1 Introduction

In the last century, industrialization and population growth have also increased environmental pollution. In addition to wastes such as metals and dyes used in many production processes, human-caused drug metabolites, pesticides, or wastes generated after use have reached a level that threatens the environment and human health. Among these pollutants, metals occupy the largest area. Mercury, one of these metals, is used in many industrial areas, as well as in areas such as cosmetics and electronics, and it pollutes environmental waters from natural sources.

Mercury is a very dangerous metal for human health. The common types of mercury, which exist in three forms, are Hg (0), Hg (I) and Hg (II). Especially the Hg (II) form is known to cause many diseases (Chalkidis et al., 2020). When it enters the human body by inhalation and ingestion, it can lead to failure and even death in many organs, especially the nervous system and kidneys (Ochedi et al., 2020). Neurological effects are seen even at doses of 0.5 mg/kg. At this dose, it causes inhibition of brain development and regression in the development of psychomotor movements, especially in fetuses. The daily intake dose should not exceed 0.1 µgKg−1 day−1, especially in lactating and pregnant women (Berlin et al., 2007). Due to the enrichment of seawater, the removal of mercury in the form of methylmercury from fish is very important in this respect.

There are many chemical and biological treatment methods for the removal of mercury from the aqueous environment. Filtration (** other parameters constant, with adsorption models based on various mathematical equations. The Langmuir, Freundlich, Temkin, and Dubinin-Radushkevich models are commonly used among these models and were used in this study (Al-Ghouti & Da'ana, 2020). For this purpose, the adsorption of solutions containing mercury at different concentrations was performed, and the equilibrium mercury concentrations were determined using the methods given in Section “Adsorption study”. The isotherm plotted between Ce and Qe obtained experimentally and the graph showing the fit of the experimental results to the theoretical models are shown in Fig. 9, while the parameters obtained from the models are given in Table 1.

Fig. 9
figure 9

Adsorption isotherms and fitting curves of models

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Table 1 Adsorption parameters Hg (II) onto EWGH@Paa
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The adsorption isotherm obtained follows the L-type adsorption isotherm in the Giles classification; however, at low concentrations of mercury, it also shows high adsorption amounts that are typical of an H-type adsorption isotherm. In this type of adsorption behavior, adsorption continues until the adsorption sites become saturated. At low initial concentrations, adsorption occurred in the solid-phase direction, whereas at intermediate concentrations, a solid–liquid equilibrium was established. At high concentrations, the adsorption sites become saturated, and a plateau is reached.

The experimental data fit the Langmuir model, and the obtained adsorption capacity was 1.808 molKg−1 (362,67 mgg−1), which is a very high adsorption capacity. The soluble content of WGH, such as tannic acid, ellagic acid, juglones, naphthoquinone glycosides, and numerous flavonoids in the composite, has been effective in adsorption (Jahanban-Esfahlan et al., 2019). The strong interaction between these structures, which are grafted/entrapped in the inert hydrogel, and mercury ions supports the adsorption energy obtained from the D-R model. The adsorption energy, which evaluates whether the binding is chemical or not, was found to be 13.88 kJ mol-1, indicating that this binding is a chemical interaction. The β value obtained from the Freundlich model is also considered to be a measure of surface heterogeneity. Simultaneously, as this value approaches zero, the adsorption energy increases with increasing adsorbate concentration on the surface (Chen et al., 2022). The Freundlich isotherm is not suitable for providing information on surface saturation or adsorption capacity.

The Temkin model assumes that the binding energy is uniform and the adsorption heat is linear at moderate concentrations, considering the interaction between the adsorbate and adsorbent. The bT value is considered the adsorption binding energy, and the AT value can be evaluated as a measure of the adsorption energy, with small AT values indicating physical adsorption (Al-Trawneh et al., 2021).

The Dubinin-Radushkevich (D-R) model is related to the adsorption energy, indicating whether the adsorption is physical or chemical. For EDR values less than 8 kJmol−1, it can be said that physical adsorption occurs. In this study, the EDR value was 13.88, which can be interpreted as chemical adsorption (Kim & Kim, 2019).

After the adsorption process, desorption studies were carried out with 0.1 M HCl, 1 M HCl, 1 M HNO3, and 1 M NaOH for the reusability study of the adsorbent, and the highest recovery of approximately 50% was achieved with 0.1 M HCl. For the reusability study, the samples desorbed with 0.1 M HCl were selected. The samples were subjected to the adsorption and desorption processes three times, and no decrease in the total adsorption amount was observed. However, it was observed that approximately half of the adsorbed mercury was not separated from the adsorbent.

It can be seen that the adsorption capacity is quite high when compared to similar adsorbents listed in Table 2, selected from the literature.

Table 2 Comparison table of various adsorbents
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5.7 Influence of Time to Adsorption

A series of experiments were carried out to find the change of adsorption over time and the kinetic parameters of adsorption, and the experimental results and the compatibility of these results with the theoretical models such as Pseudo first order (PFO), Pseudo Second order (PSO), intraparticle diffusion (IP) and Elovich (Largitte & Pasquier, 2016) are given in the Fig. 10, and the kinetic parameters found from the models are given in the Table 3.

Fig. 10
figure 10

Effect of time to adsorption and fitting curves of theoretical models

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Table 3 Kinetic parameters of adsorption and using equations
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Since the adsorption event takes place in a heterogeneous phase, it is difficult to explain with kinetic models used in homogeneous reactions. Models that are widely used in the evaluation of adsorption kinetics generally provide several parameters such as the adsorption rate constant, accurate estimation of the adsorbed amount in equilibrium, and an opportunity to comment on the change and mechanism of the reaction over time. Although PFO explains the reaction kinetics as a suitable model at the beginning of the adsorption, it is more appropriate with the PSO model to predict the long adsorption time and the amount adsorbed in equilibrium. The experimental data obtained for the change in the adsorption of Hg (II) ions to the Influence of pH of the solution to Hg (II) adsorption onto EWGH@Paa adsorbent over time were found to have high coefficients of fit for various kinetic models. However, the qe values obtained experimentally and the closeness of the qm values from the model to the found one can be considered as a measure to determine which model the adsorption kinetics is suitable for. The results show that the PFO model is suitable for describing adsorption kinetics, but the PSO model can also be used to explain adsorption. The adsorption rate constants are approximate from both models and show very fast adsorption. The half-life found in the PSO model was quite high for the adsorption. The adsorption kinetics can be explained in terms of the parameters obtained from the Elovich model. The Elovich parameters α and β are the initial adsorption rate and desorption constant, respectively (Hosseini-Bandegharaei et al., 2011). The initial velocity is high. These findings show that adsorption is very fast and that the newly synthesized EWGH@Paa adsorbent is useful for Hg (II) ion adsorption. Although the IP model has a low coefficient of fit, the multilinear adsorption curve indicates that intraparticle diffusion also occurs during adsorption.

5.8 Effect of Temperature on Adsorption and Thermodynamic Parameters

To find the thermodynamic parameters of adsorption, the study was carried out at different temperatures, and other adsorption conditions were kept constant, and the results are given in Fig. 11. Adsorption thermodynamic parameters were calculated using the Van’t Hoff equation. The results show that the adsorption is endothermic and the enthalpy is 35.17 kJmol−1. This result shows that the adsorption is in the energy-consuming direction. The adsorption entropy was found to be 183 Jmol−1, i.e. positive. This result indicates that the disorder increases during adsorption. Considering that the free ions in the solution become more regular in the solid phase during the adsorption process, a decrease in entropy is expected, but since this result is the entropy of the whole process, other secondary interactions that occur with adsorption increase the entropy of the system (Abdelmonem et al., 2024). Because together with adsorption, secondary events such as dehydration, ion exchange, and hydrolysis affect the adsorption entropy. Free enthalpy of adsorption was found to be negative for 298 K, as 19.25 kJmol−1. This result is expected because adsorption occurs spontaneously at this temperature.

Fig. 11
figure 11

Effect of temperature on adsorption

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5.9 Details of Density Functional Theory Calculations

All calculations were performed using the Perdew-Burke-Ernzerhof (GGA-PBE) exchange–correlation functional (Perdew et al., 1996) and 6-31G(d)/LANL2DZ electronic basic set (Francl et al., 1982; Hay & W.R., 1985). The dispersion corrections D3 proposed by Grimme (Grimme et al., 2010) were also included to take into account the weak non-covalent interactions. So, the PBE-D3/6-31G(d)/LANL2DZ level of theory is applied. We used the graphics processor-based TeraChem software (Goumans et al., 2009; Kästner et al., 2009; Titov et al., 2013; Ufimtsev & Martínez, 2009). Geometry optimization was carried out with the efficient geomeTRIC energy minimizer (Wang & Song, 2016). Conceptual Density Functional Theory (CDFT) considered as a branch associated with the chemical reactivity of DFT presents the following mathematical relations to define the chemical potential (µ) and chemical hardness (η) (Islam et al., 2018).

$$\mu = - \chi = \left[ {\frac{\partial E}{{\partial N}}} \right]_{\nu (r)}$$
$$\eta = \left[ {\frac{\partial \mu }{{\partial N}}} \right]_{\nu (r)} = \left[ {\frac{{\partial^{2} E}}{{\partial N^{2} }}} \right]_{\nu (r)}$$
$$\sigma = 1/\eta$$

Here, E, N, and ν(r) are total electronic energy, total number of electrons, and external potential, respectively. As can be seen from the relations presented above electronegativity (χ) corresponds to the negative of the chemical potential while softness (σ) is defined as the multiplicative inverse of the chemical hardness. If one applies the finite difference approach to the aforementioned mathematical relations, ground state ionization energy (I) and electron affinity (A) based hardness and chemical potential equations can be obtained as (Kaya et al., 2023):

$$\mu = - \chi = - \left( {\frac{I + A}{2}} \right)$$
$$\eta = I - A$$

According to Koopmans Theorem (Koopmans, 1934), via frontier orbital energies (HOMO and LUMO energy values), the ionization energy and electron affinities of molecules can be approximately predicted as:

$$I = - E_{HOMO}$$
$$A = - E_{LUMO}$$

In the present work, we used the Koopmans Theorem to predict the ionization energy and electron affinities of the predominantly found molecules in green walnut shell and their Hg (II) complexes.

5.10 Molecular Complexes

First of all, we optimized the structure of the two-molecular complexes containing Hg (II) ions. We considered the ion-containing complexes as the singlets. The electronic and energy characteristics of the considered systems are presented in Table 4. The binding energy was determined as follows:

$$E_{b} = E\left( {{\text{molecule}}} \right) + E\left( {{\text{Hg}}^{2 + } } \right) - E\left( {{\text{molecule/Hg}}^{2 + } } \right)$$

where “molecule” is tannic acid, ellagic acid, sinapic acid, juglanone A, and juglanone B.

Table 4 Calculated electronic and energy characteristics of, ellagic acid, sinapic acid, juglanone A, juglanone B, and their complexes with Hg (II) ion
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One of the most popular parameters used in the chemical reactivity analysis of the chemical system is the chemical hardness. This concept introduced by R.G. Pearson is defined as the resistance against the polarization of atoms, ions and molecules (Kaya & Kaya, 2015a, 2015b). There is a remarkable relation between quantum chemical parameters like hardness, polarizability and stability. The relations with stability of such parameters are illuminated through some electronic structure rules such as Maximum Hardness Principle (Kaya et al., 2022) and Minimum Polarizability Principle (Kaya et al., 2016). Maximum Hardness Principle (MHP) states that stable chemical states correspond to minimum softness or maximum hardness value. It is clear from this explanation that hard chemical systems are more stable and hardness can be used as a stability indicator. The verbal definition given above for chemical hardness implies the inverse relation between polarizability and chemical hardness concepts. This inverse relation introduced by Ghanty and Ghosh (Ghanty & Ghosh, 1993) has been instrumental in introducing the Principle of Minimum Polarizability (PMM) to science by Chattaraj and Sengupta (Chattaraj & Sengupta, 1996). According to PMM, polarizability is minimized at stable states unlike the chemical hardness. As a measure of the polarizabilities of the studied chemical systems, we calculated their dipole moments and presented in the related table. The emergence of the chemical hardness concept has been realized with the introducing of Hard and Soft Acid–Base (HSAB) Principle (Pearson, 1963). Through HSAB Principle, Lewis acids-base are classified as hard, bonderline and soft. Hard acids prefer the binding to hard bases and soft acids prefer the binding to soft bases because of the power of the interactions between the mentioned species.The most stable sytem among the dominant component of green walnut shell is ellagic acid with a chemical hardness value of 2. 844 eV. The most reactive or soft system is juglanone B with a chemical hardness value of 1.943 eV. It should be noted that in hard and soft classification of Pearson, Hg (II) ion is among widely known soft acids. In the light of HSAB Principle, it is not difficult to predict that this ion will more powerful interact with the most polarizable or soft molecule among the dominanat components. As expected, the binding energy (Eb) calculated for the interaction between Hg (II) and juglanone B is higher than the calculated binding energies for other chemical interactions. This situation shows that our theoretical and experimental observations are in good agreement with HSAB Principle. The mechanism of the interaction between Hg (II) and juglanone B is visually presented in Figs. 12–13. Figures regarding to the interaction with Hg (II) of other components are presented in the Supplementary File of the paper.

Fig. 12
figure 12

Juglanone B: atomic structure (a), HOMO (b), and LUMO (c)

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Fig. 13
figure 13

Juglanone B/Hg (II) complex: atomic structure (a), HOMO (b), and LUMO (c)

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6 Conclusion

The high amount of water-soluble part of the green shell, which is released in a very high amount during the walnut production process, poses a serious danger to the environment. The water-soluble component is high in terms of functional groups and consists of active biomolecules. It has been shown that by incorporating this part into an inert polymer structure, it can be an effective adsorbent, especially for metal removal. This feature of the adsorbent has been experimentally shown to be highly effective for mercury removal, with high adsorption capacity and fast adsorption. The aim of this study is to transform a structure that is currently in waste and has a limited application area for use as a usable adsorbent. The results showed that this method is promising for future studies.