Review of second-order models for adsorption systems
Yuh-Shan Ho
∗
School of Public Health, Taipei Medical University, 250 Wu-Hsing Street, Taipei 11014, Taiwan
Received 24 November 2004; received in revised form 2 April 2005; accepted 29 December 2005 Available online 7 February 2006
Abstract
Applications of second-order kinetic models to adsorption systems were reviewed. An overview of second-order kinetic expressions is described
in this paper based on the solid adsorption capacity. An early empirical second-order equation was applied in the adsorption of gases onto a solid.
A similar second-order equation was applied to describe ion exchange reactions. In recent years, a pseudo-second-order rate expression has been
widely applied to the adsorption of pollutants from aqueous solutions onto adsorbents. In addition, the earliest rate equation based on the solid
adsorption capacity is also presented in detail.
© 2006 Elsevier B.V. All rights reserved.
Keywords: Kinetics; Second-order; Pseudo-second-order; Biosorption; Sorption
1. Introduction
Predicting the rate at which adsorption takes place for a
given system is probably the most important factor in adsorption
system design, with adsorbate residence time and the
reac-tor dimensions controlled by the system’s kinetics. A number
of adsorption processes for pollutants have been studied in an
attempt to find a suitable explanation for the mechanisms and
kinetics for sorting out environment solutions. In order to
inves-tigate the mechanisms of adsorption, various kinetic models
have been suggested. In recent years, adsorption mechanisms
involving kinetics-based models have been reported. Numerous
kinetic models have described the reaction order of adsorption
systems based on solution concentration. These include
first-order
[1]
and second-order
[2]
reversible ones, and first-order
[3]
and second-order
[4]
irreversible ones, pseudo-first-order
[5]
and pseudo-second-order ones
[6]
based on the solution
concentration. On the other hand, reaction orders based on the
capacity of the adsorbent have also been presented, such as
Lagergren’s first-order equation
[7]
, Zeldowitsch’s model
[8]
,
and Ho’s second-order expression
[9–12]
.
This paper describes an earlier adsorption rate equation based
on the solid capacity for a system of liquids and solids
[7]
, the
Elovich equation for adsorption of gases onto a solid and
apply-∗Tel.: +886 2 2736 1661x6514; fax: +886 2 2738 4831.
E-mail address: [email protected].
ing a second-order rate equation for gas/solid and solution/solid
adsorption systems
[8]
, a second-order rate expression for ion
exchange reactions
[13]
, and a pseudo-second-order expression
[9]
.
2. Modeling
2.1. Second-order rate equation
A linear form of the typical second-order rate equation is
1
C
t= k
2t +
1
C
0,
(1)
where C
tis the equilibrium concentration (mg/dm
3), C
0the
ini-tial concentration (mg/dm
3), t the time (min), and k
2is the rate
constant (dm
3/mg min).
Early applied second-order rate equations in solid/liquid
sys-tems described reactions between soil and soil minerals
[14,15]
.
Others applied which the second-order rate equation included
the adsorption of fluoride onto acid-treated spent bleaching earth
[16]
; and the adsorption of water using the dealumination of
HZSM-5 zeolite by thermal treatment
[17]
. Moreover,
Varsh-ney et al. reported the kinetics of adsorption of the pesticide,
phosphamidon, on beads of an antimony(V) phosphate cation
exchanger during the first 15 min
[18]
.
0304-3894/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jhazmat.2005.12.043
2.2. Lagergren’s equation
As early as 1898
[7]
, Lagergren described liquid–solid phase
adsorption systems, which consisted of the adsorption of oxalic
acid and malonic acid onto charcoal. Lagergren’s first-order rate
equation is the earliest known one describing the adsorption rate
based on the adsorption capacity. It is summarised as follows:
d
x
d
t
= k(X − x),
(2)
where X and x (mg/g) are the adsorption capacities at equilibrium
and at time t (min), respectively, and k is the rate constant of the
first-order adsorption (1/min).
Eq.
(2)
was integrated with the boundary conditions of t = 0
to t = t and x = 0 to x = x to yield
ln
X
X − x
= kt
(3)
and
x = X(1 − e
−kt)
.
(4)
Eq.
(3)
may be rearranged to a linear form:
log(
X − x) = log(X) −
k
2
.303
t.
(5)
In order to distinguish kinetics equations based on
concentra-tions of solution from adsorption capacities of solids,
Lager-gren’s first-order rate equation has been called pseudo-first-order
[10,19–22]
. An early known application of Lagergren’s kinetics
equation to adsorption was undertaken by Trivedi et al.
[23]
for
the adsorption of cellulose triacetate from chloroform onto
cal-cium silicate. During the last four decades, the kinetics equation
has been widely applied to the adsorption of pollutants from
aqueous solutions
[24]
.
2.3. Elovich’s equation
Elovich’s equation is another rate equation based on the
adsorption capacity. In 1934
[8]
, the kinetic law of
chemisorp-tion was established though the work of Zeldowitsch. The rate of
adsorption of carbon monoxide on manganese dioxide
decreas-ing exponentially with an increase in the amount of gas adsorbed
was described by Zeldowitsch
[8]
. It has commonly been called
the Elovich equation in the following years:
d
q
d
t
= a e
−αq
,
(6)
where q is the quantity of gas adsorbed during the time t,
α the
initial adsorption rate, and a is the desorption constant during any
one experiment. The integrated form of Eq.
(6)
can be written
in the form
q =
2
.3
α
log(
t + t
0)
−
2
.3
α
log
t
0(7)
with
t
0=
1
αa
.
(8)
With a correctly chosen t
0, the plot of q as a function of log(t + t
0)
should yield a straight line with a slope of 2.3/
α; Eq.
(8)
then
gives a which obviously represents the initial rate of adsorption
for q = 0. The test thus involves one single disposable parameter,
t
0, which is found by trial; if t
0is too small, the curve is
con-vex, and if t
0is too large, it is concave to the axis of log(t + t
0)
[25]
. This Elovich equation is commonly used to determine the
kinetics of chemisorption of gases onto heterogeneous solids,
and is quite restricted, as it only describes a limiting property
ultimately reached by the kinetic curve
[26]
.
To simplify Elovich’s equation, Chien and Clayton
[27]
assumed that a
αt 1 and by applying the boundary conditions
of q = 0 at t = 0 and q = q at t = t, then Eq.
(6)
becomes
[28]
:
q = α ln(aα) + α ln(t).
(9)
Thus, the constants can be obtained from the slope and the
inter-cept of a straight line plot of q against ln(t). Recently, Rudzinski
and Panczyk
[29]
published an exhaustive analysis of existing
rationalizations for the Elovich equation found in the literature
for the kinetics of adsorption onto heterogeneous surfaces.
In earlier years, numerous applications of Elovich’s
equa-tion to the adsorpequa-tion of gases onto solid systems were reported
[30,31]
. During the last three decades, the equation has been
widely used to describe the kinetics of adsorption of gases
onto solids
[29,32–35]
. The most frequently cited paper for the
application of Elovich’s equation to adsorption systems was an
alternative to Elovich’s equation for kinetics of adsorption of
gases onto solids
[33]
. An earlier application of the rate
equa-tion of Elovich was the exchange of
32P between the goethite
(␣-FeOOH) crystal surface and the solution phase
[36]
. The
application of Elovich equation to the kinetics of phosphate
release and adsorption in soils
[27]
is the most frequently cited
paper on the adsorption in solution/solid systems. In addition, the
Elovich equation has also been used to describe the adsorption
of pollutants from aqueous solutions in recent years
[19,37,38]
.
2.4. Ritchie’s equation
In 1977
[33]
, Ritchie reported a model for the adsorption of
gaseous systems. Assumptions were made as follows:
θ is the
fraction of surface sites which are occupied by an adsorbed gas,
n the number of surface sites occupied by each molecule of the
adsorbed gas, and
α is the rate constant. Assuming that the rate
of adsorption depends solely on the fraction of sites which are
unoccupied at time t, then
d
θ
d
t
= α(1 − θ)
n.
(10)
Eq.
(10)
integrates to
1
(1
− θ)
n−1= (n − 1)αt + 1 for n = 1
(11)
or
θ = 1 − e
−αtfor
n = 1.
(12)
It is assumed that no site is occupied at t = 0. When introducing
the amount of adsorption, q, at time t, Eq.
(11)
becomes
q
n−1∞
(
q
∞− q)
n−1= (n − 1)αt + 1
(13)
and similarly Eq.
(12)
becomes
q = q
∞(1
− e
−αt)
,
(14)
where q
∞is the amount of adsorption after an infinite time.
In earlier years, Sobkowsk and Czerwi´nski
[39]
presented a
rate equation for the reaction of carbon dioxide adsorption onto
a platinum electrode:
d
θ
d
t
= k(1 − θ)
n
,
(15)
where
θ = Γ /Γ
∞denotes the surface coverage by the reaction
products,
Γ and Γ
∞the surface concentrations at time t and after
completion of the reaction, respectively, k the rate constant, and
n is the order of the reaction.
When n = 1,
−ln(1 − θ) = k
1t.
(16)
When n = 2,
θ
1
− θ
= k
2t.
(17)
Sobkowsk and Czerwi´nski
[39]
concluded that the first-order
is only for low surface concentrations of a solid, confirmed by
using plots of
−ln(1 − θ) versus time as Eq.
(16)
, and the
second-order is for higher concentrations of a solid, confirmed by using
plots of
θ/(1 − θ) versus time as Eq.
(17)
. In addition, Trasatti and
Formaro reported that the plot of
−ln(1 − θ) versus time is not
linear for very long times, when the coverage reaches a
station-ary value for the adsorption of glycolaldehyde onto a platinum
electrode
[40]
. In the case of the sorption of basic dyes from
aqueous solution onto sphagnum moss peat, Ho and McKay
[22]
found that log(q
e− qt) versus time was only applicable in
the early stage of the reaction. In the case of adsorption of gases
onto a solid surface, Sobkowsk and Czerwi´nski reported that
the first-order rate equation could only be used for a low surface
concentration of gases adsorbed onto a solid surface, and the
second-order rate evaluation could be applied to higher
concen-trations
[39]
.
Several adsorption results were examined using the Ritchie
equation
[33]
. In the early years, the Elovich equation was
applied to describe gas and vapour adsorption systems, such
as the adsorption of carbon monoxide during the oxidation
of polyvinylidene chloride
[41]
, the chemisorption of
hydro-gen onto graphon
[42]
, the measuring of the kinetics of the
chemisorption of H
2onto a MoS
2+ Al
2O
3catalyst
[43]
, and the
adsorption of water vapour by Vycor fibre
[44]
. These systems
did not fit the Elovich equation very well. Ritchie
[33]
examined
these results using Eq.
(13)
when n = 2. Eq.
(13)
becomes
q
∞(
q
∞− q)
= αt + 1.
(18)
The value for q
∞is obtained from the intercept at (1/t) = 0 on
a plot of (1/q) against (1/t). Ritchie found a good linear
rela-tionship between t and q
∞/(q
∞− q) for the results of Austin et
al.
[41]
, Bansal et al.
[42]
, Deitz and Turner
[44]
, and Samuel
and Yeddanapalli
[43]
. In recent years, the Ritchie equation
has also been applied to solution/solid adsorption systems, for
example, the adsorption of cadmium ions onto bone char
[37]
,
and the adsorption of Cd(II) onto acid-treated jackfruit peel
[45]
.
2.5. Second-order rate expressions
In 1984
[13]
, Blanchard et al. presented the overall exchange
reaction of NH
4+ions fixed in zeolite by divalent metallic ions
in the solution which can be written:
Z
(2NH4+)+ M
2+→ Z
(M2+)+ 2NH
4+,
(19)
where Z
(2NH4+)and Z
(M2+)are the amounts of NH
4+ion fixed in
the zeolite (meq/g), and M
2+and NH
4+are the concentrations
(meq/dm
3).
The authors assumed that the metallic concentration varies
very slightly during the first hours, and the kinetic order is two
with respect to the number (n
0− n) of available sites for the
exchange; thus, the differential equation can be written as
−
d
n
d
t
= K[n
0− n]
2
(20)
and integration gives
1
(
n
0− n)
− α = Kt,
(21)
where n is the amount of M
2+fixed or the amount of NH
4+released at each instant, n
0the exchange capacity, and K is the
rate constant.
Considering the boundary condition n = 0 for t = 0, it follows
that
α = 1/n
0. By plotting 1/(n
0− n) as a function of time, a
straight line must be obtained, the slope of which gives the rate
constant, K, and the intercept gives the exchange capacity. In
recent years, the Blanchard second-order expression has been
used to describe the kinetics of exchange processes between
sodium ions from zeolite A and cadmium, copper, and nickel
ions from solutions
[46]
.
An expression of second-order rate based on solid capacity
has also been presented for the kinetics of adsorption of
diva-lent metal ions onto peat
[9–12]
. Peat contains polar functional
groups such as aldehydes, ketones, acids, and phenolics. These
groups can be involved in chemical bonding and are
respon-sible for the cation exchange capacity of the peat. Thus, the
peat–copper reaction may be represented in two ways
[47]
:
2P
−+ Cu
2+↔ CuP
2(22)
and
2HP
+ Cu
2+↔ CuP
2+ 2H
+,
(23)
In an attempt to present the equation representing adsorption
of divalent metals onto sphagnum moss peat during agitation,
the assumption was made that the process may be second-order
and that chemisorption occurs involving valency forces through
sharing or the exchange of electrons between the peat and
diva-lent metal ions as covadiva-lent forces. The rate of the second-order
reaction may be dependent on the amount of divalent metal ions
on the surface of the peat, and the amount of divalent metal
ions adsorbed at equilibrium
[9,12]
. The rate expression for the
adsorption described by Eqs.
(24)
and
(25)
is
d(P)
td
t
= k[(P)
0− (P)
t]
2(24)
or
d(HP)
td
t
= k[(HP)
0− (HP)
t]
2,
(25)
where (P)t
and (HP)t
are the number of active sites occupied
on the peat at time, t, and (P)
0and (HP)
0are the number of
equilibrium sites available on the peat.
The driving force, (q
e− qt), is proportional to the available
fraction of active sites. The kinetic rate equations can be
rewrit-ten as follows:
d
q
td
t
= k(q
e− q
t)
2
,
(26)
where k is the rate constant of adsorption (g/mg min), q
ethe
amount of divalent metal ions adsorbed at equilibrium (mg/g),
and qt
is the amount of divalent metal ions on the surface of the
adsorbent at any time, t (mg/g).
Separating the variables in Eq.
(26)
gives
d
q
t(
q
e− q
t)
2= k dt
(27)
and integrating this for the boundary conditions t = 0 to t = t and
q
t= 0 to qt
= qt, gives
q
t=
q
2 ekt
1
+ q
ekt
(28)
which is the integrated rate law for a second-order reaction. Eq.
(28)
can be rearranged to obtain
q
t=
1t
kq2 e+
t qe(29)
which has a linear form of
t
q
t=
1
kq
2 e+
1
q
et
(30)
and
h = kq
2 e,
(31)
where h is the initial adsorption rate (mg/g min) as qt/t
approaches 0, and Eq.
(29)
can be rearranged to obtain
q
t=
1t
h+
qte(32)
and
t
q
t=
1
h
+
1
q
et.
(33)
The rate of a reaction is defined as the change in concentration of
a reactant or product per unit time. Concentrations of products
do not appear in the rate law because the reaction rate is studied
under conditions where the reverse reactions do not contribute
to the overall rate. The reaction order and rate constant must
be determined by experiments. In order to distinguish the
kinet-ics equation based on the concentration of a solution from the
adsorption capacity of solids, this second-order rate equation
has been called a pseudo-second-order one
[9]
. The
pseudo-second-order model constants can be determined experimentally
by plotting t/qt
against t. Although there are many factors which
influence the adsorption capacity, including the initial adsorbate
concentration
[12,48–51]
, the reaction temperature
[10,12,50]
,
the solution pH value
[52,53]
, the adsorbent particle size
[48]
and
dose
[12,48,51]
, and the nature of the solute
[12,54]
, a kinetic
model is concerned only with the effect of observable
parame-ters on the overall rate. The pseudo-second-order expression has
been successfully applied to the adsorption of metal ions, dyes,
herbicides, oils, and organic substances from aqueous solutions
(
Table 1
).
Recently, a theoretical analysis of the pseudo-second-order
model was reported
[139]
. The advantage of the Azizian
deriva-tion is that when the initial concentraderiva-tion of solute is low, then
the adsorption process obeys the pseudo-second-order model.
Conversely pseudo-first-order models can be applied to higher
initial concentrations. The rate constant of the
pseudo-second-order model is a complex function of the initial concentration of
the solute.
Table 2
shows a comparison of second-order rate equations
of Sobkowsk and Czerwi´nski
[39]
, Ritchie
[33]
, Blanchard et al.
[13]
, and Ho
[9]
. In earlier years, Sobkowsk and Czerwi´nski used
the second-order rate equation based on the adsorption capacity
of a solid for higher concentrations of solids with the rate of
reaction of carbon dioxide adsorption onto a platinum electrode
[39]
. Ritchie presented a second-order empirical equation to test
the adsorption of gases onto solids
[33]
. Blanchard et al. reported
a similar rate equation for the exchange reaction of NH
4+ions
fixed in zeolite by divalent metallic ions in solution
[13]
. Ho
described adsorption which included chemisorption and gave
a different idea of the second-order equation called a
pseudo-second-order rate expression
[9]
.
In many cases, the equilibrium adsorption capacity is
unknown, and chemisorption tends to become immeasurably
slow and the amount adsorbed is still significantly smaller than
the equilibrium amount
[140]
. On the other hand, achieving
equi-librium takes a long time in some adsorption systems
[141–143]
.
However, the pseudo-second-order equation has the following
advantages: it does not have the problem of assigning an
effec-tive adsorption capacity, i.e., the adsorption capacity, the rate
constant of pseudo-second-order, and the initial adsorption rate
all can be determined from the equation without knowing any
parameter beforehand.
Table 1
Pseudo-second-order kinetic model of various related systems from the literature
Adsorbent Adsorbate References
2-Mercaptobenzimidazole clay
Hg(II) [55]
Activated carbon 2,4-Dichlorophenoxy-acetic acid
[56]
Activated carbon Cd(II) [57]
Activated carbon Cd(II) [58]
Activated carbon Cd(II), Ni(II) [59]
Activated carbon Congo red [60]
Activated carbon Direct blue 2B, Direct green B
[61]
Activated carbon Hg(II) [62]
Activated carbon Hg(II) [63]
Activated carbon Methylene blue [64]
Activated carbon Paraquat dichloride [65]
Activated carbon Co(II) [66]
Activated carbon Pb(II) [67]
Activated carbon Pb(II) [68]
Activated carbon Pb(II), Hg(II), Cd(II), Co(II)
[69]
Activated clay Basic red 18, Acid blue 9 [70]
Aeromonas caviae Cr(VI) [71]
Alginate Ni(II) [72]
Anaerobic granular sludges Ni(II), Co(II) [73]
Aspergillus niger Acid blue 29 [74]
Aspergillus niger Basic blue 9 [75]
Aspergillus niger Congo red [76]
Aspergillus niger Pb(II), Cd(II), Cu(II), Ni(II) [77]
Azadirachta indica (Neem)
leaf
Congo red [78]
Azadirachta indica (Neem)
leaf
Pb(II) [79]
Baker’s yeast Cd(II) [80]
Banana stalk Musa
paradisiacal
Hg(II) [81]
Beech leaves Cd(II) [11]
Bentonite Acid red 57, Acid blue 294 [82]
Bi2O3 Cr(VI) [11]
Blast furnace slag, dust, sludge, carbon slurry
Chlorophenols [83]
Bottom ash Cu(II), Pb(II) [11]
Calabrian pine bark Zn(II), Pb(II) [84]
Calcined alunite Phosphorus [85]
Calcined Mg–Al–CO3
hydrotalcite
Cr(VI) [86]
Cassava waste biomass Cu(II), Cd(II) [87]
Chitin Cd(II) [88]
Chitin, chitosan, Rhizopus
arrhizus
Cr(VI), Cu(II) [38]
Chitosan Cu(II) [89]
Chitosan Ni(II) [90]
Clinoptilolite Pb(II) [91]
Coconut coir pith 2,4-Dichlorophenol [92]
Coconut coir pith Cr(VI) [93]
Coir Cu(II), Pb(II) [94]
Cypress leaves Pb(II) [11]
Date pits Methylene blue [95]
Date pits Phenol [96]
Diatomaceous clay Methylene blue [97]
Dolomite Phosphate [98]
Fly ash Congo red [99]
Fly ash Omega chrome red ME,
o-cresol, p-nitrophenol
[100]
Fly ash Victoria blue, OCL, PNP,
OCRME
[11]
Table 1 (Continued)
Adsorbent Adsorbate References
Grafted silica Pb(II), Cu(II) [101]
Grape stalks Cr(VI) [102]
Iron oxide-coated sand As(V), As(III) [103]
Jordanian low-grade phosphate
Pb(II) [104]
Juniper fiber Cd(II) [105]
Juniper fiber Phosphorus [106]
Mesoporous silicate Phosphate [107]
Mg–Al–CO3hydrotalcite Cr(VI) [108]
Microcystis Ni(II), Cr(VI) [109]
Microporous titanosilicate ETS-10
Pb(II) [110]
Mixed clay/carbon Acid blue 9 [111]
Mucor rouxii Pb(II), Cd(II), Ni(II), Zn(II) [112]
Myriophyllum spicatum Pb(II), Zn(II), Cd(II) [113]
Na-bentonite Oil [114]
Oil shale 4-Nitrophenol [115]
Peat Basic blue 69, Acid blue 25 [11]
Peat Basic green 4, Basic violet
4, Basic blue 24
[116]
Peat Cu(II) [117]
Peat Cu(II) [11]
Peat Cu(II) [118]
Peat-resin particle Basic magenta, Basic brilliant green
[119]
Perlite Cd(II) [120]
Perlite Methylene blue [121]
Pith Basic red 22, Acid red 114 [122]
Reed leaves Cd(II) [11]
Rhizopus oligosporus Cu(II) [123]
Rhodotorula aurantiaca Pb(II) [124]
Sago Cu(II), Pb(II) [125]
Sawdust Cd(II), Pb(II) [126]
Sawdust Phenol [127]
Schizomeris leibleinii Pb(II) [128]
Sepiolite Pb(II) [129]
Spent grain Pb(II), Cd(II) [130]
Sphagnum moss peat Chrysoidine, Astrazon blue, Astrazone blue
[22]
Sphagnum moss peat Cu(II), Ni(II) [131]
Sphagnum moss peat Cu(II), Ni(II), Pb(II) [12]
Sugar beet pulp Pb(II) [132]
Sugar beet pulp Pb(II), Cu(II), Zn(II), Cd(II), Ni(II) [133] Surfactant-modified clinoptilolite Phosphate [134] TNSAC Phosphate [11]
Tree fern Basic red 13 [135]
Tree fern Cd(II) [136]
Tree fern Cu(II) [49]
Tree fern Pb(II) [50]
Vermiculite Cd(II) [137]
Waste tyres, sawdust Cr(VI) [138]
Wollastonite Ni(II) [11]
Table 2
Comparison of second-order models
Author Year Linear form Plot
Sobkowsk and Czerwi´nski 1974 1−θθ = k2t 1−θθ vs. t
Ritchie 1977 qq∞ ∞−q = αt + 1 q∞ q∞−qvs. t Blanchard et al. 1984 n1 0−n− α = Kt 1 n0−nvs. t Ho 1995 qtt = 1 k2q2e + 1 qet t qtvs. t
3. Conclusion
Adsorption rate equations have considered the adsorption
capacities of solids since Lagergren’s first-order equation was
presented. Several rate equations were reported with the same
idea in the following years. In earlier years, Elovich’s
equa-tion and Ritchie’s equaequa-tion were applied to the adsorpequa-tion of
gases onto solid faces. Later, application of these equations
to the adsorption of pollutants from aqueous solutions were
investigated. A second-order rate equation was used to describe
chemisorption for the adsorption of gases used to describe ion
exchange reactions. The pseudo-second-order rate expression
was used to describe chemisorption involving valency forces
through the sharing or exchange of electrons between the
adsor-bent and adsorbate as covalent forces, and ion exchange. In
recent years, the pseudo-second-order rate expression has been
widely applied to the adsorption of pollutants from aqueous
solu-tions. The advantage of using this model is that there is no need
to know the equilibrium capacity from the experiments, as it can
be calculated from the model. In addition, the initial adsorption
rate can also be obtained from the model.
References
[1] J.E. Saiers, G.M. Hornberger, L. Liang, First- and second-order kinetics approaches for modeling the transport of colloidal particles in porous media, Water Resour. Res. 30 (1994) 2499–2506.
[2] M.A. McCoy, A.I. Liapis, Evaluation of kinetic-models for biospecific adsorption and its implications for finite bath and column performance, J. Chromatogr. A 548 (1991) 25–60.
[3] S.V. Mohan, N.C. Rao, J. Karthikeyan, Adsorptive removal of direct azo dye from aqueous phase onto coal based sorbents: a kinetic and mechanistic study, J. Hazard. Mater. 90 (2002) 189–204.
[4] K. Chu, M. Hashim, Modeling batch equilibrium and kinetics of copper removal by crab shell, Sep. Sci. Technol. 38 (2003) 3927–3950. [5] D.J. O’Shannessy, D.J. Winzor, Interpretation of deviations from
pseudo-first-order kinetic-behavior in the characterization of ligand binding by biosensor technology, Anal. Biochem. 236 (1996) 275–283. [6] C.A. Zaror, Enhanced oxidation of toxic effluents using simultaneous ozonation and activated carbon treatment, J. Chem. Technol. Biotech-nol. 70 (1997) 21–28.
[7] S. Lagergren, Zur theorie der sogenannten adsorption gel¨oster stoffe, K. Sven. Vetenskapsakad. Handl. 24 (1898) 1–39.
[8] J. Zeldowitsch, ¨Uber den mechanismus der katalytischen oxydation von CO an MnO2, Acta Physicochim. URSS 1 (1934) 364–449.
[9] Y.S. Ho, Adsorption of heavy metals from waste streams by peat, Ph.D. Thesis, University of Birmingham, Birmingham, U.K., 1995. [10] Y.S. Ho, G. McKay, Sorption of dye from aqueous solution by peat,
Chem. Eng. J. 70 (1998) 115–124.
[11] Y.S. Ho, G. McKay, Pseudo-second order model for sorption processes, Process Biochem. 34 (1999) 451–465.
[12] Y.S. Ho, G. McKay, The kinetics of sorption of divalent metal ions onto sphagnum moss peat, Water Res. 34 (2000) 735–742.
[13] G. Blanchard, M. Maunaye, G. Martin, Removal of heavy-metals from waters by means of natural zeolites, Water Res. 18 (1984) 1501– 1507.
[14] S. Kuo, E.G. Lotse, Kinetics of phosphate adsorption by calcium car-bonate and Ca-kaolinite, Soil Sci. Soc. Am. Proc. 36 (1972) 725– 729.
[15] R.A. Griffin, J.J. Jurinak, Kinetics of the phosphate interaction with calcite, Soil Sci. Soc. Am. Proc. 38 (1974) 75–79.
[16] M. Mahramanlioglu, I. Kizilcikli, I.O. Bicer, Adsorption of fluoride from aqueous solution by acid treated spent bleaching earth, J. Fluor. Chem. 115 (2002) 41–47.
[17] T. Sano, N. Yamashita, Y. Iwami, K. Takeda, Y. Kawakami, Estimation of dealumination rate of ZSM-5 zeolite by adsorption of water vapor, Zeolites 16 (1996) 258–264.
[18] K.G. Varshney, A.A. Khan, U. Gupta, S.M. Maheshwari, Kinetics of adsorption of phosphamidon on antimony(V) phosphate cation exchanger evaluation of the order of reaction and some physical param-eters, Colloid Surf. A: Physicochem. Eng. Asp. 113 (1996) 19–23. [19] Y.S. Ho, G. McKay, A comparison of chemisorption kinetic models
applied to pollutant removal on various sorbents, Process Saf. Environ. Protect. 76B (1998) 332–340.
[20] Y.S. Ho, G. McKay, Kinetic model for lead(II) sorption on to peat, Adsorpt. Sci. Technol. 16 (1998) 243–255.
[21] Y.S. Ho, G. McKay, Kinetic models for the sorption of dye from aqueous solution by wood, Process Saf. Environ. Protect. 76B (1998) 183–191.
[22] Y.S. Ho, G. McKay, The kinetics of sorption of basic dyes from aque-ous solution by sphagnum moss peat, Can. J. Chem. Eng. 76 (1998) 822–827.
[23] H.C. Trivedi, V.M. Patel, R.D. Patel, Adsorption of cellulose triacetate on calcium silicate, Eur. Polym. J. 9 (1973) 525–531.
[24] Y.S. Ho, Citation review of Lagergren kinetic rate equation on adsorp-tion reacadsorp-tions, Scientometrics 59 (2004) 171–177.
[25] H.A. Taylor, N. Thon, Kinetics of chemisorption, J. Am. Chem. Soc. 74 (1952) 4169–4173.
[26] C. Aharoni, M. Ungarish, Kinetics of activated chemisorption. Part I: the non-Elovichian part of the isotherm, J. Chem. Soc., Faraday Trans. I 72 (1976) 400–408.
[27] S.H. Chien, W.R. Clayton, Application of Elovich equation to the kinetics of phosphate release and sorption in soils, Soil Sci. Soc. Am. J. 44 (1980) 265–268.
[28] D.L. Sparks, Kinetics of reaction in pure and mixed systems, in: D.L. Sparks (Ed.), Soil Physical Chemistry, CRC Press, Boca Raton, Florida, 1986, pp. 83–145.
[29] W. Rudzinski, T. Panczyk, Kinetics of isothermal adsorption on ener-getically heterogeneous solid surfaces: a new theoretical description based on the statistical rate theory of interfacial transport, J. Phys. Chem. B 104 (2000) 9149–9162.
[30] K. Otto, M. Shelef, The adsorption of nitric oxide on chromia sup-ported on alumina, J. Catal. 14 (1969) 226–237.
[31] M. Tanaka, S. Ogasawara, n-Butene isomerization on HCl-treated alu-mina, J. Catal. 16 (1970) 164–172.
[32] N.H. Turner, Kinetics of chemisorption: an examination of the Elovich equation, J. Catal. 36 (1975) 262–265.
[33] A.G. Ritchie, Alternative to the Elovich equation for the kinetics of adsorption of gases on solids, J. Chem. Soc., Faraday Trans. I 73 (1977) 1650–1653.
[34] J.O.M. Bockris, K.T. Jeng, In situ studies of adsorption of organic compounds on platinum electrodes, J. Electroanal. Chem. 330 (1992) 541–581.
[35] J.A. Heimberg, K.J. Wahl, I.L. Singer, A. Erdemir, Superlow fric-tion behavior of diamond-like carbon coatings: time and speed effects, Appl. Phys. Lett. 78 (2001) 2449–2451.
[36] R.J. Atkinson, F.J. Hingston, A.M. Posner, J.P. Quirk, Elovich equation for the kinetics of isotope exchange reactions at solid–liquid interfaces, Nature 226 (1970) 148–149.
[37] C.W. Cheung, J.F. Porter, G. McKay, Sorption kinetic analysis for the removal of cadmium ions from effluents using bone char, Water Res. 35 (2001) 605–612.
[38] Y. Sa˘g, Y. Aktay, Kinetic studies on sorption of Cr(VI) and Cu(II) ions by chitin, chitosan and Rhizopus arrhizus, Biochem. Eng. J. 12 (2002) 143–153.
[39] J. Sobkowsk, A. Czerwi´nski, Kinetics of carbon dioxide adsorption on a platinum electrode, J. Electroanal. Chem. 55 (1974) 391–397. [40] S. Trasatti, L. Formaro, Kinetics and mechanism of the adsorption of
glycolaldehyde on a smooth platinum electrode, J. Electroanal. Chem. 1 (7) (1968) 343–364.
[41] F.E. Austin, J.G. Brown, J. Dollimore, C.M. Freedman, B.H. Harri-son, The use of partial-pressure mass spectrometry in the study of the thermal desorption and oxidation of carbon and graphite, Analyst 96 (1971) 110–116.
[42] R.C. Bansal, F.J. Vastola, P.L. Walker Jr., Studies on ultra-clean car-bon surfaces. III. Kinetics of chemisorption of hydrogen on graphon, Carbon 9 (1971) 185–192.
[43] P. Samuel, L.M. Yeddanapalli, Kinetics of hydrogen chemisorption on supported molybdenum-disulfide, J. Appl. Chem. Biotechnol. 24 (1974) 777–786.
[44] V.R. Deitz, N.H. Turner, Dynamic adsorption of water vapor by a fiber drawn from a melt of Vycor, J. Phys. Chem. 75 (1971) 2718–2727. [45] B.S. Inbaraj, N. Sulochana, Carbonised jackfruit peel as an adsorbent
for the removal of Cd(II) from aqueous solution, Bioresour. Technol. 94 (2004) 49–52.
[46] B. Biˇskup, B. Suboti´c, Kinetic analysis of the exchange processes between sodium ions from zeolite A and cadmium, copper and nickel ions from solutions, Sep. Purif. Technol. 37 (2004) 17–31.
[47] N.T. Coleman, A.C. McClung, D.P. Moore, Formation constants for Cu(II)–peat complexes, Science 123 (1956) 330–331.
[48] Y.S. Ho, G. McKay, Sorption of dyes and copper ions onto biosorbents, Process Biochem. 38 (2003) 1047–1061.
[49] Y.S. Ho, Removal of copper ions from aqueous solution by tree fern, Water Res. 37 (2003) 2323–2330.
[50] Y.S. Ho, W.T. Chiu, C.S. Hsu, C.T. Huang, Sorption of lead ions from aqueous solution using tree fern as a sorbent, Hydrometallurgy 73 (2004) 55–61.
[51] Y.S. Ho, G. McKay, Sorption of copper(II) from aqueous solution by peat, Water Air Soil Pollut. 158 (2004) 77–97.
[52] Y.S. Ho, D.A.J. Wase, C.F. Forster, The adsorption of divalent cop-per ions from aqueous solution by sphagnum moss peat, Process Saf. Environ. Protect. 72B (1994) 185–194.
[53] Y.S. Ho, D.A.J. Wase, C.F. Forster, Batch nickel removal from aqueous solution by sphagnum moss peat, Water Res. 29 (1995) 1327–1332. [54] Y.S. Ho, C.T. Huang, H.W. Huang, Equilibrium sorption isotherm for
metal ions on tree fern, Process Biochem. 37 (2002) 1421–1430. [55] D.M. Manohar, K.A. Krishnan, T.S. Anirudhan, Removal of
mer-cury(II) from aqueous solutions and chlor-alkali industry wastewater using 2-mercaptobenzimidazole-clay, Water Res. 36 (2002) 1609–1619. [56] Z. Aksu, E. Kabasakal, Batch adsorption of 2,4-dichlorophenoxy-acetic acid (2,4-D) from aqueous solution by granular activated carbon, Sep. Purif. Technol. 35 (2004) 223–240.
[57] K.A. Krishnan, T.S. Anirudhan, Removal of cadmium(II) from aque-ous solutions by steam-activated sulphurised carbon prepared from sugar-cane bagasse pith: kinetics and equilibrium studies, Water SA 29 (2003) 147–156.
[58] A. ¨Ozer, F. T¨umen, Cd(II) adsorption from aqueous solution by acti-vated carbon from sugar beet pulp impregnated with phosphoric acid, Fresen. Environ. Bull. 12 (2003) 1050–1058.
[59] M.C. Basso, E.G. Cerrella, A.L. Cukierman, Activated carbons devel-oped from a rapidly renewable biosource for removal of cadmium(II) and nickel(II) ions from dilute aqueous solutions, Ind. Eng. Chem. Res. 41 (2002) 180–189.
[60] C. Namasivayam, D. Kavitha, Removal of Congo Red from water by adsorption onto activated carbon prepared from coir pith, an agricul-tural solid waste, Dyes Pigments 54 (2002) 47–58.
[61] P.K. Malik, Dye removal from wastewater using activated carbon devel-oped from sawdust: adsorption equilibrium and kinetics, J. Hazard. Mater. 113 (2004) 81–88.
[62] K. Kadirvelu, P. Kanmani, P. Senthilkumar, V. Subburam, Separation of mercury(II) from aqueous solution by adsorption onto an activated carbon prepared from Eichhornia crassipes, Adsorpt. Sci. Technol. 22 (2004) 207–222.
[63] K.A. Krishnan, T.S. Anirudhan, Removal of mercury(II) from aque-ous solutions and chlor-alkali industry effluent by steam activated and sulphurised activated carbons prepared from bagasse pith: kinetics and equilibrium studies, J. Hazard. Mater. 92 (2002) 161–183.
[64] F. Banat, S. Al-Asheh, L. Makhadmeh, Preparation and examination of activated carbons from date pits impregnated with potassium hydroxide for the removal of Methylene blue from aqueous solutions, Adsorpt. Sci. Technol. 21 (2003) 597–606.
[65] N.K. Hamadi, S. Swaminathan, X.D. Chen, Adsorption of Paraquat dichloride from aqueous solution by activated carbon derived from used tires, J. Hazard. Mater. 112 (2004) 133–141.
[66] E. Demirbas¸, Adsorption of cobalt(II) ions from aqueous solution onto activated carbon prepared from hazelnut shells, Adsorpt. Sci. Technol. 21 (2003) 951–963.
[67] M. Abdulkarim, F.A. Abu Al-Rub, Adsorption of lead ions from aque-ous solution onto activated carbon and chemically-modified activated carbon prepared from date pits, Adsorpt. Sci. Technol. 22 (2004) 119–134.
[68] K.A. Krishnan, A. Sheela, T.S. Anirudhan, Kinetic and equilibrium modeling of liquid-phase adsorption of lead and lead chelates on acti-vated carbons, J. Chem. Technol. Biotechnol. 78 (2003) 642–653. [69] K.A. Krishnan, T.S. Anirudhan, Uptake of heavy metals in batch
sys-tems by sulfurized steam activated carbon prepared from sugarcane bagasse pith, Ind. Eng. Chem. Res. 41 (2002) 5085–5093.
[70] Y.S. Ho, C.C. Chiang, Y.C. Hsu, Sorption kinetics for dye removal from aqueous solution using activated clay, Sep. Sci. Technol. 36 (2001) 2473–2488.
[71] M.X. Loukidou, A.I. Zouboulis, T.D. Karapantsios, K.A. Matis, Equilibrium and kinetic modeling of chromium(VI) biosorption by
Aeromonas caviae, Colloid Surf. A: Physicochem. Eng. Asp. 242
(2004) 93–104.
[72] F.A. Abu Al-Rub, M.H. El-Naas, F. Benyahia, I. Ashour, Biosorption of nickel on blank alginate beads, free and immobilized algal cells, Process Biochem. 39 (2004) 1767–1773.
[73] E.D. van Hullebusch, M.H. Zandvoort, P.N.L. Lens, Nickel and cobalt sorption on anaerobic granular sludges: kinetic and equilibrium studies, J. Chem. Technol. Biotechnol. 79 (2004) 1219–1227.
[74] Y.Z. Fu, T. Viraraghavan, Removal of CI Acid Blue 29 from an aqueous solution by Aspergillus niger, AATCC Rev. 1 (2001) 36–40. [75] Y.Z. Fu, T. Viraraghavan, Removal of a dye from an aqueous solution
by the fungus Aspergillus niger, Water Qual. Res. J. Can. 3 (5) (2000) 95–111.
[76] Y.Z. Fu, T. Viraraghavan, Removal of Congo red from an aqueous solution by fungus Aspergillus niger, Adv. Environ. Res. 7 (2002) 239–247.
[77] A. Kapoor, T. Viraraghavan, D.R. Cullimore, Removal of heavy met-als using the fungus Aspergillus niger, Bioresour. Technol. 70 (1999) 95–104.
[78] K.G. Bhattacharyya, A. Sharma, Azadirachta indica leaf powder as an effective biosorbent for dyes: a case study with aqueous Congo red solutions, J. Environ. Manage. 71 (2004) 217–229.
[79] K.G. Bhattacharyya, A. Sharma, Adsorption of Pb(II) from aqueous solution by Azadirachta indica (Neem) leaf powder, J. Hazard. Mater. 113 (2004) 97–109.
[80] P. Vasudevan, V. Padmavathy, S.C. Dhingra, Kinetics of biosorption of cadmium on Baker’s yeast, Bioresour. Technol. 89 (2003) 281–287. [81] I.G. Shibi, T.S. Anirudhan, Synthesis, characterization, and application
as a mercury(II) sorbent of banana stalk (Musa paradisiaca): polyacry-lamide grafted copolymer bearing carboxyl groups, Ind. Eng. Chem. Res. 41 (2002) 5341–5352.
[82] A.S. ¨Ozcan, A. ¨Ozcan, Adsorption of acid dyes from aqueous solutions onto acid-activated bentonite, J. Colloid Interf. Sci. 276 (2004) 39–46. [83] A.K. Jain, V.K. Gupta, S. Jain, Suhas, Removal of chlorophenols using
industrial wastes, Environ. Sci. Technol. 38 (2004) 1195–1200. [84] B. Acemio˘glu, M.H. Alma, A.R. Demirkiran, Removal of Zn(II) and
Pb(II) ions by Calabrian pine bark wastes, J. Chem. Soc. Pak. 26 (2004) 82–89.
[85] M. ¨Ozacar, Equilibrium and kinetic modelling of adsorption of phos-phorus on calcined alunite, Adsorpt. J. Int. Adsorpt. Soc. 9 (2003) 125–132.
[86] N.K. Lazaridis, D.D. Asouhidou, Kinetics of sorptive removal of chromium(VI) from aqueous solutions by calcined Mg–Al–CO3
hydro-talcite, Water Res. 37 (2003) 2875–2882.
[87] M. Horsfall, A.I. Spiff, A.A. Abia, Studies on the influence of mercap-toacetic acid (MAA) modification of cassava (Manihot sculenta Cranz) waste biomass on the adsorption of Cu2+and Cd2+from aqueous
solu-tion, Bull. Kor. Chem. Soc. 25 (2004) 969–976.
[88] H. Benaissa, B. Benguella, Effect of anions and cations on cadmium sorption kinetics from aqueous solutions by chitin: experimental studies and modeling, Environ. Pollut. 130 (2004) 157–163.
[89] W.S. Wan Ngah, A. Kamari, Y.J. Koay, Equilibrium and kinetics stud-ies of adsorption of copper(II) on chitosan and chitosan/PVA beads, Int. J. Biol. Macromol. 34 (2004) 155–161.
[90] O. Gyliene, R. Tarozaite, O. Nivinskiene, Sorption of Ni(II)–citrate complex from electroless nickel plating solutions onto chitosan, Trans. Inst. Metal Finish. 82 (2004) 38–42.
[91] N. Bektas¸, S. Kara, Removal of lead from aqueous solutions by natural clinoptilolite: equilibrium and kinetic studies, Sep. Purif. Technol. 39 (2004) 189–200.
[92] C. Namasivayam, D. Kavitha, Adsorptive removal of 2,4-dichlorophenol from aqueous solution by low-cost carbon from an agricultural solid waste: coconut coir pith, Sep. Sci. Technol. 39 (2004) 1407–1425.
[93] M.R. Unnithan, V.P. Vinod, T.S. Anirudhan, Synthesis, characteriza-tion, and application as a chromium(VI) adsorbent of amine-modified polyacrylamide-grafted coconut coir pith, Ind. Eng. Chem. Res. 43 (2004) 2247–2255.
[94] S.Y. Quek, B. Al Duri, D.A.J. Wase, C.F. Forster, Coir as a biosorbent of copper and lead, Process Saf. Environ. Protect. 76B (1998) 50–54. [95] F. Banat, S. Al-Asheh, L. Al-Makhadmeh, Evaluation of the use of raw and activated date pits as potential adsorbents for dye containing waters, Process Biochem. 39 (2003) 193–202.
[96] F. Banat, S. Al-Asheh, L. Al-Makhadmeh, Utilization of raw and acti-vated date pits for the removal of phenol from aqueous solutions, Chem. Eng. Technol. 27 (2004) 80–86.
[97] R.A. Shawabkeh, M.F. Tutunji, Experimental study and modeling of basic dye sorption by diatomaceous clay, Appl. Clay Sci. 24 (2003) 111–120.
[98] S. Karaca, A. G¨urses, M. Ejder, M. Ac¸ıkyıldız, Kinetic modeling of liquid-phase adsorption of phosphate on dolomite, J. Colloid Interf. Sci. 277 (2004) 257–263.
[99] B. Acemio˘glu, Adsorption of Congo red from aqueous solution onto calcium-rich fly ash, J. Colloid Interf. Sci. 274 (2004) 371–379. [100] Y.S. Ho, G. McKay, Comparative sorption kinetic studies of dye and
aromatic compounds onto fly ash, J. Environ. Sci. Health Part A: Toxic/Hazard. Subst. Environ. Eng. 34 (1999) 1179–1204.
[101] N. Chiron, R. Guilet, E. Deydier, Adsorption of Cu(II) and Pb(II) onto a grafted silica: isotherms and kinetic models, Water Res. 37 (2003) 3079–3086.
[102] W. Fiol, J. Poch, I. Villaescusa, Chromium(VI) uptake by grape stalks wastes encapsulated in calcium alginate beads: equilibrium and kinetics studies, Chem. Speciation Bioavail. 16 (2004) 25–33.
[103] O.S. Thirunavukkarasu, T. Viraraghavan, K.S. Subramanian, Arsenic removal from drinking water using iron oxide-coated sand, Water Air Soil Pollut. 142 (2003) 95–111.
[104] F.A. Abu Al-Rub, Sorption of lead ions from simulated industrial wastewater onto Jordanian low-grade phosphate, Adsorpt. Sci. Technol. 22 (2004) 165–179.
[105] S.H. Min, J.S. Han, E.W. Shin, J.K. Park, Improvement of cadmium ion removal by base treatment of juniper fiber, Water Res. 38 (2004) 1289–1295.
[106] E.W. Shin, J.S. Han, S.H. Min, Removal of phosphorus from water using lignocellulosic material modified with iron species from acid mine drainage, Environ. Technol. 25 (2004) 185–191.
[107] E.W. Shin, J.S. Han, M. Jang, S.H. Min, J.K. Park, R.M. Rowell, Phosphate adsorption on aluminum-impregnated mesoporous silicates: surface structure and behavior of adsorbents, Environ. Sci. Technol. 38 (2004) 912–917.
[108] N.K. Lazaridis, T.A. Pandi, K.A. Matis, Chromium(VI) removal from aqueous solutions by Mg–Al–CO3 hydrotalcite: sorption–desorption
kinetic and equilibrium studies, Ind. Eng. Chem. Res. 43 (2004) 2209–2215.
[109] S. Singh, B.N. Rai, L.C. Rai, Ni(II) and Cr(VI) sorption kinetics by
Microcystis in single and multimetallic system, Process Biochem. 36
(2001) 1205–1213.
[110] G.X.S. Zhao, J.L. Lee, P.A. Chia, Unusual adsorption properties of microporous titanosilicate ETS-10 toward heavy metal lead, Langmuir 19 (2003) 1977–1979.
[111] Y.S. Ho, C.C. Chiang, Sorption studies of acid dye by mixed sorbents, Adsorpt. J. Int. Adsorpt. Soc. 7 (2001) 139–147.
[112] G.T. Yan, T. Viraraghavan, Heavy-metal removal from aqueous solution by fungus Mucor rouxii, Water Res. 37 (2003) 4486–4496.
[113] O. Keskinkan, M.Z.L. Goksu, A. Yuceer, M. Basibuyuk, C.F. Forster, Heavy metal adsorption characteristics of a submerged aquatic plant (Myriophyllum spicatum), Process Biochem. 39 (2003) 179–183. [114] T. Viraraghavan, H. Moazed, Removal of oil from water by bentonite,
Fresen. Environ. Bull. 12 (2003) 1092–1097.
[115] S. Al-Asheh, F. Banat, A. Masad, Kinetics and equilibrium sorption studies of 4-nitrophenol on pyrolyzed and activated oil shale residue, Environ. Geol. 5 (2004) 1109–1117.
[116] L. Sep´ulveda, K. Fern´andez, E. Contreras, C. Palma, Adsorption of dyes using peat: equilibrium and kinetic studies, Environ. Technol. 25 (2004) 987–996.
[117] R. G¨undo˘gan, B. Acemio˘glu, M.H. Alma, Copper(II) adsorption from aqueous solution by herbaceous peat, J. Colloid Interf. Sci. 269 (2004) 303–309.
[118] S.L.G. Petroni, M.A.F. Pires, C.S. Munita, Use of radiotracer in adsorp-tion studies of copper on peat, J. Radioanal. Nucl. Chem. 259 (2004) 239–243.
[119] Q.Y. Sun, L.Z. Yang, The adsorption of basic dyes from aqueous solu-tion on modified peat-resin particle, Water Res. 37 (2003) 1535–1544. [120] T. Mathialagan, T. Viraraghavan, Adsorption of cadmium from aqueous
solutions by perlite, J. Hazard. Mater. 94 (2002) 291–303.
[121] M. Do˘gan, M. Alkan, A. T¨urkyilmaz, Y. ¨Ozdemir, Kinetics and mech-anism of removal of Methylene blue by adsorption onto perlite, J. Hazard. Mater. 109 (2004) 141–148.
[122] Y.S. Ho, G. McKay, A kinetic study of dye sorption by biosorbent waste product pith, Resour. Conserv. Recycl. 25 (1999) 171–193. [123] F. Beolchini, F. Pagnanelli, A.P. Reverberi, F. Vegli`o, Copper
biosorp-tion onto Rhizopus oligosporus: pH-edge tests and related kinetic and equilibrium modeling, Ind. Eng. Chem. Res. 42 (2003) 4881– 4887.
[124] D.H. Cho, M.Y. Yoo, E.Y. Kim, Biosorption of lead (Pb2+) from
aque-ous solution by Rhodotorula aurantiaca, J. Microbiol. Biotechnol. 14 (2004) 250–255.
[125] S.Y. Quek, D.A.J. Wase, C.F. Forster, The use of sago waste for the sorption of lead and copper, Water SA 24 (1998) 251–256.
[126] V.C. Taty-Costodes, H. Fauduet, C. Porte, A. Delacroix, Removal of Cd(II) and Pb(II) ions, from aqueous solutions, by adsorption onto sawdust of Pinus sylvestris, J. Hazard. Mater. 105 (2003) 121–142. [127] D.N. Jadhav, A.K. Vanjara, Removal of phenol from wastewater using
sawdust, polymerized sawdust and sawdust carbon, Indian J. Chem. Technol. 1 (1) (2004) 35–41.
[128] A. ¨Ozer, Application of pseudo second order kinetic model to lead(II) biosorption on Schizomeris leibleinii, Fresen. Environ. Bull. 12 (2003) 1239–1245.
[129] N. Bektas¸, D. Soysal, Kinetics of phosphate removal using surfactant modified clinoptilolite, Fresen. Environ. Bull. 13 (2004) 366–369. [130] K.S. Low, C.K. Lee, S.C. Liew, Sorption of cadmium and lead from
aqueous solutions by spent grain, Process Biochem. 36 (2000) 59– 64.
[131] Y.S. Ho, D.A.J. Wase, C.F. Forster, Kinetic studies of competitive heavy metal adsorption by sphagnum moss peat, Environ. Technol. 17 (1996) 71–77.
[132] Z. Reddad, C. Gerente, Y. Andres, P. Le Cloirec, Lead removal by a natural polysaccharide in membrane reactors, Water Sci. Technol. 49 (2004) 163–170.
[133] Z. Reddad, C. G´erente, Y. Andres, P. Le Cloirec, Adsorption of several metal ions onto a low-cost biosorbent: kinetic and equilibrium studies, Environ. Sci. Technol. 36 (2002) 2067–2073.
[134] N. Bektas¸, B.A. A˘gım, S. Kara, Kinetic and equilibrium studies in removing lead ions from aqueous solutions by natural sepiolite, J. Hazard. Mater. 11 (2) (2004) 115–122.
[135] Y.S. Ho, T.H. Chiang, Y.M. Hsueh, Removal of basic dye from aqueous solution using tree fern as a biosorbent, Process Biochem. 40 (2005) 119–124.
[136] Y.S. Ho, C.C. Wang, Pseudo-isotherms for the sorption of cadmium ion onto tree fern, Process Biochem. 39 (2004) 759–763.
[137] T. Mathialagan, T. Viraraghavan, Adsorption of cadmium from aqueous solutions by vermiculite, Sep. Sci. Technol. 38 (2003) 57–76. [138] N.K. Hamadi, X.D. Chen, M.M. Farid, M.G.Q. Lu, Adsorption kinetics
for the removal of chromium(VI) from aqueous solution by adsorbents derived from used tyres and sawdust, Chem. Eng. J. 81 (2001) 95–105. [139] S. Azizian, Kinetic models of sorption: a theoretical analysis, J. Colloid
Interf. Sci. 276 (2004) 47–52.
[140] M. Ungarish, C. Aharoni, Kinetics of chemisorption: deducing kinetic laws from experimental data, J. Chem. Soc., Faraday Trans. I 77 (1981) 975–985.
[141] K.K.H. Choy, G. McKay, J.F. Porter, Sorption of acid dyes from efflu-ents using activated carbon, Resour. Conserv. Recycl. 27 (1999) 57–71. [142] R. Bayard, L. Barna, B. Mahjoub, R. Gourdon, Influence of the pres-ence of PAHs and coal tar on naphthalene sorption in soils, J. Contam. Hydrol. 46 (2000) 61–80.
[143] I. Czinkota, R. F¨old´enyi, Z. Lengyel, A. Marton, Adsorption of propisochlor on soils and soil components equation for multi-step isotherms, Chemosphere 48 (2002) 725–731.
