Simulation of degradation of the organic contaminants ethylene glycol and phenol by iron nanoparticles using the kinetic Monte Carlo method

Abstract

We applied kinetic Monte Carlo simulation to study the kinetics and mechanisms of the degradation of the organic pollutants ethylene glycol and phenol by iron(III) nanoparticles and hydrogen peroxide as the catalytic system. The values of the rate constants for all steps of the reaction mechanisms are obtained as adjustable parameters. In both degradation processes, an [Fe^II˙OOH] complex is formed. This complex can directly oxidize phenol, but it produces a hydroxyl radical in a separate kinetic step for the degradation of ethylene glycol. Here, ethylene glycol is oxidized by this hydroxyl radical. The kinetic Monte Carlo simulation results of this research agree qualitatively with the available corresponding experimental data for the degradation of ethylene glycol and phenol.

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1. Introduction

Organic contaminants often exist in drinking water, groundwater, and domestic and industrial wastewaters. The chemical degradation of organic pollutants by advanced oxidation processes (AOPs) is a developing method for the treatment of industrial wastewater and purification of drinking water and groundwater.^1–4 The oxidation by AOPs has been applied using Fenton's reagent (Fe²⁺/Fe³⁺/H₂O₂) as a promising and attractive treatment for the effective destruction of a wide range of organic compounds.^5–9 The Fenton process is a catalytic reaction for the generation of very reactive free hydroxyl radicals (˙OH) and it is based on an electron transfer between hydrogen peroxide (H₂O₂) and iron ions as the homogeneous catalyst. The hydroxyl radical is a highly reactive, non-selective oxidizing agent and able to degrade a large number of organic compounds under ambient conditions.^10–12 This catalytic system is used for cleaning industrial water based on AOPs.^13,14 In order to promote oxygenation of organic contaminants such as ethylene glycol and phenol, Zelmanov and Semiat reported the application of iron oxide nanoparticles using the Fenton system.¹⁵

We have set out to study the kinetic parameters and mechanisms of the degradation of organic pollutants using computational modelling. For the present work we employed an efficient method for identifying and comparing the kinetic mechanisms of the destruction of phenol and of ethylene glycol by iron oxide nanoparticles using kinetic Monte Carlo simulation, which has been shown to be a powerful tool for simulating various chemical reactions.^16–18 The rate constant of each step as well as concentration-versus-time curves for the oxidation of phenol and ethylene glycol (EG) were determined using this simulation method.

2. Kinetic Monte Carlo method

In order to simulate the experimental data for degradation of organic pollutants by iron oxide nanoparticles, we used the kinetic Monte Carlo method developed by Gillespie.¹⁹ Kinetic simulations were performed using the Chemical Kinetic Simulator program, version 1.01.²⁰ The algorithm of this simulation considers the reaction mechanism as a collection of several steps:

nN + mM + … → products (2.1)

The input parameters for the simulation are the steps, the rate constants of each step (k_i), temperature (T) and number of molecules (C_i). The algorithm of this simulation is based on the reaction probability density function (P(τ, i)) which is obtained by the master equation:

P(τ, i) = k_iC_i exp{−Σk_iC_iτ} (2.2)

In fact the reaction probability density function is a two-variable probability density function that can be written as the product of two one-variable probability density functions:

P(τ, i) = P(τ)P(i) (2.3)

Here Pτ(dτ) is the probability of occurrences of the next reaction between times t + τ and t + τ + dτ, irrespective of which reaction it could be and P(i) shows the probability that the next reaction may be an Ri reaction that happens at time t + τ.

By the addition theory for probabilities, Pτ(dτ) is equal to the summation of P(τ, i) dτ over all i-values:

P(i) is obtained by substituting eqn (2.4) into eqn (2.3) as:

These two equations clearly express the two one-variable density functions that are multiplied in eqn (2.3) to give the two-variable density function P(τ, i). By substituting eqn (2.2) into eqn (2.4) and (2.5), P(τ) and P(i) can be obtained by eqn (2.6) and (2.7).

P(τ) = a exp(−aτ), 0 ≤ τ < ∞ (2.6)

Here, a_i and a can be obtained by eqn (2.8) and (2.9)

a_i = k_iC_i(i = 1, 2, …, M) (2.8)

In this special case, P(i) is independent of τ. It is also noted that both of these one-variable density functions are properly normalized over their respective domains:

The idea of this method is to create a random value of τ according to P(τ) in eqn (2.6), and then produce a random integer i according to P(i) in eqn (2.7). The result of the random pair (τ, i) can be distributed according to P(τ, i).

A random value τ can be generated according to P(τ) in eqn (2.6) by drawing a random number r₁, from the uniform distribution in the unit interval and calculating

Then, a random integer i may be created according to P(i) in eqn (2.7) by drawing another random number r₂ from the uniform distribution in the unit interval and by taking i to be that integer for which,

In this method, two random numbers r₁ and r₂ are created and τ and i are calculated by eqn (2.10) and (2.11), respectively.

The simulation was extended by continually selecting at random among the probability-weighted steps in the mechanism and updating the reactant and product populations according to the stoichiometry of the selected step, system state variables and reaction rates. The results were obtained as concentration-versus-time curves. This stochastic numerical simulation method has been used to simulate several chemical reactions.^16–18 In this project, kinetic Monte Carlo simulation was used to study the kinetics of degradation of organic compounds by Fenton's reagent using iron nanoparticles.

3. Results and discussion

In this research the kinetics and mechanism of an experimental degradation (i.e., “destruction”) of organic contaminants were investigated by the Fenton reaction.¹⁵ Zelmanov and Semiat¹⁵ have studied the degradation of ethylene glycol and phenol using iron oxide nanoparticles and hydrogen peroxide as the catalytic system. The concentration of each organic compound was obtained as a function of time for various concentrations of Fe(III) nanoparticles. In the present work modelling of the kinetics of the degradation of ethylene glycol and of phenol were performed using kinetic Monte Carlo simulation.

3.1. Simulation of ethylene glycol degradation by iron(III) nanoparticles and H₂O₂

For simulation of ethylene glycol oxygenation, the following data were used as input: temperature (298 K), initial concentration of ethylene glycol ([EG]₀ = 25.78 × 10⁻² M), initial concentration of hydrogen peroxide ([H₂O₂]₀ = 1.83 M), initial concentration of iron oxide nanoparticles ([Fe NPs]₀ = 98.2 × 10⁻⁴ M),¹⁵ the steps of the mechanism and rate constants of each step. The values of rate constants were adjusted until a reasonable fit of the calculated data with experimental kinetic data was attained. Different mechanisms were examined for the degradation of ethylene glycol using Monte Carlo simulation. The mechanism that is used for the kinetic Monte Carlo simulation and has a good fit with experimental results is:

In the above mechanism, ethylene glycol is degraded by hydroxyl radical (˙OH). In the first step of this mechanism, the complex [Fe^II˙OOH] is formed by the reaction of nano Fe(III) with hydrogen peroxide (reaction (3.1.1)). The rate constant of this step is denoted as k₁. A reversible dissociation of this complex creates a hydroxyl radical (reaction (3.1.2)), and the rate constants of the forward and reverse reactions are denoted as k₂ and k₃, respectively. Finally, ethylene glycol is converted by ˙OH to glycoaldehyde and water (3.1.3) (rate constant = k₄).

The rate constants of each step of the proposed mechanism were obtained as adjustable parameters by the kinetic Monte Carlo simulation. The obtained mechanism was employed to simulate this reaction with different initial concentrations of iron(III) nanoparticles ([Fe NPs]₀ = 17.86 × 10⁻³, 26.79 × 10⁻³, 44.64 × 10⁻³ M). The rate constants for the degradation of ethylene glycol at various Fe(III) nanoparticle concentrations are listed in Table 1. It is shown in this table that the third step (reaction (3.1.3)) is the rate-determining step. Therefore, k₄ is more important than other rate constants in the degradation process. Also k₁, k₂ and k₃ are constant for this reaction at different concentrations of nano Fe(III) but k₄ increases with increasing of nanoparticles concentration.

Table 1 Rate constants of the simulated mechanism for degradation of ethylene glycol using different concentrations of Fe(III) nanoparticles

[Fe NPs]0 (M)	k1 (min^−1)	k2 (min^−1)	k3 (min^−1)	k4 (min^−1)
98.2 × 10^−4	1.0	0.5	1.0 × 10^−2	7.3 × 10^−3
17.86 × 10^−3	1.0	0.5	1.0 × 10^−2	2.2 × 10^−2
26.79 × 10^−3	1.0	0.5	1.0 × 10^−2	4.4 × 10^−2
44.64 × 10^−3	1.0	0.5	1.0 × 10^−2	1.4 × 10^−1

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Curves describing the concentrations of ethylene glycol as a function of time were obtained at different concentrations of Fe(III) nanoparticles by the simulation and the results are shown in Fig. 1. As seen in this figure, there is good agreement between the simulated and experimental data.¹⁵ This agreement demonstrates that the proposed mechanism can be suitable for studying the kinetics of the degradation of ethylene glycol.

Fig. 1 Kinetic data for degradation of ethylene glycol in the Fenton-like process at different concentrations of Fe(III) nanoparticles: (a) 98.2 × 10⁻⁴ (b) 17.86 × 10⁻³, (c) 26.79 × 10⁻³ and (d) 44.64 × 10⁻³ M, experimental data (open circles) and theoretical data (solid line).

A possible mechanism for oxidation of ethylene glycol by hydroxyl radical is shown in Scheme 1.²¹ Glycoaldehyde is formed by the reaction of ˙OH with ethylene glycol. At the end of this pathway, sequential ˙OH attacks result in the creation of formic acid, which then gets converted to carbon dioxide and water.

Scheme 1 A possible pathway for degradation of ethylene glycol by hydroxyl radical.

3.2. Simulation of phenol degradation by iron(III) nanoparticles and H₂O₂

The input data for the simulation of phenol degradation are temperature (298 K), initial concentration of phenol ([PhOH]₀ = 1.45 × 10⁻² M), initial concentration of iron oxide nanoparticles ([Fe NPs]₀ = 2.68 × 10⁻⁴ M), initial concentration of hydrogen peroxide ([H₂O₂]₀ = 2.13 × 10⁻¹ M),¹⁵ the steps of the proposed mechanism and rate constants of each step. The values of the rate constants were adjusted until a reasonable fit of the calculated data with the experimental results was obtained. Various mechanisms were examined for the oxygenation of phenol by Monte Carlo simulation. The mechanism which best fits with the experimental data is:

In the first step of this mechanism Fe(III) nanoparticles react with hydrogen peroxide to form the [Fe^II˙OOH] complex reaction (3.2.1) with a rate constant of k₁. Then this complex reacts with phenol to produce hydroquinone by reaction (3.2.2) (rate constant = k₂).

The rate constants k₁ and k₂ were obtained as adjustable parameters by the kinetic Monte Carlo simulation. The proposed mechanism was applied to simulate this reaction at various initial concentrations of Fe(III) nanoparticles ([Fe NPs]₀ = 2.68 × 10⁻⁴, 5.36 × 10⁻⁴, 1.07 × 10⁻³ M). Table 2 shows the values of the rate constants for phenol degradation using different initial concentrations of nanoparticles (entries 1–3). As seen in this table the rate-determining step is production of the [Fe^II˙OOH] complex (reaction (3.2.1)). Thus k₁ is more important than k₂ in the oxidation of phenol. Also k₁ and k₂ are almost constant for this reaction at different concentrations of iron nanoparticles and the rate of phenol destruction depends on the concentration of Fe(III) nanoparticles.

Table 2 Rate constants of the simulated mechanism for degradation of phenol

Entry	[Fe NPs]0 (M)	k1 (min^−1)	k2 (min^−1)
a Simulation conditions: [PhOH]0 = 1.45 × 10^−2 M, [H2O2]0 = 2.13 × 10^−1 M.b Simulation conditions: [PhOH]0 = 5.45 × 10^−2 M, [H2O2]0 = 1.07 M.
1^a	2.68 × 10^−4	1.00	6.48 × 10^1
2^a	5.36 × 10^−4	1.00	6.50 × 10^1
3^a	1.07 × 10^−3	1.00	6.50 × 10^1
4^b	2.14 × 10^−3	1.00	6.53 × 10^1
5^b	3.57 × 10^−3	1.00	6.55 × 10^1
6^b	4.28 × 10^−3	1.00	6.56 × 10^1

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The curves of phenol concentration versus time for different concentrations of iron nanoparticle were obtained using the kinetic Monte Carlo simulation and the results are illustrated in Fig. 2(a). As shown in this figure, there is perfect agreement between the simulated and existing experimental data for the degradation of phenol.¹⁵

Fig. 2 Kinetic data for degradation of phenol in the Fenton-like process (a) [PhOH]₀ = 1.45 × 10⁻² M, [H₂O₂]₀ = 2.13 × 10⁻¹ M at different concentrations of Fe(III) nanoparticles, M: (□) 2.68 × 10⁻⁴, (○) 5.36 × 10⁻⁴, (Δ) 1.07 × 10⁻³. (b) [PhOH]₀ = 5.45 × 10⁻² M, [H₂O₂]₀ = 1.07 M, concentrations of Fe(III) nanoparticles, M: (□) 2.14 × 10⁻³, (○)3.57 × 10⁻³, (◊) 4.28 × 10⁻³. Experimental data (open circles) and theoretical data (solid line).

Also the proposed mechanism (in reactions 3.2) was used to simulate degradation of phenol at different conditions ([PhOH]₀ = 5.45 × 10⁻² M, [H₂O₂]₀ = 1.07 M, [Fe NPs]₀ = 2.14 × 10⁻³, 3.57 × 10⁻³, 4.28 × 10⁻³ M).

The values of the rate constants according to the simulation with the aforementioned conditions (Table 2, entries 4–6) demonstrate that the rate-determining step of the phenol degradation is production of the [Fe^II˙OOH] complex.

As a result of these simulations, k₁ and k₂ are almost constant for this reaction at different initial concentrations of phenol, Fe(III) nanoparticles and H₂O₂.

Fig. 2(b) shows phenol concentration-versus-time curves for the aforementioned conditions using kinetic Monte Carlo simulation. As can be seen, the simulated data are in good agreement with experimental data.¹⁵ According to these results, the proposed mechanism is appropriate to study kinetics of degradation of phenol.

A probable pathway for the degradation of phenol by the [Fe^II˙OOH] complex is presented in Scheme 2. As shown in this scheme phenol is chelated to Fe in the [Fe^II˙OOH] complex followed by the reductive elimination reaction to produce hydroquinone. Organic acid is formed by sequential oxidation of hydroquinone by ˙OH, and finally carbon dioxide and water are created.^22–24

Scheme 2 The probable mechanism for degradation of phenol by [Fe^II˙OOH]_nano.

The results shown in this section indicate that the mechanism of the oxygenation of phenol differs from that of ethylene glycol. In the latter case, dissociation of the [Fe^II˙OOH] complex releases a hydroxyl radical, which then oxidizes ethylene glycol. Phenol, on the other hand, is directly oxidized by the [Fe^II˙OOH] complex. This difference may be attributed to the degradation pathways of phenol and ethylene glycol (Schemes 1 and 2). In the pathway for phenol oxidation, ˙OH is substituted on the aromatic ring which needs the metal to assist in the transfer of the hydroxyl radical. This transfer is performed on the nanoparticle surface. Therefore the [Fe^II˙OOH] complex reacts with phenol.

4. Conclusions

We used kinetic Monte Carlo simulation to predict and study the kinetics and mechanism of organic pollutant (ethylene glycol and phenol) degradation by iron oxide Fe(III) nanoparticles and hydrogen peroxide as a catalytic system. The kinetic Monte Carlo-simulated results show good agreement with existing experimental results for ethylene glycol degradation. The obtained mechanism was applied for simulation of experimental data at different initial concentrations of iron(III) nanoparticles. Also our model predictions agree well with the experimental results of the destruction phenol by oxidation at a variety of initial concentrations of reactants and Fe(III) nanoparticles. Therefore these proposed mechanisms are suitable for the study of degradation reactions. Our results showed that the [Fe^II˙OOH] complex is formed in both oxidation processes. In the degradation pathway of ethylene glycol, dissociation of this complex releases a hydroxyl radical, which then oxidizes the ethylene glycol. But for the destruction of phenol, the [Fe^II˙OOH] complex directly oxidizes the phenol.

Acknowledgements

The authors are grateful to University of Kashan for supporting this work by Grant no. (256750/I).

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