Introduction

Because of modern science and technology development, nuclear energy is now widely used for civilian purposes in fields including industry, agriculture, medicine, and scientific research. Moreover, the nuclear industry is rapidly expanding and provides a significant amount of solid, liquid, and gaseous radioactive waste, which should be treated properly before being adequately disposed of [1]. These radioactive waste forms are classified into low, intermediate, and high levels, with liquid radioactive waste representing a large segment of the total [2]. Radionuclides in liquid radioactive waste are normally categorized into two categories fission products (such as 137Cs, 90Sr, 152+154+155Eu, 133Ba, etc.) and activation products (such as 63Ni, 60Co, 56Fe) [3]. The most problematic constituents in radioactive liquid wastes are barium, europium, strontium, and cesium because they are long-lived radionuclides [4, 5]. Due to this, it is extremely important to get eliminate them from liquid waste streams before they are discharged into the environment. However, some beneficial radionuclides are recovered for use in various applications, such as creating a 137Cs/137mBa radioisotope generator used in industry and medicine for quality control and the production of sealed sources employing 152+154Eu for use in industry and health [3, 6]. Ion exchange [7, 8], chemical precipitation [9], membrane separation [10, 11], solvent extraction [12], and adsorption [13, 14] are examples of techniques and methodologies that have been developed for the treatment of aqueous radioactive waste. Adsorption is an efficient and cost-effective technique to concentrate and remove contaminants from the aqueous phases. The contaminants are recovered from the aqueous solutions and bound in artificial or natural adsorbent, where they can be properly disposed off or retrieved [15].

Silicate clay, a naturally occurring nanoparticle adsorbent produced by silicate weathering on the earth’s surface, is present in deposits totaling more than 50 million tons worldwide. Owing to its negatively charged surface, large specific surface area, robust cation exchange, and chemical pollution-free properties, clay minerals have become one of the most studied activations, modification, and functionalization topics among many scientists [16].

A typical silicate clay mineral with significant deposits and high magnesium content is talc (T) having the chemical formula of Mg3Si4O10(OH)2. Talc is distinguished by its 2:1 sheets structure, which consists of a layer of Mg(OH)2 and two layers of the Si–O tetrahedron [17]. After being broken up into talc powder and processed, the talc powder is separated. It is widely used in a variety of industries, including ceramics, paper, plastic, rubber, food, medicine, and food processing [18]. Talc’s high porosity, substantial specific surface area, rod-like structure, and the profusion of hydrophilic Si–OH make it an excellent adsorbent for the decontamination of radioactive wastewater [19,20,21]. Talc composites have been enhanced with other substances including P(AA-AN)-talc [17], Fe3O4/Talc [22], and modified talcum [23]. Investigators haven’t looked into the impregnation of talc layers with iron ions or phosphate groups. In this study, iron phosphate@talc (IPT) was developed as a novel substance and used to filter out 137Cs, 152+154Eu, and 131Ba from radioactive wastewater. Using sorption techniques, the sorption efficiency (% S.E.) of 137Cs, 152+154Eu, and 131Ba from liquid waste was investigated [24, 25].

The purpose of this research is to reduce the negative effects of 137Cs, 152+154Eu, and 131Ba by applying the sorption technique to IPT sorbent prepared by the precipitation method. Fourier-transform infrared spectroscopy (FT-IR), scanning electron microscopy (SEM), X-ray diffraction (XRD), and X-ray fluorescence (XRF) were used as analytical techniques to characterize IPT sorbent. Batch experiments were used to calculate the optimal sorption parameters for 137Cs, 152+154Eu, and 131Ba, which include time, pH, temperature, and initial metal concentration.

Experimental

Materials

The suppliers of BaCl2 and FeCl3 are Loba Chemie (India), KH2PO4 Alpha Chemika (India), Na5P3O10 Goway (China), and HNO3 Merck (Germany). NaOH, NH3, and NaCl El-Nasr Company (Egypt). For all works, double-distilled water (DDW) was used. The reagents employed in this study were of the analytical grade without any further purification.

Radioisotopes tracers

Radioactive tracers 131Ba and 152+154Eu were obtained via the activation reaction of (n, γ) by neutron irradiation of 0.05 g weight of metal chloride salts wrapped in double aluminum foil and goes to the vertical irradiation channels inside the core of the second Egyptian Training Research Reactor ETRR-2 for 3 h at a neutron flux of 1 × 1014 n cm−2 s−1 to obtain the desired radioactivity level. Then, they were left to cool for a week before dissolving and counting using the gamma spectrometry technique, to allow all undesirable short-lived radionuclides to decay. 137Cs was obtained from a standard radioactive solution purchased from Eckert and Ziegler company with an initial activity of 3.7 × 106 Bq (≈ 100 µCi).

Preparation

For the preparation of talc (T), talc phosphate (TP), and iron phosphate@talc (IPT) sorbents, a simple and ambient precipitation procedure was used through the final stage.

  1. (i)

    Preparation of talc solution by addition of 7.5 g Na5P3O10 as dispersing agent to 75 g talc powder with the addition of DDW to reach 750 mL with constant stirring for 120 min.

  2. (ii)

    Preparation of 0.2 M KH2PO4 and 0.2 M FeCl3 solutions by dissolving 14.2 g KH2PO4 with 500 mL DDW and 8.11 g FeCl3 with 250 mL DDW.

  3. (iii)

    Different ratios of the equimolar solutions from FeCl3 and KH2PO4 were added to the talc solution as the following (0:0:1, 1:0:1, 1:1:1) respectively, details are listed in Table 1.

Adding the prepared solutions together and stirring consistently for 2 h, adding 10% NH4OH solution to the mixture, as observed a color gel began to form at a pH of 7.5. The formed gel was left undisturbed overnight before being washed with DDW, dried at 60 ± 1 °C, and finally ground to get a fine powder.

Preliminary studies for sorbents selection

To perform the measurements, 5 mL each of radioactive solutions of 137Cs, 152+154Eu, and 131Ba were added to 0.05 g of three different prepared samples and shaken at 298 ± 1 K in a thermostat shaker (Kottermann D-1362, Germany). The solution and the solid are decanted as soon as the shaker is turned off after 24 h.

The activities of 137Cs, 152+154Eu, and 131Ba were measured for 3600 s using a coaxial p-type HPGe detector (GEM-series, ORTEC, USA) connected to a multichannel analyzer system (MCA, Inspector 2000 Series, Canberra, USA). The % sorption efficiency (% S.E.) can be computed by using Eq. (1) [26, 27];

$$\% \;{\text{S}}.{\text{E}}. = \left( {\frac{{\text{A}_{\text{i}} - {\text{A}}_{\text{f}}}} {{{\text{A}}_{\text{i}}}}} \right)100$$
(1)

Ai and Af are the initial and final activity of 137Cs, 152+154Eu, and 131Ba, respectively.

Table 1 Conditions for the synthesis of T, TP, and IPT sorbents and % S.E. of 137Cs, 152+154Eu, and 131Ba [Ci = 50 mg L−1, V/m = 0.1 L g−1, and shaking time 24 h]
Full size table

Instruments for sorbent characterization

Germany’s Bruker XRD diffractometer D2 Phaser II was used to examine the crystal structure of the IPT sorbent. FT-IR measurements were made in the wavenumber range of 4000–400 cm−1 using an automated spectrophotometer Alpha II Bruker (Germany). The Philips sequential X-ray spectrometer-2400 was used to identify the elemental composition of IPT sorbent. Using the Super-Q quantitative application program, the percentages of Mg, Al, Si, P, Ca, K, and Fe were estimated. SEM JSM-6510A Model (Japan) was used to study the surface morphology of the IPT sorbent material.

Chemical stability

Different solvents such as (DDW, ethanol, methyl ethyl ketone, HNO3, and NaOH) were used to study the solubility percentage of the IPT by constant shaking 0.1 g of solid and 10 mL of studied solvents for 3 days at 25 ± 1 °C. The amount of IPT sorbent left in the solution was measured gravimetrically by decantation of filtrate and then dried [24, 28].

pH titration

IPT sorbent was examined using the Topp and Pepper method to detect pH titration by the NaOH–NaCl system [29]. Each 10.0 mL of NaOH (0.1 M)–NaCl (0.1 M) mixed by different volumetric ratios was contacted with 0.1 g of the prepared sorbent and then constantly stirred. After a standard 24 h interval, the pH of the solutions was recorded using a pH meter.

Sorption experimentation

All equilibrium measurements were carried out by shaking 0.05 g of IPT sorbent with 5.0 mL of 137Cs, 152+154Eu, and 131Ba at a baseline concentration of 50 mg L−1 in a shaker thermostat model Kottermann D-1362 (Germany), and V/m = 100 mL g−1. The variation in sorption parameters such as pH (1–7), metal concentrations (50–500 mg L−1), temperatures (30, 45, and 60 °C), and contacting time (5–300 min) were checked to get the optimum sorption conditions. IPT sorbent batch-wise interacted with 137Cs, 152+154Eu, and 131Ba. Following sorption, the samples were separated by filtration. The amount sorbed qe was calculated using the following equation [30,31,32]:

$$q_{e} {\text{(mg}}\;{\text{g}}^{ - 1} {) = }\left( {\frac{{A_{i} - A_{e} }}{{A_{i} }}} \right)\left( {\frac{{C_{i} V}}{m}} \right)$$
(2)

Ae, V, Ci, and m are the activity of a solution at equilibrium, the solution volume (L), initial concentration, and the IPT weight (g), respectively. The distribution coefficients Kd and separation factors \(\alpha_{{\text{B}}}^{{\text{A}}}\) as a function of pH were determined with the subsequent equations [31, 33,34,35]:

$$K_{d} {\text{(mL}}\;{\text{g}}^{{ - {1}}} {) = }\left( {\frac{{A_{i} - A_{f} }}{{A_{f} }}} \right)\left( \frac{V}{m} \right)$$
(3)

and

$$\alpha_{{\text{B}}}^{{\text{A}}} = \frac{{{\text{K}}_{{\text{d}}} ({\text{A}})}}{{{\text{K}}_{{\text{d}}} ({\text{B}})}}$$
(4)

V is the volume of 137Cs, 152+154Eu, and 131Ba (mL). Kd(A), and Kd(B) are the distribution coefficients for the two competing species A and B in the system.

Results and discussion

Preliminary studies

The sorption efficiency (% S.E.) of the studied radiotracer either onto talc, TP, and IPT sorbents is presented in Table 1. These results prove that an enhancement was attained in the sorption behavior of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent than T and TP sorbents. So, IPT sorbent was used for all experiments.

XRD analysis

XRD was utilized to indicate the degree of crystallinity of IPT sorbent as presented in Fig. 1a. Figure 1a reveals that IPT sorbent has a uniform hexagonal crystalline nature and demonstrates the existence of characteristic peaks of talc addressed at 2θ values (8.33°, 14.46°, 16.71°, 19.86°, 24.65°, 25.18°, 28.69°, 35.35°, 36.45°, 39.4°, 42.6°, 45.22°, 55.1°, 58.12°, 60.45°, 66.3°, 67.99°, 73.3°, and 79.3°) related to Miller indices of hkl values (100, 2–10, 200, 101, 201, 300, 3–21, 4–31, 002, 2–12, 500, 302, 601, 2–13, 8–40, 8–61, 403, 8–52, and 2–14) respectively. Peaks of iron and phosphorus are significantly appeared at 2θ values (10.82°, 11.96°, 14.92°, 22.93°, 58.66°, and 67.24°). Moreover, some impurities are detected from Ca, Al, and K at 2θ values (9.57°, 12.61°, 18.91°, 19.54°, 25.19°, 26.79°, 28.02°, 28.75°, 34.72°, 35.37°, 36.79°, 55.31°, 60.18°, 61.60°, and 79.42°). This result gives a good estimation of the existence of iron and phosphorus in the present work-prepared IPT sorbent [36].

Fig. 1
figure 1

a XRD pattern and b FT-IR spectrum of IPT sorbent

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FT-IR spectrum

FT-IR analysis of IPT sorbent was existing in Fig. 1b. It is clear that from this Figure eight bands appeared in IPT sorbent at wavenumbers (3749, 3621, 1630, 1049, 941, 873, 745, and 577 cm−1). The bands at 3621 and 947 cm−1 are due to A1–A1–OH (stretching and bending vibration, respectively) [37, 38]. The band at 3749 cm−1 is related to Al–OH–Mg bonds present in talc powder [39]. The bands at 3621 and 1639 cm−1 agreed to OH frequencies of the H2O molecule (stretching and bending) respectively [24] or officially to P–OH [40, 41]. At the same time, bands at (1049, 873, and 745 cm−1) are due to Si–O, Si–O–Al, and Si–O–Mg bending, respectively [37]. Bands from 941 and 577 cm–1 are related to M–O (where M is Al or Fe) [40]. The FT-IR analysis of IPT sorbent loaded by Cs(I), Ba(II), and Eu(III) ions presented in Fig. 1b has the same bands observed in the FT-IR of IPT sorbent. The band at 577 cm−1 shifted to 640 cm−1 for IPT loaded by Cs(I), shifted to 586 cm−1 for IPT loaded by Ba(II), and shifted to 660 cm−1 for IPT loaded by Eu(III). Whereas the intensity of bands at 3621 and 1630 cm−1 was increased after loading of IPT sorbent with Cs(I), Ba(II), and Eu(III) ions. These data confirmed that the combination between Cs(I), Ba(II), and Eu(III) ions with IPT sorbent was achieved.

SEM analysis

SEM images of the proposed sorbent material are shown in Fig. 2 at different magnification powers of X500, X1000, and X2000. Results show a heterogeneous distribution of the iron and phosphate particles (white color) on the talc media (grey color), simply they are similar to a bulk of tiny islands on the ocean surface. At small magnification power of X500, the surface appears to have very small porous, and by increasing the magnification power at X1000 and X2000, these particles are rugged, and sharp and have intermolecular distances that support the physical sorption process on the material.

Fig. 2
figure 2

SEM images for the proposed IPT sorbent material at different magnification powers a X500 b X1000 c X2000

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XRF analysis

The percentage of metal present in IPT sorbent based on an X-ray fluorescence spectrometer was measured and revealed that the prepared IPT sorbent possesses the values 14.2, 4.31, 24.26, 15.11, 3.92, 3.38, and 34.82 for Mg, Al, Si, P, Ca, K, and Fe respectively. These data confirmed that the main constituents are Fe, Si, P, and Mg. Also, the reason for the appearance of Ca, K, and Al elements in XRF analysis is due to the presence of these elements in natural talc.

pH titration curve

Figure 3 displays the pH titration curve of IPT sorbent. The X-axis and Y-axis characterize the number of mL of NaOH solution interacting with 0.1 g of IPT sorbent, and the pH of the effluent, respectively. The pH titration curve for IPT sorbent reflect only one inflection point at a pH value equal 10, revealing that it is a mono-functional sorbent. This is the same behavior as ZrSnP prepared by Abass et al. [24].

Fig. 3
figure 3

pH titration curve of IPT sorbent

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Chemical stability

The solubility test of the IPT sorbent is represented in Table 2 reflecting that the prepared sorbent was stable in DDW, ethanol, methyl ethyl ketone, HNO3, and NaOH below 2 mol L−1. Table 2 exhibits that IPT sorbent has relatively high stability to chemical reagents compared to other sorbents [42,43,44].

Table 2 Chemical stability of IPT sorbent in different solvents
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Sorption studies

Influence of pH on the sorption efficiency and distribution coefficients (K d )

The sorption of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent in different pH values was studied from aqueous media as exposed in Fig. 4a. According to this Figure, the % S.E. increases with increasing pH until it reaches the maximum levels of 96.0, 83.2, and 81.0% for 131Ba, 137Cs, and 152Eu, respectively, at pH 6 for 131Ba and 137Cs and pH 4 for 152+154Eu. The sorption of 131Ba, 137Cs, and 152Eu was found to be low at low pH values, which is likely caused by the protonation of the surface-active sites and the rise in H3O+ ions in the aqueous solution [45]. As a result of competition for the accessible binding surface active site produced by the positively charged surface sites, uptakes of the radionuclides 131Ba, 137Cs, and 152Eu were reduced. With rising pH values, the concentration of H3O+ ions is reduced while the concentration of OH− is raised which causes deprotonation of the sorbent surface, such explanations mean that the surface of the IPT sorbent tends to have a negative charge. Hence, the attraction among the surface of IPT and the positive charge of 131Ba, 137Cs, and 152Eu in the solution was improved.

Fig. 4
figure 4

a Effect of pH on the % S.E. of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent and chemical speciation of b Ba(II), c Cs(I), and d Eu(III) at pH range (1–7), ionic strength 0.001, and 25 °C

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The speciation of Ba(II), Cs(I), and Eu(III) ions in a liquid solution at different pH values (1- 7), at ionic strength 0.001 M and 25 °C was performed using the MEDUSA program which gives information about the distribution of species as a function of pH [46], as exposed in Fig. 4b–d. The results showed that the speciation of Cs(I) and Ba(II) ions have no precipitate at all pHs (1–7) [7]. H+ ions concentration was decreased with increasing pH values and at pH approximately 7, H+ ions disappeared and at pH 5, OH− ions start to increase with increasing pH values. The speciation of Eu(III) ions has no precipitate at a pH range from 1 to 2.2 with no presence of these ions in the hydroxide form. The hydrolysis of Eu(III) ions begins at a pH value above 2.2, and different species can be shaped, such as EuOH2+ and Eu(OH)2+ formed at pH 5, the uptake of Eu(III) increases with pH until 4.0 and then decreased due to formation of EuOH2+ and Eu(OH)2+. After pH 6 Eu(III) precipitated as Eu(OH)3. The above data of chemical speciation are compatible with the sorption of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent at pH 6 for 131Ba and 137Cs and pH 4 for 152+154Eu.

Distribution coefficients (Kd) and separation factors \(\left( {\alpha_{{\text{B}}}^{{\text{A}}} } \right)\) at different pHs (1–7) were calculated and tabulated in Table 3 and reflected that Kd has the affinity order: 131Ba > 137Cs > 152+154Eu, this result supports that 131Ba and 137Cs uptake was carried out in the case of ionic radii [131Ba and 137Cs have ionic radius 0.142 and 0.165 nm, respectively] whereas the sorption of and 152+154Eu was done as hydrated ionic radius [152+154Eu has an ionic radius 0.107 nm]. Radionuclides with lower ionic radius (131Ba) easily enter the cavities of IPT sorbent increasing in sorption and consequently increasing Kd [47, 48]. Separation factors for studied radionuclides reflected that 131Ba has a good separation factor at different pH values. Also, the data obtained in Table 3 reveal that the best separation factors for studied radionuclides were at pH 4 (6.1 for the separation of 131Ba from 152+154Eu and 12.9 for the separation of 131Ba from 137Cs).

Table 3 Distribution coefficients and separation factors of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent at 25 ± 1 °C
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Nonlinear relationships between log Kd and pH were observed for the studied radionuclides, as shown in Fig. 5a. This relationship reveals the exchange reaction is non-ideal. The difference could be attributed to the prominence of a mechanism other than ion exchange, such as precipitation and/or surface adsorption [33].

Fig. 5
figure 5

Sorption of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent, a plots of log Kd against pH at 25 ± 1 °C and b effect of shaking time on the % S.E

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Shaking time impact

The impact of contact time on 137Cs, 152+154Eu, and 131Ba sorption onto IPT sorbent was studied at a fixed temperature (298 ± 1 K), initial concentration Ci = 50 mg L−1, V/m = 0.1 L g−1, shaking time (5 min–24 h), pH = 4 for 152+154Eu, and pH = 6 for 131Ba and 137Cs, and the data are shown in Fig. 5b. This Figure examined that the sorption of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent enhanced with contact time attain equilibrium at 1 h for 137Cs and 152+154Eu and 5 h for 131Ba. The rate of 137Cs and 152+154Eu uptake onto IPT sorbent rapidly increases with time from 5 to 60 min reaching flattened behavior. Moreover, the rate 131Ba uptake is different, it takes two stages to be flattened the first one start 5–90 min and then form rapidly rises from 150 to 300 min, and starts to flatten again till 1000 min achieving the maximum % S.E. Results can be concluded as there is no significant change of the uptake above 100 min for 137Cs and 152+154Eu but at 300 min for 131Ba.

Kinetic studies

In the present work, pseudo-1st-order (Lagergren equation), and pseudo-2nd-order were applied to study and analyze the obtained data from the sorption of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent, their equations are given below as [49, 50]:

$$\log \;({\text{q}}_{{\text{e}}} - {\text{q}}_{{\text{t}}} ) = \log \;{\text{q}}_{{\text{e}}} - \frac{{{\text{K}}_{{\text{f}}} {\text{t}}}}{2.303}$$
(5)
$$\frac{{\text{t}}}{{{\text{q}}_{{\text{t}}} }} = \frac{1}{{{\text{K}}_{{\text{s}}} {\text{q}}_{{\text{e}}}^{2} }} + \frac{{\text{t}}}{{{\text{q}}_{{\text{e}}} }}$$
(6)

in which, qt is the value of the amount sorbed per unit mass (mg g−1) at time t, Kf (min−1), and Ks (g mg−1 min−1) are the rate constants of two kinetic equations. By plotting log (qe − qt) versus t and t/qt versus t, the obtained results are displayed in Fig. 6a and b. The result shows that the obtained experimental data are well-fitted with the pseudo-2nd-order model rather than the 1st-order model. The calculated constants of the two models are tabulated in Table 4. By comparing the model data with the obtained experimental data; it proposes that pseudo-2nd-order sorption is the main mechanism, as data quality is related to R2 (a goodness-of-fit measure for linear regression models); for 137Cs, 152+154Eu, and 131Ba are almost equal to one compared with its low values obtained from the pseudo-1st-order kinetic model. Also, the values of qe calculated from the pseudo-2nd-order model were nearer to the values of qe (experimental). This means the adsorption of 137Cs, 152+154Eu, and 131Ba was found to be a chemisorption process [51, 52].

Fig. 6
figure 6

Kinetic modeling fitting of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent, a pseudo-1st-order kinetic, b pseudo-2nd-order kinetic, c intra-particle diffusion, and d Elovich models at 25 ± 1 °C

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Table 4 Kinetic parameters and correlation coefficients (R2) for pseudo-1st-order, pseudo-2nd-order, intra-particle diffusion, and Elovich models for the sorption of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent at 25 ± 1 °C
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The diffusion mechanism of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent was investigated by the intra-particle diffusion model which is presented in the next equation [53, 54].

$${\text{q}}_{{\text{t}}} = {\text{K}}_{{{\text{id}}}} {\text{t}}^{0.5} + {\text{C}}$$
(7)

Which, Kid and C are the intra-particle diffusion rate constant (mg g−1 min−0.5) and the intra-particle diffusion constant which is directly proportional to the boundary layer thickness, respectively. The plot of qt versus t0.5 is assumed in Fig. 6c. The value of the rate parameter was calculated from the slope, and the value of R2 is assumed in Table 4. Three steps were used to create the intra-particle diffusion model for 137Cs, 152+154Eu, and 131Ba sorption [55, 56]. (a) The diffusion of 137Cs, 152+154Eu, and 131Ba from the solution to the surface of the IPT sorbent (from 5 to 30 min) for 131Ba and (from 5 to 15 min) for 137Cs and 152+154Eu. (b) The gradual sorption on the surface of the IPT sorbent, which may be the rate-limiting step (from 40 to 240 min) for 131Ba, (from 30 to 50 min) for 137Cs and 152+154Eu. (c) The equilibrium saturation (from 300 to 1440 min) for 131Ba and (from 60 to 1440 min) for 137Cs and 152+154Eu. The sorption mechanism of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent was found to be fast at the initial period of contact time and then to become constant with the increase in time. The sorption mechanism, which comprises both film and intra-particle diffusion, is primarily controlled by the multi-diffusion step.

The Elovich kinetic model is used to describe the kinetics of chemisorption on highly energetically heterogeneous solid surfaces. The mathematical linear form of this model is expressed as [57]:

$${\text{q}}_{{\text{t}}} = \frac{1}{\beta }{\text{ln}}(\alpha \beta ) + \frac{1}{\beta }\ln {\text{t}}$$
(8)

where: α is the Elovich coefficient which represents the initial sorption rate (mg g−1 min−1) and β is a parameter related to the desorption constant (g mg−1) during any experiment. The plots of qt vs. ln t for the sorption of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent are shown in Fig. 6d. It gives a linear relationship with a slope of 1/β and an intercept of 1/β ln(αβ). The values of Elovich prediction model parameters were determined from the obtained linear form and listed in Table 4. The data in Table 4 declared that the Elovich equation did not fit the experimental results based on the low values of R2. This validated the inapplicability of this model for describing the sorption of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent.

Effect of concentrations

Figure 7 reveals the plots between qe of 137Cs, 152+154Eu, and 131Ba onto IPT and Ci at the range (50–500 mg L−1) at different reaction temperatures. The qe of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent rises as the initial concentration of 137Cs, 152+154Eu, and 131Ba increases. As well as, the qe increases by increasing reaction temperature indicating the endothermic nature of the sorption.

Fig. 7
figure 7

Effect of initial concentration of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent at different temperatures [V/m = 0.1 L g−1, pH = 6 for 131Ba and 137Cs and pH = 4 for.152+154Eu]

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Isothermal modeling

The Langmuir isotherm model can be represented in the equation [3, 58]:

$$\frac{{{\text{C}}_{{\text{e}}} }}{{{\text{q}}_{{\text{e}}} }} = \frac{{{\text{C}}_{{\text{e}}} }}{{{\text{Q}}_{\max } }} + \frac{1}{{{\text{bQ}}_{\max } }}$$
(9)

Qmax and b are the theoretical monolayer capacity (mg g−1) and the sorption equilibrium constant is related to the energy of sorption, respectively, and Ce is the equilibrium concentration. As shown in Fig. 8, plotting Ce/qe and Ce gives straight lines for 137Cs, 152+154Eu, and 131Ba onto IPT sorbent at temperatures (303, 318, and 333 K). The calculated data from the slopes and intercepts of the linear form of the Langmuir model for 137Cs, 152+154Eu, and 131Ba sorption onto IPT sorbent at 303, 318, and 333 K were presented in Table 5. The R2 values confirm that the high applicability of Langmuir isotherm for the sorption of these radionuclides onto IPT sorbent. The Qmax was (64.47, 73.64, and 73.75 mg g−1), (41.1, 44.37, and 46.06 mg g−1), and (39.0, 40.2, and 42.11 mg g−1) for 131Ba, 137Cs, and 152+154Eu at 303, 318, and 333 K, respectively. These data prove the endothermic nature of the sorption of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent because of rising Qmax for 131Ba, 137Cs, and 152+154Eu with increasing reaction temperature.

Fig. 8
figure 8

Isothermal modeling fitting of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent at different reaction temperatures [V/m = 0.1 L g−1, pH = 6 for 131Ba and 137Cs and pH = 4 for.152+154Eu]

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Table 5 Isotherm parameters for sorption of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent at different reaction temperatures
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The equilibrium parameter (RL) can be obtained from the Langmuir constant b as follows:

$${\text{R}}_{{\text{L}}} = \frac{1}{{1 + {\text{bC}}_{{\text{i}}} }}$$
(10)

The RL values reflect the type of isotherm to be irreversible if, RL = 0, favorable 0 < RL < 1, linear if RL = 1, or unfavorable RL > 1. Table 5 proves that the 0 < RL < 1 reveals the favorable sorption isotherms of studied radionuclides [3].

A linear form of Freundlich expression can be represented as:

$$\log \;{\text{q}}_{{\text{e}}} = \log \;{\text{K}}_{{\text{F}}} + \frac{1}{{\text{n}}}\log \;{\text{C}}_{{\text{e}}}$$
(11)

In which, KF and 1/n are the Freundlich constant and heterogeneity factors. It represents the amount of 137Cs, 152+154Eu, and 131Ba onto IPT for unit equilibrium concentration. The values of 1/n signify the deviation from the linearity of sorption as follows: (i) 1/n = 1 reflects that the sorption is linear; (ii) 1/n < 1 implies heterogeneous surface structure with minimum interaction between the adsorbed atoms, and (iii) 1/n > 1 implies homogeneous surface structure and unfavorable Freundlich adsorption processes [52]. The results of 137Cs, 152+154Eu, and 131Ba sorbed onto IPT sorbent by Langmuir and Freundlich isotherms were shown in Fig. 8. As well as the constants of both isotherm models were calculated from the slope and intercept, and the data were tabulated in Table 5. The R2 values obtained from Freundlich for 131Ba, 137Cs, and 152+154Eu were lower than the Langmuir isotherm values. Based on R2 data, the linear forms of the Freundlich model were less applicable than the Langmuir model.

Literature review of monolayer sorption capacity of different sorbents

The monolayer capacity (Qmax) of IPT sorbent for the sorption of 137Cs, 152+154Eu, and 131Ba was compared with other sorbents reported in the literature. As characterized in Table 6, the monolayer capacity of IPT is a good value compared with the previously reported values which recommended that this is a promising material to decontaminate 137Cs, 152+154Eu, and 131Ba from aqueous media [15, 35, 59,60,61,62,63,64,65,66].

Table 6 Comparison of the monolayer capacity of 137Cs, 152+154Eu, and 131Ba sorbed onto various sorbents
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Effect of temperature studies

The linear form between ln Kd of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent and 1000/T was exposed in Fig. 9 according to Van’t Hoff relation [24]:

$$\ln \;{\text{K}}_{{\text{d}}} = \frac{{\Delta {\text{S}}^{{\text{o}}} }}{{\text{R}}} - \frac{{\Delta {\text{H}}^{{\text{o}}} }}{{{\text{RT}}}}$$

where R, ∆H°, T, and ∆S° are the gas constant, the enthalpy change of adsorption, the absolute temperature, and the entropy change of adsorption, respectively. As exposed in Fig. 9, ln Kd of 137Cs, 152+154Eu, and 131Ba increased with rising reaction temperature from 303 to 333 K. This enhancement is due to the acceleration of previously slow adsorption steps and the formation of new active sites on adsorbent surfaces [52]. From both slopes and intercepts of the straight lines, ∆H° and ∆S° were obtained and tabulated in Table 7. The positive values of ∆H° and ∆S° reflect the endothermic nature of the adsorption process and the increased randomness of the solid solution interface during the adsorption of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent, respectively [24, 52, 67]. The free energy change of specific adsorption (∆G°) was obtained using the relation:

$$\Delta {\text{G}}^{{\text{o}}} = \Delta {\text{H}}^{{\text{o}}} - {\text{T}}\Delta {\text{S}}^{{\text{o}}}$$
(13)
Fig. 9
figure 9

A plot of ln Kd against 1000/T for sorption of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent [Ci = 50 mg L−1, V/m = 0.1 L g−1, pH = 6 for 131Ba and 137Cs and pH = 4 for.152+154Eu]

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Table 7 Thermodynamic parameters for the sorption of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent
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The negative values of ∆G° reflect the adsorption process is spontaneous and reflects the preferable adsorption of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent compared with the H+ ion [67].

Conclusion

The co-precipitation method was used to prepare IPT sorbent. IPT sorbent was characterized and employed for batch sorption of 137Cs, 152+154Eu, and 131Ba from an aqueous solution. The sorption data of 137Cs, 152+154Eu, and 131Ba reveal that IPT has an equilibrium time for 137Cs and 152+154Eu (1 h) and 131Ba (5 h). The optimal pH = 4 for 152+154Eu and pH = 6 for 131Ba and 137Cs. The pseudo-2nd-order kinetic described the kinetic data well, reflecting the presence of chemisorption. Isotherm models are more applicable for the Langmuir model with high monolayer capacity for studied radionuclides. Thermodynamic functions show the adsorption of 137Cs, 152+154Eu, and 131Ba onto IPT sorbent was endothermic and spontaneous. Finally, IPT sorbent could be considered a promising sorbent possessing high sorptive abilities for the studied radionuclides.