Marine Algae Biomass for Removal of Heavy Metal Ions 25.5 Modeling of Biosorption in Batch Conditions 631
Part D | 25.5
the heterogeneity of the biosorbent surface, they were
quite successful in predicting the practical biosorption
capacity and optimization of the biosorption system design [25.129]. Generally, the linear regression is used
to find the most adequate model that could describe the
biosorption isotherms of heavy metal ions on marine
algae biomass. Even though nonlinear method provides
better results, the linear least-square method is still often preferred in favor of its simplicity and convenience.
The Freundlich isotherm model is originally of
empirical nature (Table 25.7). This model is one
of the the most widely used isotherm model for
description of adsorption equilibrium, both for organic and inorganic compounds on a wide variety of adsorbents, including biosorbents [25.18]. The
Freundlich isotherm model has been interpreted as
biosorption to heterogeneous surface or surface supporting sites of different affinity, and assumed that
the stronger binding sites are occupied first and that
the binding strength decreases with increasing degree of occupation [25.87]. Generally, the Freundlich
isotherm model is used to estimate the biosorption intensity of heavy metal ions toward a given
biosorbent.
The graphical representation of lnq e versus lnc e has
a slop with the value of 1=n and an intercept magnitude
of lnK F . A favorable biosorption process tends to have
the Freundlich constant n between 1 and 10 [25.18].
Larger value of n (smaller value for 1=n) indicates
strong interactions between biosorbent and heavy metal
ions, while a value of n equal to 1, suggests linear
biosorption process, leading to identical biosorption energy for all sites [25.130].
The Freundlich isotherm model can be successfully
used to analyze most of the experimental biosorption
data, and is especially excellent for fitting data from
systems that use highly heterogeneous biosorbents, as
listed in Table 25.8. Even, the biosorption capacities for
marine algae biomasses (obtained from the Freundlich
K F constant) summarized in Table 25.8 are quite low
in comparison with commercially activated carbons,
these biosorbents are still attractive due to its biosorption advantages and cost-effectiveness for the removal
of heavy metal ions.
Nevertheless, in some cases, the Freundlich
isotherm model could not fit the experimental data well
due to the low values of obtained correlation coefficients, or is not suitable to describe the biosorption
equilibrium. Thus, the Freundlich isotherm model cannot be use to predict the biosorption equilibrium data
at extreme concentrations of heavy metal ions. This
is because the mathematical equation is not reduced
to a linear expression at very low concentrations, and
do not has limit expression at very high concentrations [25.18]. Fortunately this is not a problem, because
a moderate concentration range is frequently used in
most of biosorption studies.
The Langmuir isotherm model is probably the best
known and the most widely used sorption isotherm for
describing heavy metals biosorption on marine algae
biomass, which produced good agreement with a wide
variety of experimental data. In the simplest case, the
Langmuir model is based on the following assumptions [25.4, 18]:
i) The biosorption process is limited to monolayer
coverage,
ii) The surface of biosorbent is homogeneous and all
surface sites (constant heat of biosorption);
iii) There is only one sorbate,
iv) One sorbate molecule reacts with one active site,
and
v) The ability of a molecule to be retained on a given
site is independent of the surface occupancy.
This model assumed that biosorption forces are similar to the forces in chemical interactions, and can
be used to estimate the maximum biosorption capacity (q max , mg=g), corresponding to biosorbent surface
saturation. Usually, the parameters of the Langmuir
isotherm model (q max and K L ) are evaluated from the intercepts and the slopes of linear plots of c e =q versus c e .
Table 25.8 summarizes a number of studies that draw
upon the Langmuir isotherm to analyze the biosorption
equilibrium data of heavy metal ions onto marine algae
biomass.
According to the Langmuir model, the maximum
biosorption capacity (q max , mg=g) should coincide with
saturation of the monolayer coverage, and as a consequence it should be independent of temperature. The
experimental results have shown that a relatively small
increase or even decrease in the maximum biosorption capacity is usually observed in the case of heavy
metal ions biosorption on marine algae biomass (Table 25.8). This is because in biosorption processes that
use marine algae biomass as biosorbents, saturation
of certain biomass depends on the accessibility of the
binding sites, the chemical state, and the affinity of
studied metal ions for these sites. The temperature variation may affect one or more of these factors, and this
will lead to the variation of the maximum biosorption
capacity.
Part D | 25.5
the heterogeneity of the biosorbent surface, they were
quite successful in predicting the practical biosorption
capacity and optimization of the biosorption system design [25.129]. Generally, the linear regression is used
to find the most adequate model that could describe the
biosorption isotherms of heavy metal ions on marine
algae biomass. Even though nonlinear method provides
better results, the linear least-square method is still often preferred in favor of its simplicity and convenience.
The Freundlich isotherm model is originally of
empirical nature (Table 25.7). This model is one
of the the most widely used isotherm model for
description of adsorption equilibrium, both for organic and inorganic compounds on a wide variety of adsorbents, including biosorbents [25.18]. The
Freundlich isotherm model has been interpreted as
biosorption to heterogeneous surface or surface supporting sites of different affinity, and assumed that
the stronger binding sites are occupied first and that
the binding strength decreases with increasing degree of occupation [25.87]. Generally, the Freundlich
isotherm model is used to estimate the biosorption intensity of heavy metal ions toward a given
biosorbent.
The graphical representation of lnq e versus lnc e has
a slop with the value of 1=n and an intercept magnitude
of lnK F . A favorable biosorption process tends to have
the Freundlich constant n between 1 and 10 [25.18].
Larger value of n (smaller value for 1=n) indicates
strong interactions between biosorbent and heavy metal
ions, while a value of n equal to 1, suggests linear
biosorption process, leading to identical biosorption energy for all sites [25.130].
The Freundlich isotherm model can be successfully
used to analyze most of the experimental biosorption
data, and is especially excellent for fitting data from
systems that use highly heterogeneous biosorbents, as
listed in Table 25.8. Even, the biosorption capacities for
marine algae biomasses (obtained from the Freundlich
K F constant) summarized in Table 25.8 are quite low
in comparison with commercially activated carbons,
these biosorbents are still attractive due to its biosorption advantages and cost-effectiveness for the removal
of heavy metal ions.
Nevertheless, in some cases, the Freundlich
isotherm model could not fit the experimental data well
due to the low values of obtained correlation coefficients, or is not suitable to describe the biosorption
equilibrium. Thus, the Freundlich isotherm model cannot be use to predict the biosorption equilibrium data
at extreme concentrations of heavy metal ions. This
is because the mathematical equation is not reduced
to a linear expression at very low concentrations, and
do not has limit expression at very high concentrations [25.18]. Fortunately this is not a problem, because
a moderate concentration range is frequently used in
most of biosorption studies.
The Langmuir isotherm model is probably the best
known and the most widely used sorption isotherm for
describing heavy metals biosorption on marine algae
biomass, which produced good agreement with a wide
variety of experimental data. In the simplest case, the
Langmuir model is based on the following assumptions [25.4, 18]:
i) The biosorption process is limited to monolayer
coverage,
ii) The surface of biosorbent is homogeneous and all
surface sites (constant heat of biosorption);
iii) There is only one sorbate,
iv) One sorbate molecule reacts with one active site,
and
v) The ability of a molecule to be retained on a given
site is independent of the surface occupancy.
This model assumed that biosorption forces are similar to the forces in chemical interactions, and can
be used to estimate the maximum biosorption capacity (q max , mg=g), corresponding to biosorbent surface
saturation. Usually, the parameters of the Langmuir
isotherm model (q max and K L ) are evaluated from the intercepts and the slopes of linear plots of c e =q versus c e .
Table 25.8 summarizes a number of studies that draw
upon the Langmuir isotherm to analyze the biosorption
equilibrium data of heavy metal ions onto marine algae
biomass.
According to the Langmuir model, the maximum
biosorption capacity (q max , mg=g) should coincide with
saturation of the monolayer coverage, and as a consequence it should be independent of temperature. The
experimental results have shown that a relatively small
increase or even decrease in the maximum biosorption capacity is usually observed in the case of heavy
metal ions biosorption on marine algae biomass (Table 25.8). This is because in biosorption processes that
use marine algae biomass as biosorbents, saturation
of certain biomass depends on the accessibility of the
binding sites, the chemical state, and the affinity of
studied metal ions for these sites. The temperature variation may affect one or more of these factors, and this
will lead to the variation of the maximum biosorption
capacity.