Functionalized Magnetic Nanoparticles for Heavy Metal Removal from Aqueous Solutions: Kinetics and Equilibrium Modeling - Advanced Materials for Agriculture, Food and Environmental Safety - page 317

h e external mass transfer process was determined by:

dq KACC
dt

( )

i

(11.13)

= −

L s

h ey observed that the external mass transfer coei cients can be ordered
from high to low values as Cu(II) > Pb(II) > Zn(II) > Cd(II), while the
intraparticle dif usion coei cients were as follow: Cd(II) > Zn(II) > Cu(II)
> Pb(II).

11.7.2 Equilibrium Modeling of Adsorption

Equilibrium isotherm models are usually classii ed into the empirical equa-
tions and the mechanistic models. h e mechanistic models are based on
mechanism of metal ion adsorption, which are able to not only represent,
but also to explain and predict the experimental behavior. Some empiri-
cal models for single solute systems are listed in Table 11.2. h e Langmuir
model (based on monolayer adsorption of solute) and the Freundlich model
(developed for heterogeneous surfaces) are the most widely accepted and
used in literature [111, 112, 113, 114, 115]. h e Brunauer-Emmett-Teller
(BET) model [116] describes the multi-layer adsorption at the nanoparti-
cle surfaces and assumes that the Langmuir isotherm applies to each layer.
h ese models can provide information about metal uptake capacity and
dif erence in metal uptake between various species.

11.7.2.1 Freundlich Isotherm

h e Freundlich isotherm is an empirical equation. h is equation is among
one of the most widely used isotherms for the explanation of adsorption
equilibrium. h e Freundlich isotherm is capable of describing the adsorp-
tion of heavy metals on a wide variety of adsorbents. h is equation has the
following form [111]:

1/ n

qKC =

(11.14)

e F e

It can also be expressed in the linearized logarithmic form [117]:

1

log q = log K + log C

e F e

(11.15)

n