Kinetic and equilibrium modelling of adsorption of cadmium on nano crystalline zirconia using response surface methodology

Accepted Manuscript Title: Kinetic and equilibrium modelling of adsorption of cadmium on nano crystalline zirconia using response surface methodology Author: Deepak Gusain Prabhat Kumar Singh Yogesh C. Sharma PII: DOI: Reference:

S2215-1532(16)30021-6 http://dx.doi.org/doi:10.1016/j.enmm.2016.07.002 ENMM 50

To appear in: Received date: Revised date: Accepted date:

30-4-2016 8-7-2016 11-7-2016

Please cite this article as: Deepak Gusain, Prabhat Kumar Singh, Yogesh C.Sharma, Kinetic and equilibrium modelling of adsorption of cadmium on nano crystalline zirconia using response surface methodology, Environmental Nanotechnology, Monitoring and Management http://dx.doi.org/10.1016/j.enmm.2016.07.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

1 2 3

Kinetic and equilibrium modelling of adsorption of cadmium on nano crystalline zirconia using response surface methodology

4

Deepak Gusain1, Prabhat Kumar Singh2, Yogesh C. Sharma1*

5

1

Department of Chemistry,

6

2

Department of Civil Engineering,

7

Indian Institute of Technology (BHU) Varanasi, Varanasi 221 005, India.

8 9 10 11 12

*Corresponding author E Mail [email protected]; Tel 91 542 6702865; Fax 91542 6702876

13 14 15 16 17 18

Highlights     

A novel nanoadsorbent, nano zirconia was synthesized and characterized The process parameters were optimized by response surface methodology(RSM) Removal of Cd by nanoadsorbent was significant The nanoadsorbent could be regenerated and reused several times to cut the cost of treatment Process could be used for other metallic contaminants

19 20

Abstract

21

Nano zirconia has been employed for adsorption of cadmium from aqueous solution. Adsorption

22

parameters were optimized using Box-Behnken design. Adsorption parameters Initial

23

concentration, adsorbent dose and temperature were optimized. Optimized conditions were found

24

out at initial concentration = 1 ppm, adsorbent dose = 4 g/l and pH =7. The best-fit equations of

25

linear and non-linear forms of kinetics and isotherm models were compared among themselves.

26

Results exhibit that chi-square reduction method in Microcal origin curve fitting tool is better

27

than Error analysis method of solver add in for determination of isotherm parameters. However,

28

linear model explains the system best fit on the basis of R2adj in isotherm analysis. Experimental

29

qe values were slightly closer to theoretical q e values in linear pseudo-second order model as

30

compared to pseudo-first order non linear model. The system follows Langmuir isotherm model

31

and pseudo-second order model. Thermodynamic parameter by partition and Langmuir constant

32

method suggests that the system is spontaneous in nature. 1

33

Keywords: BBD-RSM; Isotherm, Kinetics; Nano iron oxide/ hydroxide; Thermodynamics

34

1. INTRODUCTION

35

Human body requires a few heavy metals like copper and zinc for normal metabolic activity of

36

the body. But at higher concentration these heavy metal are of grave concern to the human health

37

(Zhang et al., 2013). But, few heavy metals like cadmium mercury and lead are toxic even at

38

low concentration (Zhang et al., 2013). Itai-itai disease occurred in Japan in 1950s due to the

39

cadmium which led to studies related to its ill effects on bone and kidney (Zhang et al., 2014).

40

Cadmium is used in number of industries like metal plating, manufacturing of Ni-Cd batteries

41

and pigments application of phosphatic fertilizers, by product of mining and smelting of lead and

42

zinc (De Lurdes Dinis and Fiúza, 2011; Boparai et al., 2013b). The aqueous solutions from

43

aforementioned industry contains elevated metal concentration harmful to the aquatic

44

environment and human health (Regmi et al., 2012).Cadmium finds its way from aquatic

45

environment into the human body. Cadmium causes liver dysfunction, hypertension and act as

46

endocrine disruptor, teratogen, carcinogen, mutagen (Gloria et al., 2011; Ali et al., 2013).

47

To resolve the issues associated with cadmium a number of techniques applied, a few of them

48

are precipitation (Rojas, 2014),electro coagulation (Vasudevan et al., 2011), ion exchange

49

(Elkady et al., 2011a), reverse osmosis, nano filtration (Kheriji et al., 2015) and adsorption

50

(Boparai et al., 2013a; Luo et al., 2013; Venkatesan et al., 2014; Yaacoubi et al., 2014). In the

51

current study adsorption is used for abatement of cadmium from aqueous solution using nano

52

crystalline zirconia. Adsorption removes contaminant even at very low concentration. Maximum

53

contaminant level goal (MCLG) for cadmium is 0.005 mg/l (Sheftel, 2000). Hence adsorption is

54

used for current study. A number of adsorbents used for remediation of cadmium from water

55

like magnetite/maghemite (Chowdhury and Yanful, 2013), mesoporous silica, activated carbon

56

(Machida et al., 2012),Cerium oxide, Titanium oxide (Contreras et al., 2012). Present study use

57

nano crystalline zirconia for removal of cadmium. Zirconia is chemical inert and biocompatible

58

(Manicone et al., 2007; Gusain et al., 2014a). The fluorescence enhancement was used to

59

distinguish phases of nanomaterials(Meng and Ugaz, 2015). But here, XRD is used to identify

60

phases of synthesized nanocrystalline zirconia. Linear and non linear regression is frequently

61

used to determine the isotherm parameters. Error distribution gets altered by linearization of the

62

non linear equation (Gusain et al., 2014b). Hence, scholars are using non linear equations. 2

63

Current study deals with the use of both linear and non linear equations for their comparative

64

analysis. Non linear analysis was also conducted using error analysis by Microsoft excel Solver

65

add in (Gusain et al., 2014b) and Microcal origin curve fitting tool (Czinkota et al., 2002).

66

2. MATERIAL AND METHODS

67

K2Cr2O7, ZrOCl2.8H2O, NH4OH purchased from Merck India. Tubular Furnace (IKON),

68

Analytical balance (VIBRA), pH meter (IKON) distilled water, X ray diffraction ( MINIFLEX

69

II, Desktop XRD, RIGAKU) , DTA/TGA (Labsys™ TG–DTA 16, SETARAM Instrumentation),

70

Scanning electron microscope (Quanta 200 f, FEI), Transmission electron microscope (TECNAI

71

G2, FEI)

72

(Szhimadzu AA 7000) , Fourier transform Infrared spectroscopy (PerkinElmer Version 10.03.05)

73

were instruments used to characterize and perform the experiments.

water bath shaker (Narang scientific), atomic adsorption spectrophotometer

74 75

2.1.Design of Experiments

76 77

Conventionally experiments were conducted by variation of one variable at a time. Recently a

78

number of experimental designs were used like ANN (artificial neural network) and RSM

79

(response surface methodology) for adsorption. In the current study RSM is used to evaluate the

80

effect of parameters on the percentage removal of cadmium. RSM contains two designs one is

81

Box-Behnken design (BBD) and other one is Central composite design (CCD In the current

82

experiment BBD is used. The BBD have 3 degrees of freedom (-1, 0, +1). The three parameters

83

were studied in the BBD i.e. pH, Dose, Concentration.

84

The relationship between coded and non coded parameters

85

(Montgomery, 2012):

86

CODED VALUE = Xi–Xn/ΔX

87

Here Xi is the value of uncoded value of ith factor Xn is the midway average value of low and

88

high, ΔX is the step change. The total number of experiments was 20.

is represented as follows

(1)

3

89 90

Table 1 Level of variables chosen for BBD in adsorptive removal of cadmium utilizing nano crystalline zirconia Factors

Units

Coded value

Initial Concentration(X1) pH(X2) Adsorbent dose (X3)

ppm g/l

-1

0

+1

1 4 4

5.5 5.5 6

10 7 8

91 92

A second order polynomial is used to explain the relationship between the response and input

93

variables (Gusain et al., 2014a).

94

Y = β0 + ⅀ βi xi2 + ⅀ βii xi2 + ⅀⅀ βij xi xj + €r

95

Y is the predicted response, i and j varies from 1 to the number of independent process variables.

96

β0, βi, βii, βij were the offset term, linear effect, square effect and interaction effect calculated by

97

the least squares method, €r is the error of prediction and Xi and Xj are coded independent

98

process variables (Gusain et al., 2014a).

99

2.2.Batch experiments

(2)

100

Batch adsorption experiments were carried out to assess the removal efficacy of nano crystalline

101

zirconia for cadmium removal from aqueous solutions. In the batch experiments, a stock solution

102

of 1000 ppm of cadmium was prepared by dissolving CdCl2 and standardizing it with atomic

103

absorption spectrophotometer. Cadmium solution is further diluted in distilled water to make

104

working solutions of desired concentrations. HCl and NaOH with a strength of 0.1N used to

105

maintain the initial pH of the solution. Experiments with conditions suggested by Box-Behnken

106

with 50ml volume conducted. Thereafter, the sample was separated from the solution by

107

centrifugation (REMI PR 24) at 10000 rpm for 10 min. The residual concentrations of Cd in each

108

aliquot were analyzed with atomic adsorption spectrophotometer.

109

Adsorbed amount of cadmium is calculated by following expression (Srivastava and Sharma,

110

2013)

111

qe = (Ci - Ce) *V/M

(3) 4

112

The qe is the amount adsorbed on per unit mass of the adsorbent (mg g-1), Ci and Ce (both in

113

ppm) are the initial and the equilibrium concentration respectively; V and W are volume of

114

adsorbate solution (L) and the weight of adsorbent (g) respectively. Percentage removal of Cd

115

was calculated by applying following equation (Srivastava and Sharma, 2013)

116

% Removal of metallic ions =

(Ci - Ce / Ci) *100

(4)

117 118 119

2.3.Regeneration experiments

120

Regeneration studies were performed at room temperature. First cadmium adsorption was

121

conducted on adsorbent at following condition (initial concentration 5 ppm, pH = 7, Adsorbent

122

dose = 8 g/l). Afterwards it has been stirred at room temperature for two hours. Adsorbent was

123

then separated and dried in oven. Following this cadmium was desorbed by taking 1000 ml of

124

regenerating solution in a beaker along with cadmium loaded adsorbent. It has been stirred at 350

125

rpm on magnetic stirrer and then dried and in oven

126 127

2.4.Process and parameter determination

128

Isotherm and parameter determination were executed linear and non linear methods. Error

129

function analysis using solver add in (Gusain et al., 2014b) and curve fitting function of Microcal

130

origin were used as non linear method. The sum of the square of the errors (ERRSQ), Hybrid

131

fractional error function (HYBRID), Marquardt’s percent standard deviation (MPSD), The

132

average relative error (ARE), The sum of the absolute errors (EABS) were the error function

133

employed in error function analysis. Non-linear curve fitting for isotherm and kinetic parameter

134

determination using Microcal origin was done by customizing a non linear function for isotherm

135

and kinetic model. The parameters in Microcal origin were estimated by reducing the difference

136

between estimated values and experimental values using iteration by application of chi-square

137

minimization method (Andrae et al., 2010). The initial parameters were initially set as 1. The

138

Levenberg-Maquardt (LM) algorithm (Hagan and Menhaj, 1994) was used to adjust parameter

139

values in iterative process.

140

The square of correlation coefficient is investigated as an indicator of isotherm and kinetic model 5

141

suitability. The value of the square of correlation coefficient varied from 0 to 1 (Mendenhall et

142

al., 2012).

143

r2 = S(XY) / S(XX) S(YY)

(5)

144 145

Here, S(XY) designates the sum of squares of X and Y, S(XX) as the sum of the squares of X and

146

S(YY) as the sum of squares of Y.

147

Thermodynamic parameters especially free energy were also determined by partition method and

148

Langmuir constant method (Salvestrini et al., 2014).

149

3. RESULTS AND DISCUSSION

150

3.1.Characterization of nano crystalline zirconia

151 152

Figure 1 XRD of sample , tetragonal zirconia (crystal diffract file), monoclinic zirconia

153

(database_code_amcsd 0009231)

154

XRD depicted two phases of nano crystalline zirconia monoclinic 28.1 ( 1 11), 31.4 (111)

155

(JCPDS card no. 78- 1807) and tetragonal 30.2o (101), 50.2o (112) and 60.2o (211) (JCPDS card

156

no. 79- 1769). The peaks at 2θ c.a. 28.29o, c.a. 31.56o and c.a. 34.32o, c.a. 49.41o, c.a. 50.22o

157

were matched with nano crystalline zirconia. The crystallite size was calculated by using Scherer

158

formula:

6

Crystalline size = Kλ/ W cosθ

159

(6)

160 161

Here K (shape factor) 0.9,

λ (1.5414 Å) is wavelength of X-ray used, W= (Wb - Ws) line

162

broadening measured at half of height (FWHM), and θ is angle of reflection. Crystallite sizes of

163

monoclinic zirconia were 13.4 nm (28.1°), and 8.5 nm (31.4°). Similarly, the crystallite size was

164

also calculated by Scherrer formula and the sizes were 13.3 nm (30°), 6.3 nm (50°) and 7.6 nm

165

(60°).

166 167

Figure 2. FTIR and TEM image of synthesized nano crystalline zirconia

168 169

FTIR analysis 2A of the sample depicted -OH physioadsorbed water (c.a. 1600 cm-1 and c.a.

170

1380 cm-1 and3400 cm-1) (Guo and Chen, 2005; Tyagi et al., 2006; Deshmane and Adewuyi,

171

2012; Goharshadi and Hadadian, 2012). Peaks at 750 and 500 cm-1 indicate the presence of Zr -

172

O2 - Zr bond (Ranjan Sahu and Ranga Rao, 2000).

173

TEM analysis conducted to assess the particle size and aggregation of the adsorbent (2B)

174

(reprinted from DOI:doi:10.1016/j.molliq.2014.04.026). All particles were found to be

175

agglomerated and irregular in shape. Average particle size is c.a. 13 nm. The pHZPC has been

176

determined to examine the surface charge properties of adsorbent material and was found to be

177

6.78. SEM analysis (Figure 3) depicts irregular shape of the nano crystalline zirconia (reprinted

178

from DOI:doi:10.1016/j.molliq.2014.04.026). The surface of particle is rough and size of particle

179

is 3-5 μm. The larger size is due to the agglomeration of crystallites.

180

7

181

182 183

Figure 3. SEM image of synthesized nano crystalline zirconia

184 185

3.2.Data analysis and construction of regression model

186

Regression analysis in coded terms of the experimental data yielded the following regression

187

equation for the percentage removal of cadmium:

188

Y = 50.65-13.79 (X1) + 28.998 (X2) + 3.3653 (X3) + 2.3753 (X1)2 + 2.2484 (X2)2 - 8.6067 (X3)2 -

189

12.3116 (X1 x X2) + 0.3084 (X1 x X3) - 0.5966 (X2 x X3)

190

The final empirical model in terms of actual parameters (uncoded) is written in general form as

191

follows:

192

8

(7)

193

Table 2 Box Behnken designed experimental runs for removal of cadmium utilizing nano crystalline zirconia Run order

Initial Concentration

pH

Adsorbent dose

Percentage Removal

1 2 3 4 5 6 7 8 9 10 11 12

1 10 1 10 1 10 1 10 1 10 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5

4 4 7 7 4 4 7 7 5.5 5.5 4 7 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5

4 4 4 4 8 8 8 8 6 6 6 6 4 8 6 6 6 6 6 6

12.90 14.83 100.00 47.93 20.04 18.45 100.00 53.92 75.75 35.66 28.40 82.75 36.27 53.18 47.73 51.54 49.00 48.00 49.00 48.00

13 14 15 16 17 18 19 20

194 195

Y= -153.198+ 5.47124 (Initial concentration) + 19.5648 (pH) + 28.4080 (Adsorbent dose) +

196

0.117299 (Initial concentration*Initial concentration) +0.999272 (pH*pH) -2.15167 (Adsorbent

197

dose*Adsorbent dose) – 1.82394 (Initial concentration*pH) + 0.0342694 (Initial concentration*

198

Adsorbent dose) - 0.198858 (pH*Adsorbent dose)

199

3.3.Regression and Analysis of variance (ANOVA)

200

Regression coefficient (R2) value more than 80% depicts good fit of the regression model. In this

201

current study, R2value was 97.87and R2 (Adjusted) was found to be 95.96. Aforementioned R2

202

value suggests that the quadratic model is valid for adsorption of cadmium on nano crystalline

203

zirconia. Terms having probability value more than 0.05 considered to be non – significant. Only

204

pH and concentration and their interaction have value of p less than 0.05. Hence, pH and

205

concentration were considered as significant factors affecting the adsorption process. The pH and

206

adsorbent dose have positive sign afore to its coefficient. Positive sign afore to pH and dose 9

(8)

207

Table 3 Estimated Regression Coefficients for removal of cadmium using zirconia Term

Coef

Constant Conc pH Dose Conc*Conc pH*pH Dose*Dose Conc*pH Conc*Dose pH*Dose

SE Coef

50.6591 -13.7903 28.998 3.3653 2.3753 2.2484 -8.6067 -12.3116 0.3084 -0.5966

T

1.744 1.605 1.605 1.605 3.06 3.06 3.06 1.794 1.794 1.794

P

29.042 -8.594 18.072 2.097 0.776 0.735 -2.813 -6.863 0.172 -0.333

0 0 0 0.062 0.456 0.479 0.018 0 0.867 0.746

S = 5.07405 PRESS = 1875.84 R-Sq = 97.87% R-Sq(pred) = 84.52% R-Sq(adj) = 95.96%

208 209

depicts that percentage removal of cadmium increased with increase in pH and adsorbent dose.

210

Strength of a particular variable is assessed by the magnitude of the coefficient, among all of

211

factors pH was most dominating factor followed by concentration and dose.

212

Table 4 Analysis of Variance for removal of cadmium using zirconia Source

DF

Seq SS

Adj SS

Adj MS

Regression Linear Conc pH Dose Square Conc*Conc

9 3 1 1 1 3 1

11857.2 10423.8 1901.7 8408.8 113.3 217.1 10.4

11857.2 10423.8 1901.7 8408.8 113.3 217.1 15.5

1317.46 3474.6 1901.71 8408.85 113.26 72.38 15.52

51.17 134.96 73.86 326.61 4.4 2.81 0.6

0 0 0 0 0.062 0.094 0.456

pH*pH Dose*Dose

1 1

3.1 203.7

13.9 203.7

13.9 203.71

0.54 7.91

0.479 0.018

Interaction Conc*pH

3 1

1216.2 1212.6

1216.2 1212.6

405.4 1212.6

15.75 47.1

0 0

Conc*Dose pH*Dose

1 1

0.8 2.8

0.8 2.8

0.76 2.85

0.03 0.11

0.867 0.746

Residual Error Lack of Fit

10 5

257.5 247.5

257.5 247.5

25.75 49.5

24.82

0.002

Pure Error Total

5 19

10 12114.6

10

1.99

213 10

F

P

214

The ANOVA is applied to check the acceptability of the applied model. ANOVA (Table 4)

215

suggested the same results as by the regression model. The pH was most dominating factor

216

suggested by highest Sequential sum of squares (8408.8) followed by concentration (1901.7)

217

and dose (113.3).

218

3.4.Effect of pH

219

The pH was the most dominating factor affecting the removal of cadmium. The effect can be

220

clearly seen by comparison of experimental run1; 3 and 2; 4. The percentage removal increases

221

from 12.9 to 100% with rose of pH from 4 to 7 at 1 ppm and adsorbent dose of 4 g/l. The

222

decrease in the pH of the solution positive charge on the surface of the adsorbent elevated. Hence

223

electrostatic charge on the surface decreased between adsorbate and adsorbent.

224

3.5.Effect of adsorbent dose

225

Adsorbent dose was the least dominating factor for removal of cadmium from aqueous solution.

226

There is only slight change in the percentage removal of cadmium on changing adsorbent dose

227

(run 1:5 and run 2:6 in Table 2).

228

3.6.Effect of initial concentration

229

Initial concentration was next dominating factor after pH. The availability of the active sites on

230

the surface of the adsorbent is limited. At low initial concentration adsorbate were few in

231

numbers compare to number of active sites. Hence, there is large percentage removal at lower

232

initial concentration. At higher concentration the numbers of active sites were few in number as

233

compared to adsorbate species. So, only few adsorbate species were able to occupy the active

234

sites. This led to decrease in the percentage removal of the cadmium with increase of initial

235

concentration.

236

3.7.Confirmation experiments

11

237 238

Figure 4. Optimization plot of removal of cadmium using nano crystalline zirconia

239

Optimization results (Figure 4) suggested by the model for cadmium removal were as follows

240

initial concentration =1, initial pH =6.7, adsorbent dose = 5.2 g/l. The predicted response is

241

checked by the experimentation in addition to other confirmatory experiments. The predicted

242

responses were close to experimental results. However at pH of 5.5 and lower concentration

243

predicted response was far away from experimental results. It shows that the model is valid only

244

for higher pH above 6 only.

245 246

Table 5.Confirmation experiments for removal of cadmium using nano crystalline zirconia

247

S.No. 1. 2.

Conc 1 1

pH 5.5 5.5

Dose 4 8

3. 4. 5. 6 7

3 3 4 4 4

6 6.5 6.5 5.5 6

6 8 4 4 6

Experimental values 91.95

Predicted values 55.16

96.62 77.52 76.74 72.11 33.60

61.27 71.24 78.134 67.11 43.65

45.27 41.205

66.80 64.39

8 2 6 4 *Samples were outside the model data

12

248

Optimization of results (Table 6) was afterwards followed by varying pH, initial concentration

249

and adsorbent dose one by one and optimized condition were reached at initial concentration =1,

250

pH = 7 and adsorbent dose = 4 g/l.

251

Table 6 Cadmium optimization with nano zirconia S.No.

Conc

pH

Dose

Percentage Removal

1.

1

7

5.2

100

1

7

5

100

1 1

7 7

4 3

100 99.19

1 2

7 7

2 4

97.45 85.45

2. 3. 4. 5. 6. 7.

3

7

4

75.01

8.

4

7

4

75.94

9.

5

7

4

51.88

252 253

3.8.Desorption experiments

254

Hydrochloric acid (HCl), nitric acid (HNO3) and sulphuric acid (H2SO4) 0.1 N solutions were

255

used as desorbing agents for regeneration and reuse. The HCl, HNO3, H2SO4 show desorption

256

efficiency of 99.25 %, 91.75 % and 77.25% respectively. Among all the bases hydrochloric acid

257

showed the best result in regenerating the zirconia for reuse as an adsorbent for removal of

258

cadmium. Hydrochloric used as regenerating agent up to three cycles (Table 7).

259 260

261 262

Table 7 Cadmium removal after subsequent regeneration cycle S.No.

Regeneration cycle

Cadmium removal after regeneration cycle (percentage)

1

1st

69.16

2

2nd

52.48

3

3rd

51.65

Removal efficiency of cadmium after regeneration cycle (Initial conc. =5 ppm, pH = 7, Adsorbent dose = 4 g/l, Temperature =303 K)

263 264 13

265

3.9.Langmuir isotherm

266

Langmuir isotherm model assumes that adsorption of adsorbate molecules occurred on a

267

homogenous surface by monolayer adsorption and there is not any interaction between the

268

adsorbate (Al-Othman et al., 2012).Langmuir isotherm in its non linear form is represented as

269

follows (Sharma et al., 2014):

270 271

qe = b Qo Ce/(1+ b Ce )

(9)

272 273

Here Ce (mg/l) and qe (mg/g) are the equilibrium concentration of the solute and amount of

274

adsorbate at equilibrium respectively. Adsorption capacity and energy of adsorption are

275

represented by Qo (mg/g) and b (L/mg). The linear form of the model is described as (Yadav et

276

al., 2013):

277 278

Ce/qe = 1/Qo b + Ce/ Qo

(10)

279 280

Table 8 Langmuir and Freundlich isotherm parameter determination by linear and non linear Microcal

281

origin

Linear

Microcal origin

Langmuir

Fe Cd

Temp (K)

Qo (mg/g)

b (L/mg)

2

293 303 313

3.1886 3.1401 3.1883

8.5315 7.2536 6.5321

323 333

2.8659 2.5743

343 293

Freundlich 2

KF {(mg/g) (L/mg)1/n)

0.99246 0.99248 0.99496

0.9933 0.9933 0.9955

2.5772 2.4643 2.4878

5.0195 4.5241

0.99849 0.99093

0.9986 0.9920

2.5634

4.4623

0.98568

0.9874

3.1705

7.9353

0.9162

R

r

adj

R2adj

r2

0.2833 0.2968 0.3258

0.90923 0.93487 0.90483

0.925341 0.945274 0.921999

2.0585 1.7801

0.3064 0.3150

0.94571 0.87081

0.953967 0.896997

1.7754

0.3003

0.92309

0.936013

2.5458

0.2170

0.8894

1/n

0.9307

0.91053

303 313

3.1357 3.3595

6.7191 4.6345

0.9501 0.9282

0.9574 0.9400

2.4479 2.4822

0.2273 0.2419

0.8919 0.8258

0.9124 0.8659

323

2.8932

4.3329

0.9745

0.9778

2.0870

0.2425

0.9164

0.9309

333 343

2.5451 2.5143

4.9455 4.9436

0.9314 0.9143

0.9425 0.9292

1.8368 1.8190

0.2433 0.2441

0.8645 0.8961

0.8925 0.9154

282 14

283

3.10. Freundlich isotherm

284

Freundlich isotherm assumes that adsorption occurs on a heterogeneous surface. The equation

285

can be written in no linear form as follows (Dubey et al., 2013).

286 287

qe = KF Ce1/n

(11)

288 289

Table 9 Langmuir and isotherm parameter determination by error analysis method Langmuir

Freundlich parameters

Qo (mg/g)

b (L/mg)

R2adj

r2

1/n

R2adj

r2

1.0936

-1.7134

0.6304

293 K

ARE

3.3238

6.1596

0.8964

0.9242

ERRSQ

KF ({(mg/g) (L/mg)1/n)) 1.0704

303 K

ERRSQ

3.1358

6.7173

0.9042

0.9574

ERRSQ

1.0389

1.0697

-1.6352

0.6350

313 K

MPSD

3.3205

5.1380

0.8961

0.9383

EABS

1.0628

1.0461

-1.8573

0.6071

323 K

ARE

2.8959

4.2599

0.8946

0.9777

333 K

ERRSQ

2.5451

4.9456

0.9042

343 K

ARE

2.4627

5.8264

0.8961

Temp

0.9318

0.9274

-1.5499

0.6485

0.9425

ERRSQ HYBRID

0.8804

0.8191

-1.5962

0.6538

0.9264

HYBRID

0.8804

0.8194

-1.3911

0.6597

290 291

The linear form of the above equation is as follows:

292 293

log qe = log KF + (1/n) log Ce

294

KF and n are the Freundlich constants. Here, n giving a sign of how harmonious the adsorption

295

process is, and KF (mg/g (L/mg)1/n)represents the quantity of cadmium adsorbed on the adsorbent

296

for a unit equilibrium concentration.

(12)

297 298

3.11. Linear approach for isotherm analysis

299

Isotherm parameters revealed by linear curve fitting analysis are presented in Table 8.A graph

300

was plotted between Ce/qe and Ce. Langmuir constants Qo and b computed from slope and

301

intercept of the fitted curve. The exothermic nature of the adsorption system was depicted by

302

increasing value of Qo. Similarly, parameters of Freundlich isotherm i.e. KF and 1/n were

303

computed from the intercept and slope of linear fitted curve of log qe vs. log Ce respectively.

304

The r2 and R2adj was higher for Langmuir isotherm model as compared to Freundlich isotherm

305

model. Linear isotherm analysis suggest that adsorption of cadmium by nano crystalline zirconia

306

was better explained by Langmuir isotherm. 15

307

3.12. Non linear approach for isotherm analysis

308

The estimated isotherm parameters for non linear method calculated via using error analysis

309

method using Microsoft Solver add in and Microcal origin curve fitting tool. The estimated

310

isotherm parameters by non linear analysis presented in Table 8 and 9.

311

Error functions with minimum normalized sum of error selected as optimum error function. The

312

selected error function used for isotherm and parameter determination.

313

In Langmuir isotherm parameter determination three out of six systems were better explained by

314

ARE error function and rest two systems are explained by ERRSQ and one by MPSD. In

315

Freundlich isotherm resulted three systems out of six systems were better explained by ERRSQ

316

and one system by EABS error function and two systems jointly by HYBRID. Coefficient of

317

determination (R2adj) and r2 values of error function suggested Langmuir isotherm model

318

appropriateness for determination of model. Non linear analysis was also performed using curve

319

fitting function of Microcal origin. The (R2adj) and r2 for Langmuir isotherm model fit better as

320

compared to the Freundlich isotherm model. Hence, the system follows Langmuir isotherm

321

model. The value of R2adj and r2 values was higher for linear analysis than non linear analysis

322

of Microcal origin software. Hence, linear analysis was used to determine isotherm parameters.

323 324

3.13. Adsorption kinetic studies

325

The information about rate of adsorbate uptake was provided by adsorption kinetic studies (Chen

326

and Li, 2010). Parameters obtained by kinetic modelling were helpful in design of adsorption

327

processes by control of residual uptake. Pseudo-first order and second order kinetic models used

328

in the present study to analyze the kinetics of adsorption.

329 330

3.13.1. Pseudo-first order model

331

The linear pseudo-first order kinetic model expressed by the following equation (Srivastava et

332

al., 2015):

333

ln (qe - q) = ln qe – k1t

334

Equation can be written in non linear form as follows:

335

qt = qe (1- exp (-k1t))

(13)

(14)

336 337 16

338

Table 10 Kinetic parameter determination by linear analysis and non linear analysis by Microcal origin Pseudo-first order

R2adj

r2

4.9808

0.9993

0.9995

0.5031

2.6768

0.9987

0.9838

0.8384

0.5000

2.2072

0.9972

0.9903

0.7988

0.8459

0.4314

2.1791

0.9894

0.9974

0.0972

0.8674

0.8924

0.4856

1.0062

0.9820

0.9988

0.1431

0.1562

0.9578

0.9630

0.4566

2.6544

0.9996

0.9993

0.4899

0.4648

1.7580

0.4387

0.6602

0.4827

8.0832

0.8458

0.8761

303

0.4878

0.4554

1.3015

0.4167

0.6516

0.484

4.5868

0.8098

0.8515

313

0.4983

0.4585

0.7240

0.8377

0.8705

0.4958

2.4478

0.9279

0.9380

323

0.4415

0.3807

1.0153

0.4980

0.6848

0.4072

4.2784

0.7703

0.8260

333

0.4778

0.4039

0.5209

0.6657

0.7654

0.4513

1.6502

0.8516

0.8802

343

0.4445

0.4169

0.8669

0.8057

0.8487

0.4487

3.2459

0.9813

0.9831

Temp.

Microcal origin

R2adj

Experimental qe (mg/g)

qe

k1

(mg/g)

(min-1)

293

0.4899

0.0811

0.1234

0.9431

303

0.4878

0.1667

0.2011

313

0.4983

0.1451

323

0.4415

333

r2

qe

k2

(mg/g)

(g/mg/ min)

0.9145

0.4924

0.9032

0.9198

0.0970

0.7880

0.1368

0.0711

0.4778

0.2491

343

0.4445

293

(K) Linear

Pseudo-second order

339 340

Here k1 (min-1) is the pseudo-first order rate constant, qe and q are the amount of adsorbate

341

species adsorbed on adsorbent at equilibrium and at any time, t, respectively. The slope of the

342

graph between ‘log (qe - q) vs. t at different temperatures accounts to k1

343 344

3.13.2. Pseudo-second order kinetic model

345 346

Pseudo-second order model

347

#825;Wang, 2010 #995}.

in linear form is represented as follows {Al-Rashdi, 2012

348 349

t/qt = 1/ k2qe2 + (1/qe) t

350

The values of k2 and qe are acquired from the intercept and slope of the plot between t/qt vs. t.

351

Pseudo-second order model can be expressed non linearly as follows:

(15)

352 17

353

qt = qe2 K2 t / 1+ qe K2 t

354

Table 11 Kinetic parameter determined by Error analysis method

(16)

Pseudo-first order

Pseudo-second order

Temp

k1

qe

(K)

(min-1)

(mg/g)

R2adj

r2

k2

qe

(g/mg min)

(mg/g)

R2adj

r2

293

HYBRID

1.7803

0.4638

0.9340

0.9998

HYBRID

8.2343

0.4822

0.8397

0.8604

303

MPSD

0.9147

0.4679

0.9994

0.9995

ARE

4.0619

0.4912

0.7126

0.8534

313

MPSD

0.6096

0.4600

0.9997

0.9997

EABS

3.0183

0.4858

0.9092

0.9021

323

ARE

0.8464

0.3752

0.9996

0.9993

MPSD

6.1651

0.3947

0.8277

0.6708

333

EABS

0.5565

0.3894

0.9996

0.9990

EABS

1.7466

0.4339

0.9041

0.8428

343

ARE

0.8380

0.4168

0.9998

0.9998

HYBRID

3.3135

0.4478

0.9825

0.9827

355 356

3.13.3. Linear approach for kinetic model analysis

357

Kinetic parameters computed from linear and non linear analysis presented in Table 10 and 11.

358

Linear analysis of the data suggests that the system follows the pseudo-second order model. The

359

r2 and R2adj is high for pseudo-second order model as compared to pseudo-first order model.

360

Theoretical qe retrieved from the pseudo-second order was proximate with the experimental

361

values. Hence, linear kinetic model analysis advocated the applicability of pseudo-second order

362

model.

363 364

3.13.4. Non-linear approach for kinetic model analysis

365

Nonlinear analysis conducted by error analysis method. In pseudo-first order; out of six systems

366

one system each is explained by HYBRID and EABS and two systems each by MPSD and ARE

367

were explained better than other error function. In pseudo-second order two out of six systems

368

are better explained by HYBRID and EABS and one system each by ARE, MPSD. The

369

theoretical qe values obtained from the pseudo-second order and pseudo-first order model were

370

proximate to the experimental data. However coefficient of determination and r2 is higher for

371

pseudo-first order model.

372

Curve fitting using Microcal origin Software is also used for parameter determination for

373

pseudo-first order and pseudo-second order model respectively. On the basis of coefficient of

374

determination pseudo-second order is preferable model. 18

375

Linear analysis and non linear analysis by Microcal origin both advocated the appropriateness of

376

pseudo-second order model as compared pseudo-first order model. However, error analysis

377

method suggests suitability of the pseudo-first order model. The experiment qe values were

378

closer to theoretical qe values by linear method as compared to error analysis method. Hence,

379

pseudo-second order parameters values suggested by linear analysis method were used.

380 381

3.14. Adsorption Thermodynamics

382

Thermodynamic parameters i.e. change in standard free energy (ΔG o), standard enthalpy (ΔHo)

383

and standard entropy (ΔSo) calculated using following equations (Gupta and Rastogi, 2009; Liu,

384

2009; Salvestrini et al., 2014)

385 386

ΔGo = -RT lnKL

(17)

Ln KL = ΔSo/R - ΔHo/RT

(18)

387 388 389 390

Thermodynamic equilibrium constant i.e. KL (L mol-1) is the Langmuir constant b and R is gas

391

constant (8.314 J mol-1 K-1). A graph was plotted between lnKL and 1/T, the slope and intercept

392

furnish the ΔHo and ΔSo respectively (Elkady et al., 2011b). ΔGo, ΔHo and ΔSo calculated

393

presented in the Table 12.

394

Table 12 Thermodynamic parameters calculated by Langmuir constant method Parameter

Equation

ΔGo (K J/mol)

ΔGo = -RTlnKL

Temperat ure 293 K

Parameters using linear equation parameter b -31.8164

303 K

-32.4935

-32.3006

313 K

-33.2932

-32.4001

323 K

-33.6496

-33.2546

333 K

-34.4037

-34.6502

343 K

-35.3976

-35.6897

ΔHo (K J/mol) o

ΔS (K J/mol K)

395

ln KL = ΔSo/R – ΔHo/RT

R2adj *Except taking point of Ln KL at 333 and 343 K

396 19

Parameters using non linear equation parameter b (Microcal origin) -31.6399

-11.805

-17.242*

0.06824

0.0492*

0.9513

0.9158*

397

Comparison of thermodynamic parameter by linearly and non-linearly derived Langmuir

398

constant i.e. b showed slight variation in magnitude. The process was spontaneous, exothermic

399

and occurred with increase in entropy.

400

Enthalpy change (- 11.85 KJ mol-1) recommends the exothermic way of adsorption procedure.

401

The estimation of ΔGo decline with ascent of temperature shows that the procedure turns out to

402

be more feasible at higher temperature. Entropy change (0.913) indicates the increase of

403

disorderness at adsorbate –adsorbent interface during adsorption of cadmium.

404

In addition to this an additional mode is used for determination of thermodynamic parameters i.e.

405

partition method or distribution coefficient (Liu, 2009; Salvestrini et al., 2014). Kp or Kc is used

406

in place of KL.

407 408

Kc or Kp = CS/Ci

(19)

409 410

Here CS and Ci symbolize the concentration of adsorbate in solid and liquid phase. Following

411

determination of Kp equation 17 and 18 used for determination of thermodynamic parameters.

412

In addition to this free energy computed from the following equation (Salvestrini et al., 2014):

413 414

ΔGo = ΔHo–TΔSo

(20)

415 416

Table 13 Thermodynamic parameters calculated by partition method Parameter

Temperature

ΔGo (K J/mol)

ΔGo = -RTlnKp

293 K 303 K 313 K 323 K 333 K 343 K

-9.455 -9.291 -14.782 -5.425 -8.496

ΔHo (K J/mol)

ΔS o (K J/mol K)

lnKp = ΔSo/R – ΔHo/RT

-70.9061

-2.026

ΔG o (K J/mol)

R2adj

ΔGo= ΔHo –TΔSo

0.6267

-11.521 -94.944 -74.676 -54.409 -34.141 -13.873

417 418

The estimations of ΔGo, ΔHo and ΔSo ascertained at diverse temperature are given in Table

419

13.The negative estimations of enthalpy change (ΔHo = - 70.90 KJ mol-1) show the exothermic

420

nature of the adsorption process. ΔGo values were negative, it recommend that the procedure is 20

421

spontaneous in nature. Free energy values calculated from equation 20 were negative and

422

variable. The negative estimations of ΔS o show the diminishing of disorderliness at adsorbate-

423

adsorbent interface during adsorption of cadmium on zirconia.

424

The aforementioned stated strategy proposes that the system is spontaneous and occur with

425

decrease in entropy. In any case, Kc is equivalent to thermodynamic balance steady (KL) at

426

weaken concentration (Liu, 2009). However, Kc is equal to thermodynamic equilibrium constant

427

(KL) at dilute concentration (Liu, 2009). Hence thermodynamic parameters calculated from

428

Langmuir constant method is taken into account.

429 430

4. CONCLUSION

431

Abatement of cadmium was effectively achieved using nano crystalline zirconia. Initial pH was

432

most dominating factor followed by initial concentration and adsorbent dose. The found out at

433

initial concentration = 27 ppm, adsorbent dose = 4 g/l and pH = 7. HCl regenerates the adsorbent

434

and effectively have 50 % removal efficiency after three cycles. Langmuir isotherm model using

435

linear analysis was used to determine isotherm parameters. In addition to this the adsorption of

436

cadmium on nano crystalline zirconia follows pseudo-second order model. Thermodynamic

437

parameters suggest that the system is spontaneous in nature. The partition and Langmuir constant

438

method showed difference in coefficients of thermodynamic parameters. However both systems

439

suggest spontaneity and exothermic nature of adsorption process. The thermodynamic

440

parameters obtained by Langmuir constant (obtained by linear analysis) is taken into

441

consideration.

442

Conflict of interest

443

The authors declare that there is no conflict of interest.

444

Acknowledgement

445

The authors thank CSIR for providing financial assistance (SRF) to Deepak Gusain. We thanks

446

department of anatomy, All India Institute of Medical Sciences, New Delhi for TEM analysis of

447

the sample.

21

448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493

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