Where Ci Is the Initial Concentration of Solute and Ct Is the Concentration at Time T in Mg L-1

The percentage removal of dye/heavy metal ion concentration from aqueous solution is calculated using the following equation:

(1)

Where Ci is the initial concentration of solute and Ct is the concentration at time ‘t’ in mg L-1.

The maximum amount of dye/heavy metal ion adsorption at equilibrium is determined using the following equations: (2)

Where V is the volume of solution and M is the mass of adsorbent.

The pseudo-first order, pseudo-second order and intraparticle diffusion models are used to evaluate the kinetic mechanism, which controls the adsorption process. Validity of the models are verified by the linear equation analysis log Qe-Qt vs. t, t/Qt vs. t and Qt vs , respectively.

. The first model is the pseudo- first order equation.

Log (Qe-Qt)= log Qe - t (3 )

Where Qe and Qt (mg g-1) refer to the amount of /heavy metal ion/dye adsorbed at equilibrium and time t (min), respectively, and k1 is the rate constant.

The pseudo-second order model is represented in the following equation:

+ (4)

Where k2 is the rate constant of the pseudo-second order model.

The intra-particle diffusion model of Weber and Morris is represented by the following equation:

Qt = kit1/2 + C (5)

Where ki is an intraparticle diffusion rate constant and C is the concentration of adsorbate (mg L-1).

Langmuir model is expressed by the equation:

(6)

Where Ce, is the equilibrium concentration of the adsorbate andQmax is theadsorption capacity at saturation (mg g-1). KL is the Langmuir adsorption constant and is related to the energy of adsorption.

Freundlich model is expressed by the following equation:

ln Qe = ln KF + lnCe (7)

Where n is the Freundlich constant, KF is the other constant related to the maximum adsorption capacity.

Tempkin model is represented by the following equation:

Qe = B ln KT + B ln Ce (8)

Where KT is the equilibrium binding energy constant and B is a constant related to the energy of adsorption.

The pseudo-first order, pseudo-second order and intraparticle diffusion models were used to evaluate the kinetic mechanism, which controls the adsorption process. Validity of the models was verified by the linear equation analysis log Qe-Qt vs. t, t/Qt vs. t and Qtvs, respectively.

Fig. 1.1. Pseudo-first order plot for Cu(II) adsorption by (a) PANI and (b)PANI-Fe(III) composite.

Fig. 1.2.Pseudo-second order plot for Cu (II) adsorption by (a) Polyaniline and (b)PANI-Fe (III) composite.

Fig. 1.3.Intraparticle diffusion plot for Cu(II) adsorption by (a) PANI and (b)PANI-Fe (III) composite.

.

Adsorption isotherm

The following adsorption isotherms were used to fit the experimental data: 1) Langmuir model 2) Freundlich model and 3) Tempkin model.

Fig. 1.4.Langmuir Isotherm plot for Cu (II) adsorption by (a) PANI and (b) PANI-Fe(III) composite.

Fig. 1.5.Freundlich Isotherm plot for Cu (II) adsorption by (a) PANI and (b)PANI-Fe(III) composite.

Fig. 1.6.Temkin Isotherm plot for Cu (II) adsorption by (a) PANI and (b) PANI-Fe(III) composite.

Fig 2.1.Pseudo-first order plot for MB adsorption by (a) PANI and (b) PANI-Fe(II) composite.

Fig 2.2. Pseudo-second order plot for MB adsorption by (a) PANI and (b) PANI-Fe(II) composite.

Fig 2.3.Intraparticle diffusion plot for MB adsorption by (a) PANI and (b) PANI-Fe(II) composite.

3.2.10 Adsorption isotherm

The following adsorption isotherms are used to fit the experimental data: 1) Langmuir model 2) Freundlich model and 3) Tempkin model.

Fig 2.4.Langmuir isotherm plot for MB adsorption by (a) PANI and (b)PANI-Fe(II) composite.

Fig 2.5.Freundlich isotherm plot for MB adsorption by (a) PANI and (b) PANI-Fe(II) composite.

Fig 2.6.Temkin isotherm plot for MB adsorption by (a) PANIand (b) PANI-Fe(II) composite.