Adsorption Kinetics

The effect of TiO2 on the adsorption process of methylene blue onto activated carbon was bilaterally studied, performing not only equilibrium, but also, kinetics experimental work. In order to compare the rate of uptake of methylene blue from water under the studied conditions, the decolouration percentage, the external mass transfer rate and the intraparticle diffusion rate were calculated.

The decolouration percentage or degradation rate was determined as follows

Decoloration or Removal = (𝐶₀− 𝐶_𝑖) 𝐶⁄ ₀ (3-1)

where C0 and Ci are the initial dye concentration and the dye concentration at a given time, respectively. Each simplified kinetic model described in the Literature Review was applied to the adsorption kinetics dataset.

The rate parameter for intraparticle diffusion ki (mg g^-1 min^-0.5) was determined using Weber’s intraparticle diffusion model by plotting q versus 𝑡^1⁄2:

𝑞 = 𝑘_𝑖𝑡^1⁄2+ 𝐶 (3-2)

where C is the intercept and boundary layer effect, ki is the intraparticle diffusion rate constant (mg/g min^0.5), q is the amount of dye adsorbed (mg/g), and t the time.

The external mass transfer coefficient kF (cm s^-1) was calculated based on the following equation, derived from the film-solid diffusion model (Onal et al., 2007):

K_F=mk₂q²_e

C₀S_ext (3-3)

where k2 (g mg^-1 min^-1) is the rate constant for pseudo second-order adsorption, m is the mass of the adsorbent (g), qe is the adsorption capacity (mg g^-1), C0 is the initial dye concentration (mg m³), and Sext is the external surface area of adsorbent (m²). More details about these models can be found in the Literature Review.

Experimental design and data analysis

Five designs of experiment (DOE) and a total of 86 experiments were configured to investigate the interaction between TiO2 and activated carbon. Decolouration (methylene blue removal), the change in pH during adsorption for 207C carbon (Var-pH), the liquid film rate constant (external mass transfer KF cm/s) and the intraparticle diffusion rate constant (Ki mg/g min^0.5) were set as responses.

The mass of activated carbon, the mass of TiO2, the initial concentration of dye (C0), the time (t) and

57 the type of activated carbon (Type carbon) were the predictor variables. By default, all experiments were randomized to reduce the effect of experimental bias.

DOE 1

Five predictor variables were used to analyse their effect on decolouration. A total of 22 runs were performed by designing a fractional factorial (fraction 1/2) with 6 centre points. The resolution of this design is V (a resolution V design,2𝑉5−1 is a design with a total collection of design generators I=ABCDE which determines how the subset of runs is selected from the full factorial design), so main effects and 2-way interactions were free from aliasing. Effects which are confounded are called aliases (Antony, 2003). The term confounding is generally reserved to indicate that treatment and blocking effects are indistinguishable (Dean and Voss, 1999; NIST/SEMATECH, 2013). In this design main effects are aliased with 4-factor interactions and 2-factor interactions are aliased with 3-factor interactions, but 3 and 4-factor interactions were considered negligible (Gómez and Callao, 2008;

Montgomery, 2008). Levels and factors details for this experimental design are shown in Table 3-3.

The design from Minitab was next Session window output:

Factors: 5 Base Design: 5, 16 Resolution: V Runs: 22 Replicates: 1 Fraction: 1/2 Blocks: 1 Centre pts (total): 6

Table 3-3 Detail of assigned level values in each variable from DOE 1 Fractional Factorial (1/2)

Response: % Removal Low Middle High

Methylene blue initial concentration, mg/L 10 55 100

Activated carbon mass, mg 50 275 500

TiO2 mass, mg 50 275 500

Time, min 60 150 240

Type of carbon CA1 --- 207C

DOE 2 and 3

Three predictor variables were used to analyse their effect on decolouration. A total of 16 runs were performed by designing a full factorial with no centre points and 2 replicates. Main effects and 2-way interactions were free from aliasing. Levels and factors details for each experimental design are shown in Table 3-4. In this case the design from Minitab was the following

Session window output:

Factors: 3 Base Design: 3, 8 Runs: 16 Replicates: 2 Blocks: 1 Centre pts (total): 0

58 Table 3-4 Detail of assigned level values in each variable from DOE 2 and 3

Full Factorial per carbon (contact time, 1 h)

Response: % Removal, pH Low High

Methylene blue initial concentration, mg/L 10 100

Activated carbon mass, mg 50 500

TiO2 mass, mg 50 500

DOE 4 and 5

A Full Factorial with activated carbon, TiO2 and methylene blue, at equilibrium conditions, were used as variables. The three predictor variables were used to analyse their effect in KF and Ki. A total of 16 runs were performed by designing a full factorial with no centre points and 2 replicates. Main effects and 2-way interactions were free from aliasing. Levels and factors details for each experimental design are shown in Table 3-5. The session window output from Minitab was as given below

Session window output:

Factors: 3 Base Design: 3, 8 Runs: 16 Replicates: 2 Blocks: 1 Centre pts (total): 0

Table 3-5 Detail of assigned level values in each variable from DOE 4 and 5 Full Factorial per carbon (Equilibrium conditions)

Response: KF and Ki Low High

Methylene blue initial concentration, mg/L 10 100

Activated carbon mass, mg 50 500

TiO2 mass, mg 50 500

Experimental procedure

The experimental procedure for each run was as follows: Sorption kinetics experiments were carried out using a 500 ml capacity batch-stirrer vessel. The vessel was charged with 300 ml of methylene blue solution. Methylene blue solutions were prepared by diluting different amounts of stock solution according to the values indicated by the DOE. Photocatalyst and adsorbent were mixed as solids prior to addition in the solution at room temperature and constant agitation speed of 500 rpm. The reactor was left for the total time specified in each run of the design. Samples were taken and filtered at constant intervals of time. The collected samples were then analysed using UV-Vis spectroscopy. Zeta potential, mean particle size and pH before and after adsorption were measured in addition. Two vessels (`A` and `B`) with the same suspension and experimental conditions were

59 placed side by side. Samples were withdrawn from vessel A for analysis. To make up for the lost volume equal amount of solutions from vessel B was added to vessel A.