Experimental and robust modeling approach for lead(II) uptakeby alginate gel beads: Influence of the ionic strength and medium

composition

Salvatore Cataldo a, Antonio Gianguzza a, Marcello Merli b, Nicola Muratore a, Daniela Piazzese a,⇑,Maria Liria Turco Liveri a

aDipartimento di Fisica e Chimica, Università degli Studi di Palermo, Viale delle Scienze, I-90128 Palermo, ItalybDipartimento di Scienze della Terra e del Mare, Università degli Studi di Palermo, Via Archirafi 22, I-90123 Palermo, Italy

a r t i c l e i n f o

Article history:

Received 5 May 2014

Accepted 28 July 2014

Available online 4 August 2014

Keywords:

Alginate gel beads

Robust statistics

Metal adsorption

Wastewater treatment

Ionic strength

Differential Pulse Anodic Stripping

Voltammetry

Adsorption isotherms

Adsorption kinetics

Lead

Heavy metal

a b s t r a c t

Systematic kinetic and equilibrium studies on the lead ions removal ability by Ca-alginate gel beads have

been performed by varying several internal parameters, namely, number of gel beads, nature and com-

position of the ionic medium and pH, which allowed us to model a wastewater in order to closely repro-

duce the composition of a real sample. Moreover, the effects brought about the different ionic species

present in the reacting medium have been evaluated.

Differential Pulse Anodic Stripping Voltammetry (DP-ASV), has been systematically used to perform

kinetic and equilibrium measurements over continuous time in a wide range of concentration. Kinetic

and equilibrium data have been quantitatively analyzed by means of robust approach both for the

non-linear regression and the subsequent residuals analysis in order to significantly improve the results

in terms of precision and accuracy.

Alginate gel beads have been characterized by SEM and an investigation on their swelling behavior has

also been made. Removal efficiency of the calcium-alginate gel beads has been calculated and results

obtained have showed a relevant dependence on ionic strength, composition of ionic media, pH of solu-

tion and number of gel beads. The number of gel beads takes part as key crucial components, i.e., the

higher the number of beads the greater the amount of Pb(II) species removed from the sample, the lower

the time needed to reach the maximum removal efficiency of 90%.

� 2014 Elsevier Inc. All rights reserved.

1. Introduction

The discharge of wastewaters from various industrial activities

to the environment is more and more rigorously controlled. The

cogent problem arises from the inadequate disposal of wastewater

mainly contaminated with heavy metals, being a risk for both the

aquatic ecosystems and human health [1]. In fact, presence of

heavy metals in the aquatic ecosystem leads unambiguously to

harmful effects to living organisms because these metals are not

biodegradable and can be bio-accumulated through the food chain.

Among the heavy metals present in the wastewater a great atten-

tion has been paid to lead, which is one of the most useful metals

not only for its wide presence but also for both its effortless extrac-

tion and handle [2]. Unless these benefits, we cannot leave out of

consideration that lead has the most damaging effects on human

health, whereby it can enter the human body through uptake of

food (65%), water (20%) and air (15%) [3]. For all these reasons, lead

is one of the most controlled metal in wastewaters: its maximum

admissible concentration in drinking water was fixed to 10 lg L�1

by European Union. Several classical remediation processes have

been proposed for metal recovery from industrial effluents [4–8],

but in the majority of the situations all of the above reported treat-

ments reveal to be unsuitable, especially for very low-concentra-

tion solutions. This way, the application of these protocols

reflects not only into a waste of both time and money but on envi-

ronmental reasons trough direct or indirect impact by producing

hazardous wastes that need further treatment [9–11]. Thus, in

selecting the proper technique to apply for the wastewater treat-

ment several features have to be taken into account, i.e., environ-

mental impact, costs, competitiveness, technical efficiency, life

cycle and sustainable growth parameters.

A very promising alternative to the above reported methods for

the removal of heavy metals is the bio-sorption based on the use of

http://dx.doi.org/10.1016/j.jcis.2014.07.042

0021-9797/� 2014 Elsevier Inc. All rights reserved.

⇑ Corresponding author.

E-mail address: daniela.piazzese@unipa.it (D. Piazzese).

Journal of Colloid and Interface Science 434 (2014) 77–88

Contents lists available at ScienceDirect

Journal of Colloid and Interface Science

www.elsevier .com/locate / jc is

different materials [12–25]. In particular, bacteria [26], alga [27],

fungi [28], but also sub-products of agriculture [29] or industry,

biopolymers [30–34] have been already applied. These renewable

resources possess peculiar characteristics, which make them very

suitable for sequestering the heavy metals present in the waste.

Although they share some features with conventional resins char-

acterized by the presence of a number of reactive groups, they

present the advantages to remove the heavy metal by synergically

exploiting different processes, namely ion exchange, complexation

and also electrostatic interactions [35,36]. As the attractive interac-

tions between the heavy metal species and the functional groups of

adsorbent drive the process, the effects of the wastewaters ionic

composition cannot be leaved out of consideration because the rel-

evant presence of ionic species clearly interferes with the removal

processes of heavy metal.

Furthermore, particularly in areas of wastewater treatments by

biosorption processes, a knowledge of the kinetics of biomaterial-

metal ion uptake is very important, because knowing the temporal

scale of the process is useful as identifying the final equilibrium

state of the system. In fact, a given adsorbent could have a very

high removing efficiency but on a timeframe very long. This way,

the applied materials for the remediation process would result

both time and money consuming.

Among different biopolymers, alginate can be considered a suit-

able sorbents because of (a) the wide availability, being a major

component of the cell walls of brown algae, (b) the high affinity

for heavy metals [37–41], and (c) the ability to form gel depending

on the experimental conditions of the aqueous alginate solutions

[42].

In order to model the composition of a real wastewater samples

and to obtain a complete picture of the forces that govern the

adsorption of lead ions into alginate gel beads, we planned a sys-

tematic kinetic and equilibrium studies by methodically changing

the ionic strength and ionic medium.

Differential Pulse Anodic Stripping Voltammetry (DP-ASV) has

been used to perform kinetic and equilibrium measurements over

continuous time in a wide range of metal concentration, as this

electrochemical technique shows relevant advantages in terms of

high sensitivity, ease of application even in solutions with high

ionic strength values, low cost, high selectivity and accuracy [43].

Up to now, to the best of our knowledge, only few researchers

[44,45] have employed electrochemical techniques to study waste-

waters treatment by biosorption processes due to the contamina-

tion on the sensitive electrode by the adsorption of organic

matter in samples. In this investigation we have preliminarily ver-

ified the possibility to use the DP-ASV for direct measurements of

lead ions in solution and experimental data obtained have demon-

strated a good reproducibility and no interference by organic mat-

ter in the experimental electrochemical conditions adopted for this

study.

Both the kinetic and equilibrium data have been quantitatively

analyzed by means of the Ordinary Least-Squares regressions (OLS)

and (robust) Iteratively Reweighted Least-Squares regressions

(IRLS) by using the typical models. For the kinetic data the

pseudo-first order, pseudo-second order, double exponential

model, Higuchi and Weibull models have been applied while the

sorption characteristics were examined by using the classical mod-

els, i.e., Langmuir, Freundlich, and some others, e.g., Langmuir–Fre-

undlich, Sips, double Langmuir. The affinity of the Pb(II) species for

the binding sites was evaluated by using the Scatchard plot analy-

sis [46] that allows to gather useful information about affinity phe-

nomena of adsorbent toward the adsorbate.

The analysis of the experimental data allowed us not only to

elucidate the mechanism pathways concerning the adsorption pro-

cesses but also to establish the nature of the interactions which

govern the removing process. Complementary studies on the algi-

nate gel beads swelling behavior and their SEM characterization

provided important information for corroborating the mechanism

pathways trough which the metal ion adsorption take place.

2. Materials and methods

2.1. Chemicals

Commercial alginic acid (AA, molecular weight in the range 70–

100 kDa), as sodium salt extracted from Macrocystis pyrifera, with

an average content of mannuronic and guluronic acids of 61%

and 39%, respectively, was supplied by Sigma (lot. 60K1443). Nitric

acid and sodium hydroxide solutions used to fix the pH of the

metal ion aqueous standard solutions were prepared by diluting

concentrated Fluka ampoules and standardized against sodium

carbonate and potassium hydrogen phthalate, respectively.

Sodium nitrate, sodium chloride, lead nitrate and calcium chloride

dehydrate were supplied by Fluka and were always dried at 110 �C

before use. The purity of calcium chloride and lead nitrate was

checked by Inductively Coupled Plasma Optical Emission Spectros-

copy (ICP-OES) measurements. All the solutions were prepared

using freshly prepared CO2-free ultra pure water (qP 18 MX cm)

and grade A glassware.

2.2. Experimental procedures for the preparation and the

characterization of sorbent material

Calcium alginate gel beads (Ca-A) were prepared at the concen-

tration of 2%, using the dropping technique, as already reported in

a recent paper [47]. Different analysis were carried out in order to

determine the density, the water content, the weight and the

mechanical resistance of gel beads and the detailed experimental

procedures were recently described by Cataldo et al. [47].

The degree of swelling of calcium alginate gel beads was deter-

mined gravimetrically. Different number of calcium alginate gel

beads (NB), specifically 25, 50 and 100 beads, were placed in

25 mL of NaCl aqueous solutions at different ionic strength values

(0.1 6 I/mol L�16 0.8), at pH 5.0. The beads were allowed to swell,

under gentle stirring at room temperature for 6 h. The swollen

beads were taken out from the solution, completely dried using a

filter paper in order to remove the excess of water on their surface

and afterwards weighed. The swelling ratio (SR) was determined

by considering the following relationship

SR ¼ ws �wd

wd

ð1Þ

where ws and wd are the weights of the swollen and dry beads,

respectively.

The surface morphology and the size of calcium alginate gel

beads after lead sorption (Ca-A/Pb) was observed by using an elec-

tronic microscope ESEM FEI QUANTA 200F coupled with an EDX

(Energy Dispersive X-ray spectroscopy) system. The gel beads were

dried at T = 80 �C and their surface was coated with gold in the

presence of argon by an Edwards Sputter Coater S150A in order

to prevent charging under electronic beam. The electron beam

was opportunely set in order to avoid the damage of the samples.

SEM micrographs were registered within the micrometer range.

2.3. Experimental procedures for kinetic and equilibrium

investigations

Lead nitrate aqueous solutions have been prepared by weighing

the salt and dissolving it with the aqueous HCl or HNO3 solution at

the required pH and ionic strength. The kinetic investigations have

been performed under constant stirred conditions at room temper-

78 S. Cataldo et al. / Journal of Colloid and Interface Science 434 (2014) 77–88

ature at pH = 5.0 and keeping constant the heavy metal amount

(50 mg L�1):

1. In the absence of added electrolytes by keeping constant NB

at 25.

2. By varying the NB in the range 25–100 on varying the ionic

strength values (0.1 6 I/mol L�16 0.8) with NaCl.

3. In the presence of NaNO3 medium at I = 0.1 and 0.8 mol L�1

by keeping constant NB at 25.

The kinetic experiments have also been carried out in the pres-

ence of 25 beads

1. At pH = 3.0 in the presence of NaCl medium at I = 0.1 and

0.8 mol L�1.

2. At pH 5.0 on varying the ionic strength in the range 0.1 6

I/mol L�16 0.8 in a mixed ionic media, consisting of

mixture of NaCl + CaCl2 at different Na+/Ca2+ ratios.

The kinetic investigations were performed by monitoring the

time evolution of the Pb2+ concentration (C0 = 50 mg L�1) in the

solution during the adsorption onto the calcium alginate gel beads

by using a polarographic system (Metrohm 663 VA STAND) con-

trolled by the Autolab potentiostat in conjunction with the

IME663 interface. The whole apparatus was controlled by NOVA

1.6 software (by Metrohm Autolab). The VA STAND is fitted with

a three electrode system which consists of Multi-Mode Electrode

Pro (Metrohm, code 6.1246.120) working in the Static Mercury

Drop Electrode (SMDE) mode, a glassy carbon auxiliary electrode

(code 6.1247.000) and a double junction Ag/AgCl/KCl (3 mol L�1)

reference electrode (code 6.0728.030).

The DP-ASV measurements were performed after bubbling

purified N2 gas into the solutions for 150 s and the peak current

of lead was recorded every 3.5–7 min. The experimental electro-

chemical conditions were chosen in order to optimize the quality

parameters, as signal/noise ratio, repeatability, accuracy, etc., and

to avoid interferences; so a deposition potential of �0.55 V was

applied under stirring for 1 s; after an equilibration time of 10 s

the voltammogram was registered from �0.55 V to �0.20 V with

a scan rate of 0.01 V s�1 and a step potential of 5 mV. The modula-

tion amplitude was 50 mV with a modulation time of 0.01 s and a

time interval of 0.5 s. The hydrogen ion concentration of the solu-

tions was checked by a potentiometer (Metrohm, Model 654)

equipped with a combined ISE-H+ glass electrode (Ross type

8102). No significant pH changes have been detected during the

lead(II) sorption processes. Moreover, the applied pH values are

well below the pHpzc 6.5 ± 0.1 [48].

The equilibrium studies were carried out by means of batch

experiments, putting a variable number of beads (from NB = 5 up

to 100) in 25 mL of solution containing Pb(NO3)2 at the concentra-

tion of 200 mg L�1; experiments have been made in the single

(NaCl) and mixed (NaCl + CaCl2) ionic media at a selected ionic

strength values, i.e., 0.1 mol L�1. The solutions have been shaken

for 24 h by using an orbital rotator apparatus and then filtered.

The residual concentration of Pb2+ ion in the filtrates has been

determined by using Differential Pulse Anodic Stripping Voltam-

metry (DP-ASV) at the same experimental conditions as for kinetic

experiments.

2.4. Robust data analysis

In this investigation both the kinetic and the equilibrium mod-

els have been fitted by means of Ordinary Least-Squares regres-

sions (OLS) and (robust) Iteratively Reweighted Least-Squares

regressions (IRLS). In order to check the reliability of the regression

results and to detect the possible dangerous outliers in the data set,

subsequent residuals analysis has been performed for each regres-

sion run, using some robust regression diagnostics techniques.

Moreover, the choice of the best model has been carried out by

means of advanced decision tools belonging to the family of the

Bayesian Information Criteria, as well as the classical ANOVA com-

parison tests. We used the Excel utility SOLVERSTAT [49], in which

all of these advanced statistical procedures are implemented. In

Table. 1 the kinetics and equilibrium models used in this work

are listed.

The IRLS procedures have been performed adopting as M-esti-

mator function the Huber’s one [50] with a tuning constant

c = 1.345 (i.e., the constant which sets the Gaussian efficiency of

the M-estimator to the 95%), and using the Standardized Residuals

as a scale measure of the M-estimator, while the robust r-estima-

tor MAD (namely the Median Absolute Deviation of the residuals)

has been adopted. Note that as concerns the kinetic model regres-

sions, in this work we present just the results obtained by IRLS for

the sake of brevity. The (robust) regression diagnostics procedure

to detect the outliers in the data set have been performed by

means of statistical descriptors such as Studentized Residuals,

Cook’s distances and COVRATIO values, following the protocol

elaborated in Merli et al. [51].

2.4.1. Monitoring the regression quality

Following Neter et al. [52], the conditions that we tried to sat-

isfy (in addition to the ‘‘classical’’ observation of R, R2 and SSR

and of the standard uncertainty associated to each variable

together with the related t-test) to get the best least-squares

regression were:

(1) Absence of multi-collinearity (the presence of high or near-

perfect inter-correlations between or among the indepen-

dent variables) in the case of multiple regression analysis.

(2) Residuals normality.

(3) Residuals homoscedasticity.

(4) Independency of the residuals from each other.

Condition (1) has been verified by means of the Variance Infla-

ction Factor (VIF), i.e., a test based on the R2 obtained when each

variable is regressed on the remaining independent variables. As

well known, collinearity arises from sampling methodology,

over-defined model, model choice and presence of outliers. Multi-

collinearity, in turn, determines inaccurate estimates of the regres-

sion parameters, alters the result of various tests and degrades the

predictability of the model. A suitable upper bound for each VIF

values is 10.

The normality of the residuals (2) has been checked by mean of

the so-called Jarque–Bera Statistic (JB) based on the coefficient of

skewness and kurtosis. JB is distributed as a v2 distribution with

Table 1

Kinetic and equilibrium models tested in this work.

Kinetic model Equation

First order model (FOM) qt ¼ qeð1� e�ktÞSecond order model (SOM) qt ¼ q2e kt

ð1þqektÞDouble exponential model (DEM) qt ¼ A1ð1� e�k1tÞ � A2ð1� e�k2 tÞHiguchi model (HM) qt ¼ kH

ffiffi

tp

þ c

Weibull model (WM) qt ¼ ð1þ eð�tb=kÞ þ cÞqeEquilibrium model Equation

Langmuir Cs ¼ qm �KL �Ce

1þKL �Ce

Freundlich Cs ¼ KF � Cne

Sips qe ¼ qm �KS �CmS

1þKS �CmS

Double Langmuir Cs ¼ qm1 �K1 �Ce

1þK1 �Ceþ qm2 �K2 �Ce

1þK2 �Ce

S. Cataldo et al. / Journal of Colloid and Interface Science 434 (2014) 77–88 79

two degrees of freedom. The homoschedasticity, i.e., the constant

variance of the residuals, has been tested by means of a Modified

Levene Test (MLT. See Levene [53] for further details). The MLT

value should be less than a critical value to ensure that the resid-

uals are homoschedastic.

The independence of the residuals (4) has been tested with the

Durbin–Watson statistics (DW. See Durbin and Watson [54] and

Howard and Cassidy [55], for a practical application).

2.4.2. Choice of the model

As above mentioned, the model tested in this work were FOM,

SOM. DEM and WM among the usual kinetic models commonly

adopted in kinetics studies, while HM has been tested in order to

check if multilinear pathways occur.

The choice of the model among different tests has been per-

formed by means of a number of statistical decisions tools. The

classical, not fully satisfactory, approach is based on the evaluation

of the residuals and the error values associated to the minimized

parameters. Referring to the SOLVERSTAT manual [49], other use-

ful information can be obtained by some advanced statistics such:

(1) R2adj [52] (in addition to the usual R and R2). While the clas-

sical coefficients of determination R and R2 indicate the frac-

tion of total variability in the data shown by the regression

model, R2adj is particularly useful when comparing models

with different number of degrees of freedom, since it is sen-

sitive to addition of irrelevant variables.

(2) Predicted Residual Sums of Squares (PRESS) statistic, which

is a measure of the predictive power of the model. This sta-

tistic tell us how well the model would predict each of the

points in the data set if they were not included in the regres-

sion. In comparison with other experiments, the PRESS value

should be the smallest one.

(3) Cross-Validation Mean Error of Prediction (MEP), which

gives a rough description of the performance of the model,

and it depends on the unknown response function and the

unknown variance of the observations. Best models have

lower MEP [56].

(4) R2 prediction, which reflects the prediction ability of the

model. It is possible to have a high R2 and a low R2 predic-

tion. In a similar way as R2adj this statistic shows a maximum

for the best predictive model. The difference is that R2 pre-

diction is based on the predictive power of the model.

Higher R2 prediction values are preferred.

(5) The family of the Bayesian Information Criterion (BIC), such

as Schwartz criterion (SBC), Akaike Information Criterion

(AIC), Hannan-Quinn Information Criterion (HQC) as well

as their ‘‘corrected’’ version (AICc, HQCc, SBCc), i.e., corrected

for the number of degrees of freedom [57]. They are gener-

ally based on measuring the fit given by SSE and correcting

it for the number of regressors. In this sense, these statistics

give an idea of the relative quality of a statistical model, pro-

viding a means for model selection. These model selection

strategies deal with the trade-off between the goodness of

fit of the model and the complexity of the model itself, and

hinge on information entropy. Note that these criteria do

not provide a test of a model in the sense of testing a null

hypothesis; thus, they cannot give information about the

quality of the model in an absolute sense. The best model

will show low values of these statistical tools. For the sake

of brevity, in this work we present the results related to

AIC and AICc tests.

(6) A ‘‘classical’’ (but actually effective) F-test as commonly

adopted in econometrics. When the regression has a low

explanatory power (i.e., low R2) the F-test values will be

close to zero, while if R2 is close to 1, then the F-test value

tends to be very large. The larger is its value, the best is

the model.

An example of application of the procedure to choose the

kinetic model performed in one selected case among those investi-

gated is reported in the Supplementary Material section.

2.4.3. The outliers recognition

As mentioned above, in order to check for the presence of dan-

gerous outliers in the data set, a robust analysis of the residuals has

been performed.

In general, if one or more figures of merit among those listed

above show unacceptable values, particular care must be paid to

the residuals behavior, or, most of all, to some scaled measure of

them. In the outlier recognition particularly useful are some

(robust) regression diagnostics such as leverage, Cook’s distance,

COVRATIO and – for instance – Studentized Residuals. Combining

the analysis of these estimators one is allowed to detect in a rigor-

ous way the presence of an actually influent outlier, whose the fit-

ting would turn into an inevitable worsening of the results (overall

of the parameter estimates). A suitable regression diagnostic could

be the so-called William graph, which plots Cook’s distance and

COVRATIO vs. leverage. An outlier is present if simultaneously (i)

leverage is > 3p/n, Cook’s distance > F(0.5,n�p,n) and (iii) COVRA-

TIO < 1–3p/n. Values of COVRATIO > 1 + 3p/n (i.e., its upper bound)

are not necessarily related to outliers, but just to strongly influenc-

ing data points. Once the presence of outliers is detected, if the IRLS

procedure is not able to underweight each aberrant observation,

one is suggested to remove them from the data set.

A complete procedure to identify and remove outliers in one

selected case among those investigated is reported in Supplemen-

tary Material section.

3. Results and discussions

3.1. Swelling behavior of Ca-A gel beads

The swelling behavior of 2% calcium alginate gel beads were

investigated in NaCl aqueous solutions over a wide range of ionic

strength (0.1 6 I/mol L�16 0.8), at pH = 5.0 and room temperature.

Results obtained, expressed as swelling ratio SR according to Eq.

(1), are collected in Table 2.

The obtained results suggested that the ionic strength plays a

relevant role in influencing the swelling behavior to an extent that

depends on the number of beads. In particular, for the different

systems investigated the increase in ionic strength hampers the

swelling process by a factor of about 20% for the system containing

25 gel beads, 36% and 40% for those containing 50 and 100, respec-

tively. The effect of the ionic strength on the swelling behavior can

be reasonably explained by considering that the shrinking process

occurs due to a decrease in the repulsive interactions of negatively

charged carboxyl groups on the alginate caused by the interaction

with the positively charged Na+ from the ionic medium. Further-

Table 2

Swelling ratio for the calcium alginate gel beads in NaCl medium, at different ionic

strength values and at room temperature.

I/mol L�1 SR

NB

25 50 100

0.1 33.2 28.6 19.4

0.5 27.0 20.5 13.5

0.8 26.4 17.2 11.8

80 S. Cataldo et al. / Journal of Colloid and Interface Science 434 (2014) 77–88

more the swelling is always greater for a number of Ca-A equal to

25, probably because of the higher surface area in contact with the

aqueous solution.

3.2. Scanning Electron Microscopy (SEM)

Micrographs from Scanning Electron Microscopy (SEM) analysis

show wrinkled surfaces of gel beads with increases of pores in the

presence of Pb2+ ions with respect to the blank Ca-A gel beads. This

morphology may be attributed to the shrinkage of the beads at

higher metal concentrations [58]. As an example SEM surface

micrographs of Ca-A biopolymers after contacting with 200 mg L�1

lead(II) solutions for 24 h are depicted in Fig. 1.

SEM analysis was coupled with EDX measurements which

allow to obtain semi-quantitative results on the metal content in

the different dried gel beads. EDX results for the system investi-

gated were reported in Fig. 1, in comparison with analogous

obtained for Ca-A system, recently reported [47]. They clearly show

that calcium percentage in gel beads lowers when the calcium–

biopolymer system is in contact with the solutions containing lea-

d(II) ions. These results prove that the heavy metal species displace

to a certain extent the Ca2+ ions from the alginate gel beads.

3.3. Sorption kinetic data

In Fig. 2 is reported, as an example, the time evolution of the

current intensity (I) of the Pb2+ aqueous solution containing 25 cal-

cium alginate gel beads in NaCl 0.1 mol L�1.

Since the removal of the heavy metal species by the calcium

alginate gel beads takes place, as can be expected, the current

intensity of Pb2+ decreases as function of time till it reaches a con-

stant value. The obtained trends clearly suggest that the uptake

process is complete and no desorption occurs in the timeframe of

observation. The current intensities data have been converted into

quantity of lead ion removed qt for all systems examined.

The effects of both the nature and composition of ionic medium

on the total adsorption of Pb2+ have been evaluated by following

the sorption kinetic profiles for the aqueous system containing

25 Ca-A gel beads at pH = 5.0 both in the absence of fixing ionic

medium and in the presence of NaCl over a wide range of ionic

strength, i.e., 0.1 6 I/mol L�16 0.8 (Fig. 3a); moreover, in the same

interval of ionic strength the influence of the different number of

beads on the lead(II) biosorption at has been investigated. The

obtained results are depicted in Fig. 3b. Perusal of figures clearly

demonstrate that presence of NaCl in the reacting medium plays

a relevant role, particularly the progressively increase of the elec-

trolyte concentration in solution leads to a drastic reduction of

the Pb2+ uptake by alginate gel beads. This effect can be explained

according to literature [59–61] and our swelling results by

Inte

nsi

ty(C

ou

nts

s-1

1000

2000

3000

4000

5000

6000

7000

8000

Inte

nsi

ty(C

ou

nts

s)

0,00

0

C

O

1,00 2,00

Energy (KeV) Energy (KeV)

u

3,00

Ca

4,00

Au

(a)

5,00

It

itC

t-1

1000

1500

2000

2500

3000

Inte

ns i

ty (

Cou

nt

s)

0,000

500

C

1,00 2,00

A

Pb

3,00

Ca

4,00

Au

(b)

5,00

u

A

O

(c) (d)

Fig. 1. EDX spectra of Ca-A (a) and Ca-A/Pb (b); SEM images at 10,000� of magnification (c) of Ca-A gel bead surface and (d) after sorption of Pb2+ ions.

0 50 100 150 200 250 300

1

2

3

4

5

6

7

8

9

10

I (µ

A)

t (min)

Fig. 2. Adsorption kinetics of Pb2+ 50 mg L�1 onto 25 Ca-A beads in NaCl

0.1 mol L�1.

S. Cataldo et al. / Journal of Colloid and Interface Science 434 (2014) 77–88 81

considering that the presence of both additional cations and anions

induces double consequences. In fact, the interaction between the

negative charge present in the alginate chain back-bone and the

anions in the nearness of the polymer chains will keep the anions

concentration in the near-neighbor of the surface lower than that

of the bulk solution. Nevertheless, this difference vanishes on

increasing the ionic strength of the medium. Moreover, the Na+

ions of the salt used to adjust the ionic strength will compete with

the heavy metal for the sorption sites. Indeed, it cannot leaved out

of consideration that the increase in the concentration of the

applied salt induces a shrink of the beads, as a consequence, the

adsorption sites become less accessible for the lead ion uptake.

Thus, the complete balance of these effects reflects into a signifi-

cant decrease of the Pb(II) loaded into the gel beads.

To further establish the influence of the ionic strength on the

lead biosorption rate by Ca-A gel beads a mixed ionic media, i.e.,

NaCl + CaCl2, has been applied. The kinetic profiles have been gath-

ered for the system containing 25 beads in a wide range of ionic

strength (0.1 6 I/mol L�16 0.8) at pH = 5.0, and for I = 0.5 mol L�1

for two different Na+/Ca2+ ratios. Fig. 3b clearly shows that, analo-

gously to the ionic strength effect discussed above, the contempo-

rary presence of both Na+ and Ca2+ ions in solution brings about the

same decreasing uptake effect on the biosorption process whose

extent is significantly enhanced by an increase in the Ca2+/Na+

ratios in the ionic medium.

Once established the role played by the ionic strength on the

Pb(II) loading gel beads process, the kinetic investigation have

been carried out by keeping constant the ionic strength, ionic med-

ium nature and Pb2+ concentration, on varying the number of gel

beads from 25 up to 100. This way, a complete picture of the mech-

anism pathways trough which the beads-metal ion uptake occurs

could be drawn. For all cases examined the time necessary to the

biomaterial for achieving the complete removal of the undesired

metal was determined. The trends shown in Fig. 3b emphasize that

for the same initial concentration of metal ions, for the same con-

ditions of ionic strength, by considering the same range of time, the

removing heavy metal adsorption process is strongly dependent on

the number of applied gel beads, i.e., the higher the number of

beads the greater the amount of Pb(II) species removed.

The analysis of kinetics based on advanced statistical diagnos-

tics and robust fitting techniques suggested that experimental data

are better reproduced by the DEM which implies two reaction

pathways. One possibility to justify the DEM is that two different

species, most likely diverse type of lead(II) complexes, which

would be absorbed by the alginate gel beads with different rate.

However, this pathways have been ruled out on the base of the

kinetic data obtained in the presence of different ionic medium

(see discussion below). This way, we have reasonably proposed

that the sorption mechanism occurs via two parallel reactions

involving the lead(II) species and two non energetically equivalent

binding sites, namely the specific and non specific binding sites.

A schematic representation of the reaction pathways to which

different rate constant values are associated is depicted in Fig. 4.

It is reasonable to assume that the complex formation between

the heavy metal and the surface functional groups present in the

polymer backbone is faster with respect to the cation exchange

process, i.e., the Ca2+ displacement by the Pb2+ species. These

hypothesis take into consideration that the functional groups are

prone to form the complex with the metal ion due to their avail-

able position on the beads surface, while the calcium cation linking

–COO� groups belonging to different chains exchanges with the

Pb(II) with low rate.

The above depicted reaction pathways have been proposed on

the base of preliminary kinetic investigation on the Ca2+ ion release

by the Ca-A gel beads. The measurements have been performed

both in absence (blank) and in the presence of Pb2+ ions under

some representative experimental conditions of ionic strength,

ionic medium and pH used in the full work, e.g., NaNO3 and NaCl

0.1 mol L�1. Since the Ca2+ ion concentration cannot be determined

by the voltammetric technique the ICP-OES method was applied.

Quantitative analysis of the kinetic data unveiled that, even

though, a relationship between moles of Pb2+ adsorbed and Ca2+

released so far exists it does not respect a 1:1 ratio, i.e., the extent

of lead(II) ions uptake is higher than that of the calcium ions

release. These obtained trends suggested us that lead(II) adsorp-

tion must occur not only via the cationic-exchange mechanism

but an additional pathway could justify the extra uptake. By con-

sidering the –COO� available groups in the alginate chains we have

reasonably ascribed the additional process to the complex forma-

tion between these groups and the undesired metal ions. The attri-

bution of k1 and k2 to the fast complex formation and to the slightly

cation exchange has been intuitively proposed because the Ca2+

displacement from its binding site need more energy and time

with respect to that necessary for the complex formation.

The fast and slow kinetic constant values obtained for the

uptake of heavy metal by 25 Ca-A beads in the absence of added

electrolyte are shown in Table 3. It can be noticed that the rate con-

stant for the complex formation is roughly 6 times that of the cat-

ion exchange.

As concerns the rate of the processes, comparison of the data of

Table 4 reveals that the kinetic constant values strongly depend on

the different experimental conditions applied, namely, NB and

amount of added electrolyte. In particular the presence of NaCl in

the reaction medium leads to higher removal rates. These results

0 50 100 150 200 250

0,0

0,2

0,4

0,6

0,8

1,0

qt

t (min)

(a)

0 50 100 150 200 250

0,0

0,2

0,4

0,6

0,8

1,0

qt

t (min)

(b)

Fig. 3. (a) 25 Beads of Ca-A in 25 mL for different value of ionic strength (NaCl): 0.1 (�); 0.5 (N); 0.8 (.) mol L�1 and no salt added (j); (b) different number of beads (25 (j),

50 (d) and 100 (N)) in 25 mL of Pb 50 ppm and 0.1 mol L�1 NaCl. At room temperature and pH = 5.

82 S. Cataldo et al. / Journal of Colloid and Interface Science 434 (2014) 77–88

seem apparently in contradiction with the expected decrease of the

rate constant on augmentation of the ionic strength, however

might be justified by considering that this dependence is usually

observed for homogeneous medium, while in the present work,

the aqueous gel beads solution constitute an heterogeneous react-

ing aqueous medium. This way, the observed behavior can be

ascribed to the interplay between the diverse swell to which

undergoes the beads in the medium with different salinity and

the electrostatic effects brought about the monovalent anions.

The ‘‘sum’’ of all effects superimposes that in the presence of NaCl

the alginate chain of the gel beads offers to the Pb(II) species more

available binding sites, thus, making easy and fast the lead(II) load-

ing processes.

It has to be noticed that, at each NB and ionic strength values,

the k1 is always lower than k2, indicating that the complex forma-

tion mechanism is favorite with respect to the ion exchange.

Moreover, the obtained k1 values follows the order

k1(NB = 25) > k1(NB = 100) > k1(NB = 50) while the complex forma-

tion rate constants increases pursuing the order k2(NB = 25) < k2(NB = 50) > k2(NB = 100). The latter trends completely match the

swelling gel beads previously observed. This way, it might be rea-

sonably concluded that the peculiar rearrangements of both shape

and size of alginate gel beads induced by the presence of interact-

ing cations and anions may either favor or hamper a given process.

In order to test how the removal process is influenced by pH

changes we studied the lead(II) adsorption process in the presence

of NB = 25 at I (NaCl) = 0.1 mol L�1 and pH = 3.0. Under this exper-

imental condition, functional groups in the backbones of gel beads

are present mainly in the protonated form, i.e., –COOH [62]. Com-

parison of rate constant values determined for NB = 25, at NaCl

0.1 mol L�1 at different pH values shows that k1 at pH = 3 (see

Tables 4 and 5) decreases respect to the value reported at pH = 5,

but k2 associated to the complex formation mechanism is constant

as the pH decreases. The behavior of k2 value can be reasonably

explained by considering that the competition between the H+

and Pb2+ ions for the carboxylic groups favors at low pH the forma-

tion of Pb2+-AA complex species, as the stability of the complex is

greater than the stability of the protonated species.

These results clearly suggest that the lead(II) removal process is

not only governed by the size of the gel beads (either like they are

prepared or modified by the added electrolyte), but also the nature

of additional cations and anions have to play a relevant role.

With this aim the adsorption process has been followed on

varying either the nature of the anions, i.e., the chloride has been

replaced by the nitrate; or by differently dosing the amount of

Ca2+ ions. The obtained results are collected in Tables 5–7. Interest-

ing and clarifying results have been provided by these studies. In

particular, by comparing the effect of the nitrate with that of the

Fig. 4. Reaction scheme.

Table 3

IRLS regression figures of merit and parameters values

for the case with no salt addition, at pH = 5.

I 0

R2 0.9996

R2pred 0.9995

JB test (<9.2) 0.35

Parameters a

k1 0.0133 ± 0.0043

k2 0.0789 ± 0.0039

a min�1.

Table 4

Selected IRLS regression figures of merit and parameters values for the case NaCl at

different ionic strength values and at room temperature, at pH = 5.

Medium

NaCl 0.1 mol L�1 0.5 mol L�1 0.8 mol L�1

NB = 25

R2 0.9985 0.9966 0.9801

R2pred 0.9982 0.9902 0.9739

JB test (<9.2) 2.6 0.4 0.9

Parametersa

k1 0.01580 ± 0.00090 0.01790 ± 0.00070 0.0255 ± 0.0024

k2 0.1217 ± 0.0046 0.367 ± 0.028 0.464 ± 0.088

NB = 50

R2 0.9996 0.9979 0.9947

R2pred 0.9995 0.9975 0.9930

JB test (<9.2) 4.7 0.6 3.7

Parametersa

k1 0.0352 ± 0.0011 0.0190 ± 0.0010 0.0158 ± 0.0010

k2 0.2420 ± 0.0057 0.1537 ± 0.0074 0.270 ± 0.018

NB = 100

R2 0.9996 0.9978 0.9989

R2pred 0.9977 0.9929 0.9971

JB test (<9.2) 1.4 0.96 1.33

Parametersa

k1 0.0726 ± 0.0030 0.0291 ± 0.0241 0.03220 ± 0.00090

k2 0.528 ± 0.016 0.380 ± 0.031 0.441 ± 0.015

a min�1.

S. Cataldo et al. / Journal of Colloid and Interface Science 434 (2014) 77–88 83

chloride anions it can be evidenced that the presence of NaNO3

favors the complex formation between the heavy metal and the

anionic group of the gel beads with respect to the ionic-exchange.

These trends are in line with the different affinity of the two kind of

anions towards the Pb2+ ions. In particular, the Cl� anions exhibits

the ability to form weak complexes with lead ions, thus, its reac-

tions become competitive with those of carboxylic groups present

in alginate beads. This way, the rate of the complex formation is

enhanced by the presence of non-complexing nitrate anions while

that of the ion-exchange with calcium(II) cation is slowed down.

Moreover, both process are inhibited by the increase in the ionic

strength concentration.

Finally, to further corroborate the proposed lead(II) loading

mechanism the kinetic of the heavy metal uptake has been fol-

lowed by applying an ionic medium having different Na+/Ca2+

ratio. Indeed, all the investigated conditions resemble the real

wastewater sample composition.

As concern the alginate gel beads lead(II) removal rate on vary-

ing the composition of a mixture of electrolytes, namely NaCl and

CaCl2, by comparing these data with those above discussed in the

absence of CaCl2 it is worth noting that the simultaneous presence

of both cations affects to a different extent the kinetics of the two

processes. In particular, both uptake processes are faster than

those observed in the absence of the calcium cations, however,

while the kinetic constant associate to the complex formation

increases on increasing the ratio Na+/Ca2+ (by keeping constant

the Ca2+ concentration) the rate of the ionic exchange remains

almost the same. Moreover, an augmentation of the ratio

Na+/Ca2+ (by increasing the concentration of both cations) leads

to a significant enhancement of the removal rates.

Since it would be expected that the simultaneous presence of

the Na+ and Ca2+ cations would slow down the rate of both pro-

cesses (due to the competition with the leads(II) for the binding

sites) and, particularly, the rate of the complex formation has to

be inhibited to a larger extent while the converse has been

detected a ‘‘realistic’’ explanation is necessary.

Most likely, the negative charges of the –COO� groups in the

polymer chains are shielded by the cation species keeping the ionic

strength, even though the major role is played by the calcium(II)

ions, precisely, the higher the Ca2+ concentration the higher the

effect on the rate enhancement. These trends might be explained

by considering that a so high electrolyte content may induce con-

formational transitions in the polymer backbone and in the size of

the beads, which make the sites much more accessible for the

uptaking of the lead(II) ions by the gel beads. Although, the pres-

ence of competitive cations in the reaction medium decreases

the amount of Pb(II) uptaken by the alginate gel beads, the cations

shielding effects on the polymer backbones favor the approaching

of the lead(II) ions, thus, speeding up the bio-adsorption processes.

This way, wherever the adsorption site, namely specific and

non-specific, the heavy undesired metal is faster removed in a

medium whose electrolyte content resemble to those of the real

wastewater sample.

3.3.1. Removal efficiency

The above discussed results unveiled that the amount of loaded

lead ions into the gel beads is strongly dependent on the applied

experimental conditions. Thus, the experimental sorption kinetic

profiles have been exploited to calculate, in analogy with the drug

release profiles already reported [63,64], a parameter, the percent

removal efficiency (RE(%)) which is strictly correlated to the time

required for the removal of lead(II) from the solutions. The removal

efficiency has been calculated by means of the following equation:

REð%Þ ¼ 100SA

R

where SA corresponds to the shaded area under the adsorption

profile up to a fixed time and R is the rectangle area (y100 * t)

described by 100% adsorption in the same time.

The calculated RE% values for all the experimental condition

discussed above are shown in Table 8. It can be easily notated that

this parameter reflects the observed kinetic trends, indeed, is

strongly sensible to both the amount and the kind of electrolyte

forming the ionic reacting medium and the number of applied

gel beads, the pH also play a relevant role. The RE% dependence

from the electrolytes presence in the wastewater model samples

allow to draw the conclusion that whatever the ionic strength is

varied the lead(II) removal is hindered due to the electrostatic

interactions between the undesired metal and the alginate gel

beads. Nevertheless, it is necessary to face with the real sample

composition. However, an interesting remark regards the effect

of the number of beads on the R.E.% parameter; calculations have

given evidence that a growing number of Ca-A gel beads ensures

better performance, i.e., the higher the NB of gel beads the higher

the amount of Pb(II) removed from the sample, the lower the time

needed to reach the maximum removal.

The parameter RE% above described contributes to easily and

simple interpret the adsorption mechanism and to obtain a

detailed knowledge of the most important factors (pH, ionic

strength, composition of ionic medium, etc.) that can influence

the adsorption processes of lead onto alginate gel beads. This infor-

mation is relevant especially in the planning stage of a removal

process of lead ions from wastewaters. Moreover, comparison of

the results obtained in the present work, in the situation mimick-

ing a real wastewater sample, reveals that the uptake capacities of

our alginate gel beads result to be superior to those showed by

some other systems previously studied [65].

3.4. Sorption isotherms

The adsorption isotherms have been constructed by determin-

ing the lead(II) equilibrium concentration (Ce) in the range

3–170 mg L�1, then, the difference between the initial heavy metal

concentration and that left in the aqueous solution was used to

estimate the amount of adsorbed metal (qe) onto the gel beads.

By taking into account the results obtained from the kinetic

Table 5

Selected IRLS regression figures of merit and parameters values for

the case NaCl 0.1 mol L�1, number of beads 25 and pH = 3.0.

NaCl 0.1

R2 0.9493

R2pred 0.9438

JB test (<9.2) 8.1

Parametersa

k1 0.0096 ± 0.0028

k2 0.123 ± 0.032

a min�1.

Table 6

Selected IRLS regression figures of merit and parameters values for the case NaNO3

0.1 and 0.8 mol L�1 and at room temperature, at pH = 5.0.

NaNO3

NB = 25

I 0.1 0.8

R2 0.9949 0.9899

R2pred 0.9946 0.9819

JB test (<9.2) 0.3 1.6

Parametersa

k1 0.02890 ± 0.00080 0.0178 ± 0.0012

k2 1.05 ± 0.89 0.448 ± 0.069

a min�1.

84 S. Cataldo et al. / Journal of Colloid and Interface Science 434 (2014) 77–88

measurements, i.e., the higher the amount of gel beads the higher

the removed metal ion concentration and, indeed, the faster the

uptake velocity; we have used a significant elevated amount of

both the sorbent and sorbate to improve the loading efficiency of

the alginate gel beads, namely, the lead ions was set at 200 mg L�1

while the beads quantities was varied over the wide range

(5 6 NB 6 100). Moreover, by considering the peculiar trends

obtained for the kinetic constant as a function of the type of salt

used to fix the medium ionic strength, the isotherms have been

gathered for NaCl at 0.1 mol L�1 and for NaCl + CaCl2 at 0.1 mol L�1

([NaCl] = 0.01 mol L�1 and [CaCl2] = 0.03 mol L�1) while the pH was

fixed at 5.0.

The equilibrium voltammetric values, obtained under the dif-

ferent experimental conditions, have been used to construct the

adsorption isotherms depicted in Fig. 6, where the equilibrium

amount of heavy metal adsorbed into the gel bead (qe, mg g�1) is

plotted as a function of Ce.

Perusal of Fig. 5 clearly evidences that the amount of adsorbed

Pb(II) species increases on increasing the equilibrium metal con-

centration and depends to a significant extent on the nature of

the inorganic salt used to keep constant the ionic strength. In par-

ticular, for each Ce value the corresponding qe is higher when only

the NaCl regulates the ionic strength, while the presence of mixed

electrolytes implies a less Pb(II) uptake into the gel beads. This

result is in line with our explanation given in the previous section

dealing with the kinetic evidence of the effect of the mixed med-

ium. We briefly recall that both the Na+ and Ca2+ ions free in the

aqueous suspension compete with the heavy metal for the avail-

able active sorption sites, which in turn reflects into a noticeable

decrease of the maximum removing quantities of the heavy metal

from the aqueous solution. Moreover, by neutralizing the negative

charges present in the polymer chains they may lead to a contrac-

tion of the beads, which, in turn, reflects into a lower metal ions

uptake.

Modeling the adsorption data in terms of adsorption isotherm

equation is a cogent and crucial task in the design of application

of proper protocols for the wastewater treatment.

Several adsorption models reported in the literature [66,67] are

based either on one-binding sites or two-binding sites, in the for-

mer the sites of the adsorbent are homogeneously equivalent,

independent and characterized by the same energy while in the

latter the solid adsorbent exhibits two types of sites to which cor-

respond strong and weak binding affinities toward the adsorbate,

being consequently different energies.

The adsorption isotherm models reported in Table 1 have been

applied to analyze our data. The obtained adsorption parameters

are collected in Table 9.

Inspection of Table 9 and Fig. 5 evidences that the adsorption

isotherm model of Sips and Freundlich, for the systems NaCl and

NaCl + CaCl2, respectively, exhibit a good fit to experimental data.

These empirical equations are based on the assumption that the

adsorption process takes place on two different populations of

binding sites of the adsorbent.

The Sips equation overcame the problem of the Freundlich

equation of the continuing increase in the adsorbed amount with

an increase in concentration. In fact, the two equations are similar

Table 7

Selected IRLS regression figures of merit and parameters values for the case ‘‘Mixed NB = 25’’ for the concentrations 0.1, 0.5 (0.03 + 0.41), 0.5 (0.163 + 0.01) and 0.8 (0.03 + 0.71).

Medium

NaCl + CaCl2 0.1 mol L�1 0.5 mol L�1 (0.03 + 0.41) 0.8 mol L�1 (0.03 + 0.71)

NB = 25

R2 0.9925 0.9974 0.9913

R2pred 0.9911 0.9953 0.9818

JB test (<9.2) 4.3 8.0 1.1

Parametersa

k1 0.0221 ± 0.0012 0.02170 ± 0.00080 0.0227 ± 0.0018

k2 0.494 ± 0.070 0.597 ± 0.039 0.417 ± 0.036

NaCl + CaCl2 0.5 mol L�1 (0.163 + 0.01)

NB = 25

R2 0.9904

R2pred 0.9669

JB test (<9.2) 5.4

Parametersa

k1 0.0359 ± 0.0031

k2 0.88 ± 0.19

a min�1.

Table 8

Percent removal efficiency for the systems investigated.

Medium I/mol L�1 RE%

NB

25 50 100

No salt 0 92

NaCl 0.1 81 90 94

0.5 62 72 84

0.8 54 69 81

NaCl (pH = 3) 0.1 64

NaNO3 0.1 83

0.8 70

NaCl + CaCl2 0.1 76

0.5 (0.41 + 0.03) 58

0.5 (0.01 + 0.163) 53

0.8 (0.71 + 0.03) 44

0 40 80 120

150

300

450

600

qe (

mg

g-1

)

Ce (mg L-1)

Fig. 5. Adsorption isotherms of Pb2+ ions in NaCl (square) and NaCl + CaCl2 (circle)

0.1 mol L�1 at room temperature.

S. Cataldo et al. / Journal of Colloid and Interface Science 434 (2014) 77–88 85

but the Sips has a finite limit when the adsorbate concentration is

sufficiently high.

Comparison of the obtained binding constant values reveals

that the alginate gel beads adsorb the Pb(II) in sites with different

binding affinities, however, the estimated binding constant values

represent the average value of each binding value in each site. The

value of n lower than 1 clearly indicate that the adsorption sites in

the gel beads are heterogeneous in nature.

Thus, in the light of the kinetic results, the complementary

equilibrium data suggest that the alginate gel beads offer two types

of binding sites, heterogeneous in nature and with different affin-

ities, for the removal of lead(II) from a water waste model accord-

ingly to two pathways mechanism which occur at different rate

(see kinetic data section for the discussion).

However, to unambiguously verify these assessment we have

treated the equilibrium data through the Scatchard plot analysis,

which is also known as independent site-oriented model. The Scat-

chard equation, below reported, derives from the mathematical

transformations of the classical Langmuir equation where there

exist a relationship between amount of the adsorbed per unit con-

centration of aqueous bulk solution (qe/Ce) and qe

qe=Ce ¼ qmKL � KLqe ð2Þ

Thus, the qe/Ce values must depend linearly on qe. It is important

to evidence that the mathematical transformation of the Langmuir

equation results to be a very useful and informative process for

two main reasons. First, by normalizing the qe value the effect of

concentration on the shape of Scatchard plot is theoretically elim-

inated; second, if deviations in the qe/Ce versus qe plot from the

linearity are observed they can be attributed to different binding

sites available to the adsorbate, which, in other words, correspond

to diverse affinities phenomena.

From the Scatchard analysis of our data shown in Fig. 6(a and b)

we can highlight that the curvature of the curves is upward which

is indicative of negative cooperations. These type of interactions

implies that once the uptake of the Pb(II) species occurs, indepen-

dently of the binding sites, their presence on the alginate gel beads

hampers the further adsorption, as a consequence, the removed

heavy metal amount decreases. Moreover, the existence of two

regions of behavior can be detected. Usually, the region with high

slope is associate to specific binding site (high affinity), while that

with low slope corresponds to non-specific binding (low affinity).

It can be noticed that, at low Pb(II) concentration, the binding is

specific while at high concentration the binding becomes non-spe-

cific. These trends can be explained by considering that the Pb(II)

ions at low concentration adsorb into the gel beads in sites, being

high affinities, by forming the complex with the available –COO�

groups of the alginate chains ion while, at high heavy metal ions

concentration, the metal cations displace the Ca2+ crosslinked in

the alginate chains. As more metal ions are bound to alginate,

the alginate chains have to rearrange to coordinate them. This

way, the polymer backbones undergo to a tighter conformation

that hinders further chain rearrangement hence making some

sorption sites non-accessible.

Finally, in order to obtain information about the nature of the

heavy metal/gel beads interaction, the analysis of the equilibrium

data has been also performed by means of the Dubinin–Radushke-

vich (DR) equation:

100 200 300 400 500 600 700

0

10

20

30

40

50

60

70

80q

e/C

e (

L g

-1)

qe (mg g

-1)

(a)

100 200 300 400 500

0

5

10

15

20

qe

(mg g-1

)

qe/C

e (

L g

-1)

(b)

0,0 0,5 1,0 1,5 2,0 2,5

4,5

5,0

5,5

6,0

6,5

ln q

e

e2

(kJ2 mol

-2)

(c)

0,00 0,05 0,10 0,15 0,20 0,25

4,5

5,0

5,5

6,0

6,5

ln q

e

ε2

(kJ2 mol

-2)

(d)

Fig. 6. Scatchard plots of Pb2+ adsorption at t = 25 �C in 0.1 mol L�1 of NaCl (a) and NaCl + CaCl2 (b); Dubinin–Radushkevich adsorption isotherms of Pb2+ at t = 25 �C in

0.1 mol L�1 of NaCl (c) and NaCl + CaCl2 (d).

86 S. Cataldo et al. / Journal of Colloid and Interface Science 434 (2014) 77–88

ln qe ¼ ln qm � ke2 ð3Þwhere k is a constant related to adsorption energy and e is RT ln

(1 + 1/Ce).

The DR approach gave rise to curved plots which means that

free energy of adsorption changes on changing the amount of sor-

bate already adsorbed (Fig. 6(c) and (d)). Thus, we can say that

each equilibrium data treatment drives to the conclusion that the

lead(II) adsorption into alginate gel beads takes place trough two

different pathways at two independent binding sites. At this stage,

we can conclude that the affinity analysis represents an efficient

tool for setting up the proper experimental conditions to be

applied for achieving a quantitative removing of the heavy metal

system. Moreover, the gathered information could be fruitful

exploited to significantly diminish both the cost and the time of

the whole process.

4. Conclusion

In the present work we have realized a very efficient, perfor-

mant and low cost system for removing undesired heavy metal

ions, namely Pb(II) species, from a model wastewater sample.

The information provided by kinetic and equilibrium comple-

mentary studied have been exploited to elucidate the adsorption

mechanism of the lead(II) species into alginate gel beads.

The proposed mechanism pathways have been corroborated

through the SEM characterization of the blank and Pb(II)-loaded

gel beads. Swelling behavior of the alginate gel beads has com-

pleted the picture.

DP-ASV can be considered an appropriate experimental tool to

perform kinetic and equilibrium investigations in terms of accu-

racy, high sensitivity and selectivity.

The obtained removal efficiency of the calcium-alginate gel

beads has been found to strongly depend on the internal parame-

ters, i.e., number of gel beads, nature and concentration of the

added electrolyte and pH, of the applied system. All parameters

play a role in influencing the wastewater treatment process, how-

ever, the number of gel beads take part as key crucial components,

i.e., the higher the number of beads the greater the amount of

Pb(II) species removed from the sample, the lower the time needed

to reach the maximum removal.

The effectiveness of the robust procedures involved in this work

suggests to systematically adopt robust data treatment in regres-

sion and related diagnostics in a research, in order to draw a com-

plete picture for real processes.

Acknowledgments

The authors carried out this work thanks to a grant from the

project ‘‘Development of innovative technologies for the treatment

of fluid wastes from shipping activities and for marine environ-

ment protection’’ (PON02_00153_2849085 ‘‘Ricerca e competiti-

vità 2007–2013, asse 1’’).

Appendix A

n number of observations

p number of refined parameters

SSM Model Sum of Squares

SSR Regressional Sum of Squares

SST Total Sum of squares

R correlation coefficient

R2 coefficient of determination

R2adj adjusted R-squared

p1, p2, p3,

p4

parameter 1–4 refined. Referring to Table 2., for

FOM p1 = Qe, p2 = k1; for SOM p1 = Qe, p2 = k; for

DEM p1 = A1, p2 = k1, p3 = A2, p4 = k2; for HM

p1 = kH, p2 = C; for WM p1 = k, p2 = b, p3 = C

s.u. (pn) standard uncertainty for the nth parameter

t (pn) t-statistic value for the nth parameter

VIF variance inflation factors for each parameter,

defined as in this work the threshold of 5 has been

adopted (VIF < 5)

ME mean error

r standard deviation of the residuals

DW Durbin–Watson test for the autocollinearity of the

residuals

MLT Modified Levene Test for constant variance [53]

(continued on next page)

Table 9

Sorption isotherm parameters of Pb2+ by alginate gel beads at room temperaturea. Symbols as in Appendix A.

Langmuir Freundlich

NaCl NaCl + CaCl2 NaCl NaCl + CaCl2

qm (mg g�1) 673 ± 20 540 ± 43 KF (mg(1�n) g�1 Ln) 139 ± 24 47.0 ± 2.0

KL (L g�1) 0.117 ± 0.011 0.030 ± 0.010 n 0.331 ± 0.040 0.463 ± 0.010

R2 0.99399 0.97688 R2 0.93456 0.99911

AICc 45.16 44.49 AICc 61.88 24.90

Sips

NaCl NaCl + CaCl2

qm (mg g�1) 728 ± 24 2300 ± 1000

KS (L mg�1) 0.090 ± 0.010 0.00050 ± 0.00070

n 0.840 ± 0.044 0.526 ± 0.036

R2 0.99848 0.99956

AICc 42.54 30.64

Double Langmuir

NaCl NaCl + CaCl2

qm1 (mg g�1) 580 ± 150 790 ± 100

K1 (L g�1) 0.069 ± 0.028 0.0050 ± 0.0010

qm2 (mg g�1) 130 ± 160 158 ± 23

K2 (L g�1) 0.61 ± 0.87 0.192 ± 0.047

R2 0.998857 0.99982

AICc 54.51 55.36

a qm, qm1 and qm2 are maximum adsorption capacities while K (with the proper subscript) state for equilibrium constant.

S. Cataldo et al. / Journal of Colloid and Interface Science 434 (2014) 77–88 87

Res+,Res- number of the residuals greater than ME and less

than ME respectively for the Residuals Run Test

(Wald Wolfowitz One Tail Distributions Runs

Test)

P. prob. Passed probability for the sign Residuals Run

Tests

PRESS Predicted Residual Sums of Squares

RMSE Root Mean Square Error, defined as (SSR/n)1/2

RMSP Root Mean Square Press error, defined as (PRESS/

n)1/2

R2 pred R2 prediction, defined as [1 � (PRESS/SST)] * 100

AIC Akaike Information Criterion, defined as

n�(log(SSR/n) + 2(p/n))

AICc corrected Akaike Information Criterion defined as

n�(log(SSR/n) + 2(p/n)�log(log(n)))F-test F statistics defined as R2/p/(1�R2)/(n�p�1)

Appendix B. Supplementary material

Supplementary data associated with this article can be found, in

the online version, at http://dx.doi.org/10.1016/j.jcis.2014.07.042.

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