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# Adsorption mechanism of Cr(VI) onto GO/PAMAMs composites

## Abstract

Graphene oxide/polyamidoamine dendrimers (GO/PAMAMs) composites were used to remove Cr(VI) from simulated effluents, the adsorption kinetics and thermodynamics of Cr(VI) onto GO/PAMAMs were systematically investigated. The results showed that the optimum pH value was 2.5, the removal percentage reached 90.7% for 30 mg/L of Cr(VI) within 120 min. The adsorption process was well described by pseudo-second-order kinetic model. The maximum adsorption capacities of Cr(VI) onto GO/PAMAMs were found to be 131.58, 183.82 and 211.42 mg/g at 293.15, 303.15 and 313.15 K, respectively, which were calculated from the Langmuir model equation. The adsorption thermodynamic parameters indicate that the adsorption of Cr(VI) onto GO/PAMAMs is a spontaneous endothermic process. The XPS analysis reveals the adsorption and removal mechanism of Cr(VI) on GO/PAMAMs that first the Cr(VI) binds to the protonated amine of GO/PAMAMs, then Cr(VI) be reduced to Cr(III) with the assistance of π-electrons on the carbocyclic six-membered ring of GO in GO/PAMAMs, and then Cr(III) was released into solution under the electrostatic repulsion between the Cr(III) and the protonated amine groups.

## Introduction

Chromium is widely used in the industries of leather-tanning1, mining, textile dyeing, manufacturing processes of anti-corrosion agents and pigments2, which means that it’s unavoidable to generate large amounts of chromium-containing wastewater. As is known that hexavalent [Cr(VI)] and trivalent [Cr(III)] are the most stable forms in aquatic environment and Cr(VI) is about 1000 times more poisonous than Cr(III)3. Due to its highly poisonous and extremely mobile in the surface-water and groundwater in a broad pH range, Cr(VI) has been identified as a potential carcinogenic substance by the Environmental Protection Agency of USA. Long-term exposure to Cr(VI) can lead to nose perforation, skin ulceration, liver damage and lung cancer4,5. Hence, Cr(VI) has been placed as one of eight prior toxic chemical substances listed by the World Health Organization (WHO), and the maximum amount of Cr(VI) for discharging to inland surface water must be restricted to 0.2 mg/L according to the industrial wastewater discharge standard, which set by the Ministry Environmental protection of China6, meanwhile the guideline of Cr(VI) content for drinking water established by the WHO must be below 0.05 mg/L4.

In this paper, we used 2.0 G GO/PAMAMs composites, which were prepared by grafting 2.0 G PAMAM to GO in our previous study31. The influence factors such as pH value, initial Cr(VI) concentration, temperature and contact time were investigated. During the investigation process, we focused on studying the kinetics and thermodynamics of Cr(VI) adsorption onto GO/PAMAMs. The adsorption kinetics was investigated by pseudo-first, pseudo-second equation and intraparticle diffusion model. In order to obtain the qm values of Cr(VI) adsorption on PAMAMs-GO, the Langmuir and Freunlich model are used for fitting the adsorption isotherm data. To investigate the influence of temperature on the thermodynamic parameters, thermodynamic parameters, e.g. ΔH0, ΔS0and ΔG0 for the adsorption of Cr(VI) on PAMAMs-GO were also calculated. The effect of Cl and SO42− on the adsorption of Cr(VI) by GO/PAMAMs and XPS analysis were especially explored in the paper.

## Results and Discussion

### Characterization

The GO/PAMAMs were analyzed by FT-IR, TGA Raman spectra, the Surface Area Analyzer in our published paper31. The BET specific surface area of GO/PAMAMs is 25 m2/g, which was much lower than that of previous graphene oxide sample data31. This might be due to the incomplete exfoliation of graphene oxide and the agglomerations occurred during preparation process31.

Figure 1 showed that the surface morphology of GO/PAMAMs was changed after adsorbing Cr(VI). It was easily found that the GO/PAMAMs had relatively fluffy and foam-like structures, which certainly provide good platform for heavy metal adsorption. After adsorbing Cr(VI), the GO/PAMAMs became flakes but retained its fluffy characteristic, this may favor the regeneration of GO/PAMAMs as an adsorbent for Cr(VI) adsorption.

### Effect of pH on removal of Cr(VI)

As the pH value has a significant effect on most adsorbents for removal of heavy metals, so it should be given priority consideration. As depicted in Fig. 2, there is a relatively high removal efficiency for Cr(VI) in the pH range of 1.5–2.5, the maximum removal efficiency for Cr(VI) reached 80.70% at pH = 2.5. While in the pH range of 2.5–7.0, there is a sharp decline in removal efficiency of Cr(VI), the removal efficiency of Cr(VI) decrease as the increase in pH. The highly dependence on pH of Cr(VI) adsorption onto the GO/PAMAMs can be explained as follows: the most probable species of Cr(VI) present in aqueous solution are Cr2O72−, CrO42−, HCrO4 and H2CrO4, which depend on the solution pH, Cr(VI) concentration and redox potential32. In the acid medium with pH ranging from 1.0 to 4.0, HCrO4 is the major species of Cr(VI)32, and the surface of GO/PAMAMs was surrounded by adequate H+. Hence, the amine groups of the adsorbent were easily protonated and positively charged, which promoted the approach of negatively charged Cr(VI) species (HCrO4) attributed to the electrostatic interaction as Eq. (1). This point was supported by the curve of zeta potentials of GO/PAMAMs versus pH values in our published literature31. While in the relatively neutral solution with pH ranging from 4.0 to 7.0, CrO42− is the predominant species, which means that adsorbing one Cr(VI) anion must consume two active sites (showed as Eq. (2)) on GO/PAMAMs compared with that of HCrO4 species6. Meanwhile, due to the lacking of proton, there are few protons to form protonated amine groups for adsorption of CrO42− species. Therefore, low pH medium is favorable for the removal of Cr(VI). Since at pH = 2.5, the GO/PAMAMs has the maximum removal efficiency, so we choose pH = 2.5 as the optimal pH medium for adsorption of Cr(VI) in the following experiments

$${\rm{R}}\,{({{\rm{NH}}}_{2})}_{{\rm{n}}}\mathop{\longrightarrow }\limits^{{{\rm{H}}}^{+}}{\rm{R}}\,{{(\mathrm{NH}}_{{\rm{3}}}^{+})}_{{\rm{n}}}\mathop{\longrightarrow }\limits^{{{\rm{HCrO}}}_{4}^{-}}{\rm{R}}\,{{[\mathrm{NH}}_{{\rm{3}}}^{+}{{\rm{HCrO}}}_{4}^{-}]}_{{\rm{n}}}$$
(1)
$${\rm{2R}}\,{({{\rm{NH}}}_{2})}_{{\rm{n}}}\mathop{\longrightarrow }\limits^{{{\rm{H}}}^{+}}{\rm{2R}}\,{{(\mathrm{NH}}_{{\rm{3}}}^{+})}_{{\rm{n}}}\mathop{\longrightarrow }\limits^{{{\rm{CrO}}}_{4}^{2\,-}}[\mathrm{2R}(\,-\,{{\rm{NH}}}_{{\rm{3}}}^{+}{)}_{{\rm{n}}}{{\rm{nCrO}}}_{4}^{2\,-}]$$
(2)

where R represents the skeleton of GO/PAMAMs, the value of n is between 1 to 8.

### Effect of contact time and adsorption kinetics

In order to obtain the minimum contact time for equilibrium adsorption, the time-dependent behavior of Cr(VI) adsorption of two different initial concentration (50 and 100 mg/L) were carried out in the time range of 10–720 min as shown in Fig. 3. From the Fig. 3 we can be observed that the adsorption rate was very quick for the first 20 minutes and then became slow until nearly zero. For both C0 = 50 and 100 mg/L of Cr(VI), 180 min of contact time is enough to reach equilibrium of adsorption at 303.15 K. Generally, the pseudo-first-order equation (3) and pseudo-second-order equation (4)4 are utilized to investigate the adsorption kinetics, and usually the Eq. (4) offered a better description of adsorption kinetics. Besides, the Intraparticle model is also the most widely used model to describe the kinetic mechanism of the adsorption process since it gives information of the diffusion of Cr(VI) anions onto GO/PAMAMs particles in the liquid adsorption system, the most commonly used intraparticle diffusion model is expressed in Eq. (5)33. In this paper, pseudo-first, pseudo-second equation and intraparticle diffusion model were used to fit the adsorption data.

$${\rm{The}}\,{\rm{pseudo}} \mbox{-} {\rm{first}} \mbox{-} {\rm{order}}:\,\mathrm{ln}(\frac{{q}_{e}-{q}_{t}}{{q}_{e}})=-\,{k}_{1}t$$
(3)
$${\rm{The}}\,{\rm{pseudo}}-{\rm{second}}-\,{\rm{order}}:\frac{t}{{q}_{t}}=\frac{1}{{q}_{e}}t+\frac{1}{{k}_{2}{q}_{e}^{2}}$$
(4)
$${\rm{The}}\,{\rm{Intraparticle}}\,{\rm{diffusion}}\,{\rm{model}}:{q}_{t}={k}_{i}{t}^{1/2}+C$$
(5)

where qe and qt are the mass of Cr(VI) adsorbed (mg/g) at equilibrium and time t, respectively, k1 is the first-order reaction rate constant of adsorption (min−1), and k2 is the pseudo-second order reaction rate constant (g.mg−1.min−1), ki is the intraparticle diffusion rate constant (mg.g−1·min−1/2), and C is the thickness of the boundary layer. The values of k1 and qe were calculated from the slope and intercept of the plot of ln(qe − qt) versus t. While the values of qe and k2 were calculated from the slope and intercept of the plot of t/qt versus t, and the value of ki and C were calculated from the plot and intercept of qt versus t1/2, respectively. Table 1 summarized the values of all the three different kinetic model parameters.

As shown in Figs. 1(A,B), the adsorption kinetic data of Cr(VI) on PAMAMs/GO were much more in agreement with the pseudo-second-order model than the pseudo-first-order model and intraparticle diffusion model, whose values of correlation coefficient were closer to 1 than the other two models, which were listed in Table 1. In addition, the values of qe calculated from equation of the pseudo-second-order model were well agreed with the experimental values, while the qe obtained from the pseudo-first-order model were poorly agreed with the experimental values. Besides, increasing the initial concentration of Cr(VI) caused a decrease in the values of k2. Furthermore, the Figs. 1(C) shows that the values of correlation coefficient R2 from the linear plot of qt versus t1/2 in t = 60 to 720 min were 0.9240 and 0.9529 respectively, which represented the diffusion of Cr(VI) anions within the sorbent. Above all, the adsorption kinetics analysis clearly indicates that the mechanism of adsorption of Cr(VI) on GO /PAMAMs could be interpreted by the intraparticle diffusion model.

### Effect of initial Cr(VI) concentration, temperature and adsorption isotherm

Figure 4 shows the effect of initial ion concentration on the adsorption of Cr(VI) at 303.15 K, as the initial Cr(VI) concentration increased from 30 to 240 mg/L, the equilibrium adsorption capacity keeps increasing from 54.41 to 169.09 mg/g, while the removal efficiency keeps deceasing from 90.69% to 35.22%. When the initial Cr(VI) concentration reached 180 mg/L, the adsorption capacity is almost no increasing, which means the adsorption reached saturation. This could be interpreted that when the concentration of Cr(VI) is lower than 180 mg/L, there are adequate amine groups and adsorption sites on the surface of GO/PAMAMs for removing of Cr(VI). However, when the concentration of Cr(VI) is larger than 180 mg/L, there are not enough amine groups and active sorption sites for binding with Cr(VI). Moreover, the electrostatic repulsion between negative charges of Cr(VI) oxygen anions resulted in the decline of removal percentage.

Figure 5 has shown the relation curves between the equilibrium adsorption capacity and equilibrium concentration of Cr(VI) under 3 different temperatures. The equilibrium adsorption capacities of Cr(VI) is 114.55, 169.09 and 200.56 mg/g at 293.15, 303.15 and 313.15 K, respectively, the change showed that the equilibrium adsorption capacity increase with the increasing of temperature, which means that raising the temperature from 293.15 to 313.15 K favors the adsorption of Cr(VI).

In order to obtain the saturate capacity qm of Cr(VI) adsorption on PAMAMs-GO, the Langmuir and Freunlich model are widely used for fitting the adsorption isotherm data34. So the Langmuir and Freundlich model were applied to fit the adsorption isotherm data in our work, and the linearized forms of these models are expressed in Eqs (6) and (7)6, respectively.

$${\rm{Langmuir}}\,{\rm{model}}:\frac{{C}_{e}}{{q}_{e}}=\frac{1}{{q}_{m}}{C}_{e}+\frac{1}{{K}_{L}{q}_{m}}$$
(6)

where KL (L/mg) and qm (mg/g) represent the Langmuir equilibrium constant and the saturated adsorption capacity, respectively.

$${\rm{Freundlich}}\,{\rm{model}}:\,\mathrm{ln}\,{q}_{e}=\frac{1}{n}\,\mathrm{ln}\,{C}_{e}+\,\mathrm{ln}\,{K}_{F}$$
(7)

where KF (mg/g)·(L/mg)1/n is the measure of adsorption capacity and 1/n is the adsorption intensity.

The adsorption equilibrium data on PAMAMs/GO were fitted with the Langmuir and Freundlich isotherm models at 293.15, 303.15 and 313.15 K and listed in Fig. 6 and Table 2. The results showed both the correlation coefficient R2 of the Langmuir and Freundlich model were all very close to 1, which indicated that the two models fitted well with the adsorption isotherm data. However, the R2 value of Langmuir isotherm is closer to 1 than that of Freundlich isotherm, which means adsorption obeys Langmuir isotherm more than Freundlich model. Langmuir model indicates the adsorption of Cr(VI) is more likely on a homogenous surface by monolayer adsorption, and no interaction occurred between adsorption targets28. The essential characteristic of the Langmuir isotherm in terms of the dimensionless constant separation factor RL can be calculated from Eq. (8)35. According to the Langmuir isotherm equation, the calculated maximum adsorption capacities for Pb2+ by PAMAMs/GO are 131.58, 183.82 and 211.42 mg/g at 293.15, 303.15 and 313.15 K, respectively.

$${R}_{L}=\frac{1}{1+{K}_{L}{C}_{0}}$$
(8)

where the value of KL is the parameter listed in Table 2 and the C0 is the initial ion concentration whose value lies between 30 and 240.

The values of parameter KL from Langmuir model and 1/n from Frundlich model lies between 0 and 1 indicate the favorable condition for the adsorption33. Furthermore the values of qm, KL and KF increased with the raise of temperature reveals the endothermic nature of the adsorption process33. Table 3 summarizes the maximum adsorption capacities of some adsorbents for Cr(VI), which reported in recent years, it shows that the adsorption capacity of GO/PAMAMs for Cr(VI) is exceed or comparable to those of other adsorbents. So, the GO/PAMAMs can be used for treating wastewater containing Cr(VI) anions.

### Thermodynamic analysis

The influence of temperature on the thermodynamic parameters is related to the adsorption process. Several thermodynamic parameters were calculated according to Eqs (9) and (10)31.

$$\mathrm{ln}\,{K}^{0}=-\,\frac{{\rm{\Delta }}{{\rm H}}^{0}}{R}\frac{1}{T}+\frac{{\rm{\Delta }}{S}^{0}}{R}$$
(9)
$${\rm{\Delta }}{G}^{0}={\rm{\Delta }}{H}^{0}-T{\rm{\Delta }}{S}^{0}$$
(10)

where K0 is the adsorption distribution coefficient, which was determined from the intercept of plotting ln(qe/Ce) versus Ce at different temperature by extroplotting Ce to zero according to Khan and Singh method1, and ΔH0 is the standard enthalpy change (J·mol−1), ΔS0 is the standard entropy change (J·mol−1·K−1), ΔG0 is the standard Gibbs free energy change, R is the gas constant (8.314 J·mol−1·K−1) and T is the absolute temperature in Kelvin (K), respectively. ΔH0 and ΔS0 were obtained from the slope and intercept in the curve of ln K0 versus T−1.

The graph of ln(qe/Ce) versus Ce and ln K0 versus T−1 were plotted and showed in Figs 2 and 3, respectively. The values of ln K0, ΔH0, ΔS0 and ΔG0 were listed in Table 4. It is clear that there’s a highly good linear relationship between ln K0 and T−1, whose values of slope, intercept and correlation coefficient R2 determined to be −9610.81, 33.985 and 0.9846, respectively.

### Effect of competitor anions

As we known, the Cl and SO42− are widely existed in industrial wastewater, the presences of Cl and SO42− certainly have impact on the removal Cr(VI) on adsorbents3,33. Figure 7(a,b) have shown the effect of Cl and SO42− in the range of 0.02 ~ 0.10 mol/L on the adsorption of Cr(VI) by GO/PAMAMs. It can be seen that the existences of Cl and SO42− have significant influence on the adsorption of Cr(VI) on GO/PAMAMs, this may be the strong competition between anions and Cr(VI) for available adsorption sites.

### XPS analysis

In order to conform that Cr(VI) was actually adsorbed on GO/PAMAMs and investigate thoroughly whether the Cr(VI) was reduced to Cr(III) due to the presence of π electrons donor on GO/PAMAMs, XPS characterization was carried out for GO/PAMAMs before and after adsorbed Cr(VI). Seen from Fig. 8(a), Cr 2p peak was occurred after adsorption of Cr(VI), which conformed that Cr(VI) was actually adsorbed onto GO/PAMAMs. The composition change in GO/PAMAMs before and after adsorbed Cr(VI) by the XPS semi-quantitative surface element analysis (Table 5) further conformed the adsorption of Cr onto GO/PAMAMs. There are four different peaks at 288.04 eV, 286.60 eV, 285.60 eV and 284.70 eV (Fig. 8(b)), which corresponds to C=O, C-O, C-N and C-C of GO/PAMAMs, respectively30. After adsorbing Cr(VI), all the binding energies of C in GO/PAMAMs decreased a little, this may be due to the interaction between neighbor N and metal ions45. It has been reported that Cr(VI) can be removed from aqueous solution by adsorbents through a direct or an indirect mechanism30,46. In order to explore the main mechanism of Cr(VI) removal by GO/PAMAMs, the valence of Cr bound to GO/PAMAMs was also analysed by XPS characterization (Fig. 8(c)). Seen from Fig. 8(c), Cr 2p peaks can be curve-fitted with four components at binding energies of 589.2 eV, 586.9 eV, 579.2 eV and 577.2 eV, the peak components at 577.2 eV and 579.2 eV correspond to Cr 2p3/2 orbitals, while those at 586.9 eV and 589.2 eV correspond to Cr 2p1/2 orbitals. The peaks at binding energies of 579.2 eV and 589.2 eV can be regarded as the signals of Cr(VI), while the peaks at 577.2 eV and 586.9 eV can be attributed to Cr(III)30. The results indicate that both Cr(III) and Cr(VI) exist on GO/PAMAMs. Hence, it can be concluded that Cr(VI) was removed from aqueous solution through an indirect mechanism, and part of Cr(III) was bound to the surface of GO/PAMAMs.

It can be speculated that the removal mechanism of Cr(VI) on GO/PAMAMs consists of three steps as follows: the Cr(VI) binded to the surface of GO/PAMAMs under the electrostatic interaction between the negative charged Cr(VI) species and the protonated amine groups, then the Cr(VI) was reduced to Cr(III) with the assistance of π-electrons on the carbocyclic six-membered ring of GO in GO/PAMAMs, and then the Cr(III) was released into solution under electrostatic repulsion between the Cr(III) and the protonated amine groups, and part of Cr(III) on GO/PAMAMs was existed for the electrostatic attraction between Cr(III) and negatively charged –COO of GO/PAMAMs30,46.

### Regeneration study

The regeneration experiments are significant complements of adsorption studies, which could evaluate the feasibility of regeneration of the adsorbent. Figure 9 has shown the removal efficiency of Cr(VI) at each cycle after desorption with 50 mL 0.02 mol/L NaOH solution. It can be observed that the removal efficiency of Cr(VI) by GO/PAMAMs just has a little decrease after 5 times regeneration, and the removal efficiency of Cr(VI) only decreased from 72.8% to 65.2% for 100 mg/L of Cr(VI) at pH = 2.5, which indicates a good regeneration property of the adsorbent of GO/PAMAMs for removal of Cr(VI).

## Conclusions

The GO/PAMAMs is an effective adsorbent for the removal of Cr(VI) from aqueous solutions. The adsorption of Cr(VI) on GO/PAMAMs is highly pH and initial Cr(VI) concentration dependent. The optimal pH lies at 2.5, with the highest Cr(VI) removal efficiency 80.7% for C0 = 50 mg/L of Cr(VI) at 30 °C, while the percentage removal of Cr(VI) decreased with the increase of Cr(VI) concentration. The adsorption equilibrium experimental data fitted well with the pseudo-second-order model. The adsorption isotherm fitted well with the Langmuir model and the maximum adsorption capacity reached 211.42 mg/g at 40 °C. The thermodynamic parameters indicatethat the adsorption belongs to chemical-adsorption and the nature of spontaneous endothermic process, which is driven by entropy. The regeneration experiments showed 0.05 mol/L of NaOH solution is suitable for the regeneration of GO/PAMAMs. The XPS analysis reveals the adsorption and removal mechanism of Cr(VI) on GO/PAMAMs that first the Cr(VI) binds to the protonated amine of GO/PAMAMs, then Cr(VI) be reduced to Cr(III) with the assistance of π-electrons on the carbocyclic six-membered ring of GO in GO/PAMAMs, and then Cr(III) was released into solution under the electrostatic repulsion between the Cr(III) and the protonated amine groups.

## Experimental Section

### Materials

Chemical reagents include graphite powder, K2Cr2O7, K2S2O8, P2O5, H2O2, NH2CH2CH2NH2, methylacrylate, NaOH and HNO3 were purchased from Tianjin Kemiou Chemical reagent Co., Ltd, Tianjin, China. 1,5-diphenylcarbazide was purchased from Guangfu fine chemical research institute, Tianjin. All the chemical reagents are analytical grade and all the water used were double distilled water.

### Synthesis of GO/PAMAMs

The dimethylformamide (DMF) solution of Graphene Oxide (GO) was prepared via the modified Hummers method46. The generation 2(G2) PAMAMs were prepared according to the procedures described in the literature47. The GO/PAMAMs were synthesized and characterized in our reported literature31. Briefly, 5.0 g of G2-PAMAMs dissolved in 20 mL of absolute methanol, then mixed with 120 mL of DMF solution which contains 1.0 g of exfoliated GO with magnetic stirring in 250 mL of three-neck glass flask. After the mixture being refluxed for 24 h under 80 °C in a water bath, the warm solution was filtered and washed with 200 mL of absolute methanol until all excess G2-PAMAMs were removed from the precipitates. Finally, the colloidal sediment was transferred into a glass dish and dried in a vacuum oven at 100 °C for 12 h, thus the GO/PAMAMs composites were obtained.

### Analysis method

A stock solution containing Cr(VI) 500 mg/L was prepared by dissolving 0.7206 g of potassium dichromate with distilled water in a 500 mL of measuring flask and diluted to desired concentration, the pH of Cr(VI) solution were adjusted to desired value with 0.1 M of HNO3 and NaOH solution under the pH meter (Jingke, Shanghai Co. Ltd). Concentration of Cr(VI) was determined using a Ultraviolet-visible spectrophotometer (UV-2250, SHIMADZU, Japan), which analyzed through the purple red complex with 1, 5-diphenylcarbazide in acid medium at λ = 540 nm. The standard curves of Cr(VI) concentration was obtained through determining the absorbance of known concentration of Cr(VI) with 0–2.0 mg/L (seen in Fig. 4), the linear equation of absorbance (A) versus Cr(VI) concentration (C, mg/L) was calculated as follow: A = 0.31693 C + 0.00296, the scope of A is 0–0.7 and the correlation coefficient of the standard curve is 0.9973.

The batch experiments of investigating influence factors for adsorption were performed in a series of 100 mL of Cr(VI) solution in 250 mL of stand-up bottom flask under the conditions of constant magnetic stirring speed, adsorbent dosage 0.05 g and contact time 24 h. The effect of different initial aqueous pH values were investigated in the range of 1.5–7.0 with initial Cr(VI) concentration 50 mg/L at 303.15 K, the optimum pH value medium was adopted for all the following experiments. The effect of initial Cr(VI) concentration was performed in the range of 30–240 mg/L. the adsorption isotherm experiments were performed by varying initial Cr(VI) concentration from 30–240 mg/L at three different temperatures of 293.15, 303.15, and 313.15 K within 6 h, respectively. The batch adsorption equilibrium experiments were performed in a 1000 mL three-neck bottom flask where 500 mL Cr(VI) solution mixed with 0.5 g adsorbent by varying the initial Cr(VI) concentration (50, 100 mg/L) at 303.15 K and constant stirring speed in the water bath, 2 mL of supernatant sample was taken out at various time intervals (10–720 min) and filtered immediately through 0.45 μm filter paper. The residual concentration of Cr(VI) was determined, then the equilibrium adsorption capacity (qe, mg/g) and removal efficiency (R) of Cr(VI) were calculated according to Eqs (11) and (12)4, respectively:

$${q}_{e}=\frac{({C}_{0}-{C}_{e})V}{m}$$
(11)
$$R \% =\frac{{C}_{0}-{C}_{e}}{{C}_{0}}\times 100 \%$$
(12)

where C0 and Ce represent the initial and equilibrium concentration (mg/L), respectively, V represents the volume of solution (L), m represents the mass of PAMAMs/GO (g).

### Regeneration studies

Regeneration studies of PAMAMs/GO was performed four times for initial C0 = 50 mg/L of Cr(VI) at 303.15 K after desorption by 0.05 M of NaOH solution. After Cr(VI) desorption, the PAMAMs/GO was air dried and dissolved in 100 mL Cr(VI) solution for 6 h adsorption, then the residual concentration of Cr(VI) was determined.

All the experiments were duplicated and only the average values were chosen for plotting. Furthermore, the maximum errors were being controlled within 5%.

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## Acknowledgements

The work is supported by National Natural Science Foundation of China (21566010, 31760196), Special research project from Jishou University (Jdy1826), P. R. China.

## Author information

This manuscript is original, unpublished, and not being considered for publication elsewhere. Han Liu and Fan Zhang wrote the main manuscript text and Zhiyuan Peng prepared the Supplementary Material. All authors read and approved the final manuscript.

Correspondence to Fan Zhang.

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