Functionalized Magnetic Nanoparticles for Heavy Metal Removal from Aqueous Solutions: Kinetics and Equilibrium Modeling - Advanced Materials for Agriculture, Food and Environmental Safety - page 314

with an interplanar spacing of 0.296 nm for the {220} plane, 0.210 nm for
the {400} plane, and 0.172 nm for the {422} plane, respectively. Figure 11.2b
shows that the γ-Fe 2 O 3 nanocages included two single crystalline obviously
with an interplanar spacing of 0.374 nm for the {210} plane and 0.295 nm for
the {220} plane, respectively. h e studies by the authors have coni rmed that
the nanocages consist of randomly small iron oxide nanocrystals, and the
nanocages present polycrystalline feature on the whole.

11.7 Modeling of Adsorption: Kinetic and Isotherm

Models

Assessment of a solid-liquid sorption system is usually based on two types
of investigations: equilibrium batch sorption tests and dynamic continuous-
l ow sorption studies. h e kinetic study of adsorption processes provides
useful data regarding the ei ciency of the adsorption and the feasibility for
scale-up operations. h e kinetic data of adsorption can be evaluated using
dif erent types of mathematical models, of which the one most widely used
is Lagergren's rate equation [99]. Equilibrium isotherm model equations
such as Langmuir, Freundlich, Temkin, and Redlich-Peterson are used
to describe experimental adsorption data in batch mode [100, 101, 102,
103]. It is important to i nd best-i t isotherm to evaluate the ei cacy of
the prepared adsorbent to develop suitable industrial adsorption system
designs.

11.7.1 Kinetic Studies in Adsorption of Heavy Metals

Adsorption equilibria studies are important to conclude the ei cacy of
adsorption. In spite of this, it is also necessary to identify the adsorp-
tion mechanism type in a given system. For the purpose of investigating
the mechanism of adsorption and its potential rate-controlling steps that
include mass transport and chemical reaction processes, kinetic models
have been exploited to test the experimental data. In addition, information
on the kinetics of metal uptake is required to select the optimum condition
for full-scale batch metal removal processes.
Several adsorption kinetic models have been established to understand
the adsorption kinetics and rate-limiting step. h ese include pseudo-i rst-
order and pseudo-second-order rate model, Weber and Morris sorption
kinetic model, Adam-Bohart-h omas relation, i rst-order reversible
reaction model, external mass transfer model, i rst-order equation of
Bhattacharya and Venkobachar, Elovich's model and Ritchie's equation.