Bio Adsorption: An Eco-friendly Alternative for Industrial Effluents Treatment 45

3.4 Equilibrium Isotherms

Another extremely important data to work with the software and to be able to estimate the reactor’s

design dimensions is the qmax (maximum adsorption capacity that comes from the study of

equilibrium isotherms).

For a given solid-liquid system, the dynamics of the adsorption equilibrium of the solute on

the solid is expressed by the ratio between the amount adsorbed at equilibrium per unit mass of

original adsorbent qe (mmol g^–1) and the residual concentration at equilibrium in the liquid phase

Ce (mmol L^–1), at a constant temperature. The graphical representation of these parameters is known

as adsorption isotherm. The study of the isotherms serves to obtain parameters that characterize

the adsorption phenomenon for a given adsorbent-adsorbate pair and to be able to establish the

experimental conditions that maximize adsorption. In addition, the mathematical correlation of the

process constitutes an important role for the analysis of the assumptions implied by the models and

provide an idea of the adsorption mechanism, the surface properties, as well as the degree of affinity

of the adsorbent (Foo and Hameed 2010).

The Langmuir (1918) and Freundlich (1906) models happen to be the most widely used

isotherm models mentioned in literature. In Table 3.1 a comparison of the characteristic parameters

and assumptions between each model is shown.

As an example, the nonlinear fit of the experimental data and the obtained parameters to the

Langmuir and Freundlich adsorption isotherms for a biomass system of the aquatic macrophyte

Azolla for the adsorption of Cu from an aqueous solution can be represented (Figure 3.4). The R²

value closer to 1 is indicating that the experimental data fits better to the Langmuir model for the

studied system, from which the model parameters are obtained (Figure 3.5).

For the proposed system, the model that best fits the data happens to be Langmuir. This model

is the one that generally results best for lignocellulosic adsorbents as observed in other works

(Guo et al. 2008, Boeykens et al. 2018).

Table 3.1. Comparison between Langmuir and Freundlich model with their respective parameters and assumptions.

Model

Langmuir 1918

Freundlich 1906

Mathematical

expression

qe =

qmaxKLCe

1 + KLCe

qe = Kf Ce

1/n

Parameters

Graph qe vs Ce

● KL (L mmol^–1) = constant. Langmuir, related

to adsorption intensity

● qmáx (mmol g^–1) = maximum adsorption

capacity

Graph qe vs Ce

● Kf (mmol g^–1) constant. Freundlich, related to the

adsorption capacity

● n = related to the intensity of adsorption or

heterogeneity of the system

● n > 1 → favorable adsorption

● n < 1 → unfavorable adsorption

Assumptions

● Maximum adsorption in monolayer

● Adsorption sites with constant energy

● There is no lateral interaction between

neighboring molecules

● Adsorption in multilayers

● Adsorption sites with different affinities

● Adsorption energy varies exponentially

depending on the covered surface