Introduction

Demand for developmental strides and industrialization has led to more toxic effluents being discharged with little or no treatment into the environment especially water bodies. Quality water is indispensable and essential to life (Fawole et al. 2002) but meeting the quality for different purposes has been a huge task because of loads of wastes received by it from domestic, municipal and industrial sources (Lateef 2004; Adewoye and Lateef 2004; Pal and Deb 2014; Azeez et al. 2015). Most of these wastes have detrimental effects on environment, human health, agricultural produce, aquatic lives and are also known to be genotoxic (Bakare et al. 2003; Lateef et al. 2007). Dyes are examples of such wastes and are increasingly being used in pharmaceutical, paint, textile industries and laboratories as indicators. They are non-biodegradable pollutants that affect water quality by causing foul odour, preventing light penetration, increasing chemical oxygen demand, decreasing dissolved oxygen level, and eventually leading to death of aquatic lives. They have been found to be nephrotoxic and also induce toxicity on reproductive system (Das et al. 2006, 2008; Baskaran et al. 2011; Chen et al. 2012; Ramalingam et al. 2015; Tan et al. 2015).

Rhodamine B (Rh-B) belongs to xanthene dyes and is highly soluble in water. It has high fastness and possesses fluorescent property. These characteristics have made it to be widely applicable in textile, glass, paint, paper, and leather dyeing (Das et al. 2006, 2008; Satapathy et al. 2013). However, it is carcinogenic causing hypothalamic cell apoptosis leading to hormonal imbalances. It has also been reported to cause eyes, skin, and respiratory tract irritations (Satapathy et al. 2013; Pal and Deb 2014; Bhattacharyya et al. 2014; Sulistina et al. 2014; Shen et al. 2015; Mahmoud et al. 2015; Huang et al. 2016). Wastewater containing Rh-B, therefore, needs to be effectively, efficiently and qualitatively treated before being discharged into the environment (Inyinbor et al. 2015, 2016a, b).

Several studies have reported different methods for dye removal from aqueous solutions such as photochemical degradation, biological degradation, coagulation–flocculation, chemical oxidation, adsorption, membrane separation process, electrochemical, reverse osmosis, aerobic and anaerobic microbial degradation, but their shortcomings have limited their applications (Majumdar et al. 2015; Das et al. 2013; Sadaf and Bhatti 2014; Sadhukhan et al. 2014; Shen et al. 2015). Adsorption has proved to be the most effective physicochemical method in removing dye from effluents with activated carbon as the most widely used adsorbent. Activated carbon has been found useful, and effective in dye removal but high cost of preparation and regeneration maintenance have made its use economically burdensome (Tan and Hameed 2010; Giwa et al. 2015; Santhi and Kumar 2015). This has led to the use of effective alternative adsorbents such as hen feather (Mittal et al. 2007), cassava pellets (Okewale et al. 2013), perlite (Vijayakumar et al. 2012), Rhizopus oyrzae biomass (Das et al. 2006, 2008), Mucor rouxii (Majumdar et al. 2015) Raphia hookeri epicarp (Inyinbor et al. 2016a), Chitosan (Inyinbor et al. 2016b), silk (Jiwalak et al. 2010), phosphoric acid-modified rice husk (Dada et al. 2012) and sawdust of Parkia biglobosa (Giwa et al. 2015) for the removal of dyes. However, as microparticles, these materials will require long time for maximum adsorption.

Presently, the applications of metal nanoparticles as adsorbents have been on increase due to their morphology such as highly reactive sites, controlled size and high surface area. Multi-walled carbon nanotube (Yang and Xing 2010), MgO (Li et al. 2012; Mahmoud et al. 2015), chitosan–zinc oxide (Salehi et al. 2010), zero-valent iron (Satapanajaru et al. 2011), silver (Satapathy et al. 2013), gold (Xu, 2010), NiO (Samiey and Farhadi 2013), TiO2 (Hsiao et al. 2014; Lyu et al. 2014) nanoparticles have been employed in wastewater purification and have proved to be faster in action and more effective in performance. Also, catalytic degradation of dyes has been achieved using nanoparticles (Bogireddy et al. 2015; Han et al. 2013; Kumari and Philip 2015; Lateef et al. 2016a, b, c; Ojo et al. 2016; Oladipo et al. 2017). Despite the excellent adsorptive capacity of nanoparticles, toxicity arising from their use has been of great concern. Nano-TiO2 has limited adsorption affinity for anionic dyes, and was reported to cause unusual sedimentation, haemagglutination, haemolysis of erythrocytes in humans and physical changes to aquatic ecosystem (Li et al. 2008; Canesi et al. 2010). Nano-Fe3O4, nano-ZnO and nano-MgO were found to be toxic to human lung alveolar epithelial cells, neurons as well as animal cells (Choi and Choy 2009; Lu et al. 2009; Zhao et al. 2009). Carbon nanotubes are reported to be toxic to human dermal fibroblast cells. This might not be unconnected with their methods of preparation which are chemical/reduction methods (Patlolla et al. 2010). To avoid toxicities arising from physical and chemical-based synthetic routes, green (biological) synthesis of nanoparticles which does not involve the use of hazardous chemicals provides effective route for non/less toxic and eco-friendly nanoparticles (Vanaja et al. 2014; Adelere and Lateef 2016; Lateef et al. 2016d, e; Pavya et al. 2016; Shukla and Iravani 2017).

In this study, novel eco-friendly silver nanoparticles biosynthesized from extracts of cobweb (as source of biomolecules that serve as reducing agents in reducing Ag+ to zero-valent Ag0 to form AgNPs) were used for the adsorption of Rhodamine B from aqueous solution.

Materials and methods

Biosynthesis and characterization of AgNPs

AgNPs used in this study were biologically synthesized from cobweb as earlier described (Lateef et al. 2016f). The scheme of the synthesis is shown in Fig. 1. Cobweb extract was prepared through hydrolysis of 0.1 g of washed and air-dried cobweb with 10 ml of 0.1 M NaOH at 90 °C for 1 h. The resulting liquid was centrifuged at 4000 rpm for 30 min to obtain the crude cobweb extract. Biosynthesis was carried by reacting 1 ml of cobweb extract with 40 ml of AgNO3 under ambient condition. The biosynthesized AgNPs were characterized by UV–Vis spectroscopy, Fourier transform infrared spectroscopy (FTIR) and transmission electron microscopy (TEM) as previously described by Lateef et al. (2016f).

Fig. 1
figure 1

Scheme for the biosynthesis of AgNPs using cobweb extract

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pH point of zero charge (pHpzc)

The pH point of zero charge (pHpzc) was determined as previously reported (Giwa et al. 2015; Inyinbor et al. 2015). A weighed amount (0.1 g) of AgNPs was added to 50 ml of 0.1 M NaCl with predetermined pH in 250-ml conical flask. The pH of the resultant solution was adjusted between pH 2 and 10 with either 0.1 M NaOH or HCl. The conical flasks were sealed and shaken in an orbital shaker (Stuart SSLI, Barlword Scientific Ltd Britain) for 24 h, after which the final pH values were measured. The difference between the initial and final pH was calculated and plotted against the initial pH. pHpzc was obtained from the point of intersection with pH axis.

Adsorbate characteristics and preparation

The dye Rhodamine B (Fig. 2) with molecular formula C28H31N2O3Cl, λmax 554 nm was purchased from Sigma-Aldrich (Germany) and was used without further purification. All other reagents were of analar grade. A stock solution of Rhodamine B (Rh-B) was prepared by dissolving 0.1 g in 1000 ml deionized–distilled water.

Fig. 2
figure 2

Structure of Rhodamine B (Rh-B) dye (Inyinbor et al. 2015)

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Adsorption studies

Effects of initial solution pH (1–9), contact time (5–60 min), AgNPs dosage (0.2–1 g/l), initial Rh-B concentration of dye (10–50 mg/l) and temperature (303–333 K) on the adsorption of Rh-B on AgNPs were studied in batches. The pH of the Rh-B solution was adjusted with 0.1 M HCl or 0.1 M NaOH. 1 g/l of AgNPs was weighed and added to 100 ml of 50 mg/l Rh-B solution in a 250-ml conical flask. The flask was shaken in a thermostat-regulated water bath shaker (Uniscope water bath shaker) at 30 °C, agitated at 150 rpm for 30 min. The solution was centrifuged at 1500 rpm. The pH was measured with Jenway 3505 pH meter. The concentration of unadsorbed dye was determined using a Jenway 6405 UV–Visible spectrophotometer (Buch Scientific Inc. USA) at 554 nm. Percentage removal and quantity adsorbed at a given time t were calculated using the following equations:

$$\%\,{\text{Removal}} = \frac{{\left( {C_{\text{i}} - C_{\text{f}} } \right) \times 100}}{{C_{\text{i}} }}$$
(1)
$$q_{\text{t}} = \frac{{(C_{\text{i}} - C_{\text{t}} )V}}{M}$$
(2)

where qt is the amount of dye adsorbed per unit mass of adsorbent (mg/g), Ci is the initial dye concentration (mg/l), \(C_{\text{f}}\) is the final dye concentration (mg/l), Ct is the residual concentration at time t, V is the volume of dye solution (l) and M mass of adsorbent (g).

Adsorption isotherms

Adsorption isotherms were studied on the adsorption of Rh-B on AgNPs with Langmuir (Eqs. 3 and 3a), Freundlich (Eq. 4), Tempkin (Eqs. 5 and 5a) and Dubinin–Radushkevich (Eqs. 6, 6a and 6b) adsorption models.

The Langmuir isotherm is a monolayer type of adsorption which assumes that adsorption process takes place uniformly within the adsorbent surface and with uniform distribution of energy level (Langmuir 1918). Freundlich isotherm explains the heterogeneous nature of adsorption sites having non-uniform distribution of energy level (Freundlich 1906). Tempkin isotherm explains the influences of indirect adsorbate/adsorbent interactions on adsorption isotherms and also explains the interactions of these with the heat of adsorption (Tempkin and Pyzhev 1940). The Dubinin–Radushkevich model explains the relationship between energy of adsorption and type of adsorption process involved (Dubinin and Radushkevich 1947).

$$\frac{{C_{\text{e}} }}{{q_{\text{e}} }} = \frac{\text{Ce}}{{q_{ \hbox{max} } }} + \frac{1}{{q_{ \hbox{max} } K_{\text{L}} }}$$
(3)
$$R_{\text{L}} = \frac{1}{{1 + K_{\text{L}} C_{\text{o}} }}$$
(3a)
$$\log q_{\text{e}} = \frac{1}{n}\log C_{\text{e}} + \log K_{\text{f}}$$
(4)
$$q_{\text{e}} = B\ln A + B\ln C_{\text{e}}$$
(5)
$$B = {\raise0.7ex\hbox{${\text{RT}}$} \!\mathord{\left/ {\vphantom {{\text{RT}} b}}\right.\kern-0pt} \!\lower0.7ex\hbox{$b$}}$$
(5a)
$$\ln q_{\text{e}} = \ln q_{\text{o}} - \beta \varepsilon^{2}$$
(6)
$$\varepsilon = {\text{RT}}\ln \left( {1 + \frac{1}{{C_{\text{e}} }}} \right)$$
(6a)
$$E = \surd {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {2\beta }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${2\beta }$}}$$
(6b)

where Ce is the equilibrium concentration of Rh-B dye (mg/l), qe is the quantity of Rh-B dye adsorbed onto the AgNPs at equilibrium (mg/g), qmax is the maximum monolayer adsorption capacity of adsorbent (mg/g) and KL is the Langmuir adsorption constant (l/mg).

A graph of \(\frac{\text{Ce}}{\text{qe}}\) against Ce should give a straight line graph with the slope \({\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {q_{\hbox{max} } }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${q_{\hbox{max} } }$}}\) and \(\frac{1}{{q_{\hbox{max} } K_{\text{L}} }}\) as intercept. The value of RL is in the range 0 < RL < 1 indicating whether the adsorption is favourable or not: unfavourable (RL > 1), linear (RL = 1) or irreversible (RL = 0).

Kf and n are Freundlich constants corresponding to adsorption capacity and adsorption intensity or surface heterogeneity, respectively. They are obtained from linear plot of log qe versus log Ce with the slope \({\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 n}}\right.\kern-0pt} \!\lower0.7ex\hbox{$n$}}\) and intercept log Kf.

A (l/g) and B are Tempkin isotherm and Tempkin constants, respectively, which are obtained from the plot of qe against ln Ce. The value of b (J/mol) which is related to the heat of absorption is calculated using Eq. (5a), T is the absolute temperature (K), and R is the gas constant (8.314 J/mol/K).

The value of E in Dubinin–Radushkevich (D–R) model gives information about the type of adsorption whether chemical or physical involved during the uptake of Rh-B by AgNPs. A linear graph of ln qe against ɛ gives a slope of β and intercept of ln qo.

Adsorption kinetics

Adsorption kinetics were studied with pseudo-first-order (Eq. 7), pseudo-second-order (Eq. 8), Elovich kinetic models (Eq. 9) and intra-particle diffusion model (Eq. 10). Adsorption kinetics were validated with non-linear Chi-square test (Eq. 11) and correlation coefficient. Boyd model (Eqs. 12 and 13) was used to further confirm rate controlling step of adsorption process.

$$\ln (q_{\text{e}} - q_{\text{t}} ) = \ln q_{\text{e}} - K_{1} t$$
(7)
$$\frac{t}{{q_{\text{t}} }} = \frac{1}{{K_{2} q_{\text{e}}^{2} }} + \frac{t}{{q_{\text{e}} }}$$
(8)
$$q_{t} = \frac{1}{\beta }\ln \left( {\upalpha \upbeta } \right) + \frac{1}{\beta }\ln t$$
(9)
$$q_{t} = K_{\text{diff}} t^{1/2} + C$$
(10)
$$X^{2} = \mathop \sum \limits_{i = 1}^{n} \frac{{(q_{\exp } - q_{cal} )^{2} }}{{q_{cal} }}$$
(11)
$$F = \frac{{q_{\text{t}} }}{{q_{\text{e}} }}$$
(12)
$$B_{t} = - 0.4977 - { \ln }(1 - F)$$
(13)

where qe is the quantity adsorbed at equilibrium (mg/g) and qt is the quantity absorbed at time t (mg/g) and K1 is the rate constant for the pseudo-first-order sorption in min−1 obtained from the plot of ln (qe − qt) against \(t, t\) is time for adsorption in min.

K2 is the rate constant of the pseudo-second-order kinetic model in g/mg/min obtained for the plot of \(\frac{t}{{q_{t} }} {\text{aganist}}\, t\). \(K_{\text{diff}}\) is the rate constant of intra-particle diffusion (mg/g min−1/2). α and β are constants depicting chemosorption rate and the extent of surface coverage respectively, which are obtainable from the plot of qt against ln t.

F is the fraction of solute adsorbed at any time t. Bt is a mathematical function of F.

Adsorption thermodynamics

Thermodynamic parameters that explain spontaneity, energetics and the nature of adsorbate–adsorbent interactions are calculated using the following equations:

$$\ln K_{o} = \frac{{\Delta S^{o} }}{R} - \frac{{\Delta H^{o} }}{\text{RT}}$$
(14)
$$\Delta G^{o} = - {\text{RT}}\ln K_{o}$$
(15)
$$S^{*} = (1 - \theta )e^{{ -^{{{\raise0.7ex\hbox{${E_{a} }$} \!\mathord{\left/ {\vphantom {{E_{a} } {\text{RT}}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\text{RT}}$}}}} }}$$
(16)
$$\theta = 1 - \frac{{C_{\text{e}} }}{{C_{\text{o}} }}$$
(17)

Ko is calculated from \({\raise0.7ex\hbox{${q_{e} }$} \!\mathord{\left/ {\vphantom {{q_{e} } {C_{\text{e}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${C_{\text{e}} }$}}\), T is temperature (K), R is gas constant. \(\Delta S^{o}\) is change in entropy and \(\Delta H^{o}\) is change in enthalpy obtained from the plot of ln Ko against \(\frac{1}{T}\). \(\Delta G^{o}\), change in free energy is calculated using Eq. (15). E a is activation energy which is obtained from the plot of (1 − θ) against \(\frac{1}{T}\). S* is the sticking probability which is a function of adsorbate–adsorbent system and its value ranges between \(0 < S^{*} < 1\).

Results and discussion

Biosynthesized AgNPs

The pH of biosynthesized AgNPs was 6.72 and pHpzc was 7.82 (Fig. 3) which was fairly neutral. pHpzc is a parameter used to express the degree of adsorbent surface ionization. At a pH below pHpzc of the adsorbent, the surface of the adsorbent is positively charged and attracts anions while at pH above it, the surface of the adsorbent is negatively charged and attracts cations (Giwa et al. 2015; Torres et al. 2007). Earlier data revealed that cobweb extract-mediated AgNP biosynthesis gave dark brown nearly spherical crystalline AgNPs with surface plasmon resonance obtained at 436 nm. The polydispersed particles having size range of 3–50 nm were formed due to the activities of proteinous materials in the cobweb extract (Lateef et al. 2016f). The AgNPs mediated by cobweb extract have shown tremendous activities; including antimicrobial (Lateef et al. 2016f), desulphurization (Olajire et al. 2017), hydrogen peroxide scavenging, anticoagulant and thrombolytic applications (Lateef et al. 2017). However, until now, there is no report on the use of cobweb-mediated AgNPs for the removal of dyes.

Fig. 3
figure 3

pH point of zero charge (pHpzc)

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Effect of initial pH on the adsorption of Rh-B on AgNPs

Effect of various pH on adsorption of Rh-B on AgNPs is presented in Fig. 4. Adsorption process is dependent on pH where a change would either increase or reduce percentage adsorption. pH influences the charge on the surface of adsorbent and mobility of adsorbate (Majumdar et al. 2015; Das et al. 2013; Giwa et al. 2015). Percentage removal of Rh-B increased from 72 to 78% with increase in pH from pH 2 to 3.4 where maximum adsorption was observed. This decreased to the minimum (55%) at pH 9. At a pH below 7.82 (pHpzc for AgNPs), the surface of AgNPs was highly cationic, while Rh-B surface at pH less than 3.22 was also cationic, thus caused repulsion between adsorbent and adsorbate resulting in poor rate of adsorption. But as the pH increased especially at pH 3.4 (which is above 3.22 for Rh-B), the surface of Rh-B became anionic, therefore, resulting to high rate of adsorption. This could be due to electrostatic interaction between cationic adsorbent and anionic adsorbate leading to favourable adsorption of Rh-B (Majumdar et al. 2015; Das et al. 2013). With increase in pH, the surface of AgNPs became less cationic as it was nearing its pHpzc and thereafter became anionic at pH above it. This was responsible for reduction in rate of adsorption obtained at pH above 7.82. Similar trends have been previously reported in different studies (Giwa et al. 2015; Inyinbor et al. 2015; Ramalingam et al. 2015). Consequently, all batch adsorption experiments were, therefore, carried out at pH 3.4.

Fig. 4
figure 4

Effect of different pH on the adsorption of Rh-B on AgNPs. 1 g/l of AgNPs in 100 ml of 50 mg/l Rh-B, agitation speed 150 rpm, agitation time 30 min, temp. 303 K

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Effects of initial concentrations of Rh-B

The result of effect of initial dye concentrations on percentage uptake of Rh-B on AgNPs is presented in Fig. 5. It was discovered from the plot that percentage removal of Rh-B increased with increasing concentration of the dye. Maximum adsorption of 93% was recorded for highest concentration (50 mg/l), while the least adsorption (67%) was obtained for lowest concentration (10 mg/l). This could be attributed to the increase in the driving force from higher concentration which enhances the sorption process as earlier reported (Inyinbor et al. 2016a, b; Satapathy et al. 2013).

Fig. 5
figure 5

Percentage removal of Rh-B on AgNPs at different concentrations. 1 g/l of AgNPs in 100 ml of 50 mg/l Rh-B, agitation speed—150 rpm, agitation—30 min at 303 K, pH 3.4

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Effect of contact time

Contact time is one of the most effective factors in batch adsorption process and its effect on the adsorption of Rh-B on AgNPs is presented in Fig. 6. It is evident from the plot that the adsorption capacity (qt) at time t increased steadily with increase in time until it reached equilibrium at 30 min. The increase was from 7 mg/g at 5 min to 30.55 mg/g at 30 min. This is in agreement with earlier reports (Amuda et al. 2014; Mahmoud et al. 2015) where the noticed action could be due to the available surface sites before equilibrium was reached.

Fig. 6
figure 6

Adsorption capacity of AgNPs for the removal of Rh-B at different contact times. 1 g/l of AgNPs in 100 ml of 50 mg/l Rh-B, agitation speed—150 rpm at 303 K, pH 3.4

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Effect of adsorbent dosage

The result of effect of AgNPs dosage on the removal of Rh-B from aqueous solution is presented in Fig. 7. Percentage Rh-B adsorbed increased with increase in AgNPs dosage from 0.2 to 1 g/l. The increase was from 52 to 87%. The increase in the percentage removal with adsorbent dosage may be adduced to the increase in the nanoparticle’s surface area available for adsorption. This is in consonance with earlier reports (Satapathy et al. 2013; Amuda et al. 2014; Inyinbor et al. 2016a, b).

Fig. 7
figure 7

Effect AgNPs dosage on the adsorption of Rh-B. 50 mg/l Rh-B, agitation speed—150 rpm, agitation time—30 min at 303 K, pH 3.4

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Effect of temperature

Temperature influences adsorption capacity and its effect on the adsorption of Rh-B onto AgNPs is presented in Fig. 8. The temperature dependency of adsorption of Rh-B on AgNPs was studied at 303, 313, 323, 333 K, and it was observed that percentage removal of Rh-B reduced with increase in temperature. This phenomenon indicates that the adsorption process was exothermic in nature and it is in consonance with earlier reports (Satapathy et al. 2013; Girish and Murty 2014; Inyinbor et al. 2016a, b).

Fig. 8
figure 8

Effect of temperature on the adsorption of Rh-B on AgNPs at different temperatures. 1 g/l of AgNPs in 100 ml of 50 mg/l Rh-B, 150 rpm 60 min, pH 3.4

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Adsorption isotherms

For the explicit examination of the relationship between quantity of Rh-B adsorbed and its concentration, Langmuir, Freundlich, Tempkin and Dubinin–Radushkevich isothermal models were employed. Figures 9, 10, 11 and 12 show the plots of Langmuir, Freundlich, Tempkin and Dubinin–Radushkevich adsorption isotherms, respectively, for the adsorption of Rh-B on AgNPs. The parameters obtained from the plots are presented in Table 1. Correlation coefficient (R2) was used to determine which model best describes the adsorption process. The closer the R2 to unity (1), the better the agreement between experimental data, and model predicted value and the best fit it is. Comparing R2 of each isotherm, Langmuir (0.9901), Freundlich (0.9860), Tempkin (0.9740) and Dubinin–Radushkevich (0.9441), it is evident that Langmuir isotherm best fits the adsorption of Rh-B on AgNPs which indicates monolayer and homogenous adsorption process with all adsorption sites possessing equal affinity for adsorbate (Foo and Hameed 2010). The favourability of the adsorption process is confirmed if the value of RL is in the range 0 < RL < 1. As obtained in this study (Table 1), RL is 0.18, confirming that the adsorption process was favourable (Majumdar et al. 2015; Satapathy et al. 2013; Inyinbor et al. 2016a, b).

Fig. 9
figure 9

Langmuir adsorption isothermal plot for the adsorption of Rh-B on AgNPs

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Fig. 10
figure 10

Freundlich adsorption isothermal plot for the adsorption of Rh-B on AgNPs

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Fig. 11
figure 11

Temkin adsorption isothermal plot for the adsorption of Rh-B on AgNPs

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Fig. 12
figure 12

Dubinin–Radushkevich adsorption isothermal plot for the adsorption of Rh-B on AgNPs

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Table 1 Adsorption isotherm parameters for the uptake of Rh-B on AgNPs at 30 °C
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The maximum monolayer adsorption (qmax) obtained from Langmuir plot is 59.85 mg/g and when compared with previously published reports in other studies (Table 2), it shows that AgNPs is a relatively better adsorbent in terms of performance than some previously used adsorbents (Majumdar et al. 2015; Das et al. 2006; Satapathy et al. 2013; Amuda et al. 2014; Inyinbor et al. 2015, 2016a; Mahmoud et al. 2015; Shen et al. 2015).

Table 2 Comparison of monolayer adsorption capacity of Rh-B on AgNPs with other adsorbents
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\(K_{\text{f}}\) and n were calculated from Freundlich isotherm plot with the value of n (1.647) greater than 1 indicating a favourable adsorption of Rh-B on AgNPs and the chemical nature of adsorption (Foo and Hameed 2010; Amuda et al. 2014).

Adsorption energy (E) calculated from slope of Dubinin–Radushkevich plot is 19.38 kJ/mol suggesting that chemosorption was involved in the uptake of Rh-B on AgNPs as it was earlier reported (Inyinbor et al. 2015, 2016a, b).

Adsorption kinetics

The rate of removal of Rh-B and its controlling mechanism were studied as part of kinetics. Pseudo-first-order, pseudo-second-order, Elovich kinetic models and intra-particle diffusion model were employed to describe Rh-B uptake onto AgNPs. The parameters obtained for pseudo-first-order, pseudo-second-order, Elovich kinetic models and intra-particle diffusion model are presented in Table 3. Correlation coefficient (R2) was used to determine the goodness of fit between experimental and calculated data. R2 of the best fit model must be the closest to 1. Also, similarities between experimentally determined and calculated data expressed using non-linear Chi-square test (χ2) (Eq. 11) must exist. A relatively low (χ2) value indicates the model successfully describes the equilibrium kinetics (Al-Meshragi et al. 2008; Boulinguiez et al. 2008). Comparison of correlation coefficients of pseudo-first-order (R2 = 0.9421), pseudo-second-order (R2 = 0.9882) and Elovich (R2 = 0.9723) kinetic models shows that pseudo-second-order best describes the mechanism and rate of uptake of Rh-B on AgNPs. Equally, lower value of χ2 validates pseudo-second-order as the kinetic model describing the rate of adsorption. This suggests that the controlling process of adsorption of Rh-B on AgNPs may be by chemosorption (Girish and Murty 2014).

Table 3 Adsorption kinetics of Rh-B on AgNPs
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Many factors control the rate of adsorption, one of which is intra-particle diffusion. The possibility of involvement of intra-particle diffusion affecting the adsorption process was studied and is presented in Fig. 13. To further investigate rate controlling step in the adsorption process, the Boyd model as given in Eqs. 12 and 13 was used and the result is presented in Fig. 14. The parameters obtained from the plot in Fig. 13 are presented in Table 3. A single linear plot obtained for intra-particle diffusion of AgNP–Rh-B did not pass through the origin and has high correlation coefficient (R2 = 0.9971) indicating that intra-particle diffusion was involved in the adsorption but it was not the sole rate-controlling step. This was confirmed by Boyd plot which also did not pass through the origin. Therefore, surface adsorption and intra-particle diffusion were both concurrently occurring during adsorption process (Cheung et al. 2007; Hameed et al. 2008; Abou-Gamra and Medien 2013; Girish and Murty 2014). The value of C (intercept) gives the idea about the thickness of the boundary, the larger the value of C, the greater the boundary layer diffusion effect (Konicki et al. 2013).

Fig. 13
figure 13

Intra-particle diffusion of adsorption of Rh-B on AgNPs

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Fig. 14
figure 14

Boyd plot for adsorption of Rh-B on AgNPs

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Activation energy and adsorption thermodynamic

Thermodynamic parameters (∆G°, ∆H° and ∆S°) calculated from Van’t Hoff’s plot (Fig. 15) for adsorption of Rh-B on AgNPs are presented in Table 4. These parameters give information about the spontaneity of adsorption process (Satapathy et al. 2013). Activation energy (Ea) of the adsorption process obtained using Eqs. 16 and 17 is presented in Table 4. The magnitude of activation energy gives idea about the type of adsorption, which mainly can either be physiosorption or chemosorption (Mahmoud et al. 2015).

Fig. 15
figure 15

Van’t Hoff’s plot for adsorption of Rh-B on AgNPs. 1 g/l of AgNPs in 100 ml of 50 mg/l Rh-B, 150 rpm 60 min, pH 3.4

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Table 4 Thermodynamic parameters of Rh-D adsorption on AgNPs
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The Ea of the adsorption calculated was 103.273 kJ/mol which depicts the adsorption process as chemosorption because its range for chemosorption is usually between 40 and 800 kJ/mol. (Satapathy et al. 2013; Mahmoud et al. 2015).

Negative enthalpy (− ∆H°) and entropy (− ∆S°) values obtained indicate the adsorption process was exothermic in nature with decreased randomness during adsorption. The ∆G° values calculated at all temperatures were negative indicating the adsorption was spontaneous and feasible. The adsorption process became less spontaneous with higher values of ∆G° at higher temperature (Majumdar et al. 2015; Inyinbor et al. 2015; Mahmoud et al. 2015).

Conclusion

This study has reported the adsorption of Rh-B onto AgNPs biosynthesized using cobweb extract. Initial pH, contact time, initial dye concentration, adsorbent dosage and temperature significantly affected the adsorption of Rh-B and maximum adsorption was observed at pH 3.4. Four adsorption isotherms were used to describe the adsorption process with Langmuir isotherm suitably fitted best. Maximum monolayer adsorption capacity showed a relatively high performance. Pseudo-second-order kinetics best fitted the rate of adsorption which was both controlled by intra-particle diffusion and surface adsorption. Thermodynamic parameters indicated exothermic spontaneous adsorption process. The adsorption process was found to be chemical in nature as showed by the values of energy of adsorption and activation energy. This study has shown that low-cost and eco-friendly biosynthesized AgNPs with 93% dye removal from aqueous solution possess potential adsorbent capacity to remove dye.