Introduction

No-carrier-added (NCA) radioisotopes are of immense importance for in vivo and in vitro studies owing to their high specific activity and high degree of sensitivity towards various physiological systems. In addition, NCA Cd radionuclides are also regularly employed in material research, environmental studies, industrial analysis and other fields. 111mCd (T 1/2 = 49 min) was used long back as a radioactive source in perturbed angular correlation studies with biomolecules like DNA [1]. Recently, similar studies have also been reported for the interactions of 111mCd with complex molecular assemblies like fullerene [2]. On the other hand, 109Cd is a common radiotracer for environmental study of Cd pollution. It also has biomedical applications in monitoring long term metabolic activity of cadmium at subcellular and molecular level for its suitable half-life (T 1/2 = 462.6 days) [3]. Several experiments with short lived 107Cd (T 1/2 = 6.5 h) radionuclide are reported [4,5,6] which find applications in nuclear medicine when used as 107Cd/107mAg (T 1/2 = 44.3 s) generator system [7]. Applications of other radioisotopes of Cd viz., 111Cd–113Cd, 114/110Cd can also be found in the field of analytical and geological sciences [8, 9]. Numerous industrial applications of Cd including rechargeable nickel–cadmium batteries [10], electroplating [11], nuclear fission [12], petroleum industry [13, 14] are also reported in literature.

Besides all these industrial and medical use of cadmium, everyday chunks of cadmium compounds are dumped in municipal dumping ground or thrown to public sewage which is a big threat to the environment as cadmium is a potential carcinogen and accumulates in the human body through food chain affecting the function of kidneys, lungs, bones and other organs [15]. It is also a main constituent of polluted air as particulate matter due to its extreme toxic effect which causes acute and chronic health problems such as bronchial and pulmonary irritation of lung, long term damage of the kidneys, liver, bones, immune system, blood, and nervous system [16,17,18]. Therefore, studies on immobilization of cadmium and its extraction behavior have important bearings in today’s science.

Present work is a report on the study of adsorption characteristics of 109Cd into a polymeric microporous hydrogel, calcium alginate (CA) through radiochemical method at different conditions. CA beads can be used for the oral treatment for removal of Cd poisoning due to its versatile adsorption properties together with biodegradability, biocompatibility and non-toxicity. Owing to their internal structure, several metal ions can be efficiently trapped in the cage like structure [19,20,21]. Again CA beads are enormously used towards tissue engineering as well as designing wound dressing material due to their mucoadhesion and bioadhesion characteristics [22]. So it could be suitable in both ways for recovery of skin ailment as well as for remediation of Cd poisoning from the wounded site if designed properly. Adsorption isotherms (Langmuir, Freundlich, Temkin and Dubinin–Radushkevich) were investigated at different temperatures using different concentrations of cadmium (0.1–50 ppm in 10−4 M HNO3) spiked with 109Cd (T 1/2 = 1.2665 a) radioisotope and hence, production and separation of 109Cd was a foremost mission for the aforesaid purpose.

Enormous production route of NCA 109Cd from natural Ag target are reported in the literature [23,24,25]. The aforementioned articles described several extraction methods of 109Cd by ion-exchange chromatography using Dowex and Aminex, co-precipitation method, liquid–liquid extractions (LLX) using trioctyl amine (TOA) and di-(2-ethylhexyl)phosphoric acid(HDEHP), solvent extraction, aqueous biphasic system (ABS), ABS using room temperature ionic liquid (RTIL) and so on. In all the above methods except ABS, NCA 107,109Cd were separated using many organic solvents/reagents like pyridine, naphthyl substituted thiourea, cyclohexane, chloroform, etc., of which, many are carcinogenic as well as environmentally hazardous. So a greener alternative was searched for the adsorption and accumulation of the said radioisotope.

In the present article, we produced 109Cd following natAg(α,pxn)109Cd reaction and separated it from the bulk silver target by simple classical precipitation method. The adsorption studies of NCA 109Cd into CA beads were performed and the adsorption isotherms were evaluated at different temperatures and different Cd concentrations with NCA 109Cd spiked solutions using radiometric method. To the best of our knowledge, this is the first report on radiometric adsorption isotherm analysis of Cd2+ onto calcium alginate using NCA radionuclide.

Experimental

CA bead preparation

CA beads were prepared by drop wise addition of 3% (w/v) sodium alginate (Sisco Research Laboratories Pvt. Ltd.) solution from a burette into 20% w/v calcium chloride dehydrate (Merck, India) solution maintaining the temperature at ~4 °C with constant stirring using a magnetic stirrer [26,27,28]. The beads were kept overnight in the mother liquor and then washed with deionized water prior to their use in the experiment.

Irradiation

A natural silver foil of thickness 2.8 mg/cm2 was irradiated by 30 MeV α-particles for 7.25 h with an average beam current of 15.48 µA at the Variable Energy Cyclotron Centre, Kolkata, India. The total current was measured with the help of an electron suppressed Faraday cup placed at the rear side of the target holder flange. At the end of bombardment (EOB), the target was taken out and cooled for 2 days, and assayed by a CANBERRA p-type high purity germanium (HPGe) detector with a resolution of 2.3 keV at 1.33 MeV in conjunction with DSA 1000 and Genie 2000 software was used for γ-ray spectrometric analysis. 111In (2.8 days), 109Cd (462.4 days) and 106mAg (8.28 days) radionuclides were detected in the target matrix. The target was allowed for a complete decay of 111In for 90 days. The 106mAg also decayed out during this period and hence the target contained only 109Cd radioisotope in bulk Ag matrix. The energy and the efficiency calibration of the detector was performed using standard sources of known activity such as 152Eu (13.528 a), 133Ba (10.551 a), 137Cs (30.08 a) and 60Co (5.27 a).

Dissolution and separation of bulk silver

The α-irradiated silver target was dissolved in minimum volume of conc. HNO3 medium. To monitor the fate of bulk Ag in the radiochemical separations it was spiked with a solution of 110mAg (249.79 days) prepared in 0.1 M HNO3. The 110mAg was procured from the Board of Radiation and Isotope Technology (BRIT), India. The solution was evaporated to dryness thrice and was finally taken in 10−2 M HNO3. A 10 mL active stock solution containing NCA 109Cd and bulk Ag spiked with 110mAg was then prepared for radiochemical separation process. Bulk Ag was separated by precipitating as AgCl, by drop wise addition of 0.1 M HCl to the stock solution following the same procedure described by Maiti et al. [23]. The solution was centrifuged and filtered, and the filtrate contains only NCA 109Cd radioisotope. This solution was evaporated to dryness twice, taken in 10 mL water and with this final stock solution, adsorption studies of NCA 109Cd onto CA beads were performed.

Adsorption of NCA 109Cd onto CA beads

The adsorptions of NCA 109Cd from the aqueous solution into CA beads were examined using batch mode. Each batch containing 30 beads of CA were exposed to 1.9 mL of HNO3 solutions of different pH (1–5) and 0.1 mL radioactive stock solution containing 109Cd. The sets were shaken and settled for 10 min each and then the beads were removed from the contact of the solutions and 1.8 mL aliquots from the supernatant were taken in eppendorf. The solutions were then assayed for γ-spectrometry of 109Cd radioisotope by monitoring the characteristic photo peaks at 22.4 and 88.2 keV. The extent of adsorption was calculated from the difference in activity with a suitable standard. At the best pH condition with respect to HNO3, shaking time, settling time and the number of beads were varied to get the optimum condition for the aforesaid extraction. The effect of bulk Cd on adsorption of NCA 109Cd was also monitored. For this experiment, several sets of bulk Cd concentration (0.1, 1, 10, 30, 50 ppm) were chosen and number of beads were varied at all these bulk Cd concentrations.

Desorption

Subsequent to adsorption, study of desorption was an essential job. The desorption of NCA 109Cd from CA beads was tested in different desorbing media like 0.5 M oxalic acid, 0.1 and 1 M HNO3. A satisfactory desorption was obtained in both 0.1 and 1 M HNO3 medium and hence desorption of bulk Cd (0.1, 1, 10, 30, 50 ppm) from CA beads was performed in 0.1 M HNO3. The beads were found intact, with no visual degradation in its physical as well as in chemical aspect and may be reused after desorption in this medium. All the adsorption and desorption studies were carried out at 25 °C.

Adsorption isotherm modeling of Cd2+ ions

At the best condition of adsorption of 109Cd into CA beads, (pH 4, 30 min shaking and 10 min settling time, using 50 beads) the adsorption isotherms were performed at fixed temperatures of 288, 298,308 and 318 K and with different concentrations of Cd (0.1, 1, 10, 30, 50 ppm). 25 mL solution of each concentration was spiked with 1 mL of stock solution of NCA 109Cd separately. Then all the five sets were evaporated to dryness twice and made the volume up to 25 mL with 10−2 M HNO3 keeping the resulting concentration same as that with the initial. 2 mL of each set of solution were treated with 50 CA beads, shaken and settled at a fixed temperature and the amount of adsorbed Cd was measured by radiometric method with the help of the characteristics photo peak of 109Cd. The adsorption data was analyzed by fitting to isotherm models like Langmuir, Freundlich, Temkin and Dubinin–Radushkevich.

The Langmuir adsorption isotherm model

The Langmuir adsorption model assumes monolayer formation on the adsorbent surface. It also assumes uniform energy of adsorption and that drifting of adsorbate does not occur on surface [29]. Adsorption is assumed to occur until an equilibrium distribution of metal ions occurs between the solid and mobile phases [30]. Langmuir equation is therefore represented as:

$$ q_{\text{e}} = \frac{{q_{\text{m}} K_{\text{a}} C_{\text{e}} }}{{1 + K_{\text{a}} C_{\text{e}} }} $$
(1)

where C e is the equilibrium concentration of adsorbate (mg/L), q e is the amount of metal adsorbed per gram of the adsorbent at equilibrium (mg/g), q m is the maximum monolayer coverage capacity (mg/g), and K a is Langmuir isotherm constant (mg/g) (L/mg)1/n.

The Langmuir Eq. (1) was transformed into a linear Eq. (2) as shown below for obtaining the Langmuir adsorption parameters:

$$ \frac{1}{{q_{\text{e}} }} = \frac{1}{{q_{\text{m}} }} + \frac{1}{{q_{\text{m}} K_{\text{a}} C_{\text{e}} }} . $$
(2)

A plot of 1/q e versus 1/C e was used for calculating the values of q m and K a. An essential feature of the Langmuir isotherm, the equilibrium parameter R L (a dimensionless constant also referred to as separation factor) was calculated using Eq. 3 [31]:

$$ R_{L} = \frac{1}{{1 + (1 + K_{a} C_{0} )}} . $$
(3)

where C 0 is the initial concentration.

The value of R L is the indicating factor for deciding whether the adsorption process is favorable or not. It is favorable if R L value lies between 0 and 1, linear if R L = 1, irreversible if R L = 0 and unfavorable if R L is greater than 1.

The Freundlich adsorption isotherm model

This isotherm model is suitable to describe the features of those surfaces that have both homogeneous and heterogeneous features [32]. The adsorption data in such cases often fit the empirical equation proposed by Freundlich as in Eq. 4:

$$ Q_{\text{e}} = K_{\text{f}} C_{\text{e}}^{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 n}}\right.\kern-0pt} \!\lower0.7ex\hbox{$n$}}}} . $$
(4)

where K f is the Freundlich isotherm constant (mg/g)(L/mg)1/n, n is the adsorption intensity, C e is the equilibrium concentration of adsorbate (mg/L), and Q e is the amount of metal adsorbed per gram of the adsorbent at equilibrium (mg/g).

Equation 4 can be further linearized as

$$ \log Q_{\text{e}} = \log K_{\text{f}} + \frac{1}{n} {\text{log}}\,C_{\text{e}} . $$
(5)

where constant K f is a measure of the adsorption capacity at unit concentration, while 1/n indicates the intensity of adsorption and can be calculated from the slope and intercept respectively of the plot of log Q e versus log C e. The partition behaviour is independent of the adsorbate concentration if n = 1. If 1/n < 1 the partition behavior varies directly with the adsorbate concentration, and cooperative adsorption takes place if 1/n > 1 [33]. Therefore 1/n is a heterogeneity parameter. A smaller 1/n value indicates greater heterogeneity and this expression reduces to a linear adsorption isotherm when 1/n = 1. If n lies between one and ten, a favorable sorption process is predicted [34].

The Temkin adsorption isotherm model

Temkin isotherm model [35] assumes adsorbate-adsorbent interactions ignoring the extreme concentration (low and high). The heat of adsorption of all the adsorbate molecules in every layer decreases linearly with exposure to adsorbent surface. The equation is as follows [36]:

$$ q_{\text{e}} = \frac{RT}{b}\ln \left( {A_{\text{T}} C_{\text{e}} } \right) . $$
(6)

where C e is the equilibrium concentration of adsorbate (mg/L), q e is the amount of metal adsorbed per gram of the adsorbent at equilibrium (mg/g), A T is Temkin isotherm equilibrium binding constant related to the maximum binding energy (L/g), b T is Temkin isotherm constant (J/mol), R is the Universal gas constant (8.314 J/mol/K), T is the temperature (K).which is further linearized as

$$ q_{\text{e}} = \frac{RT}{{b_{\text{T}} }}\ln A_{\text{T}} + \frac{RT}{{b_{\text{T}} }}\ln C_{\text{e}} \,{\text{and}}\, q_{\text{e}} = B\ln A_{\text{T}} + B\ln C_{\text{e}} . $$
(7)

where \( B = \frac{RT}{{b_{\text{T}} }} \); and is a constant related to heat of sorption (J/mol).

The derivation of the equation relies on a uniform distribution of binding energies (up to a maximum limit). The equilibrium binding constant (A T) and the heat of adsorption (B) were calculated from the intercept and slope respectively of the q e versus ln C e plot.

The Dubinin–Radushkevich adsorption isotherm model

Multilayer adsorption process involving van der Waals forces of attraction are well described by the Dubinin–Radushkevich isotherm model. It involves a semi-empirical equation and is used to describe the pore filling mechanism of the adsorbent material. This isotherm is most suitable for physical adsorption processes [37] and the linear form is represented as:

$$ \ln Q_{\text{e}} = \ln Q_{\text{D}} - K_{\text{ad}} \varepsilon^{2} . $$
(8)

where Q D is the Dubinin–Radushkevich monolayer adsorption capacity (mg/g), Q e is the amount of metal adsorbed per gram of the adsorbent at equilibrium (mg/g), K ad is Dubinin–Radushkevich isotherm constant (mol2/kJ2), and ε is Polanyi potential.

The model is also represented as

$$ \ln Q_{\text{e}} = \ln Q_{\text{D}} - \beta \,\varepsilon^{2} $$
(9)

where β = constant related to free energy of sorption (mol2/kJ2).

The Polanyi potential is calculated using the Eq. 10 as

$$ \varepsilon = RT \ln \,\left( {1 + \frac{1}{{C_{e} }}} \right) $$
(10)

where C e is the equilibrium concentration of adsorbate (mg/L).

The values of β and Q D were calculated from the slope and intercept of straight line plots of ln Q e versus \( \varepsilon^{2} \) espectively. A decrease in the β value with increasing temperature is associated with a decrease in adsorption capacity (Q D) is observed.

The mean free energy of adsorption denoted by E D–R (kJ/mol) is the amount of free energy produced in the system owing to transfer of 1 mol of ions from solution to the adsorbent surface and was calculated using the β values from the relationship:

$$ E_{D - R} = \frac{1}{{\sqrt {( - 2\beta )} }} $$
(11)

The nature of adsorption mechanism can be predicted from the value of ED–R. If this value lies between 8 and 16 kJ/mol the process is designated as chemisorption, while a physical adsorption process is predicted if the values are below 8 kJ/mol [38].

Thermodynamic parameters

The mechanism of adsorption process can further be understood with the help of the thermodynamic parameters such as change in standard free energy (ΔG), enthalpy (ΔH) and entropy (ΔS).

These parameters can be determined from the following equations [39]

$$ \ln K_{\text{c}} = - \frac{{\Delta {\text{G}}}}{RT} $$
(12)
$$ \Delta {\text{G }} = \, \Delta {\text{H}} - {\text{T}}\Delta {\text{S}} $$
(13)

and hence

$$ \ln K_{\text{c}} = \frac{\Delta S}{R} - \frac{\Delta H}{RT} $$
(14)

where R is the gas constant (8.314 J/mol K), T is the temperature (K) and K c (L/mol) is the standard thermodynamic equilibrium constant which is calculated by

$$ K_{\text{c}} = \frac{{F_{\text{e}} }}{{1 - F_{\text{e}} }} $$
(15)

Here F e is the fractional conversion of the sorption at equilibrium and is expressed as follows

$$ F_{\text{e}} = \frac{{C_{\text{ad}} }}{{C_{i} }} . $$
(16)

C i is the initial concentration (mg/L) of the metal ion in the solution and C ad is the concentration (mg/L) of the metal ion on the adsorbent at equilibrium. All these thermodynamic parameters of our study have been obtained from the intercept and slope of ln K c versus 1/T plot using the van’t Hoff Eq. 14.

A positive value of ΔH reflects the endothermic nature of the process. Positive ΔS° values confirm the affinity of the adsorbent for adsorbate and increase in randomness at the interface of solid and solution during adsorption. Negative ΔG values indicate that the adsorption process is spontaneous and thermodynamically feasible [40].

Results and discussion

The present study involves the use of no-carrier-added 109Cd to study the Cd uptake properties of biocompatible calcium alginate gels and to spike the bulk cadmium solutions for the adsorption isotherm experiments with the CA gels. To have an idea about the probable chemical species involved in the reactions, CHemical Equilibria in AQuatic Systems (CHEAQS) software was used [41]. From the results it is clear that, cadmium exists as Cd2+ (~100%) in the pH range 2–5, whereas at pH 1, it exits as a mixture of Cd2+ (92.03%) and Cd(NO3)+ (7.77%). For the adsorption phenomenon of heavy metals onto adsorbent materials, pH takes a decisive role as shown in Fig. 1. The figure illustrates that the adsorption is more or less same in the range of pH 3–5, slightly decreases at pH 2, and falls very sharply at pH 1. This is presumably because of the pKa value of the carboxylic acids which lies in the range 3–5 and a considerable amount of free carboxylate ions are present in this pH range which is also indicated by the Henderson–Hasselbalch equation. Therefore strong electrostatic attractions and van der Waals forces come into play between COO− group and Cd2+ metal ion. Additionally, cationic exchange between Cd2+ and Ca2+ in CA beads also has a large impact on the adsorption and hence greater adsorption percentage (~60%, at pH 4) was found. But at the lower pH (1,2) COO− group gets protonated [42] and due to excessive protonation of active sites, surface of adsorbent (CA) becomes positively charged which repels the entering Cd2+ along with a competition between H3O+ and Cd2+ for binding sites resulting in a smaller extent of adsorption of Cd2+ into the CA matrix.

Fig. 1
figure 1

Adsorption profile of NCA109Cd onto CA beads with varying pH of HNO3 medium, (with 30 beads, 10 min shaking and 10 min settling time)

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To obtain better adsorption, contact time (including shaking and settling) of CA beads with aqueous Cd2+ solution were varied. The results are shown in Fig. 2. Adsorption percentage increased with increasing shaking time up to 30 min and became static after this. No significant change in adsorption was obtained with varying the range of settling time. The numbers of beads were then varied. Figure 3 shows that the number of binding sites available was large enough to bind NCA Cd2+ at all the experimental conditions and hence any significant change in the adsorption was not observed. An optimum condition was obtained at pH 4, shaking time 30 min and settling time 10 min and 50 CA beads, when around 87% NCA Cd2+was adsorbed.

Fig. 2
figure 2

Adsorption profile of NCA109Cd onto 30 CA beads with variation of shaking and settling time at pH 4 of HNO3 medium

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Fig. 3
figure 3

Adsorption profile of NCA109Cd onto varying number of CA beads at pH 4 of HNO3 medium (30 min shaking and 10 min settling time)

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Now, we tried to find the adsorption capability of bulk metallic cadmium into CA beads. A new experimental set was designed with a wide range of bulk Cd2+ (0.1–50 ppm) solution spiked with NCA 109Cd to monitor the adsorption using radiometric method via the characteristic photo-peaks of 109Cd at 22.4 and 88.2 keV. The number of CA beads were varied (30, 50, 90) in this concentration range. At all the concentrations, adsorption was found to be more or less equal and lies in the range 80–85% in each set of experiment (Fig. 4). It implies that the number of beads in our experiment was sufficient to adsorb a satisfactory amount of bulk Cd2+ and consequently adsorption isotherm experiment was performed with 50 CA beads at pH 4, shaking time 30 min and settling time 10 min.

Fig. 4
figure 4

Adsorption profile of NCA109Cd onto different number of CA beads at pH 4 of HNO3 medium in presence of different bulk Cd concentration (30 min shaking and 10 min settling time)

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Desorption of NCA 109Cd from CA beads was then performed in different desorbing media such as 0.5 M oxalic acid, 0.1 and 1 M HNO3 (Fig. 5). ~10% NCA 109Cd was desorbed in 0.5 M oxalic acid, whereas ~92% of the same was desorbed in both 0.1 and 1 M HNO3 media as it offers a strong acidic condition. As both the 0.1 and 1 M HNO3 media are equally capable towards desorption, we chose 0.1 M HNO3 avoiding higher acid concentration for bulk Cd2+ removal. Figure 6 shows that ~95% bulk Cd2+ was desorbed successfully in 0.1 M HNO3 medium at all the bulk concentrations.

Fig. 5
figure 5

Desorption profile of NCA109Cd from CA beads in different desorbing media

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Fig. 6
figure 6

Desorption of bulk Cd of different concentrations from CA beads in 0.1 M HNO3

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The Langmuir constants q m and K L (which is also represented as b in linear form of Langmuir) were obtained from the slope and intercept of 1/q e vs. 1/C e plot obtained from linearized form of non-linear Langmuir equation shown in Fig. 7 and the Langmuir isotherm parameters are tabulated in Table 1. The maximum adsorption capacities (q m) of Cd2+ by the CA were 4.92, 2.42, 2.48, 8.09, mg/g calculated from non-linear Langmuir equation at 288, 298, 308 and 318 K respectively. The regression coefficient (R 2) values 0.998, 0.999, 0.998, 0.999 at the experimental temperatures show that the data were fitted very well in this method and the adsorption process could be described by the Langmuir equation which indicates a homogeneous monolayer adsorption process. The constant K L expresses the affinity between the adsorbent and adsorbate [43] and a low value of K L (0.0076–0.026) obtained from our experimental results indicated that CA beads have a high affinity for Cd2+ ion. Finally, the values of equilibrium parameter (R L) at all the experimental temperatures and all the starting concentrations lie between 0 < R L < 1 which indicates that the adsorption process is very much favorable.

Fig. 7
figure 7

Langmuir adsorption isotherm plots

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Table 1 Isotherm model parameters and coefficient of determination (R 2) for cadmium adsorption by CA beads at different temperatures
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Figure 8 shows the plot of log Q e versus log C e obtained from linear Freundlich equation and the isotherm parameters n and K f were obtained from the slope and intercept respectively and are given in Table 1. As all the n values are found to be ~1, it implies a beneficial adsorption phenomenon as according to Kadirvelu and Namasivayam [44], the n values lying in the range 1–10 indicates adsorption processes independent of the initial concentration. The n value also indicates that the CA bead has a high affinity for Cd2+ ions in solution and a heterogeneous adsorption is expected. Maximum adsorption capacity (q m) were calculated with the help of K f values and 50 ppm as the initial concentration at all the temperatures and were found to be 1.80, 2.19, 2.80, 2.77 mg/g for 288, 298, 308 and 318 K respectively. The regression coefficient (R 2) value was 0.999 for all the set of data, which implies excellent fitting of the experimental data, thus obey the Freundlich isotherm and a multilayer adsorption process is expected [45].

Fig. 8
figure 8

Freundlich adsorption isotherm plots

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Temkin isotherm model was applied by a linear plot of q e against ln C e shown in Fig. 9, the constants B and A T were calculated from the slope and intercept respectively and Temkin isotherm constants (b T) were calculated from B values. The Temkin isotherm parameters A, B, b T and R 2 are presented in Table 1. The magnitudes of A T (15.66, 16.47, 22.10, 21.68 L/g) and b T (41.43, 43.09, 41.57, 40.49 kJ/mole) at 288, 298, 308, 318 K respectively were high which indicates a very strong interaction of Cd2+ with CA beads and therefore, the process might be chemisorption along with the physical adsorption. Again, the regression coefficient (R 2) value was ~0.7 for all the set of data and shows a weaker fitting of the data as well as applicability of this isotherm model as compared to the Langmuir and Freundlich models.

Fig. 9
figure 9

Temkin adsorption isotherm plots

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The values of β and Q D were calculated from the slope and intercept of straight line plots of ln Q e versus ε 2 following the Dubinin–Radushkevich isotherm model represented in Fig. 10. Then the mean free energy of adsorption (E D–R) was calculated from β values and all the isotherm parameters are summarized in Table 1. The Q D values were 7.159, 7.159, 6.486, 6.497 mg/g at 288, 298, 308, 318 K respectively and matches with the non-linear Langmuir isotherm. E D–R values were calculated as 2.837, 2.957, 3.30 and 3.43 kJ/mol and the adsorption process is designated to be predominated by physical adsorption as compared to chemical interactions. The values of regression coefficient (R 2) were ~0.84 for all sets of data which indicates that this isotherm did not provided a very good fit to the experimental data, though it is slightly higher than that of Temkin adsorption isotherm.

Fig. 10
figure 10

Dubinin–Radushkevich isotherm plots

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The values of some thermodynamic parameters like ΔH and ΔS were calculated from the slopes and intercepts of the plots of ln K c as a function of 1/T for different Cd2+ concentrations and are shown in Fig. 11. Then the change in free energy (ΔG) was calculated from ln K c values and all the thermodynamic parameters are tabulated in Table 2.The negative values of Gibbs free energy (ΔG) of the interactions for all the sets of data (in the range of −3 to −5) demonstrate that the process is spontaneous, feasible and favorable towards formation of electrostatic interaction between Cd2+–CA beads [46]. Zhang et al. [47] reported that the change in enthalpy (ΔH) should be lower than that of 20.0 kJ/mol for physical adsorption. The ΔH values of our experiments were found positive, and numerical values were 13.30, 6.86, 11.79, 10.59 and 13.63 kJ/mol for 0.1, 1, 10, 30 and 50 ppm initial concentration of Cd2+ metal ion respectively indicating the physical adsorption of Cd2+ onto CA beads. These positive values of ΔH also demonstrate the endothermic nature of the process involving weak interactions. Again, the high positive values of ΔS, i.e., 57.40, 36.04, 52.05, 47.86 and 56.99 J/mol K for 0.1, 1, 10, 30 and 50 ppm initial concentration of Cd2+ metal ion respectively indicate the increase in the degree of freedom of the adsorbing system with spontaneity and higher randomness of the metal ions near the adsorbent surface during the sorption process.

Fig. 11
figure 11

The plot of ln K c versus 1/T for obtaining thermodynamic parameters

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Table 2 Thermodynamic parameters for adsorption of Cd2+ ions from aqueous solutions onto the CA beads
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There are numerous reports on adsorption of Cd2+ in bare CA beads [48, 49] and modified CA beads [50,51,52,53] in the literature. Some of them report better results while the others are comparable with the present study. However, most of the reports have certain limitations in the experimental procedure as well as in the detection methods. Several of them suffer from low adsorption capacity at high Cd2+ concentration and high pH even after a long contact time [54, 55] and with high adsorbent dosage [56]. Some others have low adsorption capacity in the acidic pH range [57, 58] and at higher temperatures [59]. In contrast, our method is capable to work in a very wide range of metal ion concentrations (0.1–50 ppm) and shows high adsorption capacity in a wide pH range (2–5) even with low contact time and lesser amount of adsorbent. Additionally, the sensitivity of our detection method is better over other methods as we have used radiometry using NCA radionuclides for the studies of adsorption isotherm phenomena.

Conclusion

CA beads were used for the adsorption studies of radiopharmaceutically important NCA 109Cd radioisotope from bulk free aqueous solution with a high efficiency. The capacity of CA beads for high concentration of bulk Cd2+ adsorption was also examined with the help of radiometric method. Adsorption capability of environmentally hazardous, toxic and carcinogenic bulk Cd2+ was in agreement with that in NCA scale and hence the adsorption isotherm experiment was performed and our experimental data were excellently fitted to both non-linear Langmuir and linear Freundlich adsorption isotherm equations followed by Dubinin–Radushkevich and then Temkin isotherm models. With the isotherm data, all the thermodynamic parameters were calculated and it can be concluded that the adsorption process is monolayer as well as multilayer and it is a heterogeneous physisorption process predominating over the chemisorptions. In addition, it is a spontaneous endothermic process which suggests a high feasibility of the adsorption process involving electrostatic as well as van der Waal’s interactions.