Functionalized Magnetic Nanoparticles for Heavy Metal Removal from Aqueous Solutions: Kinetics and Equilibrium Modeling - Advanced Materials for Agriculture, Food and Environmental Safety - page 320

Langmuir model, the saturation capacity q max is supposed to coincide with
the saturation of a i xed number of identical surface sites, and as such, it
should logically be independent of temperature.
Sometimes, these empirical models do not rel ect any mechanisms of
sorbate uptake and hardly have a meaningful physical interpretation for
adsorption. Some authors have pointed out that the results from the empir-
ical models cannot be extrapolated, and no predictive conclusions can be
drawn for systems operating under dif erent conditions [120]. Also, since
both are simple, basic models (Langmuir and Freundlich models) they do
not incorporate the ef ects of any external variable environmental factors,
although they are capable of describing many biosorption isotherms in
most cases. h e mechanistic conclusions from the good i t of the models
alone should be avoided. Moreover, adsorption isotherms may exhibit an
irregular pattern due to the complex nature of both the adsorbents and
their varied multiple active sites, as well as the complex solution chemistry
of some metallic compounds.

11.7.2.3 Two Additional Parameter Isotherms

A particular model might be invalid in a particular circumstance, and
in most cases, more than one model can explain the adsorption mecha-
nism. Several models initially developed for gas-phase adsorption can
be implemented to correlate heavy metals adsorption processes. Some of
these equations contain two i tting parameters (Temkin isotherm, Flory-
Huggins, and Dubinin-Raduskevich equations), whereas others can have
more than two parameters (Redlich-Paterson and Sips isotherms) [104].
Superior adsorption performance and magnetic properties of nanomate-
rials tend to be a promising approach to deal with a variety of environmen-
tal pollutants in aqueous media. Advances in magnetic nanoparticles could
provide opportunities for developing new generation adsorbents with high
surface area, new functionalities, high capacity, easy separation, and recy-
clability. h e novel physicochemical and magnetic properties of nanoparticles
can facilitate many advanced applications in the development of adsorptive
technologies, and thus generate more ei cient and cost-ef ective remediation
approaches as compared with conventional technologies [121].

11.8 h ermodynamic Analysis

h e Langmuir isotherm constant can be used in biosorption to estimate the
thermodynamic parameters of Gibbs free energy (ΔG), change in enthalpy