adsorption isotherm modeling of phenol onto natural soils ... · pdf file266 subramanyam, b....

Int. J. Environ. Res., 6(1):265-276, Winter 2012ISSN: 1735-6865

Received 15 Nov. 2010; Revised 6 Sep. 2011; Accepted 16 Sep. 2011

*Corresponding author E-mail:[email protected]

265

Adsorption Isotherm Modeling of Phenol Onto Natural soils – Applicabilityof Various Isotherm Models

Subramanyam, B.1* and Ashutosh, D.2

1 School of Civil Engineering, SASTRA University, Thanjavur-613402, Tamil Nadu, India2 Director, Centre for Environmental Engineering, PRIST University, Tamil Nadu, India

ABSTRACT: Liquid-phases adsorption equilibrium of phenol onto two naturally available soils namelyKalathur soil (Kr) and Adhanur soil (Ar) were studied. The experimental data were analyzed using fourteenisotherm models, ranging from single-parametric model to multi-parametric models (up to 5 parameters) of thesystem. Results show that in general the accuracy of models to fit experimental data improves with the degreeof freedom. To understand the mechanism involved with different types of sorbate-sorbent system as well asto find out the best fitting isotherm model, the correlation coefficients, and average percentage error andstudent t-test were carried out. Temkin isotherm model, Langmuir-Freundlich isotherm model and Fritz-Schlunder model as well as Baudu model were found to be the best fit models amongst the two-parametricmodels, three parametric models and four parametric isotherms modeling, respectively. This study brings outthe need of simultaneous solution of multi-parametric equations (using relevant softwares, MATLAB, inpresent case) than solution of their linearized forms, which is mostly followed by contemporary investigators.

Key words: Sorption,Wastewater, Multi- parametric,Correlation,t-test, MATLAB

INTRODUCTIONTraditionally the study of adsorption capacities of

various adsorbents has mostly been based on study of2-3 parametric models, (Sevil & Bilge, 2007). With betterunderstanding the adsorption mechanisms and fast-computational facilities, of late there have beenextensive attempts by various researchers in evaluatingthe characteristics of specific adsorbent-adsorbatesystems and evaluating the degree of applicability ofexisting models for the specific systems concerned(Johnson & Arnold, 1995; Allen et al., 2004; Kundu &Gupta, 2006; Ofomaja, 2009; Akhtar et al., 2007; Tahir &Naseem, 2006; Oualid & Naffrechoux, 2007).

The applicability of isotherm models ontobentonite and activated carbon for removal of dyes,cationic dye and phenols from aqueous solution werestudied using three well-known isotherms to modelequilibrium data, revealing the significance of higherparametric-models over lower parametric-models. (Allenet al., 2004; Tahir & Naseem, 2006; Maury &Mittal,2006; Oualid & Naffrechoux, 2007). In fact, a minimumof three parametric models was recommended by severalinvestigators, based on their independent study, to beused to fit a non-linear isotherm model (Alexander &

Erling, 1998; Oualid & Naffrechoux, 2007; Maury&Mittal, 2006; Malek & Farooq, 1996; Ting & Mittal,1999). On contrary, Malek and Farooq (1996), usedseven different parametric-isotherm models for hydro-carbon adsorption on activated carbon, found all theisotherm models performing reasonably well, withlower parametric model as the best, though. Thisfinding was further supported by, Ting and Mittal(1999), on their study of adsorption of gold by solventsobtained from dead fungus.

The present research work, fourteen isothermmodels were used for modeling the experimentalequilibrium data for phenol adsorption onto naturallyavailable soils with an objective of estimation ofspecific adsorption characteristics using variousisotherm models (associated with a range ofparameters) and evaluating their relative applicationwith regards to the soil under consideration.

MATERIAL & METHODSTwo soil samples, namely, Kalathur(Kr) and

Adhanur (Ar), were collected from Thanjavur districtsof the state of Tamil Nadu (India) and were dried ( at105 0C in an electric oven for 2 hours), followed bycrushing and sieving (100 - 635 SIEVE NO ASTM E11-

266

Subramanyam, B. and Ashutosh, D.

87), to obtain the samples having an average diameterof 0.05mm. To remove organic matter, the samples wereplaced in a water bath at 80.0 °C and treated withincrements of 5 mL of 30% H2O2. These soil sampleswere free of organic matter. This was indicated by thelack of effervescence. The sample, thus obtained wasdried, desiccated and preserved in airtight containers,for subsequent analysis and experiments. Phenol(C6H5OH) of analytical reagent (AR grade; suppliedby Ranbaxy Laboratories Ltd., India), was used for thepreparation of synthetic adsorbate of concentration100 mg/l. The required quantity of phenol accuratelyweighed and dissolved in distilled water to obtain stocksolutions of 1 liter, which was prepared fresh everyday (and stored in a brown color glass bottles toprevent photo-oxidation). For equilibrium study, batchexperiments were conducted at room temperature(30±20C) for an adsorption period of 24h (to attain theequilibrium condition) and the effect of adsorbentdosage on the uptake of phenol onto the soils studied.The adsorption equilibrium data of phenol were fittedto different isotherm models (one, two, three, four andfive degree parameters), as described in the followingparagraphs, to evaluate their suitability for the twosoils studied.

ONE PARAMETER MODELHenry’s Law model equation can be given as follows(Ruthven, 1984):

(1)

(2)

(3)

(5)

(4)

(6)

(7)

Where qe is the adsorbed amount at equilibrium (mg/g), Ce is the adsorbed equilibrium concentration (mg/L) and K is the Henry’s constant. (All the terms usedhave the same connotation as that in Mono-parametricmodel).Modified Langmuir – 1 model equation can be givenas follows (Yang &Doong, 1985)

Where qe is the adsorbed amount (of adsorbent inadsorbate) at equilibrium with respect to the totaladsorbents used in adsorption (mg/g), Ce is theconcentration of adsorbate on adsorbent at equilibrium(mg/L) and K is the Henry’s constant.

TWO-PARAMETER MODELHenry’s Law (with constant) model equation can begiven as follows:

Where qe is the adsorbed amount at equilibrium (mg/g), qmLF is the Langmuir-Freundlich maximumadsorption capacity (mg/g), Ce is the adsorbedequilibrium concentration ( mg/L), KLF is the equilibrium

Where qe is the adsorbed amount at equilibrium (mg/g), Ce is the adsorbed equilibrium concentration (mg/l), A and b are the isotherm constants.

THREE PARAMETER MODELSLangmuir–Freundlich isotherm model equation can begiven as follows (Sip, 2003)

Where, qe is the adsorbed amount at equilibrium (mg/g), Ce is the adsorbed equilibrium concentration (mg/l), KDR relates to free energy of sorption, and b is theDubinin-Radushkevich isotherm constants related tothe degree of sorption.Temkin isotherm (Aharoni &Tompkins, 1970) modelconsidered that the effect of adsorbate interactionson adsorption isotherms and suggested that becauseof these interactions the heat of adsorption of all themolecules in the layer would decrease linearly withcoverage. The Temkin isotherm expressed in thefollowing form:

Where qe and Ce represent their usual connotations(as given above) and σ is the isotherm constantsrelated to the degree of sorption.Dubinin-Radushkevich (D-R) isotherm (Akhtar et al,2007) often used to estimate the characteristic porosityin addition to the apparent free energy of adsorption.Thus, for evaluating these parameters the Dubinin-Radushkevich isotherm is being used in the followingform:

Where qe and Ce represent their usual connotations(as given above); T is the temperature (in Kelvin) andb is the constant related to the free energy of adsorption(expressed as, L/ mg).Modified Langmuir – 2 model equation can be givenas follows (Brien & Myers,1984)

Int. J. Environ. Res., 6(1):265-276, Winter 2012

267

(8)

(9)

(10)

respect to the interactions, which it engages with theadsorbate

(11)

(13)

(14)

Where qe is the adsorbed amount at equilibrium (mg /g), qmRP is the Radke–Prausnitz maximum adsorptioncapacities (mg/g), Ce the adsorbate equilibriumconcentration (mg /L), KRP is the Radke–Prausnitzequilibrium constants and mRP is the Radke–Prausnitzmodels exponents.Toth has modified the Langmuir equation to reducethe error between experimental data and predictedvalues of equilibrium adsorption data. The applicationof his equation is best suited to multilayer adsorptionsimilar to BET isotherms, which is a special type ofLangmuir isotherm and has very restrictive validity.The Toth model (Toth, 2000) equation given as

Where qe is the adsorbed amount at equilibrium (mg/g), Ce the equilibrium concentration of the adsorbate(mg/ L), qmT the Toth maximum adsorption capacity(mg/ g), KT the Toth equilibrium constant, and mT isthe Toth model exponent.The Jossens model (Akira et al., 1984) described bydistribution of energy (interactions adsorbate–adsorbent on adsorption sites). It considers that theactivated carbon surface is heterogeneous, with

constant for a heterogeneous solid and mLF Langmuir-Freundlich heterogeneity parameter lie between 0 and1. The Langmuir-Freundlich isotherm model at lowsorbate concentrations is effectively gets reduced toa Freundlich isotherm and thus does not follow Henry’slaw. At high sorbate concentrations, it behavesmonolayer sorption and shows the Langmuir isothermcharacteristics.

Fritz-Schlunder model equation given as follows(Mutassim & Bowen, 1992)

Where qe is the adsorbed amount at equilibrium (mg /g), Ce the equilibrium concentration of the adsorbate(mg/L), qmFS the Fritz–Schlunder maximum adsorptioncapacity (mg/g), KFS the Fritz–Schlunder equilibriumconstant (L/mg) and mFS is the Fritz–Schlunder modelexponent.

Radke - Prausnitz model equation given as follows(Ramakrishna &Viraraghavan, 1997)

Where qe is the adsorbed amount at equilibrium (mg/g), Ce the equilibrium concentration of the adsorbate(mg/L) and H, F, and p are the parameters of the equationof Jossens. H and F depend only on temperature. Thisequation can reduce to Henry’s law at low capacities.

FOUR PARAMETER MODELSFritz-Schlunder model equation can be given as follows(Fritz & Schluender, 1974)

Where qe is the adsorbed amount at equilibrium (mg /g), Ce the equilibrium concentration of the adsorbate(mg /L), A and B are the Fritz–Schlunder parametersand α and β are the Fritz–Schlunder equationexponents.

Baudu model equation given as follows (Oualid&Emmanuel, 2007)

(12)

Where qe is the adsorbed amount at equilibrium (mg/g), Ce the equilibrium concentration of the adsorbate(mg/L), qm the Baudu maximum adsorption capacity(mg /g), b0 the equilibrium constant, and x and y arethe Baudu parameters.

FIVE-PARAMETER MODELFritz-Schlunder model equation given as follows (Fritz& Schluender, 1974)

Where qe is the adsorbed amount at equilibrium (mg/g), Ce the equilibrium concentration of the adsorbate(mg/L), qmFSS the Fritz–Schlunder maximum adsorptioncapacity (mg /g) and K1, K2, m1, and m2 are the Fritz–Schlunder parameters.

RESULTS & DISCUSSIONThe various isotherms obtained were analyzed by

non-linear curve fitting (instead of linearization), usingMATLAB-7 software. The criteria for selection of the

268

Adsorption Isotherm Modeling of Phenol

(15)

ONE PARAMETER MODELOne parameter model (i.e., Henry’s law) is applied

to the experimental data obtained from the adsorptionof phenol onto naturally available soils. As indicatedin Fig.1and 2, this model failed in predicting theequilibrium isotherm model. The linear relation betweenQ and Ce, was slightly improved by introducingHenry’s law in the intercept model. In fact, the additionof a constant term in the model found to render bettercharacteristics of the equilibrium isotherm curve,especially at higher effluent concentrations. Asindicated by Fig.1 and 2, the adsorption of phenol bytwo naturally soils (Kalathur and Adhanur soils), wasquite evident of the improvement in the predictabilityof the values by Henry’s law with intercept over thatwithout intercept (Table 1). The present study supportsthe failure of the Henry’s law at initial concentration ofphenol and improvement in plot characteristics byintroducing the intercept in Henry’s model, whichconfirms with the findings (Maurya & Mittal, 2006;Faust & Aly, 1987).

TWO-PARAMETER MODELModified Langmuir-1, Modified Langmuir-2, Temkinand Dubinin-Rdushkevich isotherms were modified byrearranging the constants without changing the degreeof freedom with regards to the original second-degreeisotherm models (namely Langmuir andFreundlich)(Yang & Doong,1985). The present paperfocused more on Modified Langmuir-1, ModifiedLangmuir-2, Temkin and Dubinin-Rdushkevich modelsinstead of regular (namely, the Langmuir, Freundlich,Sip and Redlich–Peterson) isotherm models, whichwere already studied by the authors with confirmationof isotherm models fairly obeying by both the soils,yet the best models explaining the adsorption werefound to be the Sip and Redlich–Peterson isothermmodels (Subramanyam& Das, 2009). Model fits forthe two-parameter isotherms along with experimentaldata are presented in Fig. 03 and Fig. 04, respectively.The values of model constants along withcorresponding correlation coefficient, averagepercentage error and t-test values of paired student’st-test (95% confidence interval) for all sorbent-sorbatesystem studied are presented in Table 1. In fact theModified Langmuir model-1 was explained to accountfor temperature variability of the system, whereasModified Langmuir model-2, introduced by Brien andMyers (1984) was meant to account for heterogeneityof the adsorbent used. On study, for both the soils,the modified Langmuir -2 was found to fail in t-test(95% confidence interval) in addition to high averagepercent error (31.276 and 40.15 for Kr and Ar soilrespectively) and poor correlation coefficients (r2 =0.231 and 0.356 for Kr and Ar soil respectively).However, Modified Langmuir -1 isotherm model wasfound to obey the experimental data fairly well i.e., r2

=0.9952, APE = 1.204 and t > 0.05 for 95% confidenceinterval for Kr soil & r2 = 0.998, APE = 0.836 and t > 0.05

Fig. 2. Henry’s Law one degree of freedom isothermmodel fits (for Adhanur soil)

Fig. 1. Henry’s Law one degree of freedom isothermmodel fits (for Kalathur soil)

best isotherm model essentially based on correlationcoefficient and the average percentage errors (APE).The correlation coefficient shows the fit betweenexperimental data and isotherm model, while the averagepercentage errors (APE) were calculated using equation(15) indicating the fit between the experimental dataand calculated data used for plotting isotherm curves

269

Tabl

e 1. I

soth

erm

par

amet

ers (

one a

nd tw

o pa

ram

eter

s) a

vera

ge p

erce

ntag

e err

or, c

orre

latio

n co

effic

ient

s and

t-va

lues

Kal

athu

r so

il A

dhan

ur so

il

Isot

herm

mod

el

Deg

ree

of

Free

dom

C

onst

ants

Pa

ram

eter

va

lues

Ave

rage

pe

rcen

t er

ror

R2

t Pa

ram

eter

va

lues

Ave

rage

pe

rcen

t er

ror

R2

t

He

nry’

s Law

1

K

0.28

7

0.64

2

0.38

6

0.40

9

2

K

0.39

8

0.89

8

0.24

8

0.91

9

Henr

y’s L

aw

with

line

ar

inte

rcep

t

m

12.3

1

7.26

7

2

b 0.

0433

3 1.

2041

23

0.99

52

.764

0.

0352

9 0.

8355

98

0.99

8 0.

68

Mod

ified

La

ngm

uir-1

n -0

.690

9

-0.6

186

Mod

ified

La

ngm

uir 2

2

b 0.

2619

31

.275

98

0.23

11

.041

0.

187

40.1

4976

0.

3566

0.

012

σ^2

0.04

25

0.

0552

b 15

.6

13.0

09

0.81

5 0.

435

13.9

3 3.

8211

96

0.82

69

0.72

8 Du

bini

n–

Radu

shke

vich

2

KDR

35

.97

21

.73

Tem

kin

2 b

0.22

62

0.57

4123

0.

9821

1

0.33

25

0.58

8056

0.

9929

1

A

0.44

83

0.

3429


270


for 95% confidence interval for Ar soil. In this case,the value of exponent ‘n’ was found to be negative;this indicates that phenol adsorption could be anendothermic reaction (which means, it is likely to favorsthe adsorption at higher temperature). This finding wasquite akin to finding by Singh and Rawat (Binay &Narendra, 2004) based on their studies of sorption ofphenol by fly ash and impregnated fly ash, who reportedthe increase in sorption of phenol by fly ash withincreasing temperature (in the range of 300 – 500 C).

Application of Dubinin–Radushkevich isotherm,which was mostly used for gas phase adsorption onactivated carbon [9], was also found applicable to theliquid-solid phase adsorption, of late (Maury & Mittal,2006).In the present study, when Dubinin-Rdushkevichmodel applied to study the adsorption of phenol, themodel found to fit experimental data (for two soils)fairly well, though not adequate, as shown in Fig. 3

Fig. 4. For Adhanur soil (Two-parameter isotherm models)

and Fig. 04. [(r2 = 0.815, APE =13 and t > 0.05 for 95%confidence interval for Kr soil and r2 = 0.827, APE=3.83and t > 0.05 for 95% confidence interval for Krsoil)].

The Temkin isotherm model, also widely used ingas phase adsorption (with its application, ratherlimited to liquid-solid adsorption equilibrium) assumesadsorption to be characterized by a uniform distributionof binding energies up to some maximum value (Maurya& Mittal, 2006; Malek & Farooq, 1996). In the presentstudy, the experimental data for phenol onto two soils,analyzed by non-linear regression analysis to fit theTemkin isotherm model are presented in Fig. 3 and Fig.4. The parameters of Temkin model (Table 1) as well asthe higher values of the correlation coefficient i.e., r2 =0.9821 and r2 = 0.993 for Kr and Ar soil, lower averagepercentage error i.e., APE=0.574 and 0.588 for Kr andAr soil and better t-test values at 95 % confidence

Fig. 3. For Kalathur soil (Two-parameter isotherm models)

271

interval for (Kr and Ar soil) indicate adequate match ofthe data with the model.

THREE PARAMETER MODELSThe experimental adsorption data of phenol

adsorption onto two soils was also analyzed using thewell-known three-parameter isotherm models (namely,Langmuir–Freundlich, Redlich-Peterson, Sip, Fritz-Schlunder, and Radke - Prausnitz, Toth and Jossensmodel). The model seemed to fit well for both soilsstudied (Fig. 5 and 6; Table 2). The Langmuir-Freundlich isotherm model includes the characteristicsof Langmuir and Freundlich isotherm and provide abetter fit i.e., r2 =0.996, APE =0.50 and t > 0.05 for 95%confidence interval for Kr Soil and r2 =0.998, APE =0.155and t > 0.05 for 95% confidence interval for Ar Soil.However, the Toth isotherm equation was not less

satisfactory, compared to Langmuir-Freundlichequation with regard t-test values (95% confidenceinterval). Radke – Prausnitz, Jossens and Fritz-Schlunder isotherm models were also found similar tothe Langmuir-Freundlich and Toth isotherm models,showing good fits, yet with no significant improvementin the model’s data fitting. However, based on the t-test (t> 0.05 for 95% confidence level), it was observedthat the isotherms for all the systems were significantlycorrelated regarding the three-parameter models.These models can be presented in the following ordersof fitness (1) based on correlation coefficient andaverage percent error: Jossens > Langmuir–Freundlich> Toth > Radke–Prausnitz > Fritz– Schlunder and (2)based on maximum adsorption equilibrium capacity:Toth > Langmuir–Freundlich > Radke–Prausnitz >Fritz– Schlunder.

Fig. 6 . For Adhanur soil (Three-parameter isotherm models)

Fig. 5. For Kalathur soil (Three-parameter isotherm models)


272

Tabl

e 2. I

soth

erm

par

amet

ers (

thre

e par

amet

ers)

ave

rage

per

cent

age e

rror

, cor

rela

tion

coef

ficie

nts a

nd t-

valu

es

Kal

athu

r soi

l A

dhan

ur so

il

Isot

herm

m

odel

D

egre

e of

Fre

edom

C

onst

ants

Pa

ram

eter

va

lues

Ave

rage

p

erce

nt

erro

r R

2 t

Para

met

er

valu

es

Ave

rage

p

erce

nt

erro

r R

2 t

3

q mLF

55

.71

37

.83

La

ngm

uir-

Freu

ndlic

h

K LF

0.03

635

0.50

2493

0.

9958

0.

901

0.02

785

0.15

5025

0.

9988

0.

937

mLF

0.

9165

0.90

44

Fritz

- Sc

hlun

der

3 q m

FS

43.7

9

22.9

KFS

0.

0536

9 0.

9285

41

0.99

53

0.81

9 0.

0584

9 0.

2770

59

0.99

86

0.88

6

m

FS

0.96

34

0.

9138

Ra

dke-

Pr

ausn

itz

3 q M

RP

48.9

3

25.7

3

KRP

0.

0465

2 1.

0928

68

0.99

53

0.66

3 0.

05

1.53

0964

0.

9985

0.

862

mR

P 0.

9717

0.86

79

Toth

3

q mT

56.0

8

39.5

1

KT

0.06

649

0.71

9655

0.

9955

0.

863

0.06

771

0.21

387

0.99

87

0.91

3

m

T 0.

8718

0.80

9

Jo

ssen

s 3

F -0

.302

2

-0.3

221

H

0.

2853

0.

6103

38

0.99

68

0.86

7 0.

173

0.14

1336

0.

999

0.93

8

p

0.42

48

0.

3991


273

FOUR- PARAMETER MODELSThe experimental equilibrium data were also

analyzed using four-parametric models - Fritz-Schlunder, and Baudu model. These models, withparameters obtained using non-linear curve fittinganalysis, was found to fit experimental data better thanlower parameter models for both soil-types (Fig. 7and8,Table 3). For Kr soil, the values of correlationcoefficient (r2 =0.998), average percentage error (APE=0.18) and t-test value (0.995, 95% confidence interval)were almost equal. For Ar soil, the values of correlationcoefficients was greater than 0.95 (for both Fritz-Schlunder and Baudu isotherms), whereas averagepercentage error was found to vary with the models,such as 0.061 (in case of Baudu isotherm) and 1.36 (incase of Fritz isotherm). Thus, the studies indicate thatBaudu isotherm was seemingly a better isotherm model

than Fritz isotherm model, which were further supportedby t-test values, as well (0.52 and 0.92, respectively).

FIVE- PARAMETER MODELSWhen the experimental equilibrium data was

analyzed using a five-parameter model, namely, Fritz-Schlunder model (a model with higher complexities,and necessitate nonlinear regression techniques forits solution). Although, several researchers hadindicated its poor performance in aqueous phaseadsorption (Brien &Myers,1984), yet in the presentstudies, Fritz-Schlunder isotherm model was found toprovide a good fit for both the soils are presented inFig.9 and Fig.10 (Table 3). Probably, the increasednumber of parameters was able to simulate the modelmore accurately, better than two, three and fourparameters.

Fig. 8. For Adhanur soil (Four-parameter isotherm models)

Fig.7. For Kalathur soil (Four-parameter isotherm models)


274


Fig.10.For Adhanur soil (Five-parameter isotherm models)

Table 3. Isotherm parameters (four and five parameters) average percentage error,correlation coefficients and t-values

Kalathur soil Adhanur soil Isotherm model

Degree of

Freedom Constants Parameter

values Average percent

error R2 t Parameter

values Average percent

error R2 t

Fritz- Schluender 4 A 3.5 2.73 B 0.000555 0.180569 0.998 0.95 0.000457 1.358441 0.986 0.521 α 0.658 0.547 β 1.58 1.32 Baund 4 qm 3.495 1.97 bo 1801 0.180569 0.9979 0.95 1645 0.061063 0.9976 0.92 x -2.582 -2.45 y 0.6583 0.85 Fritz-Schlunder 5 qmFSS 14.54 9.883 K1 0.2404 0.1808 K2 0.0005551 0.180569 0.9979 0.95 0.004462 0.1282 0.9991 0.981 m1 0.6583 0.7302 m2 1.582 0.7302

Fig. 9. For Kalathur soil (Five-parameter isotherm models)

275

CONCLUSIONThe study of adsorption equilibrium data for

phenol on two types of adsorbent, i.e., Kalathur andAdhanur soil using 14 well-known isotherm modelsindicated that higher parametric models seemed to bebetter options for their modeling in comparison tolower parametric models. Out of all isotherm modelsstudied, most of the isotherm models could predictthe adsorption equilibrium well (Except Henry’s,Modified Langmuir-2 and D-R isotherm models), yetwith a varying degree of correlation, averagepercentage error and student t-test. As reported invarious literatures, and quoted in precedingparagraphs, which report varying degree of obedienceto different models, specific to each adsorbent-adsorbate system. However, for a complexheterogenous mass like soils, the study of higher-parameter models using non-linear analysis seems tobe more preferable than lower-parameter and linear(ized) models.

ACKNOWLEDGEMENTSThe author(s) thank the anonymous editor for

helping us to present this research in a more effectivemanner. Authors also gratefully acknowledge thesupport received from SASTRA University.

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