Contrasting hydrogen peroxide- and persulfate-driven oxidation systems: Impact of radical scavenging on treatment efficiency and cost

Abstract

For the first time, the fate of radicals generated in heterogeneous chemical oxidation treatment systems has been accounted for and used to assess treatment performance in three reaction compartments; reaction with the target compound, rhodamine B (RhB), the aqueous phase scavengers, and the solid phase scavengers. Radicals formed during the ultra-violet (UV) activation of hydrogen peroxide (H₂O₂) (UV-AHP) and persulfate (S₂O₈²⁻) (UV-APS) include hydroxyl (•OH) and sulfate radicals (SO₄^•−), respectively. •OH and SO₄^•−, used in oxidation treatment systems to degrade a broad spectrum of environmental contaminants, may also react with non-target chemical species (scavengers) that limit treatment efficiency. UV-AHP and UV-APS treatment systems were amended with solid phase alumina to assess scavenging by solid surfaces. The overall rate of reaction and rate of radical scavenging was greater for •OH than SO₄^•−. Scavenging by dissolved constituents was dominated by the oxidant used (H₂O₂, S₂O₈²⁻); and the rate of radical scavenging by alumina was greater than the rate of RhB oxidation in all cases. Treatment efficiency was lower in the UV-AHP than in the UV-APS treatment system and was attributed to greater aqueous and solid phase scavenging rates. The cost of commercially available H₂O₂ ($0.031 mol⁻¹) and PS ($0.24 mol⁻¹) was used in conjunction with the overall treatment efficiency to assess specific cost of treatment. The specific cost to treat the probe compound with UV-AHP was greater than UV-APS and was attributed to the much lower treatment efficiency with UV-AHP. The much-desired high reaction rate constants between •OH and environmental contaminants, relative to SO₄^•−, may come at the cost of greater combined scavenging rates, and consequently lower treatment efficiency.

1. Introduction

Chemical oxidation processes utilizing activated hydrogen peroxide (H₂O₂) and persulfate (S₂O₈²⁻) (PS) are common methods for treatment of contaminated water, wastewater and aquifer media [1–4]. The reactive intermediates formed during H₂O₂ and PS activation involve hydroxyl radicals (•OH) and sulfate radicals (SO₄^•−), respectively, both capable of reacting with a broad spectrum of environmental contaminants [5–9]. Although both radicals are strong electrophiles and reactions with the majority of contaminants are highly favorable, the reaction of these radicals are uniquely different and involve non-target reactive species (i.e., scavengers).

The kinetics of contaminant transformation reactions involving •OH and SO₄^•− are strongly influenced by the presence of scavengers in the treatment system. Aqueous and solid phase scavengers compete with the contaminant for •OH and SO₄^•− and contribute to treatment inefficiency. Until recently, only radical scavenging in the aqueous phase has been quantified [10–13], predominantly utilizing the concentrations of the dissolved species and the second-order rate constants. Recently, laboratory and competition kinetics methods have been developed to estimate the surface scavenging reaction rate constants (k_≡S) between solid phase mineral species (≡S_i) and •OH [14], and SO₄^•− [15]. A description of the method of kinetic analysis is provided in the Supporting Information (S.1). The radical-specific surface scavenging rate constants estimated in these studies [14,15] were used to quantify the relative roles of solid and aqueous phase scavengers in the activated H₂O₂ and activated PS treatment systems. Results indicated that in heterogeneous systems, surface scavenging significantly reduced the rate of contaminant degradation and was the leading cause of treatment efficiency.

Alumina (Al₂O₃), a naturally occurring mineral in soil and aquifer systems [16,17], was selected as model mineral and tested. The physicochemical properties of alumina were previously established and used in this study (S.2; Table S1; Fig. S1) [14,15]. The previous studies involved heterogeneous UV-activated persulfate (UV-APS) and UV-activated hydrogen peroxide (UV-AHP) treatment conditions using alumina suspensions ([Al₂O₃] = 10 g L⁻¹) were conducted using similar experimental procedures and methods of competition kinetics analysis. Additional treatment experiments were conducted in this study to augment the kinetic parameters used in the analysis. Rhodamine B dye (RhB) served as the target compound and was used as an indicator of radical activity for •OH and SO₄^•−. Reactions and rate constants involving UV activation of H₂O₂ and S₂O₈²⁻, and associated reactions in the heterogeneous oxidative treatment system are summarized (Table 1).

Table 1.

Chemical reactions associated with UV-activated hydrogen peroxide (H₂O₂) and UV-activated persulfate (S₂O₈ ²⁻) oxidative treatment systems.

Hydrogen peroxide related reactions
UV activation: ${\text{H}}_2{\text{O}}_2\to 2•\text{OH}$		R1
•$\text{OH}+\text{RhB}\to \text{products}$	k2 = 2.5 × 1010 M−1 s−1 [5]	R2
•$\text{OH}+{{\text{∑}}_{\text{i}=1}}^{\text{n}}\left[{\text{S}}_{\text{i}}\right]\to \text{products}$		R3
•$\text{OH}+{\text{H}}_2{\text{O}}_2\to {\text{HO}}_2{•}^{-}+{\text{H}}_2\text{O}$	k4 = 2.7 × 107 M−1 s−1 [5]	R4
•OH + ≡Si → products		R5
${\text{H}}_2{\text{O}}_2\to {\text{H}}_2\text{O}+½{\text{O}}_2$		R6
Persulfate related reactions
UV activation: S2O8 2− → 2SO4 •−		R7
SO4 •− + RhB → products	k8 = 3.02 × 10 8 M −1 s −1 [15]	R8
${{\text{SO}}_4}^{•-}+{{\text{∑}}_{\text{i}=1}}^{\text{n}}\left[{\text{S}}_{\text{i}}\right]\to \text{products}$		R9
SO4 •− + S2O8 2− → SO4 2− + S2O8 •−	k10 = 6.1 × 10 5 M −1 s −1 [6]	R10
SO4 •− + OH − → SO4 2− + HO•	k11 = 7.0 × 10 7 M −1 s −1 [6]	R11
SO4 •− + H2O → SO4 2− + HO• + H +	k12 = 6.6 × 10 2 s −1	R12
SO4 •− + ≡Si → products		R13
S2O8 2− → 2 SO4 2−		R14

Previously, only reaction rate constants involving dissolved reactive species in aqueous solutions have been quantified and used to determine the fate of •OH and SO₄^•− with respect to radical scavenging, and to assess treatment inefficiency. To our knowledge, the reaction rate constants for solid phase media and •OH or SO₄^•− have not been measured and published, and thus, never considered in treatment efficiency assessments. Collectively, the data and information developed in these studies [14,15] provided a unique opportunity to establish and to contrast radical production and reaction, treatment efficiency, and the cost associated with these two oxidants in heterogeneous treatment systems. The objective of this research was to utilize the kinetic parameters from the two studies involving radical production and reaction, and to contrast treatment efficiency and cost metrics. This would establish the underlying basis for a detailed critical assessment of UV-AHP and UV-APS heterogeneous treatment systems and provide a better understanding of the strengths and limitations of each system.

2. Experimental

2.1. Experimental conditions

RhB was selected as a probe due to the favorable properties that allow rapid analysis and processing of samples, thus eliminating the quenching step of the remaining oxidant (PS). RhB is non-volatile, hydrophilic and adsorbs poorly to alumina surfaces at pH conditions applied in the study, which minimizes non-oxidative losses and simplifies the kinetic analysis [15]. RhB (λ_max = 556 nm) concentrations were determined (n = 3) spectrophotometrically on the Jenway 6505. A spectrophotometric method was also used for analyzing the persulfate concentration (λ_max = 450 nm) [18]. Regression analysis of the spectrophotometric response and the concentration of RhB and PS yielded linear calibration curves (r² = 0.99). The method detection limits (MDL) for RhB was 0.0015 mg/L. All samples were analyzed in replicate or triplicate. The pH was measured using the Orion Star A215 pH meter (EPA Method 150.1). The 95% confidence intervals were used as a statistical metric to assess the range of potential values of the measured parameter. The experiments were carried out at room temperature (22.0 ± 0.5 °C). The UV-AHP and UV-APS tests were conducted in 40 mL borosilicate volatile organic analysis (VOA) vials (temperature 21–23 °C) under a UV Lamp (High-Performance UVP Transilluminator, Model TFM-20) containing 4 UV-A tube bulbs (25 W bulbs, 115 V, 60 Hz, 2.0 amps, 365 nm), where H₂O₂ and S₂O₈²⁻ both undergo photolytic cleavage of the peroxo bond under UV activation. The UV wavelength used resulted in different rates of H₂O₂ and PS activation. However, the approach used in this critical analysis was to contrast the relative radical activity and fate, once formed, in the alumina-amended heterogeneous systems. Normalization of parameter values in this manner allows a direct comparison method of analysis.

Reaction conditions were established to quantify differences between the two systems originating from aqueous phase scavenging (i.e. reaction between •OH and H₂O₂; SO₄^•− and S₂O₈²⁻), and solid phase scavenging. Specifically, the second-order reaction rate constants for the reaction between RhB, and •OH and SO₄^•−, are quite different (k₂ = 2.5 × 10¹⁰ M⁻¹ s⁻¹, R2, Table 1; k₈ = 3.02 × 10⁸ M⁻¹ s⁻¹, R8, Table 1). It was assumed that the rate of RhB loss could potentially be much greater in the UV-AHP treatment system. Further, H₂O₂ and S₂O₈²⁻ are notorious scavengers of •OH (k₄ = 2.7 × 10⁷ M⁻¹ s⁻¹, R4, Table 1) and SO₄^•− (k₁₀ = 6.1 × 10⁵ M⁻¹ s⁻¹, R10, Table 1), respectively. Consequently, experimental conditions were used where [RhB]₀ and [alumina] were constant in all test systems. Oxidant concentrations were designed such that the rate of reaction between •OH and the aqueous scavenger, H₂O₂, and the reaction between •OH and RhB were less than a factor of 6; similarly, the rate of reaction between SO₄^•− and the aqueous scavenger, S₂O₈²⁻, and the reaction between SO₄^•− and RhB were less than a factor of 6 (i.e., k₄ [H₂O₂]/k₂ [RhB] and k₁₀ [S₂O₈²⁻]/ k₈ [RhB] < 6). Through this method, it was assured that neither reaction would predominate by masking scavenging reactions in either system, and that potential effects from scavenging by the solid phase media could be measured. Additional experiments were carried out for comparison purposes where equimolar concentrations of oxidants, [H₂O₂]₀/[S₂O₈²⁻]₀ = 1, were used ([H₂O₂]₀ = [S₂O₈²⁻]₀ = 29.4 mM). The chemicals, experimental procedures, and controls are described in detail (S.3; Figs. S2–S3). Through these experiments, direct comparison between the UV-AHP and UV-APS systems could be carried out. Parameter values, •OH and SO₄^•− activity, and scavenging rate constants used to contrast oxidation results from the UV-APS and UV-AHP heterogeneous treatment systems are tabulated (Table 2). These parameters were further used to calculate kinetic parameters including the radical production rates, normalized reaction rates, reaction rate constants, relative rates of reaction, and estimation of cost efficiency. These parameters served as the basis to contrast treatment results between the UV-AHP and UV-APS systems.

Table 2.

Parameter values and alumina surface scavenging rate constants used to contrast •OH and SO₄ ^•− activity in UV-APS and UV-AHP oxidative treatment systems.

Parameter	UV-APS 2	UV-APS	UV-AHP 2
${\left[{\text{S}}_2{{\text{O}}_8}_1^{2-}\right]}_0,{\left[{\text{H}}_2{\text{O}}_2\right]}_0$ (nM)1	2.1	29.4	29.4
[RhB]0 (mM)	1.04 × 10 −2	1.04 × 10 −2	1.04 × 10 −2
[alumina] (g L −1)	10	10	10
SA (m 2 g −1)	1.5	1.5	1.5
pHinitial, pHfinal	6.0, 4.5	6.0, 4.1	6.8, 6.0
[SO4 •−]SS,10, [•OH]SS,10 (M)	6.25 × 10 −13 (n = 13)	1.25 × 10 −11 (n = 13)	4.73 × 10 −15 (n = 7)
Test reactor volume (L)	0.025	0.025	0.025
${\text{k}}_{\equiv \text{S},\text{SO}4}{}^{•-},{\text{k}}_{\equiv \text{S},•\text{OH}}\left({\text{m}}^{-2}{\text{s}}^{-1}\right)$	2.42 × 10 4 (n = 13)	2.42 × 10 4 (n = 13)	7.45 × 10 6 (n = 7)

¹The basis for selecting the concentration of oxidant was (1) to assure that the rate of aqueous phase scavenging did not mask RhB oxidation and that changes in [RhB] could be measured (i.e. k₄ [H₂O₂]/k₂ [RhB] and k₁₀ [S₂O₈ ²⁻]/k₈ [RhB] < 6), and (2) equal [H₂O₂]₀ and [S₂O₈ ²⁻]₀.

²Data and calculated parameters derived for 2.1 mM PS and 29.4 mM H₂O₂ are from [15] and [14], respectively; data and calculated parameter values for 29.4 mM PS are from this study.

It is important to clarify that the use of UV-based oxidation systems in in-situ systems (i.e., in-situ treatment of contaminated groundwater and aquifer material) is not proposed nor should it be inferred by this study. Rather, UV activation is used in this study to generate •OH and SO₄^•− under comparable systems. Consequently, the relative fate of the radicals with aqueous or solid phase species can be determined, once produced in the treatment system. Until recently, this was only possible for aqueous phase reactants.

2.2. Metrics for determining treatment efficiency

2.2.1. Rate of radical production

Invoking the quasi-steady state assumption, the radical production rate for •OH (P_•OH) was set equal to the overall rate of •OH consumption (C_•OH); where C_•OH is represented as the sum of •OH reaction rates with the probe (R_P,•OH), scavengers in the aqueous phase (R_S,•OH), and scavengers in the solid phase (R_≡S,•OH) (Eq. (1A)). Similarly, the radical production rate for SO₄^•− (P_SO4^•−) was equal to the overall rate of SO₄^•− consumption and is the sum of reaction rates with the probe (R_P,SO4^•−), scavengers in the aqueous phase (R_S,SO4^•−), and scavengers in the solid phase (R_≡S,SO4^•−) (Eq. (2A)). UV-AHP and UV-APS heterogeneous test systems (i.e., 10 g L⁻¹ alumina suspensions) (Eqs. (1B), (2B)) were used as the basis to contrast radical activity. P_•OH and P_SO4^•− were normalized to the respective steady-state radical concentrations (i.e., [•OH]_SS,10, [SO₄^•−]_SS,10; subscript refers to 10 g L⁻¹ Al₂O₃; Table 2). This metric (N_•OH, N_SO4^•−) provides a relative measure of the overall radical reaction rate constant (Eqs. (3)–(4)). N_•OH and N_SO4^•− are independent of [•OH]_SS and [SO₄^•−]_SS when calculated in this manner and represent the overall combined reaction rate constant (s⁻¹) for RhB, the oxidant scavenger, and the alumina scavenging sites. This metric is used to assess the relative reactivity of •OH and SO₄^•− under the applied reaction conditions.

$${\text{P}}_{•\text{OH}}={\text{R}}_{\text{P},•\text{OH}}+{\text{R}}_{\text{S},•\text{OH}}+{\text{R}}_{\equiv \text{S},•\text{OH}}$$ (1A)

$${\text{P}}_{•\text{OH}}={\text{k}}_2[\text{RhB}]{[•\text{OH}]}_{\text{SS}}+{\text{k}}_4\left[{\text{H}}_2{\text{O}}_2\right]{[•\text{OH}]}_{\text{SS}}+{\text{k}}_{\equiv \text{S},•\text{OH}}{\text{S}}_{\text{A}}{\text{m}}_{\text{S}}{[•\text{OH}]}_{\text{SS}}$$ (1B)

$${\text{P}}_{{}_{•}\text{SO}4}{}^{•-}={\text{R}}_{\text{P},\text{SO}4}{}^{•-}+{\text{R}}_{\text{S},\text{SO}4}{}^{•-}+{\text{R}}_{\equiv \text{S},\text{SO}4}{}^{•-}$$ (2A)

$${{\text{P}}_{\text{SO}4}}^{•-}={\text{k}}_8[\text{RhB}]{\left[{{\text{SO}}_4}^{•-}\right]}_{\text{SS}}+k_{10}\left[{\text{S}}_2{{\text{O}}_8}^{2-}\right]{\left[{{\text{SO}}_4}^{•-}\right]}_{\text{SS}}+{\text{k}}_{\equiv \text{S},\text{SO}4}^{•-}{\text{S}}_{\text{A}}{\text{m}}_{\text{S}}{\left[{{\text{SO}}_4}^{•-}\right]}_{\text{SS}}$$ (2B)

$$\begin{gathered} {{\text{P}}_{\text{SO}4}}^{•-}={\text{k}}_8[\text{RhB}]{\left[{{\text{SO}}_4}^{•-}\right]}_{\text{SS}}+k_{10}\left[{\text{S}}_2{{\text{O}}_8}^{2-}\right]{\left[{{\text{SO}}_4}^{•-}\right]}_{\text{SS}}+{{\text{k}}_{\equiv \text{S},\text{SO}4}}^{•-}{\text{S}}_{\text{A}}{\text{m}}_{\text{S}}[{{\text{SO}}_4}^{•} \\ {\text{N}}_{•\text{OH}}={{\text{P}}^{•}}_{\text{OH}}/{[•\text{OH}]}_{\text{SS}}={\text{k}}_2[\text{RhB}]+{\text{k}}_4\left[{\text{H}}_2{\text{O}}_2\right]+{\text{k}}_{\equiv \text{S},•\text{OH}}{\text{S}}_{\text{A}}{\text{m}}_{\text{S}} \end{gathered}$$ (3)

$${\text{N}}_{\text{SO}4}{}^{•-}={\text{P}}_{\text{SO}4}{}^{•-}/{\left[{{\text{SO}}_4}^{•-}\right]}_{\text{SS}}={\text{k}}_8[\text{RhB}]+k_{10}\left[{\text{S}}_2{{\text{O}}_8}^{2-}\right]+{\text{k}}_{\equiv \text{S,SO}4}{}^{•-}{\text{S}}_{\text{A}}{\text{m}}_{\text{S}}$$ (4)

Where, P_•OH, P_SO4^•− rate of •OH and SO₄^•− production (M s⁻¹), [•OH]_SS, [SO₄•−]_SS pseudo-steady state hydroxyl and sulfate radical concentration (M), [RhB] rhodamine B concentration (M), k₂, k₈ second-order degradation rate constant of RhB with •OH, SO₄^•− (M⁻¹ s⁻¹), k₄ second-order degradation rate constant of H₂O₂ with •OH (M⁻¹ s⁻¹), k₁₀ second-order degradation rate constant of S₂O₈²⁻ with SO₄^•− (M⁻¹ s⁻¹), k_≡S,•OH, k_{≡S, SO4}^•− alumina surface scavenging rate constants for •OH and SO₄^•− (m⁻² s⁻¹), S_A surface area of alumina (m² g^−1, )m_S mass of alumina (g), N_•OH, N_SO4^•− overall radical reaction rate constant (s⁻¹).

2.2.2. Relative rates of reaction

The reaction of radicals with the target, RhB, relative to all reactive species present is estimated as an indicator of the potential rate of RhB transformation. Specifically, the rate of RhB reaction with •OH or SO₄^•− relative to the overall reaction rate constant (N_•OH, N_SO4^•−) is represented as RP_•OH, and RP_SO4•−, respectively (Eqs. (5)–(6)). Contrasting these values reveal the relative effectiveness of RhB transformation by each oxidant under the specific experimental systems used.

$${\text{RP}}_{•\text{OH}}={\text{k}}_2[\text{RhB}]/\left({\text{k}}_2[\text{RhB}]+{\text{k}}_4\left[{\text{H}}_2{\text{O}}_2\right]+{\text{k}}_{\equiv \text{S},•\text{OH}}{\text{S}}_{\text{A}}{\text{m}}_{\text{S}}\right)$$ (5)

$${\text{RP}}_{\text{SO4}•-}={\text{k}}_8[\text{RhB}]/\left({\text{k}}_8[\text{RhB}]+k_{10}\left[{\text{S}}_2{{\text{O}}_8}^{2-}\right]+{\text{k}}_{=\text{S},\text{SO}4•-}{\text{S}}_{\text{A}}{\text{m}}_{\text{S}}\right)$$ (6)

In a similar manner, the rate of radical scavenging by the aqueous and alumina mineral surfaces in the UV-AHP and UV-APS test reactors, relative to the overall reaction rate can be quantified (Eqs. (7)–(8)). Contrasting these values reveal radical vulnerability to aqueous and surface radical scavenging and provide a metric for treatment inefficiency.

$${\text{RS}}_{•\text{OH}}=\left({\text{k}}_4\left[{\text{H}}_2{\text{O}}_2\right]+{\text{k}}_{\equiv \text{S},•\text{OH}}{\text{S}}_{\text{A}}{\text{m}}_{\text{S}}\right)/\left({\text{k}}_2[\text{RhB}]+{\text{k}}_4\left[{\text{H}}_2{\text{O}}_2\right]+{\text{k}}_{\equiv \text{S},•\text{OH}}{\text{S}}_{\text{A}}{\text{m}}_{\text{S}}\right)$$ (7)

$${\text{RS}}_{\text{SO4}•-}=\left(k_{10}\left[{\text{S}}_2{{\text{O}}_8}^{2-}\right]+{\text{k}}_{\equiv S,\text{SO}4•-}{\text{S}}_{\text{A}}{\text{m}}_{\text{S}}\right)/\left({\text{k}}_8[\text{RhB}]+k_{10}\left[{\text{S}}_2{{\text{O}}_8}^{2-}\right]+{\text{k}}_{\equiv \text{S},\text{SO}4•\text{−}}{\text{S}}_{\text{A}}{\text{m}}_{\text{S}}\right)$$ (8)

2.2.3. Treatment efficiency and cost estimates

The reaction efficiency (η) associated with the H₂O₂ oxidation mechanism is the product of efficiencies associated with H₂O₂ activation-dependent •OH formation (E₁), and •OH reaction with the target compound (E₂). Specifically, inefficiency in H₂O₂ activation is attributed to non-productive reactions of H₂O₂ (NPR) that do not yield •OH [1]. Reaction inefficiency between •OH and the target compound (P), here rhodamine B, (R2; Table 1) is functionally dependent on competing •OH reactions with aqueous (R3−R4; Table 1) and solid phase scavengers (R5; Table 1) in oxidation treatment systems. Similarly, reaction efficiency in UV-APS treatment systems is estimated using the same approach (R8−R13; Table 1) [15].

The impact of •OH scavenging by aqueous and solid phase surfaces can be examined in the context of treatment efficiency (η_•OH). The efficiency (E₁) (Eq. (9)) of H₂O₂ activation dependent •OH formation is the ratio of the rate of •OH formed, defined here as the overall rate of •OH consumption (Eq. (1B)), and the rate of H₂O₂ reaction (i.e., k_H2O2 [H₂O₂]). The efficiency (E₂) (Eq. (10)) of •OH reaction with the target compound relative to other reactants is defined here as the ratio of the rate of probe (P) oxidation by •OH, and the overall rate of •OH consumption (Eq. (1B)). It is noted that the term, [•OH]_SS Σ_i=1ⁿ k_i [S_i], is the sum of products of individual aqueous phase scavengers [S_i] and respective •OH reaction rate constants (k_i). This term reduced to [•OH]_SS k₄ [H₂O₂] since the reaction of •OH with H₂O₂ was significantly greater than all other aqueous phase scavenging reactions. The product of E₁ and E₂ simplifies to the ratio of the rate of probe oxidation and the rate of H₂O₂ reaction. Experimentally determined rates of RhB reaction (k_P,•OH) and H₂O₂ reaction (k_H2O2) were used to quantify η_•OH (Eqs. (11)–(12)). The least-square regression of semi-logarithmic plots of RhB concentration versus time were linear indicating that •OH concentrations were at steady-state ([•OH]_SS) and were used to determine the pseudo-first order degradation rate constants for RhB (k_P,•OH) (Table S3). The least-square regression of semi-logarithmic plots of H₂O₂ concentration versus time were linear indicating that H₂O₂ loss was pseudo-first order. These plots were used to determine k_H2O2 (Table S3).

2.2.4. Hydroxyl radical treatment efficiency

$${\text{E}}_1=({[•\text{OH}]}_{\text{SS}}{\text{k}}_2[\text{P}]+{[•\text{OH}]}_{\text{SS}}{\sum }_{\text{i}=1}^n{k}_{\text{i}}\left[{\text{S}}_{\text{i}}\right]+{[•\text{OH}]}_{\text{SS}}{\sum }_{\text{i}=1}^n{k}_{\equiv \text{,i}}\left[{\text{S}}_{\equiv ,\text{i}}\right])/{\text{k}}_{{\text{H}}_2{\text{O}}_2}\left[{\text{H}}_2{\text{O}}_2\right]$$ (9)

$${\text{E}}_2={[•\text{OH}]}_{\text{SS}}{\text{k}}_2[\text{P}]/\left({[•\text{OH}]}_{\text{SS}}{\text{k}}_2[\text{P}]+{[•\text{OH}]}_{\text{SS}}{{\sum }_{\text{i}=1}}^n{\text{k}}_{\text{i}}\left[{\text{S}}_{\text{i}}\right]+{[•\text{OH}]}_{\text{SS}}{{\sum }_{\text{i}=1}}^n{\text{k}}_{=,\text{i}}\left[{\text{S}}_{=,\text{i}}\right]\right)$$ (10)

$${\mathrm{\eta }}_{•\text{OH}}={\text{E}}_1\times {\text{E}}_2=\left({[•\text{OH}]}_{\text{SS}}{\text{k}}_2[\text{P}]\right)/\left({\text{k}}_{{\text{H}}_2{\text{O}}_2}\left[{\text{H}}_2{\text{O}}_2\right]\right)$$ (11)

$${\mathrm{\eta }}_{•\text{OH}}={\text{k}}_{\text{P},•\text{OH}}[\text{P}]/{\text{k}}_{{\text{H}}_2{\text{O}}_2}\left[{\text{H}}_2{\text{O}}_2\right]$$ (12)

Where, k_P,•OH = [•OH]_SS k₂k_P,•OH experimentally determined pseudo-first order degradation rate of RhB (s⁻¹), k_H2O2 experimentally determined pseudo-first order degradation rate of H₂O₂ (s⁻¹).

Similarly, the impact of SO₄^•− scavenging by aqueous and solid phase surfaces can also be examined in the context of treatment efficiency (η_SO4^•−). The efficiency (E₃) (Eq. (14)) of PS activation dependent SO₄^•− formation is the ratio of the rate of SO₄^•− formed, defined here as the overall rate of SO₄^•− consumption (Eq. (2B)), and the rate of PS reaction (i.e., k_PS [PS]). Inefficiency in PS activation can be attributed to non-productive reactions of PS that do not yield SO₄^•− [19–21]. The efficiency (E₄) (Eq. (15)) of SO₄^•− reaction with the target compound relative to other reactants is defined here as the ratio of the rate of probe (P) oxidation by SO₄^•−, and the overall rate of SO₄^•− consumption (Eq. (16)). It is noted that the term, [SO₄^•−]_SS Σ_i=1ⁿ k_i [S_i], is the sum of products of individual aqueous phase scavengers [S_i] and respective SO₄^•− reaction rate constants (k_i). This term reduced to [SO₄•−]_SS k₁₀ [S₂O₈²⁻] since the reaction of SO₄^•− with S₂O₈²⁻ was significantly greater than all other aqueous phase scavenging reactions. The product of E₃ and E₄ simplifies to the ratio of the rate of probe oxidation and the rate of PS reaction. Experimentally determined rates of RhB reaction (k_P,SO4^•−) and PS reaction (k_PS) were used to quantify η_SO4^•− (Eqs. (16)–(17)). The least-square regression of semi-logarithmic plots of RhB concentration versus time were linear indicating that SO₄^•− concentrations were at steady-state ([SO₄^•−]_SS) and were used to determine the pseudo-first order degradation rate constants for RhB (k_P,SO4^•−) (Table S3). The least-square regression of semi-logarithmic plots of PS concentration versus time were linear indicating that PS loss was also pseudo-first order (Table S3). These plots were used to determine k_PS.

2.2.5. Sulfate radical treatment efficiency

$${\text{E}}_3=\left({\left[{{\text{SO}}_4}^{•-}\right]}_{\text{SS}}{\text{k}}_{\text{8}}[\text{P}]+{\left[{{\text{SO}}_4}^{•-}\right]}_{\text{SS}}{{\sum }_{\text{i}=1}}^n{\text{k}}_{\text{i}}\left[{\text{S}}_{\text{i}}\right]+{\left[{{\text{SO}}_4}^{•-}\right]}_{\text{SS}}{{\sum }_{\text{i}=1}}^n{\text{k}}_{\equiv ,\text{i}}\left[{\text{S}}_{\equiv ,\text{i}}\right]\right)/{\text{k}}_{PS}[PS]$$ (14)

$${\text{E}}_4={\left[{{\text{SO}}_4}^{•-}\right]}_{\text{SS}}{\text{k}}_8[\text{P}]/\left({\left[{{\text{SO}}_4}^{•-}\right]}_{\text{Ss}}{\text{k}}_8[\text{P}]+{\left[{{\text{SO}}_4}^{•-}\right]}_{\text{SS}}{{\sum }_{\text{i}=1}}^n{\text{k}}_{\text{i}}\left[{\text{S}}_{\text{i}}\right]+{\left[{{\text{SO}}_4}^{•-}\right]}_{\text{SS}}{{\sum }_{\text{i}=1}}^n{\text{k}}_{\equiv \text{,i}}\left[{\text{S}}_{\equiv \text{,i}}\right]\right)$$ (15)

$${\mathrm{\eta }}_{{\text{SO}}_4•-}={\text{E}}_3\times {\text{E}}_4=\left({\left[{{\text{SO}}_4}^{•-}\right]}_{\text{SS}}{\text{k}}_8[\text{P}]\right)/{\text{k}}_{\text{PS}}[\text{PS}]$$ (16)

$${\mathrm{\eta }}_{{\text{SO}}_4•-}=\left({\text{k}}_{\text{P}}[\text{P}]\right)/\left({\text{k}}_{\text{PS}}[\text{PS}]\right)$$ (17)

Where, k_P,SO4^•− = [SO₄^•−]_SS k₈k_P,SO4^•− experimentally determined pseudo-first order degradation rate of RhB (s⁻¹), k_PS experimentally determined pseudo-first order degradation rate of PS (s⁻¹).

Coupling the cost of oxidant ($ mol⁻¹ H₂O₂; $ mol⁻¹ S₂O₈²) used in the treatment system, and the treatment efficiency (η_•OH, η_SO4^•−), provides a quantitative measure of the costs associated with radical scavenging, and the relative costs of H₂O₂ versus PS. The basis used to estimate the specific cost of treatment, $_PS and $_H2O2 (Eqs. (18)–(19)), was to treat 1 mol of RhB.

$${\text{\$}}_{\text{PS}}=\left(\text{mol RhB}\times {\text{\$ mol}}^{-1}\text{PS}\right)/{\mathrm{\eta }}_{{\text{SO}}_4•-}$$ (18)

$${\text{\$}}_{{\text{H}}_2{\text{O}}_2}=\left(\text{mol RhB}\times {\text{\$ mol}}^{-1}{\text{H}}_2{\text{O}}_2\right)/{\mathrm{\eta }}_{•\text{OH}}$$ (19)

3. Results and discussion

3.1. Controls

Results from the controls indicated that the rates of H₂O₂ reaction (k_H2O2) were approximately equal in the solids-free and solids-amended treatment systems [14]. This suggests that the •OH production (P_•OH) was also equal (S.4). Similarly, P_SO4•− was approximately equal between solids-free and solids-amended treatment systems (S.4) [15]. Overall, results demonstrated that RhB oxidation by •OH and SO₄^•− was the predominant fate mechanism, and that dissolved species associated with the amendment of solids did not play a role in radical scavenging.

3.2. Radical production in UV-APS and UV-AHP

Under heterogeneous, non-equimolar oxidant conditions (i.e., [S₂O₈²⁻]₀ = 2.1 mM; [H₂O₂]₀ = 29.4 mM), P_SO4•−/ P_•OH was 0.46. Thus, UV-AHP had greater production of radicals than UV-APS and could mainly be attributed to the very high [H₂O₂]₀, relative to [S₂O₈²⁻]₀. On an equimolar basis, (i.e., [S₂O₈²⁻]₀ = [H₂O₂]₀ = 29.4 mM), P_SO4•−/P_•OH was > 24, indicating a significant increase in P_SO4•−, and that P_SO4•− is functionally dependent on [S₂O₈²⁻]₀ in this concentration range. The UV activation rate of S₂O₈²⁻ (k_PS = 4.83 × 10⁻⁵ s⁻¹) was 4 × greater than UV activation rate of H₂O₂ (k_H2O2 = 1.21 × 10⁻⁵ s⁻¹) (Table 2) and partially accounted for PSO4_•− > P_•OH.

3.3. Metrics used to contrast UV-AHP and UV-APS

The overall combined reaction rate constant (N_•OH, N_SO4•−) of •OH is much greater than SO₄•− under both non-equimolar and equimolar oxidant conditions, N_•OH/N_SO4•−=265 and 119, respectively (Table 3). This is attributed to greater •OH reaction rate constants for RhB (k₂), H₂O₂ (k₄), and alumina (k_≡S,•OH) relative to the respective SO₄^•− reaction rate constants k₈, k₁₀, k_{≡S,SO4•−} (Tables 1–2). However, with respect to RhB oxidation loss, •OH had a lower potential to react with RhB than SO₄^•− under both non-equimolar and equimolar oxidant conditions where RP_•OH / RP_SO4•−=0.29 and 0.65, respectively (Eqs. (5)–(6); Table 3). Specifically, the potential for greater loss of RhB in these heterogeneous systems was in the UV-APS system than the UV-AHP system.

Table 3.

Parameters and metrics used to contrast treatment efficiency and cost in heterogeneous UV-APS and UV-AHP oxidative treatment systems.

Parameter	UV-APS	UV-APS	UV-AHP
[PS], [H2O2] (mM)	2.1	29.4	29.4
kPS, kH2O2 (s −)	2.47 × 10 −5 (n = 4)	4.83 × 10 −5 (n = 4)	1.21 × 10 −5 (n = 9)
kP,SO4 •−, kP,•OH (s −1)	1.88 × 10 −4 (n = 4)	3.78 × 10 −3 (n = 3)	1.18 × 10 −4 (n = 3)
P•OH (M s −1)	–	–	1.82 × 10 −8
RP,•OH (M s −1)	–	–	1.23 × 10 −9
RS,•OH (M s −1)	–	–	3.75 × 10 −9
R≡S,•OH (M s −1)	–	–	1.32 × 10 −8
PSO4 •− (M s −1)	8.44 × 10 −9	3.77 × 10 −7	–
RP,SO4 •− (M s −1)	1.97 × 10 −9	3.94 × 10 −8	–
RS,SO4 •− (M s −1)	8.01 × 10 −10	2.24 × 10 −7	–
R≡S,SO4 •− (M s −1)	5.67 × 10 −9	1.13 × 10 −7	–
N•OH (s −1)	–	–	3.58 × 10 6
NSO4 •− (s −1)	1.35 × 10 4	3.02 × 10 4	–
RP•OH (unitless)	–	–	0.068
RPSO4•− (unitless)	0.233	0.105	–
RS•OH (unitless)	–	–	0.932
RSSO4•− (unitless)	0.767	0.895	–
[PS], [H2O2] (mM)	2.1	29.4	29.4
E1, E3 (unitless)	0.132	0.342	0.049
E2, E4 (unitless)	0.287	0.081	0.073
ηSO4•−, η•OH (unitless)	0.019	0.0139	0.00174
Oxidant cost ($ mol −1) 1	0.24	0.24	0.03
$PS, $H2O2 ($ mol −1 RhB)	12.6	17.3	18.2

¹Costs of PS and H₂O₂ range depending on quantity, concentration, and shipment. Average value for PS and H₂O₂ used in calculations were obtained online (alibaba.com) where average values were reported for sodium persulfate ($1000 per metric ton; 99% purity) and hydrogen peroxide ($450 per metric ton; 50%; 1.18 g mL ₋₁). Here, conversion to a mole basis was calculated.

Contrasting the rates of radical scavenging between the UV-AHP and UV-APS treatment systems revealed that a greater rate of •OH was scavenged than SO₄^•− (i.e., RS_•OH > RS_SO4•−; Table 3). The rate of RhB reaction in the test reactors is functionally dependent on the [•OH]_SS or [SO₄^•−]_SS that develops under the specific set of reaction and scavenging conditions. The pseudo-first order degradation rate constants (k_RhB) in the heterogeneous (10 g L⁻¹ alumina) non-equimolar UV-AHP and UV-APS systems were k_RhB,•OH = 1.18 × 10⁻⁴ s⁻¹ (n = 3) [14] and k_{RhB,SO4•−}=1.88 × 10⁻⁴ s⁻¹ (n = 4) [15]. The small difference in the RhB reaction rates were measured despite [H₂O₂]₀ ≫ [S₂O₈²⁻]₀. On an equimolar basis of oxidants, the [S₂O₈²⁻] was increased from 2.1 to 29.4 mM resulting in an increase in P_SO4•− and [SO₄^•−]_SS (Table 2) and in k_{RhB,SO4•−}=3.78 × 10⁻³ s⁻¹ (n = 3), demonstrating that RhB degradation was significantly faster in the UV-APS system than the UV-AHP system using the same oxidant concentrations.

Relative to the total •OH reaction (i.e., R_T,•OH = R_P,•OH + R_S,•OH + R_≡S,•OH, Eq. (1A); Table 3), the rates of radical reaction with RhB (R_P,•OH/R_T,•OH), oxidant (R_S,•OH/R_T,•OH), and alumina surfaces (R_≡S,•OH/R_T,•OH) can be differentiated (Fig. 1). Similarly, relative to the total SO₄^•− reaction (i.e., R_T,_SO4•−=R_P,SO4•−+R_S,SO4•−+R_{≡S,SO4•−}, Eq. (2A); Table 3), the rates of radical reaction with RhB (R_P,SO4•−/R_T,SO4•−), oxidant (R_S,SO4•−/R_T,SO4•−), and alumina surfaces (R_{≡S,SO4•−}/R_T,_SO4•−) can be differentiated (Fig. 1). Results indicated that the alumina surfaces dominated the reaction with RhB in all test systems. Persulfate scavenging (R10) dominated alumina in the UV-APS where SO₄•− reaction was attributed to the high initial persulfate concentration ([S₂O₈²⁻]₀ = 29.4 mM) (Fig. 1). The combined loss of radicals via aqueous and solid phase scavenging dominated reactions with the RhB (Eqs. (7)–(8)); approximately, 77%, 90%, 93% of the radicals were scavenged in the PS (2.1 mM), PS (29.4 mM), and H₂O₂ (29.4 mM) treatment systems, respectively.

Fig. 1.

Relative reaction rates of •OH and SO₄^•− with RhB, oxidants, and alumina surfaces in the UV-AHP and UV-APS treatment systems.

3.4. Treatment efficiency calculations

Activation-dependent radical formation in the UV-AHP (E₁) was less efficient than in the UV-APS treatment system (E₃) (Table 3). This indicated that SO₄^•− were produced more efficiently than •OH and was due to fewer non-productive reactions in the UV-APS system. Similarly, the efficiency of radical reaction with the target compound was lower in the UV-AHP treatment system (E₂), than in the UV-APS treatment system (E₄) (Table 3). Despite k₂ ≫ k₈ (Table 1), greater scavenging of •OH by H₂O₂ and Al₂O₃ occurred than in the UV-APS system. Examination of the overall treatment efficiency (η), the UV-AHP was less efficient in RhB oxidation (Table 3) and was attributed to greater scavenging of •OH; (η_SO4•−/η_•OH) ~ 11 in the non-equimolar, and (η_SO4•−/η_•OH) ~ 8 in the equimolar oxidant conditions (Table 3). The cost of commercially available oxidant ($ mol⁻¹ H₂O₂; $ mol⁻¹ S₂O₈²; Table 3), in conjunction with the treatment efficiency (η_•OH, η_SO4•−), was used as a metric to estimate the specific cost of RhB transformation. Using this approach, $_PS ranged from $12.6 mol⁻¹ RhB (2.1 mM PS) to $17.3 mol⁻¹ RhB (29.4 mM PS); and $_H2O2 was $18.2 mol⁻¹ RhB (29.4 mM H₂O₂) (Eqs. (18)–(19); Table 3). On this basis, the low cost of H₂O₂ in the UV-AHP treatment system was offset by the much lower overall treatment efficiency (η_•OH). Further, the much greater treatment efficiency associated with the UV-APS (η_SO4•−) offset the higher cost of PS contributing to a more favorable specific cost. In general, the much-desired high reaction rate of •OH with environmental contaminants, relative to SO₄^•−, comes at the cost of a greater combined scavenging rate, and lower treatment efficiency. The cost of oxidant in this manner is one factor to consider in oxidant selection. In other oxidation systems involving radical formation and reaction, additional factors must be considered that play a key role in oxidant selection including contaminant specificity, oxidant transport and persistence, oxidant delivery and loading requirements, etc. [1,3].

3.5. Environmental implications

It is evident that •OH and SO₄^•− scavenging reactions attributed to solid surfaces is a leading cause of treatment inefficiency, even in relatively clean systems (i.e., in the absence of anions, organic matter, higher solids content). It is anticipated that in subsurface treatment systems involving unconsolidated porous media, surface scavenging will play an even greater role given the high solids to water ratio. For example, assuming ISCO in 1 m³ aquifer material, and common parameter values for porosity (30%) and bulk density (1.6 g cm⁻³), the solids to liquid ratio is high (1600 kg L⁻¹). Whereas the solids to liquid ratio used here was comparatively lower (10 g L⁻¹ Al₂O₃). The sheer magnitude of aquifer solids and mineral surfaces in aquifer systems, compared to the dilute suspensions in this study, will strongly amplify the role of surface scavenging.

Contrasting scavenging results with the non-radical based oxidant, permanganate (MnO₄⁻), suggests that more efficient treatment would likely occur with respect to contaminant loss than radical-based oxidants. For example, results indicate that repeated and aggressive PS treatments of the alumina (i.e., 50 g PS/kg alumina (×3); 150 g PS/kg alumina), did not significantly diminish the rate of SO₄^•− scavenging by the alumina surfaces indicating that this source of treatment inefficiency is not easily eliminated for solid phase media [15]. Silicon (Si) and aluminum (Al) are unlikely species that scavenge •OH, as these elements exhibit their highest oxidation state. Surface hydroxyl groups or surface defect sites are abundant and can serve as potential electron donors and surface scavenging sites [22–25]. Conversely, in MnO₄⁻ treatment systems, the background oxidant demand often attributed to natural organic matter is finite [26–27] despite being greater than the demand expressed by the target contaminants [28–29]. Consequently, contaminant oxidation efficiency is inversely correlated with the natural oxidant demand. Specifically, improved oxidation efficiency using MnO₄⁻ occurs as background oxidant demand diminishes, MnO₄⁻ persistence improves, and greater contact occurs between the oxidant and contaminant.

4. Conclusions

The rates at which •OH and SO₄^•− were produced and reacted under heterogeneous UV-AHP and UV-APS treatment conditions were examined. Kinetic parameters used in this analysis were derived from this laboratory study, and from previous studies involving similar oxidative treatment conditions [14–15]. These parameters included the surface scavenging rate constants for alumina (k_≡S), steady state •OH and SO₄^•− concentrations, and H₂O₂, S₂O₈²⁻ and RhB degradation rate constants. The reactions were differentiated based upon the rates at which the radicals reacted with the probe compound, aqueous phase scavengers (H₂O₂, S₂O₈²⁻), and the mineral surfaces of solid phase alumina (Al₂O₃). In comparing the overall reaction rate for the three classes of reactants (i.e., probe, aqueous scavenger, solid phase scavenger), the overall reaction rate was greater for •OH than SO₄^•− (i.e., N_•OH, N_SO4•−). This result was supported by the fact that the second-order reaction rate constants for the RhB, oxidant, and surface scavenging were all greater for the •OH than SO₄^•−. Consequently, the rate of scavenging was also greater for •OH than SO₄^•−. Scavenging by dissolved constituents in the aqueous phase was dominated by the oxidant used to form the radicals (i.e., H₂O₂, S₂O₈²⁻). Although reaction rate constants (i.e., k₄, k₁₀) are not necessarily high for these oxidants, the elevated concentrations of oxidants in these treatment systems was the main cause for aqueous phase radical scavenging. The rate of radical scavenging by alumina was greater than the rate of probe oxidation in all cases; persulfate scavenging dominated alumina scavenging in the UV-APS under the condition where high initial persulfate concentration was present ([S₂O₈²⁻]₀ = 29.4 mM). Overall, a low concentration of suspended Al₂O₃ solids (i.e., 10 g L⁻¹) caused significant radical scavenging effects in both the UV-AHP and UV-APS laboratory-based treatment systems. In aquifer systems where the solids content is much higher, the solid surface scavenging reaction rates will be amplified, and treatment efficiencies are projected to be much lower than measured in the slurry treatment systems.

Activation-dependent radical formation in UV-AHP (E₁) was less efficient than in the UV-APS treatment system (E₃). This was attributed to the non-productive consumption of oxidant which diminished radical production. The radical reaction with the target compound was also less efficient in the UV-AHP treatment system (E₂), than in the UV-APS treatment system (E₄) and was attributed to greater aqueous and solid phase scavenging rates. The price of commercially available H₂O₂ ($0.031 mol⁻¹) was less costly than S₂O₈²⁻ ($0.24 mol⁻¹). However, using these oxidant costs, in conjunction with the overall treatment efficiency (η), indicated that the specific cost to treat the probe compound with UV-AHP was greater than with UV-APS ($_H2O2 was > $_PS; $ mol⁻¹ RhB oxidized). In summary, the low cost of H₂O₂ in the UV-AHP system was diminished by the low treatment efficiency relative to much greater treatment efficiency in the UV-APS. The much-desired, high reaction rate constants between •OH and environmental contaminants, relative to SO₄^•−, may come at the cost of greater combined scavenging rate, and consequently lower treatment efficiency.

5. Notice

This research was performed while Dr. Klara Rusevova Crincoli held an NRC Research Associateship award with the U.S. Environmental Protection Agency at the Robert S. Kerr Environmental Research Center, Ada, OK 74820. The views expressed in this article are those of the authors and do not necessarily represent the views or policies of the U.S. Environmental Protection Agency.