Results and discussion

Effect of contact time
The results showed that the percentage removal of copper increased briskly up to 60 min reaching 93.925 % (Fig. 1a). Beyond 60 min, the % of adsorption remained the same indicating the attainment of equilibrium conditions. Equilibrium indicates utilization of the more readily available adsorbing sites especially the carboxyl and the amino groups present on the DNES–CH composite surface. Initial rates of sorption are faster due to the availability of adequate vacant surface binding sites and the vanderwaal forces of attraction between the adsorbate and the adsorbent. With the advancement of time, sorption becomes gradually tapered due to repulsive forces between the solute molecules of the solid and the bulk phases; consequently, the remaining vacant binding sites fail to bind with the metals (Srivastava et al. 2014). The reported contact time of 150 min for removal of copper by chick egg shells by packed-bed sorption (Nabil and Sameer 2009) is much higher than the optimum contact time of 60 min for the composite in the present study.
Fig. 1  a Effect of contact time on % adsorption of copper. b Effect of pH on % adsorption and metal uptake of copper. c Effect of initial metal concentration on % adsorption and metal uptake of copper. d Effect of adsorbent dosage on % adsorption and metal uptake of copper. e Effect of temperature on % adsorption and metal uptake of copper

Effect of pH on adsorption
The pH of the aqueous metal solution affects sorption through the adsorbent surface charge, the degree of ionization and speciation of the adsorbate as well. Maximum  % removal of copper was 94.47 % at pH 6 (Fig. 1b) and this is in agreement with the earlier research reports (Rafatullah et al. 2010; Chen et al. 2012). At pH < 5, the number of sites available for metal adsorption will be low as most of the functional groups are protonated and H3O+ ions compete with the metal for the adsorption sites on the adsorbent. At pH 6, the increase in adsorption could be attributed to the weak inhibitory effect of H3O+ ions. At pH above 6, the adsorption rates were unpredictable due to accumulation of metal ions on the adsorbent.

Effect of initial metal ion concentration
The maximum percentage removal of copper observed was 94.47 % when the initial copper concentration was 20 mg/L (Fig. 1c). The plot suggests that the metal ion adsorption increased sharply in the beginning and then decreased slowly with further increase in the initial concentration. This can be attributed to the increase in adsorbate concentration to a fixed number of available active sites on the adsorbent (Malkoc 2006).

Effect of adsorbent dosage
The experiments were carried out by varying the adsorbent loading from 3 to 9 g/L. The percentage removal of copper by DNES-CH composite at different adsorbent doses is presented in Fig. 1d. Experimental studies were carried out at 30 °C with an initial metal concentration of 20 mg/L at pH 6. The removal of copper increased rapidly from 89.215 to 94.51 % with an increase in the adsorbent dose from 3 to 8 g/L. As shown in the figure, the percentage removal increased initially with the increase of the adsorbent dose due to increased surface area of the adsorbent and the number of binding sites. For a fixed initial metal concentration, although the adsorbent dose was increased, there was no significant change in the adsorption after attaining the equilibrium (Witek-Krowiak et al. 2011; Moreno-Pirajan et al. 2011).

Effect of temperature
Adsorption is expected to increase by an increase in temperature owing to the increase in the rate of diffusion of the adsorbate molecules across the external boundary layer and into the internal pores of the adsorbent particles. In this case, copper uptake marginally increased from 93.43 to 94.51 % for DNES–CH composite with increasing temperature from 10 to 30 °C indicating that the adsorption of copper on to the adsorbent is an endothermic process. With further rise in temperature beyond 30 °C, the increase in copper uptake was only marginal (Fig. 1e).

Adsorption kinetics
The kinetics of adsorption of copper at different contact times was found out using the pseudo-first order, pseudo-second order, and intra-particle diffusion models. The pseudo-first order equation is4 logqe-qt=logqe-K1/2.303twhere q e and q t are the amount of metal adsorbed at equilibrium and at time t; K 1 is the rate constant of pseudo-first order (min−1).5 The pseudo-second order equation ist/qt=1/K2qe2+1/qe(t)where K 2 (min−1) is the pseudo-second order rate constant.
Intra-particle diffusion equation is6 qt=Kintt1/2+Cwhere K int is intra-particle diffusion rate constant (mg/g min1/2) and C is the boundary layer thickness.
The pseudo-first order, pseudo-second order and intra-particle diffusion kinetic plots are given in Fig. 2a–c respectively. In the pseudo-first order, the K 1 and q e values were 0.0582 (min−1) and 1.2103 (mg/g) respectively with a correlation coefficient (R 2) of 0.9586. In the pseudo-second order, the K 2 and q e values were 0.1104 (min−1) and 3.2362 (mg/g) respectively with a correlation coefficient (R 2) of 0.9989. The intra-particle diffusion, a plot of solute sorbed against square root of contact time, should normally yield a straight line passing through the origin but the line in the present case, did not pass through the origin and the values of K int and C were 0.1341 (mg/g min½) and 2.0427 (mg/g) respectively with a correlation coefficient (R 2) of 0.8942. From the experiments, q e obtained was 3.1308 mg/g which is suggestive that the adsorption of copper by DNES–CH composite could be by chemisorption, appropriately explained by the pseudo-second order model.
Fig. 2  a Pseudo-first order kinetics for adsorption of copper using DNES–CH composite. b Pseudo-second order kinetics for adsorption of copper using DNES–CH composite. c Intra-particle diffusion kinetics for adsorption of copper using DNES–CH composite

Adsorption isotherm
The experimental data were tested and compared with the three isotherm models viz. Langmuir, Freundlich and Temkin. Langmuir isotherm is the most widely used model and the equation is given as7 ce/qe=1/bqm+ce/qmThe equation obtained for the Langmuir isotherm (Fig. 3a) for the current data was c e/q e = 0.0207c e + 0.3339 with a correlation coefficient of 0.9934 indicating the strong binding of copper ions on to the surface of the adsorbent. The maximum metal uptake (q max) obtained was 48.3 mg/g and the separation factor (R L) was 0.9358, indicating that the adsorption is favorable (0 < R L < 1). Freundlich isotherm, applied in the cases of low and intermediate concentration ranges, is given by8 qe=KfCe1/nwhere K f and n are the adsorption capacity and intensity respectively. Freundlich equation linearized in logarithmic form as follows:9 logqe=logKf+nlogCewith the experimental data represented in Fig. 3b, the Freundlich equation obtained was log q e = 0.8334 log C e + 0.4684 with a correlation coefficient of 0.999. As the n value was 0.8334, which is in between 0 < n < 1, good adsorption of copper ions over the entire range of concentrations studied was inferred. The K f value obtained was 2.9403 mg/g. Temkin isotherm equation describes the behavior of many adsorption systems on the heterogeneous surface. The linear form of the equation10 qe=RT/bTlnAT+RT/bTlncewas used for analyzing the experimental data and presented in Fig. 3c. The equation obtained for copper adsorption was q e = 6.3177 ln c e + 1.6182 with a correlation coefficient of 0.9609.
Fig. 3  a Langmuir isotherm for adsorption of copper using DNES–CH composite. b Freundlich isotherm for adsorption of copper using DNES–CH composite. c Temkin isotherm for adsorption of copper using DNES–CH composite
The applicability of each model was evaluated using error analysis (χ 2). To find out the best-fit isotherm, the non-linear Chi square test statistic (χ 2)11 χ2=Σqe,exp-qe,cal2/qe,calwhere, q e,exp q e,cal are experimental and calculated adsorption capacity values respectively, was used (Ho and Ofomaja 2005).
The good agreement of the data acquired by each model needs that the χ 2 value is a smaller number while the non-applicability of the model has larger χ 2 value. The isothermal constants and χ 2 values are indicated in Table 2. With the use of the Chi square test (χ 2) characteristic and the regression correlation coefficient R 2, the best isothermal model was identified as the Langmuir followed by the Temkin and the Freundlich isothermal models.
Table 2 Isotherm constants of copper adsorption onto DNES–CH composite
Langmuir Freundlich Temkin
q max = 48.3 mg/g  n = 0.8334  A T = 1.2918
R L = 0.9358  K f = 2.9403 mg/g  b T = 398.743
R 2 = 0.9934  R 2 = 0.999  R 2 = 0.9609
χ 2 = −0.00054  χ 2 = 11.4896  χ 2 = 0.2242

Thermodynamic studies
To investigate the nature of adsorption, thermodynamic parameters viz. enthalpy (ΔH°), entropy (ΔS°) and Gibbs free energy (ΔG°) were estimated. The following Van’t Hoff equation was used to evaluate thermodynamic parameters:12 logqe/ce=ΔH/2.303RT+ΔS/2.303RThe negative value of ΔH indicates an exothermic reaction; a positive value denotes an endothermic reaction. If the value of ΔS is less than zero, it indicates the process is highly reversible and if more than or equal to zero, it indicates the irreversibility of the process. The negative value of ΔG indicates the spontaneity of adsorption whereas a positive value of ΔG indicates the non spontaneity of adsorption. Van’t Hoff plot is represented in Fig. 4 and the equation obtained was log (q e/c e) = 0.3105(1/T) + 1.3481. The positive experimental ΔH° value indicates that the adsorption process was endothermic in nature and there was a possible strong bonding between the metal ion and the adsorbent. As ΔS° was more than zero, the adsorption process appears to be irreversible (Desorption studies were hence not attempted). The Gibbs free energy is negative, suggesting the spontaneous nature of the adsorption process. The free energy change (ΔG°) increased with increase in temperature (10–50 °C), presumably due to activation of more sites on the surface of the adsorbent (Sengil and Ozacar 2008). The thermodynamic parameters at different temperatures are given in Table 3.
Fig. 4 Van’t Hoff plot for adsorption of copper using DNES–CH composite
Table 3 Thermodynamic parameters calculated by Van’t Hoff equation
Temperature (°K) ∆G° (kJ/mol) ∆H° (kJ/mol) ∆S° (kJ/mol K)
283 −7298.9075 5.9451 25.8122
293 −7557.0295
303 −7815.1515
313 −8073.2735
323 −8331.3955
The maximum adsorption capacities of a few common adsorbents for copper are shown in Table 4. When compared to the synthetic adsorbents, the maximum adsorption capacity of the natural DNES–CH composite is low. But the advantages of the composite are good enough in minimizing sludge generation and the recovery of the metal from the effluents.
Table 4 Comparison of the adsorption capacities (q max) of different adsorbents
Adsorbent  q max (mg/g) References
Pseudomonas aeruginosa 5.83 Tuzen et al. (2008)
Saw dust 4.9 Grimm et al. (2008)
Wheat bran 8.62 Wang et al. (2009)
Chitosan supported on porous glass beads 7.27 Shen et al. (2013)
n-HAp, n-HAp/chitin (n-HApC) composite and n-HAp/chitosan (n-HApCs) composite 4.7, 5.4 and 6.2 Rajiv gandhi et al. (2011)
Immobilization of a synthesized (3-(3-(methoxycarbonyl)benzylidine)hydrazinyl)benzoic acid onto mesoporus silica monoliths 145.98 Awual et al. (2013)
5-Tert-butyl-2-hydroxybenzaldehyde thiosemicarbazone immobilized on to the mesoporus silica 176.27 Awual (2015)
DNES–CH composite 48.3 Present study

Statistical analysis
Experimentally, highest adsorption capacity was obtained at an adsorbent dosage of 8 g/L, initial metal ion concentration 20 mg/L, and pH 6. With these preliminary results, further experiments on the factors affecting adsorption were carried out using three level full factorial design under RSM with varying levels of adsorbent dosage, metal ion concentration and pH.
The coded and the actual values of the test variables are as given in Table 1. Multiple regression analysis of the data for adsorption yielded the following regression equation.13 Y=+95.25-1.74X1+0.56X2-0.089X3-5.84X1X2-2.09X1X3-1.00X2X3-16.11X12-2.29X22-0.82X32where Y is the % adsorption of copper, X 1 adsorbent dosage, X 2 is the metal ion concentration and X 3 is the pH. Solving the regression equation using fmincon function, the optimum set of values for the three variable X 1, X 2 and X 3 were −0.0960, +0.2651 and −0.0936. Hence, it was inferred that for maximum adsorption of copper with the DNES-CH composite, the adsorbent dosage, metal ion concentration and pH should ideally be kept at 7.90 g/L, 20.2651 mg/L and 5.906 respectively.

Interpretation of the regression analysis
Statistical testing of the model by the Fischer’s statistical test for analysis of variance (ANOVA) yielded a F-value of 46.25 with a low p value (p < 0.0001) indicating the significance of the model (Table 5). Determination coefficient nearer to unity (R 2 = 0.9585) indicates that only 4.15 % of the total variations are not explained by the model. The predicted R 2 of 0.8977 is in reasonable agreement with the adjusted R 2 of 0.9378 (difference is less than 0.2). The results of the full factorial design are represented in Table 6 and it is inferred that the quadratic model is the best fit for the observed biosorption of copper by DNES–CH composite.
Table 5 Regression coefficients for adsorption of copper by DNES–CH composite
Model term Coefficient estimate Standard error  F value  p value
Intercept 95.25 1.06 46.25 <0.0001
X 1 −1.74 0.55 9.87 0.0056
X 2 0.56 0.55 1.03 0.3240
X 3 −0.089 0.55 0.026 0.8739
X 1 X 2 −5.84 0.68 74.48 <0.0001
X 1 X 3 −2.09 0.68 9.59 0.0062
X 2 X 3 −1.00 0.68 2.19 0.1563
X 12 −16.11 0.93 301.46 <0.0001
X 22 −2.29 0.93 6.11 0.0236
X 32 −0.82 0.93 0.78 0.3898
All the linear, interaction and squared terms are significant (p < 0.5), excluding linear X 3
Table 6 Results from full factorial design for copper adsorption by DNES–CH composite
Source of variation Sum of squares  df Mean square  F value  p > F
Model 2285.25 9 253.92 46.25 <0.0001
Lack of fit 98.82 17 5.81
Pure error 0.000 1 0.000
Total 2384.08 27

Interaction effects of biosorption variables
To know the interactive effects of biosorption variables, surface plots drawn using Matlab 2008 are provided in Fig. 5a–c. From the curvature of the contour, it was identified that the biosorpiton of copper is strongly influenced by the adsorbent dosage, initial metal concentration and pH.
Fig. 5  a Surface plot for the effects of adsorbent dosage and initial metal concentration of copper on % removal. b Surface plot for the effects of adsorbent dosage and pH of copper on % removal. c Surface plot for the effects of pH and initial metal concentration of copper on % removal

SEM–EDS analysis
SEM analyses of the biosorbent material, DNES–CH composite, before and after adsorption of copper are presented in Fig. 6a, b, respectively. After adsorption of copper, the surface morphology of the adsorbent changed to rough, more uneven and heterogeneous nature which could probably be due to the reorganization of surface functional groups binding the metal ions. From the EDS analysis before biosorption, the major constituent of the eggshells—CaCO3, along with the elements N (chitosan provides amino groups), P and the metals Mg, Na, K, Mn, Zn, Fe, Al, Sr etc. is evident to be present in the composite (Fig. 7a). After adsorption of copper (Fig. 7b), the EDS analysis showed the presence of copper ions (3.71 %) with a concomitant decrease in the percentages of Mg, Na and Zn, suggesting that the adsorption of copper by the composite may also include the ion-exchange mechanism.
Fig. 6  a SEM micrograph of native DNES–CH composite. b SEM micrograph of DNES–CH composite after adsorption of copper
Fig. 7  a EDS micrograph of native DNES–CH composite. b EDS micrograph of DNES–CH composite after adsorption of copper

Adsorption mechanism through FTIR spectral analysis
The adsorption mechanism was investigated using FTIR analysis of the native DNES, native and the metal loaded DNES-CH composite in the range of 400–4000 cm−1 (Fig. 8a–c). The native DNES FTIR spectra showed sharp peaks at 874, 1418 cm−1 but after forming composite with chitosan, provided a number of functional groups which correspond to the amino and the carboxyl. In DNES-CH composite, ES is porous in nature and provides an efficient and strong support for the CH in forming the scaffold with more number of hydroxyl, carboxyl, amino and alcohol groups available to chelate the copper metal ions. FTIR spectra showed marked differences before and after adsorption of copper. Broadly, the spectrum could be divided into three distinct regions viz. 630–1000, 1180–3000, and 3300–3700 cm−1 wherein there are significant variations in the absorption patterns and the groups assigned for biosorption as given in Table 7.
Fig. 8  a FTIR spectrum of native DNES. b FTIR spectrum of native DNES–CH composite. c FTIR spectrum of copper loaded DNES–CH composite
Table 7 FTIR peaks and their corresponding groups
DNES–CH composite spectrum peaks (λ) Copper treated DNES–CH composite, spectrum peaks (λ) Assignment
3747 3755, 3717 O–H & N–H groups
3357 3376
3304 3338
2986 3001 Carboxyl groups
1741 1717 Amines
1550 1508 N–H bending vibration
1398 1389 C-N, Amines
1224 1182
1022 963
869 872 NH3 rocking vibration
651 632 Cu–O stretching
After interaction with the copper ions, it was identified that the sharp band at 3747 split into 3755 and 3717 cm−1 indicating that both O and N atoms present on the adsorbent surface played a significant role in binding the metal ions (Table 7); the bands at 3357 and 3304 cm−1 were assigned to O–H & N–H, and inter hydrogen bonds’ vibration shifted to 3376 and 3338 cm−1. A shift of band at 2986 cm−1 to a broad wide band at 3001 cm−1 indicates the involvement of carboxyl groups. After exposure to copper, the bands corresponding to amine shifted from 1741 to 1717 cm−1 and the bands at 1684, 1646 cm−1 disappeared. Moreover, the adsorption intensity for the N–H bending vibration at 1550 and 1508 cm−1 shifted to 1495 cm−1 and decreased after copper uptake. This observation is supported by an extreme change in absorption intensity for C–N stretching vibrations at 1398–1389 cm−1. The metal ion uptake has led to a significant change in the absorption intensity of NH3 rocking vibration from 869 to 872 cm−1. Variations in the absorption peaks at 630–700 cm−1 in the two samples (before and after treatment with copper) are indicative of Cu–O stretching in the copper loaded DNES-CH (Vinod and Miroslav 2013). In general, the adsorption capacity depends upon the porosity as well as functional groups present on the adsorbent surface (Kumar et al. 2010). Accordingly, the observed changes in the adsorption intensity and the wave number of functional groups strongly suggest the occurrence of complexation between N and O atoms on the adsorbent binding sites and the copper ions. The FTIR analysis suggests that the maximum adsorption of copper by the DNES–CH composite is due to the availability of more number of N and O atoms.

X-ray diffraction (XRD) analysis
The native DNES–CH X-ray diffractogram (as shown in Fig. 9a) exhibited sharp peaks at 2θ positions 29°, 34°, 44°, 48°, 49°, 58°, 61°, 65°, 74°, 82°, 84°, 94°, 95° and 100°. X-ray diffractogram analysis of the copper loaded DNES–CH composite (as shown in Fig. 9b) showed the amorphous nature, with sharp peaks at 2θ positions of 20°, 22°, 23°, 25°, 27°, 28°, 30°, 48° and 85°. In addition, the peaks at 43.7°, 50° and 74.2° (JCPDS copper: 04-0836) suggest the presence of copper while the peaks at 2θ positions of 32.3°, 35.2°, 38°, 46.2°, 48.6°, 51.7°, 53.4°, 56.8°, 58.1°, 65.9°, 66.1°, 68.0°, 71.5°, 72.7°, 74.7°, 82.2°, 83.0°, 83.6°, 87.6° and 89.5° (JCPDS CuO: 80-1916) indicate the formation of CuO by the reaction of the metal with the hydroxyl and the carboxyl groups present on the adsorbent. The said reaction may be due to the electron pair sharing between the copper metal and the reactive carboxyl/hydroxyl groups in the DNES–CH composite.
Fig. 9  a XRD of native DNES–CH composite. b XRD of DNES–CH composite treated with copper