energy gap of CNT-DHA and hydrated metal ion was evaluated to obtain a better insights of molecular level interaction and the calculated values are tabulated in Table 6. The hard nature of both the Th⁴⁺ and UO₂²⁺ ions were evident from the high value of E_LUMO–HOMO, χ and η. Hydrated Th⁴⁺ ion was found to be harder than that of hydrated UO₂²⁺ ion which is also reflected in the higher interaction of Th⁴⁺ ion with CNT-DHA over UO₂²⁺ ion. In addition, for the ligand–ion donor acceptor complexation, the amount of charge transfer, ΔN was also estimated and the calculated values are given in Table 6. The calculated large ion–ligand interaction energy can be correlated with the higher amount of charge transfer, ΔN which is seen to be higher with Th⁴⁺ ion over UO₂²⁺ ion.

Table 6 Calculated quantum chemical descriptors in gas phase at B3LYP/TZVP level of theory

System	ΔELUMO–HOMO	η	χ	ΔN
UO2^2+–(H2O)5	5.55	2.77	14.64	1.81
Th^4+–(H2O)8	7.83	3.91	21.62	2.16
CNT-DHA	0.43	0.21	3.77	—

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Conclusion

N,N-Dihexyl amide functionalized carbon nano tube was explored for the effective separation of uranyl and thorium. The sorption was found to follow ‘Langmuir isotherm’ for both uranyl and tetra valent thorium ion. The sorption kinetics was found to be best fitted by the pseudo 2nd order model with the rate constant 0.044 and 0.095 g mg⁻¹ min⁻¹. This sorbent was demonstrated as highly radio-resistant and selective for the Th⁴⁺ ion. 0.05 M sodium carbonate was effectively used for almost quantitative back extraction of hexavalent uranium while 0.05 M oxalic acid served as the best eluent for thorium. The DFT based calculations were performed to understand the experimental selectivity of Th⁴⁺ ion over UO₂²⁺ ion with CNT-DHA. The structural parameters of UO₂²⁺ and Th⁴⁺ ions with CNT-DHA were predicted using DFT calculations. The calculated large ion–ligand interaction energy can be correlated with the higher amount of charge transfer, ΔN which is seen to be higher with Th⁴⁺ ion over UO₂²⁺ ion. The gas phase binding energy and free energy values showed the very high selectivity of Th⁴⁺ ion towards CNT-DHA over UO₂²⁺ ion as observed in the experiment. Although the gas phase values shows the experimental selectivity it is always preferable to calculate selectivity in the solvent phase as it represents the real system. Consideration of solvent effects using COSMO though reduce the magnitude of binding and free energy, the high exergonic nature was still maintained and also the experimental selectivity.

Acknowledgements

Computer division, BARC is acknowledged for providing the Anupam supercomputing facility. We sincerely acknowledge Dr S.B. Roy, Associate Director, ChEG and Mr K.T. Shenoy, Head, ChED, for continuous encouragement. The authors (AS, Jayabun) also acknowledged the constant support of Dr P.K.Pujari, Head, Radiochemistry Division and Dr R.M.kadam, head, Actinide Spectroscopy Section, Radiochemistry Division, Bhabha Atomic Research centre, Mumbai.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra07986e

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