Abstract

Activated coal fly ash (FA) treated with NaOH and hexadecyltrimethylammonium bromide (HDTMABr) was used as adsorbent for removal of cadmium(II) ions and rhodamine B (RB) from an aqueous solution. Characterization of fly ash and FA-HDTMABr were done using Fourier transform infrared spectroscopy (FT-IR), scanning electron microscopy (SEM) and X-ray diffraction (XRD). The sorption equilibrium in the system was analysed using isotherm models, such as Freundlich, Langmuir, generalized Langmuir-Freundlich, Redlich-Peterson, Jovanović, extended Jovanović, Tóth, Frumkin-Fowler-Guggenheim, Fowler-Guggenheim-Jovanović-Freundlich, Temkin, Dubinin-Radushkevich, Halsey, Brunauer, Emmett and Teller. The evaluation of the fit of the isotherms studied experimentally was carried out by means of the reduced chi-square test and the coefficient of determination. The maximum monolayer adsorption capacity of the FA-HDTMABr was found to be 744 mg·g−1 and 666 mg·g−1 for Cd(II) and RB, respectively. The PFO, PSO, Elovich mass transfer, liquid film diffusion and intra-particle diffusion models were analysed. Sorption kinetics data were well fitted by the PSO model. The Elovich and intra-particle model also revealed that there are two separate stages in the sorption process, namely, external diffusion and intra-particle diffusion.

ABBREVIATIONS

Latin letters

     
  • aR

    Redlich-Peterson constant, (L·mg−1)βR

  •  
  • bi

    film thickness, mg·g−1

  •  
  • C0

    initial concentration of sorbate in the solution, mg·L−1

  •  
  • Ce

    unadsorbed concentration of the component in an aqueous solution at the sorption equilibrium, mg·L−1

  •  
  • CEC

    cation exchange capacity, mmol·g−1

  •  
  • Ct

    concentration of sorbate in the solution after sorption, mg·L−1

  •  
  • DoF

    degrees of freedom

  •  
  • E

    free energy, kJ·mol−1

  •  
  • F

    fractional attainment of equilibrium

  •  
  • FA

    fly ash

  •  
  • FAAS

    flame atomic absorption spectrometry

  •  
  • FT-IR

    Fourier transform infrared spectroscopy

  •  
  • k1

    first order rate constant, min−1

  •  
  • k2

    second order rate constant, g·mg−1·min−1

  •  
  • KBET

    Brunauer-Emmett-Teller sorption coefficient, L·g−1

  •  
  • KDR

    Dubinin-Radushkevich sorption coefficient, mol2·kJ−2

  •  
  • KF

    Freundlich sorption coefficient, mg1–1/n ·L1/n ·g−1

  •  
  • Kfd

    liquid film diffusion rate constant, mg·g−1·min−1

  •  
  • KFGJF

    Fowler-Guggenheim-Jovanović-Freundlich sorption coefficient, L·g−1

  •  
  • KFFG

    Frumkin-Fowler-Guggenheim sorption coefficient, L·g−1

  •  
  • Kh

    Halsey sorption coefficient, mgn−1·g−n·L

  •  
  • ki

    intra-particle diffusion rate constant, mg·g−1·min−1/2

  •  
  • KJ

    Jovanović sorption coefficient, L·mg−1

  •  
  • KJE

    extended Jovanović sorption coefficient, L·mg−1

  •  
  • KL

    Langmuir sorption coefficient, L·mg−1

  •  
  • KLF

    generalized Langmuir-Freundlich sorption coefficient, L·mg−1

  •  
  • KR

    Redlich-Peterson sorption coefficient, L·g−1

  •  
  • KT

    Temkin sorption coefficient, L·g−1

  •  
  • KTh

    Tóth sorption coefficient, (L·mg−1)Th

  •  
  • LOI

    loss on ignition, %

  •  
  • m

    sorbent mass, g

  •  
  • n

    heterogeneity factor

  •  
  • P

    sorption percentage, %

  •  
  • PFO

    pseudo-first-order kinetic model

  •  
  • PSO

    pseudo-second-order kinetic model

  •  
  • PSD

    particle size distribution

  •  
  • q0

    initial amount of adsorbate in the solution, mg·g−1

  •  
  • qe

    amount of sorbate adsorbed on sorbent at equilibrium (equilibrium sorption capacity), mg·g−1

  •  
  • q

    maximum content of sorbate in sorbent at the sorption equilibrium, mg·g−1

  •  
  • qt

    amount of sorbate adsorbed on sorbent at time t, mg·g−1

  •  
  • R

    universal gas constant (8.314 J·K−1 mol−1)

  •  
  • R2

    linear regression coefficient

  •  
  • SEM

    scanning electron microscope

  •  
  • T

    absolute temperature, K

  •  
  • t

    sorption time, min or hour

  •  
  • t1/2

    half sorption time, min or hour

  •  
  • Th

    Tóth heterogeneity factor

  •  
  • u

    initial sorption rate, mg·g−1·min−1

  •  
  • V

    initial volume of the aqueous phase under adsorption, L

  •  
  • XRD

    X-ray diffraction

Greek letters

     
  • α

    Elovich initial sorption rate, mg·g−1·min−1

  •  
  • αFGJF

    Fowler-Guggenheim-Jovanović-Freundlich constant

  •  
  • αFFG

    Frumkin-Fowler-Guggenheim constant

  •  
  • β

    constant related to the extent of surface coverage and activation energy for chemisorption in the Elovich model, g·mg−1

  •  
  • βR

    Redlich-Peterson heterogeneity factor

  •  
  • βT

    Temkin heat of sorption, J·mol−1

  •  
  • χ2

    chi-square test

INTRODUCTION

Highly coloured wastewater containing hazardous dyes and heavy metals is a serious environmental problem (Crini 2006; Gupta & Suhas 2009; Li et al. 2010; Mittal et al. 2010; Sarma et al. 2016). Synthetic dyes are being increasingly used in textile industries, dye manufacturing industries, paper and pulp mills, tanneries, electroplating factories, food companies, etc. (Sun et al. 2010). Dyes can be classified as anionic (direct, acid, and reactive dyes), cationic (basic dyes) or non-ionic (disperse dyes) (Ӧzdemir et al. 2006; Alver & Metin 2012). In general, dyes are stable in light, heat and oxidizing agents, and are usually non-biodegradable (Anirudhan & Ramachandran 2015). It is therefore necessary to study the adsorption phenomena of other classes of dyes.

Rhodamine B (RB) is a highly water soluble, basic red dye of the xanthene class (Panneer et al. 2008; Li et al. 2010). It is a typical cationic dye that has been widely used as a colorant in textile products (Adak et al. 2005; Amodu et al. 2015). RB is also used as the active medium in pulsed and continuous wave lasers, as a staining fluorescent dye in biology, and as a tracer dye to track the movement of water. RB in an aqueous solution exists in optically active protonated and zwitterionic forms and the colourless lactone form (Zhang et al. 2015).

Cadmium is toxic to the kidneys, and the skeletal and respiratory systems, and it is classified as a human carcinogen (WHO 2004). Cadmium is known to accumulate in the liver and to change the constitution of bones and blood (UNEP 2008). Consumption of rice containing high concentrations of cadmium led to a surge of itai-itai disease in Japan in 1955. Cadmium can travel long distances from the source of emission by atmospheric transfer. Human exposure is mainly due to consumption of contaminated food, active and passive inhalation of tobacco smoke, and inhalation by workers in the non-ferrous metal industry (WHO 2008).

Coal fly ash is specific material produced in coal-fired heat and power plants. Large quantities are stored in slag heaps. In recent years, research interest has increased in the production of low-cost alternatives to activated carbon, which remains an expensive material in spite of its prolific use. Commercially activated carbon is regarded as the most effective adsorbent for controlling organic and inorganic contaminants. Coal fly ash may prove to be a much cheaper adsorbent than activated carbon. Coal fly ash has a potential application in wastewater treatment because of its major chemical components, which are alumina, silica, ferric oxide, calcium oxide, magnesium oxide and carbon, and because of its physical properties, such as porosity, particle size distribution and surface area. Thus, fly ash and modified fly ash are promising candidate materials as the adsorbent and ion exchanger in water and wastewater treatment. The equilibrium and kinetic studies which contributed to understanding of the properties of a new adsorbent, chemically modified coal fly ash (FA) treated with a surfactant solution of hexadecyltrimethylammonium bromide (HDTMABr) were carried out. Importantly, the effect of pH, initial concentration of sorbate, and time of the sorption process of cadmium and RB by FA-HDTMABr was explored, and the key physical and chemical characteristics of the product were described.

EXPERIMENTAL

Apparatus

RB concentration in solution was analysed spectrophotometrically by means of a UV–VIS spectrophotometer (JASCO, type V-670, Japan). Cadmium concentration in extracts was determined by a flame atomic absorption spectrometer (FAAS, model SavantAA, GBC Scientific Equipment, Australia). Determination of non-metals (C, H, N, S) in the sample was carried out by Elemental Analyser EA 1108 (Carlo Erba, Italy). The crystallographic structure of the fly ash, FA-NaOH and FA-HDTMABr were characterized by X-ray diffraction (XRD). XRD was carried out on a D2 Phaser (Bruker, Germany) X-ray diffractometer using Cu-Kα radiation and measuring the angle (2Θ) from 5 to 65° and the scanning rate of 0.02°s−1 at 30 kV and 10 mA. The morphologies of the fly ash, FA-NaOH and the FA-HDTMABr were observed by scanning electron microscopy (SEM). The SEM micrographs were obtained using VEGA 3 (Tescan, USA). The chemical structures of coal fly ash samples were performed by infrared spectroscopy applying Fourier transformation (FT-IR) on an Alpha (Bruker, Germany). The adsorbents were investigated from 4,000 to 400 cm−1 at a resolution of 0.7 cm−1. FT-IR measurements were made on samples suspended in KBr discs.

Materials and methods

Sample of coal fly ash

In this experiment, high-temperature fly ash produced by a thermal power plant in Poland (the Rzeszów-Załęże power plant) was used. According to the American Society for Testing Materials (ASTM C618-05), the ash used in this study can be classified as group F. This group has pozzolanic properties and are characterized by SiO2 + Al2O3 + Fe2O3 > 70% and CaO <10%.

Preparation of the modified coal fly ash sample

The coal fly ash treated with NaOH (FA-NaOH) was performed in the following way: the fly ash was treated with a 2 M solution of NaOH (at a solution to fly ash ratio of 10:1 by weight). The sample of the adsorbent mass and the NaOH solution were placed into a round-bottomed flask closed reflux condenser. The suspension of the fly ash was then mixed for 6 hours at 100 °C. The solid product was decanted, filtered and washed repeatedly distilled water until the pH of the filtrate dropped to the pH of the distilled water, and then it was dried in an electric dryer at 105 °C for 24 hours. After the first modification 100 g FA-NaOH was placed in a oven and then saturated with an aqueous solution of the surfactant HDTMABr. The suspension was mixed for 24 hours at 20 °C. Next, the solution was filtered, washed several times with distilled water and dried to a solid residue at 90 °C for 8 hours to obtain surfactant-modified fly ash (FA-HDTMABr). The amount of HDTMA+ corresponds to the full cation exchange capacity (CEC). The CEC value was determined by HDTMA+ adsorption, which was carried out using 2 g of FA-NaOH with a 25 mL surfactant solution at varied concentrations in the range between 1·10−3 and 8·10−3 mol·L−1. Based on the content of non-metals in the determination of solid samples, the difference in the content of carbon, hydrogen and nitrogen between FA-NaOH and FA-NaOH treated with surfactant was used to calculate the CEC (0.12 mol HDTMA+/1 kg of FA-NaOH) (Szala et al. 2015).

Reaction of the fly ash with NaOH:
formula
Reaction of the FA-NaOH with HDTMABr:
formula

Determination of analytes

RB (Figure 1), which is also known as [9-(2-carboxyphenyl)-6-diethylamino-3-xanthenylidene]-diethylammonium chloride was used (Wang et al. 2009).

Figure 1

The structure of rhodamine B (RB).

Figure 1

The structure of rhodamine B (RB).

The calibrant solutions containing 0.0; 0.5; 1.0; 1,5 and 2.0 mg L−1 Cd(II) ions were prepared by diluting a stock solution of 1,000 mg L−1 Cd(II) for concentrations of Cd(II) ions determination by the FAAS method.

Sorption of analytes

The experiments involving adsorption of Cd(II) ions and RB onto modified coal fly ash were conducted by the batch method, which allows for complete evaluation of the parameters influencing the process of adsorption. In this method, a series of 100 mL glass flasks were filled with a 50 mL metal ion and dye solution of varying concentrations (10–500 mg·L−1). Then, 0.5 g of FA-HDTMABr nanoparticles were added to each flask and agitated at pH 9.0 for between 1 min and 5 hours. The resultant solutions were centrifuged and the supernatant liquids were subjected to the determination of Cd(II) ions and RB.

RESULTS AND DISCUSSION

The crystallography, morphology and chemical structure studies of fly ash, FA-NaOH and FA-HDTMA

The XRD study was carried out to understand the crystalline phases of the fly ash. The X-ray diffractogram of fly ash is shown in Figure 2(1a). Various peaks confirmed the presence of minerals like quartz, mullite, magnetite and hematite. The main peaks of quartz were found at 2Θ value of 20.8862, 26.5912 and 50.3040, mullite was identified at 16.4036, 25.9896 and 40.8538 and kaolinite at 26.2225 (Szala et al. 2015; Mor et al. 2018). Moreover, the fly ash also contained a trace amount of magnetite at 29.3855 and 30.9573. The XRD pattern of the FA-NaOH showed the amounts of minerals in the FA-NaOH were less than in the fly ash, as was observed from the reduction of these peak intensities (Figure 2(1b)). We also observed the appearance of zeolites, which were NaX and sodalite. This observation indicated the conversion of fly ash into a zeolite-like material under alkaline conditions. Previous studies have also reported a similar observation (Sarbak & Kramer-Wachowiak 2002). After treatment with NaOH, the ball-shaped particles of fly ash partly transformed into smooth surfaces and agglomerations of various shapes with some crystal formation (Styszko-Grochowiak et al. 2004), e.g., plates and rods (Figure 2(2b)). The particle surface of FA-NaOH showed the transformation of fly ash into a zeolite-like structure, as was confirmed by the XRD data of this study (Figure 2(1b)); this was also observed in other studies (Sarbak & Kramer-Wachowiak 2002; Penilla et al. 2006). The diffraction pattern of the FA-HDTMABr indicated that the modification process by HDTMABr did not crystallize it but instead attached to the FA-NaOH surface (Figure 2(1c)). SEM observation of the fly ash (Figure 2(2a)) showed the presence of smaller particles and microspheres in the shape of smooth balls (Aslam et al. 2015). Modification of fly ash with NaOH changed the ball-shaped surfaces into agglomeration of micro-particles. This indicated a change and increase in the roughness of the surface (Figure 2(2b)), which is similar to Mor et al. (2018). Moreover, after treatment with a surfactant solution the surface morphology did not change (Figure 2(2c)).

Figure 2

(1) XRD patterns, (2) SEM images and (3) FT-IR spectra of (a) coal fly ash, (b) fly ash treated with NaOH (FA-NaOH), (c) FA-NaOH treated with surfactant (FA-HDTMABr).

Figure 2

(1) XRD patterns, (2) SEM images and (3) FT-IR spectra of (a) coal fly ash, (b) fly ash treated with NaOH (FA-NaOH), (c) FA-NaOH treated with surfactant (FA-HDTMABr).

Based on the spectrum obtained from the FT-IR analysis of the coal fly ash, absorption bands were observed at 3,400 cm−1, 1,600 cm−1 and at about 1,050 cm−1 (Figure 2(3)). The band at 3,440 cm−1 is from the –OH group stretching vibrations (Deng & Yu 2012). This indicates the presence of both free and hydrogen bonded –OH groups on the adsorbent surface.

The spectrum was recorded at air atmosphere; that is why clear-cut interpretation of this band was difficult because it could derive from –OH groups, chemically bonded with the surface of fly ash, FA-NaOH and FA-HDTMABr (Figure 2(3)), and also from stretching vibrations H-O-H of water molecules adsorbed (peak at 3,400 cm−1) on to the ash surface (Deng & Yu 2012). The increase of band intensity in the field of 3,440 cm−1 in the spectrum of FA-HDTMABr can be observed (Figure 2(3c)). Coal fly ash modified by HDTMABr was more hydrophilic than the corresponding untreated sample. The presence of polar groups on the surface was likely to provide considerable cation exchange capacity of the adsorbents. The surface structures of functional groups were by far the most important structures in influencing the surface characteristics and surface behaviour of FA-HDTMABr. The stretching of the –OH groups bound to methyl radicals presented a very weak signal, ∼2,900 cm−1, for fly ash and FA-NaOH (Figure 2(3a) and 2(3b)). Two consecutive, strong signals for FA-HDTMABr at 2,920 and 2,850 cm−1 were observed only on surfactant-modified coal fly ash (Figure 2(3c)), where there additional bands appeared, derived from HDTMABr (Szala et al. 2015).

The bands indicated that the –OH groups bound to aliphatic compounds corresponded, respectively, to symmetric and asymmetric stretching vibrations of the methylene group –CH2– (Rožić & Miljanić 2011). The band at 1,630 cm−1 related to bending vibrations of water molecules. The 1,450 cm−1 band in fly ash, FA-NaOH and FA-HDTMABr could be attributed to aromatic CH and carboxyl-carbonate structures. The highest intensity of bands in the spectrum of the samples was in the field of 1,050 cm−1 and could be described as asymmetric stretching vibrations of bridge bounds νas Si-O-Si and νas Si-O-Al, occurring in tetrahedral or aluminium- and silicon-oxygen bridges, typical for aluminosilicate framework structures (Mozgawa et al. 2006). The doublet of low intensity at ca. 800 cm−1 (integral at 798 and 780 cm−1) indicated the presence of quartz in the analysed samples. The symmetrical stretching of νs Si-O-Al band (broad-strong) corresponded to the variation in frequency at 730 cm−1 and symmetrical stretching of νs Si-O-Si band at 660 cm−1. Pseudolattice vibrations, originating from overtetrahedral structural units and the double ring of secondary building unit (SBU) could be observed to be present in the zeolite structure in the fly ash (rings made of silicon-oxygen and aluminium-oxygen tetrahedra), corresponding to the infrared frequency, at 550 cm−1. Moreover, the bands at about 550 cm−1 corresponded to symmetric stretching vibrations of νs Si-O-Si bridge bonds and bending vibrations of δ O-Si-O as complex band (Mozgawa et al. 2006). Based on the FT-IR spectrum, it could be observed that were pore openings corresponding to the band at 460 cm−1 in the fly ash, FA-NaOH and FA-HDTMABr, which could be attributed to the dissolution of the minerals (viz., quartz and mullite) present in samples (Kantiranis et al. 2006).

Kinetic studies

The influence of mixing time (contact time) on the amount of metal ion remaining in the solution after adsorption by FA-HDTMABr was studied in the solution containing 50 mg·L−1 of Cd(II) ions and RB dye in the range of 15 min to 5 hours at room temperature (20 ± 2 °C).

It can be seen in Figure 3 that adsorption took place more rapidly in the initial stages within the first hour and gradually slowed down as it reached the equilibrium state. The rate of adsorption of Cd(II) onto the FA-HDTMABr surface was faster than that of RB. The capacity of Cd(II) ion was greater than RB because of smaller ionic size.

Figure 3

Dependence of mixing time on Cd(II) and RB adsorption onto FA-HDTMABr.

Figure 3

Dependence of mixing time on Cd(II) and RB adsorption onto FA-HDTMABr.

The kinetic rate constants were calculated by using the pseudo-first-order (PFO) (Lagergren 1898; Ho 2004), the pseudo-second-order (PSO) kinetic models (Ho &McKay 1999; Ho 2006), and the Elovich kinetic models (Chien & Clayton 1980), whereas the intra-particle diffusion model (Weber & Morris 1963; Cabal et al. 2009; Figaro et al. 2009) and the liquid film diffusion model (Boyd et al. 1947) helped to determine the rate controlling stage. Table 1 presents the values of these parameters. The kinetic sorption experimental data fit were performed by using linear PFO and PSO equations. The values of the reduced chi-square test and the coefficient of determination in the PSO model (R2 = 0.996) were slightly lower for Cd(II) than those of the PFO model (R2 < 0.7), which is an indication that the PSO model is better than the PFO model. The PSO model is based on the assumption that chemisorption occurs (Ho & McKay 1999). The kinetic sorption experimental data fit using linear PSO equations are shown in Figure 4(a). The initial adsorption rate, u=k2qe2 and qe=q0, when t0, can be calculated from the PSO rate of equation. The initial adsorption rate of Cd(II) and RB were 4.90 and 4.95 [mg·g−1·min−1] respectively. The half time of adsorption of Cd(II) and RB were 1 min for both sorbates. Multilinear plots qt=k’it1/2+bi indicated two separate regions for adsorption of Cd(II) and RB (Aslam et al. 2015). The micropore diffusion constant k'2 values for Cd(II) and RB were lower than those for the macropore diffusion constants k'1 of 0.639 and 0.645, respectively for Cd(II) and RB (Figure 4(b)). Moreover, the rate of micropore diffusion is a slower step that is the rate-controlling step (Boyd et al. 1947).

Table 1

Kinetic model constants and correlation coefficients for the adsorption systems

Kinetic modelParameterCd(II)RB
Pseudo-first-order
dqt/dt = k1(qe − qt)
ln(qe − qt)= −k1t + lnqe 
k1 [min−16.4·10−3 3.3·10−3 
R2 0.686 0.738 
Pseudo-second-order
dqt/dt = k2(qe − qt)2
t/qt = 1/k2qe2 + t/qe 
k2 [g·mg−1·min−10.197 0.198 
R2 0,996 0,964 
Elovich mass transfer
dqt/dt = αexp(−βqt)
qt = 1/β lnt + 1/β lnαβ 
α [mg·g−1·min] 0.22 1.44 
β [g·mg−10.72 1.15 
R2 0.962 0.734 
Liquid film diffusion
ln(1 − F)= −kfd
kfd [mg·g−1·min−11.1·10−2 1.4·10−2 
R2 0.667 0.866 
Intra-particle diffusion
qt = k’it1/2 + bi 
k’1 [mg·g−1·min−1/20.639 0.645 
b1 [mg·g−1– – 
R2 0.994 0.999 
k’2 [mg·g−1·min−1/21.14·10−7 1.51·10−5 
b2 [mg·g−14.9 4.5 
R2 1.000 0.997 
Initial adsorption rate
u = k2 qe2 
u [mg·g−1·min−14.90 4.95 
Half-adsorption time
t1/2 = 1/k2qe 
t1/2 [min] 1.0 1.0 
Kinetic modelParameterCd(II)RB
Pseudo-first-order
dqt/dt = k1(qe − qt)
ln(qe − qt)= −k1t + lnqe 
k1 [min−16.4·10−3 3.3·10−3 
R2 0.686 0.738 
Pseudo-second-order
dqt/dt = k2(qe − qt)2
t/qt = 1/k2qe2 + t/qe 
k2 [g·mg−1·min−10.197 0.198 
R2 0,996 0,964 
Elovich mass transfer
dqt/dt = αexp(−βqt)
qt = 1/β lnt + 1/β lnαβ 
α [mg·g−1·min] 0.22 1.44 
β [g·mg−10.72 1.15 
R2 0.962 0.734 
Liquid film diffusion
ln(1 − F)= −kfd
kfd [mg·g−1·min−11.1·10−2 1.4·10−2 
R2 0.667 0.866 
Intra-particle diffusion
qt = k’it1/2 + bi 
k’1 [mg·g−1·min−1/20.639 0.645 
b1 [mg·g−1– – 
R2 0.994 0.999 
k’2 [mg·g−1·min−1/21.14·10−7 1.51·10−5 
b2 [mg·g−14.9 4.5 
R2 1.000 0.997 
Initial adsorption rate
u = k2 qe2 
u [mg·g−1·min−14.90 4.95 
Half-adsorption time
t1/2 = 1/k2qe 
t1/2 [min] 1.0 1.0 
Figure 4

Kinetics of Cd(II) and RB removal by FA-HDTMABr according to the models (a) PSO, (b) intra-particle diffusion, (c) liquid film diffusion and (d) Elovich mass transfer.

Figure 4

Kinetics of Cd(II) and RB removal by FA-HDTMABr according to the models (a) PSO, (b) intra-particle diffusion, (c) liquid film diffusion and (d) Elovich mass transfer.

The boundary layer effect (the second line from the plots of qt versus t1/2) shows greater effect on the micropore diffusion stage (4.9 and 4.5, respectively for Cd(II) and RB, than in the macropore stage, where it is close to zero. This indicates that intraparticle diffusion is not only a rate controlling step; some other processes may also control the rate of adsorption (Garg et al. 2003; Sarma et al. 2016). Considering that the big dye molecules may diffuse very slowly across the liquid film over the adsorbent before interacting with the surface active sites, and that this may be the rate determining step, the plots of ln(1F) vs. t were drawn to validate the liquid film diffusion model (Boyd et al. 1947), where F=qt/qe (the fractional attainment of equilibrium), kfd – the diffusion rate coefficient. The film diffusion parameters were obtained from the intercepts and slopes of Figure 4(c), and given in Table 1. The intercept values for both Cd(II) (1.1·10−2) and RB (1.4·10−2) are higher than zero, but are close to the origin showing the significance of liquid film diffusion in the rate determination of the adsorption process. The Elovich equation, which is applied to heterogeneous surfaces (Chien & Clayton 1980), was also applied in an effort to describe better the chemisorption process. A plot of qt versus lnt gives a linear trace with a slope of 1/β and an intercept of 1/β lnαβ. Linear plots with reasonable R2 values indicate agreement with chemisorption processes contributing significantly to adsorption rates (Figure 4(d)). However, experimental data again showed better agreement with the PSO kinetic model (Table 1).

Error analysis

In order to quantitatively compare the applications of each model, the coefficients of determination (R2) and a reduced chi-square test (χ2/DoF) were calculated (Wang 2012). The linear and non-linear regression (reduced chi-square) value was calculated by using Origin Pro 7.5 software:
formula
where DoF, qei and qei,m are degrees of freedom, experimental data and model data. The error bars in the line graph represent a confidence interval of t-distribution; the significance was set at p = 95% and n = 3.

Equilibrium studies

The adsorption isotherm in the studied system was obtained by applying the equations of: Freundlich, Langmuir, generalized Langmuir-Freundlich, Redlich-Peterson, Jovanović, extended Jovanović, Tóth, Frumkin-Fowler-Guggenheim, and Fowler-Guggenheim-Jovanović-Freundlich, Temkin, Dubinin-Radushkevich, Halsey, Brunauer Emmett and Teller (Figure 3). The interpretation of Figure 5 is described below.

Figure 5

The plot of isotherm models (a) Freundlich, (b) Langmuir, (c) generalized Langmuir-Freundlich, (d) Redlich-Peterson, (e) Jovanović, (f) extended Jovanović, (g) Tóth, (h) Halsey, (i) Frumkin-Fowler-Guggenheim, (j) Fowler-Guggenheim-Jovanović-Freundlich, (k) Temkin, (l) Dubinin-Radushkevich, (m) Brunauer, Emmett and Teller.

Figure 5

The plot of isotherm models (a) Freundlich, (b) Langmuir, (c) generalized Langmuir-Freundlich, (d) Redlich-Peterson, (e) Jovanović, (f) extended Jovanović, (g) Tóth, (h) Halsey, (i) Frumkin-Fowler-Guggenheim, (j) Fowler-Guggenheim-Jovanović-Freundlich, (k) Temkin, (l) Dubinin-Radushkevich, (m) Brunauer, Emmett and Teller.

The Freundlich isotherm is an empirical equation employed to describe heterogeneous systems (Freundlich 1906; Liu & Zhang 2015). The obtained values of 1/n showed the favourable nature of Cd(II) and RB adsorption and the heterogeneity of the adsorbent sites at the studied temperature. The data in Table 2 show the values of 1/n = 0.56 and 1/n = 0.59 while n= 1.8 and n= 1.7, indicating that the sorption of Cd(II) and RB unto FA-HDTMABr is favourable and the R2 values are 0.999 and 0.982 for Cd(II) and RB, respectively. Furthermore, adsorption firstly occurs on the high energy sites of sorbents followed by the low energy sites, which indicates that adsorption isotherm followed L-type curves (n > 1) (Baocheng et al. 2008).

Table 2

The values of isotherm adsorption parameters for the removal of Cd(II) and RB by FA-HDTMABr

IsothermParameterCd(II)RB
Freundlich
 
KF mg1–1/n ·L1/n ·g−1 35.9 21.8 
1.8 1.7 
R2 0.999 0.982 
χ2/DoF 0.38 6.4 
Langmuir
 
KL L·mg−1 1.9·10−2 1.3·10−2 
q mg·g−1 744 666 
R2 0.991 0.997 
χ2/DoF 3.3 1.0 
Generalized Langmuir and Freundlich
 
KLF L·mg−1 1.9·10−2 1.3·10−2 
q mg·g−1 11.3 4.9 
1.5·10−2 7.3·10−3 
R2 0.988 0.996 
χ2/DoF 4.4 1.4 
Redlich-Peterson KR L·g−1 92.2 7.2 
aR (L·mg−1)βR 1.9 7.2·10−4 
βR 0.5 1.5 
R2 0.999 0.999 
χ2/DoF 0.38 0.54 
Jovanović
 
KJ L·mg−1 2.4·10−2 1.6·10−2 
q mg·g−1 539 501 
R2 0.990 0.998 
χ2/DoF 0.04 0.67 
Extended Jovanović KJE L·mg−1 9.6·104 1.3·103 
q mg·g−1 539 501 
4.0·106 8.0·105 
R2 0.986 0.997 
χ2/DoF 4.9 0.89 
Tóth
 
KTh (L·mg−1)Th 12.9 0.098 
q mg·g−1 5.3 103 
Th 0.47 0.60 
R2 0.999 0.992 
χ2/DoF 0.33 4.4 
Halsey
 
Kh mgn−1·g−n·L 2.0·10−3 1.0·10−3 
3.6·10−4 5.4·10−4 
R2 0.914 0.880 
χ2/DoF 31.2 41.7 
Frumkin-Fowler-Guggenheim KFFG L·g−1 9.5 12.1 
q mg·g−1 25 74 
αFFG 60.6 85.3 
R2 0.013 0.023 
χ2/DoF 82 86 
Fowler-Guggenheim-Jovanović-Freundlich KFGJF L·g−1 87.6 58.7 
q mg·g−1 201 153 
αFGJF 856 643 
962.1 893.6 
R2 0.012 0.022 
χ2/DoF 1.2·103 7.8·102 
Temkin  KT L·g−1 3.63 0.84 
βT J·mol−1 66 76 
38 33 
R2 0.846 0.841 
χ2/DoF 69.9 69.4 
Dubinin-Radushkevich
 
KDR mol2·kJ−2 1.1·10−7 4.9·10−7 
q mg·g−1 121.5 101.5 
E kJ·mol−1 2.1 1.0 
R2 0.676 0.625 
χ2/DoF 0.013 0.015 
Brunauer, Emmett and Teller KBET L·g−1 – – 
q mg·g−1 – – 
R2 0.331 0.312 
χ2/DoF 1.9·10−11 4.7·10−9 
IsothermParameterCd(II)RB
Freundlich
 
KF mg1–1/n ·L1/n ·g−1 35.9 21.8 
1.8 1.7 
R2 0.999 0.982 
χ2/DoF 0.38 6.4 
Langmuir
 
KL L·mg−1 1.9·10−2 1.3·10−2 
q mg·g−1 744 666 
R2 0.991 0.997 
χ2/DoF 3.3 1.0 
Generalized Langmuir and Freundlich
 
KLF L·mg−1 1.9·10−2 1.3·10−2 
q mg·g−1 11.3 4.9 
1.5·10−2 7.3·10−3 
R2 0.988 0.996 
χ2/DoF 4.4 1.4 
Redlich-Peterson KR L·g−1 92.2 7.2 
aR (L·mg−1)βR 1.9 7.2·10−4 
βR 0.5 1.5 
R2 0.999 0.999 
χ2/DoF 0.38 0.54 
Jovanović
 
KJ L·mg−1 2.4·10−2 1.6·10−2 
q mg·g−1 539 501 
R2 0.990 0.998 
χ2/DoF 0.04 0.67 
Extended Jovanović KJE L·mg−1 9.6·104 1.3·103 
q mg·g−1 539 501 
4.0·106 8.0·105 
R2 0.986 0.997 
χ2/DoF 4.9 0.89 
Tóth
 
KTh (L·mg−1)Th 12.9 0.098 
q mg·g−1 5.3 103 
Th 0.47 0.60 
R2 0.999 0.992 
χ2/DoF 0.33 4.4 
Halsey
 
Kh mgn−1·g−n·L 2.0·10−3 1.0·10−3 
3.6·10−4 5.4·10−4 
R2 0.914 0.880 
χ2/DoF 31.2 41.7 
Frumkin-Fowler-Guggenheim KFFG L·g−1 9.5 12.1 
q mg·g−1 25 74 
αFFG 60.6 85.3 
R2 0.013 0.023 
χ2/DoF 82 86 
Fowler-Guggenheim-Jovanović-Freundlich KFGJF L·g−1 87.6 58.7 
q mg·g−1 201 153 
αFGJF 856 643 
962.1 893.6 
R2 0.012 0.022 
χ2/DoF 1.2·103 7.8·102 
Temkin  KT L·g−1 3.63 0.84 
βT J·mol−1 66 76 
38 33 
R2 0.846 0.841 
χ2/DoF 69.9 69.4 
Dubinin-Radushkevich
 
KDR mol2·kJ−2 1.1·10−7 4.9·10−7 
q mg·g−1 121.5 101.5 
E kJ·mol−1 2.1 1.0 
R2 0.676 0.625 
χ2/DoF 0.013 0.015 
Brunauer, Emmett and Teller KBET L·g−1 – – 
q mg·g−1 – – 
R2 0.331 0.312 
χ2/DoF 1.9·10−11 4.7·10−9 

The obtained results indicated that the surface of FA-HDTMABr had a stronger affinity to Cd(II) ions than to dye cations. The selectivity sequence of metal and dye is generally explained on the basis of properties of the ion size, such as the smallest hydrated ionic radii (4.26 Å) and RB cation weight. It is possible that Cd(II) ions with fewer weakly bonded water molecules tended to move faster to potential adsorption sites on FA-HDTMABr, compared to the RB cations with higher ionic radii (Sočo & Kalembkiewicz 2016).

The Langmuir isotherm is often used to describe the adsorption of solutes from liquid solutions and the model assumes monolayer adsorption onto a homogeneous surface with a finite number of identical sites (Langmuir 1916; Baocheng et al. 2008; Liu & Zhang 2015). The adsorption parameters obtained from this model are given in Table 2. The maximum monolayer adsorption capacity q of the FA-HDTMABr was unaffected at pH 9, but decreased at lower pHs, and was found to be 744 and 666 mg·g−1 for Cd(II) and RB respectively.

The generalized Langmuir-Freundlich (LF) isotherm (Umpleby et al. 2001) is a function that describes a specific relationship between the qe and Ce in heterogeneous systems with three fitting coefficients: q, KLF, and n. In contrast to the heterogeneous Freundlich isotherm, the Langmuir–Freundlich model has the advantage that it does not require an independent measure of the total number of binding sites q, which is very difficult to measure in heterogeneous sorbent. The total number of binding sites q of the FA-HDTMABr was found to be 11.3 and 4.9 mg·g−1 for Cd(II) and RB respectively. The obtained values of n: 1.5·10−2 and 1.3·10−2 for Cd(II) and RB, respectively, indicated that the FA-HDTMABr is heterogeneous sorbent.

The Redlich-Peterson (R-P) isotherm contains three parameters and is an improvement over the Langmuir and Freundlich isotherm. It can be applied in homogenous as well as heterogeneous systems (Alver & Metin 2012; Anirudhan & Ramachandran 2015; Bedin et al. 2016). Examination of the data showed that the R-P isotherm provided appropriate descriptions of the data for Cd(II) sorption on the FA-HDTMABr in the studied concentration range (χ2/DoF = 0.38; R2 = 0.999). The R-P constant βR normally varies between 0 and 1, indicating favorable adsorption. At high concentrations (βR0) the R-P model approaches the Freundlich isotherm and at low concentrations (βR1) it approaches the Langmuir isotherm. As can be seen in Table 2, the value of βR was in this range (0.5) only for Cd(II). The adsorption sequence was found to be in the order of increasing molecular weight and ionic radius, i.e. Cd(II) > RB.

The model of an adsorption surface considered by Jovanović (Jovanović 1969) is essentially the same as that considered by Langmuir. Figure 5(e) and 5(f) show the comparison of the experimental data (Jovanović and Extended Jovanović (JE) model). The values for the Jovanović model were lower than for the JE model. The JE isotherm takes into account the adsorption intensity (1/n); it also indicates the relative distribution of the energy and the heterogeneity of the adsorbate sites.

The Dubinin–Radushkevich (D-R) isotherm (Foo & Hameed 2010) is applied to express the adsorption mechanism (Gunay et al. 2007) with a Gaussian energy distribution onto a heterogeneous surface (Dąbrowski 2001). The D-R model has often fitted high-concentration data well, but has poor properties at low concentrations of metal ions. The calculated mean free energy E per molecule of adsorbate is usually applied to distinguish the physical and chemical adsorption of metal ions (Ӧzdemir et al. 2006). The D-R isotherm at different temperatures is plotted as a function of the logarithm of the amount adsorbed vs the square of potential energy because this model is dependent on temperature (Foo & Hameed 2010). The experimental data for sorption of Cd(II) and RB do not correlate as well with the D-R model and this is confirmed by the error parameter shown in Table 2. The value of free energy was between 1 and 8 kJ·mol−1; on the basis of linear plot of the D-R model, E was determined at 2.1 kJ·mol−1 and 1.0 kJ·mol−1 for Cd(II) and RB respectively, indicating that physisorption may play a significant role in the adsorption process (Ho et al. 2002; Liu & Zhang 2015). The typical bonding energy range for the ion-exchange mechanism is in the range of 8–16 kJ·mol−1 (Ho et al. 2002). The obtained maximum content of sorbate in FA-HDTMABr at the sorption equilibrium was 121.5 mg·g−1 (R2 = 0.676) and 101.5 mg·g−1 (R2 = 0.625) for Cd(II) and RB, respectively.

The Temkin isotherm (Temkin & Pyzhev 1940) contains a factor taking into account adsorbent-adsorbate interactions. The model describes the adsorption heat as a function of the temperature of all molecules in the layer that decreases linearly rather than in a logarithmic way (Foo & Hameed 2010). The Temkin isotherm fits the gas phase equilibrium well, but this model is not appropriate to express the adsorption process in the liquid systems (Kim et al. 2004). From the linear plot of the Temkin model (Figure 5(k)), the free energy was determined to be 66 J·mol−1 and 76 J·mol−1 for Cd(II) and RB respectively, indicating a physisorption process and the R2 = 0.846 and R2 = 0.841 higher than that of the D-R isotherm.

The Frumkin-Fowler-Guggenheim (FFG) and Fowler-Guggenheim-Jovanović-Freundlich (FGJF) equations have been defined and applied to adsorption, where αFFG and αFGJF indicate the number of interacting molecules (interaction energy) (Kurth et al. 2005). For the studied system (Cd(II) and RB), when the values of surface coverage were calculated using the Langmuir or L-F maximum adsorption capacities, the FFG and FGJF models were unable to simulate the experimental results of the adsorption isotherms. The isotherms using the equation of FFG and FGJF are shown in Figure 5(i) and 5(j).

Multilayer adsorption isotherms are suitable for proving the heteroporous nature of adsorbent. One example is the Tóth isotherm model, which has been applied for modeling of several multilayer and heterogeneous adsorption systems (Tóth 1971; Hamdaouia & Naffrechoux 2007; Bedin et al. 2016). The parameter Th characterizes the heterogeneity of the adsorption system and when Th = 1, this equation reduces to the Langmuir isotherm equation. The model assumes asymmetrical quasi-Gaussian energy distribution, with most sites having a sorption energy lower than the maximum peak or mean value (Ho et al. 2002). The application of this isotherm is best suited to multilayer adsorption similar to Halsey (Halsey 1952; Gholitabar & Tahermansouri 2017) and Brunauer–Emmett–Teller (BET) (Brunauer et al. 1938). The BET model is a theoretical equation, most widely applied in gas-solid equilibrium systems, but its extended model can be also related to the liquid–solid interface (Foo & Hameed 2010). The researched equations are based on a kinetic principle assuming that the adsorption sites increase exponentially with adsorption, which implies multilayer adsorption. The values of (Table 2) for the Halsey, BET and Tóth models are high in comparison to other models, suggesting that the multilayer model could not describe the experimental data satisfactorily for the adsorption of Cd(II) and RB on FA-HDTMABr.

The comparison of the obtained values indicated that the Langmuir, Jovanović and R-P models are best to fit Cd(II) and RB adsorption on the FA-HDTMABr. As shown in Figure 5(b), 5(d) and 5(e) and Table 2, this confirms the good fit of the researched isotherms with the experimental data for removal of Cd(II) and RB from the aqueous solution. These models show a high degree of correlation with low reduced chi-square values. On the basis of error values obtained for both sorbates of the considered isotherms, the fitting degree follows the following sequence: Langmuir > Jovanović > R-P > Tóth > Freundlich > L-F > JE > Halsey > Temkin > D-R > FFG > FGJF > BET. The D-R approach was applied to distinguish the physical and chemical adsorption of Cd(II) and RB on the basis of its mean free energy per mole of FA-HDTMABr. The energy value obtained according to this model (2.1 kJ·mol−1 and 1.0 kJ·mol−1 for Cd(II) and RB) was less than 8.0 kJ·mol−1. This result indicates that the adsorption of Cd(II) and RB onto FA-HDTMABr follows the physisorption process. As can be inferred from the data calculated in Table 2, the value of the maximum monolayer adsorption capacity q on the FA-HDTMABr for both sorbates from the Langmuir model was very close to the experimental value and was found to be 744 and 666 mg·g−1 for Cd(II) and RB respectively. The maximum monolayer adsorption capacity values of various low-cost adsorbents have been reported in the literature. A comparison between these values and the obtained results for FA-HDTMABr show a reasonable adsorption efficiency and therefore that it can be used as a good and inexpensive adsorbent for removal of Cd(II) and RB from aqueous solution.

CONCLUSIONS

The particle surface of FA-NaOH showed the transformation of fly ash into a zeolite-like structure. The modification process by HDTMABr did not crystallize it but attached to the FA-NaOH surface. The obtained results showed that FA-HDTMABr is a more effective adsorbent than fly ash. Kinetic studies demonstrated that the mechanism for adsorption of Cd(II) and RB followed the PSO rate model, providing the best fit for the experimental data. The intra-particle diffusion model suggested that the initial adsorption rate was controlled by film diffusion, followed by pore diffusion or external mass transfer effects. The mechanism of Cd(II) ions and RB dye sorption includes ion-exchange and surface adsorption. The adsorption equilibrium was described well by the Langmuir, Jovanović and R-P isotherms. It can be concluded that FA-HDTMABr can be used for the removal of Cd(II) and RB from solution, with a maximum uptake of 744 and 666 mg·g−1 respectively. The obtained results suggest that the chemical enhancement of fly ash from coal combustion modified by NaOH and next by HDTMABr was an effective and economically feasible material and a promising way of enhancing the inhibition of Cd(II) and RB mobility in polluted waters.

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