Sulfate Radical Scavenging by Mineral Surfaces in Persulfate-Driven Oxidation Systems: Reaction Rate Constants and Implications

Abstract

Activated persulfate (PS) is a common method used to generate sulfate radicals (SO₄^•−), a powerful oxidant capable of degrading a broad array of environmental contaminants. The reaction of SO₄^•− with nontarget species (i.e., scavenging) contributes significantly to treatment inefficiency. Radical scavenging in this manner has been quantified for nontarget chemical species in the aqueous phase but has never been quantified for solid phase media. Kinetic analysis and laboratory methods were developed to quantify the SO₄^•− scavenging rate constant (k_≡S) for alumina, a naturally occurring mineral in soil and aquifer materials. SO₄^•− generated in UV and thermally activated persulfate (UV-APS, T-APS) batch systems, and the loss of rhodamine B (RhB) served as an indicator of SO₄^•− activity. k_≡s for alumina was 2.42 × 10⁴ and 2.03 × 10⁴ m⁻² s⁻¹ for UV-APS and T-APS oxidative treatment systems, respectively. At [alumina] >5 g L⁻¹, the reaction of SO₄^•− with solid phase media increased over the aqueous phase reactions with RhB and aqueous scavengers. SO₄^•− scavenging by solid surfaces was orders of magnitude greater than the reaction with the target compound and scavengers in the aqueous phase, underscoring the significant role of solid surfaces in scavenging SO₄^•−.

Graphical Abstract

INTRODUCTION

Inefficiency in oxidative treatment processes involving radical intermediates can be attributed to two general mechanisms, radical scavenging and nonproductive reactions (NPRs). Radical scavenging involves the reaction between radicals and nontarget chemical species; and NPR involves reactions that do not yield radicals and consequently deplete the source of oxidants, such as persulfate (S₂O₈²⁻) (PS) or hydrogen peroxide (H₂O₂), which in turn diminishes radical production. PS reaction with natural media involves NPR^1–5 and contributes to treatment inefficiency. Radical scavengers may either be soluble in the aqueous phase or may be present as a solid phase. In either case, radicals can react with scavengers found in the aqueous phase or on the surfaces of solid phase media. Radical scavenging, including sulfate radicals (SO₄^•−) and/or hydroxyl radicals (^•OH) in oxidative treatment systems, has predominantly been focused on soluble constituents in the aqueous phase.^6–9 Radical scavenging by solid phase media has not been specifically investigated. The focus of this study was to quantify radical scavenging by solid surfaces in persulfate-driven oxidation systems and to assess the relevance.

PS is a reagent utilized in chemical oxidation technologies, including in situ chemical oxidation (ISCO), for contaminant transformation and treatment of groundwater and soil.^3,4,10 Persulfate is highly soluble and persists in subsurface environments from days to weeks,¹ allowing greater potential for oxidant distribution and contact with the targeted contaminants. PS is a relatively strong oxidant (E⁰ = 2.1 V), but upon activation, the more powerful reaction intermediate SO₄^•− (E⁰ = 2.6 V) is produced and is capable of degrading a broad spectrum of environmental contaminants.^11–14 Several reaction pathways occur during PS activation including thermolysis^14,15 and photolysis¹⁵ of the peroxy bond ([O–O]²⁻) to generate SO₄^•− (R1 and R2; Table 1). PS reduction can be initiated by reduced transition metals,^16–18 carbonaceous-based materials,^15,19 or organic substrates^15,20 (R3; Table 1). Alkaline activation (pH > 10.5) is a common activation method where nucleophilic attack of [O–O]²⁻ is considered a main activation pathway.¹⁵ Under basic pH conditions, the generation of ^•OH becomes significant.²¹

Table 1.

Summary of Persulfate Activation, Related Reactions, and Rate Constants

persulfate activation
Heat (>35 °C)
S2O82− → 2SO4•− (R1)
UV Irradiation (<400 nm)
S2O82− → 2SO4•− (R2)
e− Transfer
S2O82− → SO4•− + SO42− (R3)
S2O82− → 2SO42− (R4)
sulfate radical reaction
SO4•− + RhB → products (R5)	k5 = 3.02(±0.03) × 108 M−1 s−1 (this study)
SO4•− + MTBE → products (R6)	k6 = 3.13(±0.02) × 107 M−1 s−1 (ref 22)
SO4•− + S2O82− → SO42− + S2O82− (R7)	k7 = 6.1 × 105 M−1 s−1 (ref 12)
SO4•− + OH− → SO42− (R8)	k8 = 7.0 × 107 M−1 s−1 (ref 12)
SO4•− + H2O → SO42− + •OH + H+ (R9)	k9 = 6.6 × 102 M−1 s−1 (ref 12)
${{\text{SO}}_4}^{•-}+\sum _{i=1}^n\left[S_i\right]\to \text{products}$ (R10)
SO4•− + ≡Si → products (R11)	k≡Si,alumina (this study)

In treatment systems, PS also undergoes decomposition reactions without yielding SO₄^•−. These NPRs undergo 2e⁻ transfer to form two sulfate anions (R4; Table 1). Such NPRs are also applicable to H₂O₂-based oxidative treatment systems^4,5 and are a significant source of inefficiency. The origin of NPRs involving PS has been attributed to the amorphous iron content or soil organic matter in the aquifer material.^1–3 Other NPRs with PS include acid-catalyzed (pH < 3) PS decomposition or uncatalyzed PS decomposition to hydrogen sulfate and oxygen.²³ However, these reactions occur at relatively slow rates (>80 days)¹ and are not applicable to the short-term reaction conditions used in this study.

The reaction efficiency (η) associated with the PS oxidation mechanism is the product of efficiencies associated with PS activation-dependent SO₄^•− formation (E₁), and SO₄^•− reaction with the target compound (E₂). Specifically, inefficiency in PS activation is attributed to NPRs that do not yield SO₄^•−. Inefficiency in the reaction between SO₄^•− and the target compound (P) [rhodamine B (RhB), methyl-tert butyl ether (MTBE)] (R5 and R6; Table 1) is attributed to competing SO₄^•− reactions with aqueous (R7–R10; Table 1) and solid phase scavengers (R11; Table 1) in oxidation systems.

Radical scavenging in the aqueous phase has largely been quantified utilizing various concentrations of dissolved species and their known second-order rate constants with SO₄^•−,¹⁰ whereas SO₄^•− scavenging by solid surfaces has not been quantified. In this study, competition kinetic analysis and laboratory methods were developed to quantify the SO₄^•− scavenging rate constant (k_≡S) for solid phase media. Subsequently k_≡S was used to assess the relative contribution of SO₄^•− scavenging in the aqueous and the solid phases Further, projection of SO₄^•− scavenging by homogeneous and heterogeneous species in an ideal aquifer system was carried out using k_≡S derived from this study.

EXPERIMENTAL SECTION

Chemicals.

The chemicals used in this study were of reagent grade and used as received. RhB dye (21.33% w/w) was from Turner Designs, and sodium persulfate, methyl tert-butyl ether (MTBE), tert-butyl alcohol, alumina (α-phase), and ascorbic acid were from Aldrich. All glassware and containers were acid-washed and rinsed with deionized water (DIW) before use. Stock solutions and dilutions of PS and probes (RhB, MTBE) were prepared using DIW prior to each experiment.

Solid Selection and Characterization.

In the development of the kinetic analysis model, three reaction conditions were considered where: (1) the solid phase media does not react with PS, (2) the solid phase media reacts with PS but does not produce SO₄^•− (i.e., NPR), and (3) the solid phase media reacts with PS, forms SO₄^•−, and may also include NPRs.²⁴ Here, methods of kinetic analysis were developed to estimate k_≡S for condition 1, where alumina (Al₂O₃), a naturally occurring mineral in soil and aquifer systems,²⁵ was selected as the model mineral and tested. Laboratory testing of alumina indicated no reaction with PS.

The specific surface area (SSA) of alumina was determined by the BET method using N₂ adsorption–desorption isotherms measured on Quantachrome NOVA 4200e (Boynton Beach, FL). Metal impurities in alumina were determined by inductively coupled plasma, optical emission spectroscopy (ICP–OES) using PerkinElmer Optima 8300DV ICP–OES, based on the EPA Method 200.7. Filtered solutions of alumina (50 g L⁻¹) were analyzed for Cl⁻ and Br⁻ using Lachat flow injection analyzers. The alumina composition was confirmed by the Rigaku MiniFlex X-ray diffractometer, which provides a qualitative identification of minerals present in solid matrices and is based on a comparison to reference diffraction data for known compounds.

Batch Experiments.

Selection of a Probe and PS Activation.

RhB (Supporting Information S.1, Figure S1) was selected as a probe because of the favorable properties that allow rapid analysis and processing of samples, thus eliminating the quenching step of the remaining oxidant (PS). RhB is nonvolatile, hydrophilic, and adsorbs poorly to alumina surfaces at pH conditions applied in the study, which minimizes nonoxidative losses and simplifies the kinetic analysis. Various methods are available for PS activation. However, thermal- and UV-activated PS are most efficient in terms of SO₄^•− formation. Metal activation (e.g., Fe²⁺) of PS was ruled out because of possible physicochemical changes of Fe²⁺ in solution and potential effects on the fate of PS (e.g., by initiation of NPRs). Base-activated PS introduces a pool of potential reactive species including ^•OH, which would compete for the species present in the reaction mixture, thus complicating the kinetic analysis.

UV and Thermally Activated PS.

UV activation of PS (UV-APS) was conducted in 40 mL borosilicate VOA vials under a UV Lamp (High-Performance UVP Transilluminator, Model TFM-20) containing four UV-A tube bulbs (25 W bulbs, 115 V, 60 Hz, 2.0 amps, 365 nm). The base case homogeneous oxidation test system was comprised of a RhB probe ([RhB]₀ = 5 mg L⁻¹; 0.01 mM) and PS ([PS]₀ = 500 mg L⁻¹; 2.1 mM) and involved a total volume of 25 mL. The heterogeneous test system was prepared in the same manner but was amended with alumina (1–50 g L⁻¹). Uncovered test reactors were then placed on a 10-spot magnetic stirrer (500 rpm) under a UV light lamp to insure a complete mixed system during the experiments. Thermal activation of PS (T-APS) was carried out as a second method to estimate and validate the surface scavenging rate for alumina. Solutions of RhB ([RhB]₀ = 5 mg L⁻¹; 0.01 mM) and/or suspensions of alumina ([alumina] = 1–10 g L⁻¹) were adjusted to an elevated temperature (40 °C) and then spiked with PS ([PS]₀ = 500 mg L⁻¹; 2.1 mM) to initiate the reaction. At selected time intervals, samples were collected and analyzed immediately for RhB and PS.

Prior to analyses, aqueous samples were separated from the suspended alumina solid phase media by centrifugation (Eppendorf MiniSpin; 3000 rpm; 2 min). The starting reaction pH was set to pH 6 and together with temperature was monitored throughout all the experiments. No buffers were introduced to avoid additional reactions with SO₄^•−, as most of the frequently used buffers react at appreciable rates with the sulfate radical.⁹ Data shown in the figures and tables are the mean values of at least two experiments. Unless stated otherwise, the reported error represents the deviation of the mean value.

Semicontinuous Mode Experiment.

Subsequent amendments (in three cycles) of freshly prepared reaction solution (RhB + PS) to the alumina was performed to assess whether the alumina scavenging changes over time. After each cycle, the suspension was decanted to eliminate the aqueous solution, and the remaining alumina was air-dried overnight. RhB (5 mg L⁻¹) and PS (500 mg L⁻¹) were added to create another suspension of the original alumina particles (10 g L⁻¹). The reaction vessels were placed under UV light on the magnetic stirrer (500 rpm) to initiate the reaction. The experiment was carried out in duplicate.

Estimation of the Second-Order Rate Constant for RhB with SO₄^•− (k₅).

Because of the lack of kinetic data published in the scientific literature involving RhB oxidation by SO₄^•−, competition kinetic experiments were carried out to determine k_{SO4^•−,RhB}, which was used as k₅ in this study. MTBE, a structurally distinct compound, served as the reference probe with a well-established rate constant with SO₄^•−, k₆ = 3.13(±0.02) × 10⁷ M⁻¹ s⁻¹.²² The relative losses of RhB and MTBE were used to estimate k₅ (M⁻¹ s⁻¹). Batch reactors (n = 2) containing a mixed aqueous solution of RhB ([RhB]₀ = 5 mg L⁻¹; 0.01 mM) and MTBE ([MTBE]₀ = 15 mg L⁻¹; 0.17 mM) were spiked with PS ([PS]₀ = 1000 mg L⁻¹; 4.2 mM). The reactors were sealed to avoid volatile losses of MTBE and placed inversely in the UV chamber on the magnetic stirring plate (500 rpm) to uniformly expose the vials to the UV-light source. The initial reaction pH was 3.9. At selected time intervals, samples were collected for MTBE and RhB analyses. RhB was measured immediately using a spectrophotometric method. Diluted samples of MTBE were preserved using ascorbic acid (moles PS/moles ascorbic acid = 1/4)²⁶ prior the gas chromatography (GC)–mass spectrometry (MS) measurements.

Controls.

Control experiments were designed to evaluate the fate mechanisms of the RhB probe, PS, and SO₄^•−. The potential for a direct reaction between RhB (5 mg L⁻¹) and persulfate (500 mg L⁻¹) was tested in 40 mL VOA vials in the dark. The impact of the UV irradiation and elevated temperature on the stability of RhB was tested in PS-free systems. The possible impact of radical scavenging by dissolved species originating from alumina amendments to the test reactors was also investigated. The filtrate (25 mL) derived from 1 g L⁻¹ (n = 2) and 10 g L⁻¹ (n = 2) alumina batches was amended with RhB and PS and the [RhB] was measured over time under UV-APS conditions. The potential for light scattering by alumina particles and impact on UV-APS was investigated. The [PS] was measured over time and contrasted with results involving an alumina-free system (i.e., the homogeneous base case system).

Analytical Methods.

RhB was determined spectrophotometrically (λ_max = 556 nm) on the Jenway 6505. A spectrophotometric method was used for analyzing the persulfate concentration (λ_max = 450 nm) as described elsewhere.²⁷ MTBE analysis was performed via the headspace GC–MS method using Thermo Scientific Trace GC Ultra coupled with Thermo DSQ II MS. Regression analysis of the spectrophotometric response and the concentrations of these analytes yielded linear calibration curves (r² = 0.99). The pH was measured using the Orion Star A215 pH meter.

Kinetic Analyses.

The development of the kinetic analysis method used to estimate c scavenging by alumina surfaces is based on the kinetic analysis previously reported.^24,28 The rate of SO₄^•− accumulation is calculated as the difference between the rates of SO₄^•− production (P_SO4^•−) and SO₄^•− consumption (C_SO4^•−) (eq 1). SO₄^•− are highly reactive and a quasi-steady-state approximation for SO₄^•− is assumed where d[SO₄^•−]/dt ≈ 0, and $C_{{{\text{SO}}_4}^{•-}}\approx P_{{{\text{SO}}_4}^{•-}}$ (eq 2). RhB was used as a probe and the loss of RhB in alumina-amended and alumina-free test reactors served as a quantitative metric to estimate the of SO₄^•− surface scavenging rate constant (k_≡S). The overall rate SO₄^•− consumption (eq 3) is the sum of rates of SO₄^•− reaction with the probe (R_P) (eqs 4 and 5), scavengers in the aqueous phase, R_S (eqs 6 and 7), and scavengers in the solid phase, R_≡S (eqs 8 and 9). The individual aqueous and solid phase scavengers are grouped into terms k_S and k_≡S, respectively. eqs 4 and 5 were combined and used to estimate [SO₄^•−]_SS (eq 10), where k₅ was established based on competition kinetics, and k_RhB is the pseudo-first-order rate constant determined from laboratory data in this study. [SO₄^•−] was assumed to be at a steady state (i.e., [SO₄^•−]_SS) as semilogarithmic plots of [RhB] versus time were linear, indicating that [SO₄^•−] did not appreciably change over the course of the experiment.

$$\text{d}\left[{{\text{SO}}_4}^{•-}\right]/\text{d}t=P_{{{\text{SO}}_4}^{•-}}-C_{{{\text{SO}}_4}^{•-}}$$ (1)

$$C_{{{\text{SO}}_4}^{•-}}\approx P_{{{\text{SO}}_4}^{•-}}$$ (2)

$${\text{C}}_{{{\text{SO}}_4}^{•-}}=R_{\text{p}}+R_{\text{s}}+R_{\equiv \text{S}}$$ (3)

$$R_{\text{p}}=k_5[\text{RhB}]{[{{\text{SO}}_4}^{•-}]}_{\text{SS}}$$ (4)

$$R_{\text{p}}=k_{\text{RhB}}[\text{RhB}]$$ (5)

$$R_{\text{s}}=\sum _{i=1}^n{k}_i[S_i]{[{{\text{SO}}_4}^{•-}]}_{\text{SS}}$$ (6)

$$R_{\text{s}}=k_{\text{s}}{[{{\text{SO}}_4}^{•-}]}_{\text{SS}}$$ (7)

$$R_{\equiv S}=\sum _{i=1}^n{k}_{\equiv ,i}[S_{\equiv ,i}]S_{\text{A}}{m}_{\text{S}}{[{{\text{SO}}_4}^{•-}]}_{\text{SS}}$$ (8)

$$R_{\equiv \text{S}}=k_{\equiv \text{S}}{S}_{\text{A}}{m}_{\text{S}}{[{{\text{SO}}_4}^{•-}]}_{\text{SS}}$$ (9)

$${[{{\text{SO}}_4}^{•-}]}_{\text{SS}}=k_{\text{RhB}}/k_5$$ (10)

where $P_{{{\text{SO}}_4}^{•-}}$ and $C_{{{\text{SO}}_4}^{•-}}$ are rates of SO₄^•− production and consumption, respectively (M s⁻¹); R_p, R_s, and R_≡S are the SO₄^•− reaction rates with the probe (RhB), scavengers in the aqueous phase (S_i) and surface scavengers (S_≡,i), respectively (M s⁻¹); [SO₄^•−]_SS is the steady-state sulfate radical concentration (M); [RhB] is the rhodamine B concentration (M); k₅ is the second-order degradation rate constant of the RhB probe and SO₄^•− (M⁻¹ s⁻¹); k_RhB is the pseudo-first-order degradation rate constant for the RhB probe (s⁻¹); k_S is the sum of products of individual aqueous phase scavengers (S_i) and respective SO₄^•− reaction rate constants (k_i) (M⁻¹ s⁻¹); k_i is the second-order rate constant of an individual aqueous phase scavenger (M⁻¹ s⁻¹); [S_i] is the individual aqueous phase scavenger concentration (M); k_≡S is the surface scavenging rate constant, sum of products of individual solid phase scavengers (S_≡,i) and respective SO₄^•− reaction rate constants (k_≡,i) (m⁻² s ⁻¹); k_≡,i is the specific second-order rate constant of an individual solid phase scavenger (M⁻¹ s⁻¹ ); [S_≡,i] is the individual specific solid phase scavenger concentration (M m⁻²); S_A is the surface area of the solid phase media (i.e., mineral) (m² g⁻¹); and m_S is the mass of the solid phase mineral (g).

The kinetic analysis method used to estimate k_≡S involved contrasting results between a solid-free, homogeneous system and a solid-amended, heterogeneous system. Alumina was incrementally amended to the test reactors to determine whether it played a role in scavenging SO₄^•−. Equations R1–R10 formed the basis to solve for $P_{{{\text{SO}}_4}^{•-}}$ (eq 11) (e.g., amended with 10 g L⁻¹ alumina). In an oxidative system without surface scavenging (i.e., mineral-free), the surface scavenging term in eq 11 is eliminated and results in eq 12. The subscripts in eqs 11 and 12 represent 0 and 10 g L⁻¹ alumina, respectively.

$$\begin{gathered} P_{{{\text{SO}}_4}^{•-},10}=k_5[\text{RhB}]{[{{\text{SO}}_4}^{•-}]}_{\text{SS},10}+k_{\text{S}}{[{{\text{SO}}_4}^{•-}]}_{\text{SS},10} \\ +k_{\equiv S}{S}_{\text{A}}{m}_{\text{S},10}{[{{\text{SO}}_4}^{•-}]}_{\text{SS},10} \end{gathered}$$ (11)

$$P_{{{\text{SO}}_4}^{•-},10}=k_5[\text{RhB}]{[{{\text{SO}}_4}^{•-}]}_{\text{SS},0}+k_{\text{S}}{[{{\text{SO}}_4}^{•-}]}_{\text{SS},0}$$ (12)

The experimental method used to differentiate between SO₄^•− scavenging in the solid phase and aqueous phase required two identical test conditions where one reactor was mineral-free (i.e., homogeneous base case) and the other was amended with alumina. The mineral-free, base case system contained [RhB]₀ = 5 mg L⁻¹ and [PS]₀ = 500 mg L⁻¹, and the mineral-amended system contained the same concentrations of these reactants, and alumina (1–50 g L⁻¹). The [PS]₀ and [RhB]₀ were identical in all test reactors used in the UV-APS and T-APS testing systems indicating favorable conditions for $P_{{{\text{SO}}_4}^{•-}}$ and k_S to be approximately equal. The pseudo-first-order degradation rate constant for PS (k_PS (s⁻¹)) and the ΔPS (M) over the duration of the experiments were approximately equal between the base case and alumina-amended treatment systems. Therefore, time-dependent differences in [RhB] were attributed to surface scavenging effects in the alumina-amended system. The steady-state SO₄^•− [SO₄^•−]_SS,0, [SO₄^•−]_SS,10, were determined experimentally (eq 10); and the pseudo-first-order reaction rate constants for RhB in alumina-free (k_RhB,0 (s⁻¹)) and alumina-amended systems (1–50 g L⁻¹, where k_RhB,10 (s⁻¹) contained 10 g L⁻¹) were determined via semi-log plots of [RhB] versus time. On this basis, the rate of SO₄^•− production was similar between systems, allowing eqs 11 and 12 to be equated and permitting the surface scavenging rate constant, k_≡S, to be determined (eq 13).

$$k_{\equiv \text{S}}=\frac{({[{{\text{SO}}_4}^{•-}]}_{\text{SS},0}(k_5[\text{RhB}]+k_S))-({[{{\text{SO}}_4}^{•-}]}_{\text{SS},10}(k_5[\text{RhB}]+k_{\text{S}}))}{S_{\text{A}}{m}_{\text{S},10}{[{{\text{SO}}_4}^{•-}]}_{\text{SS},10}}$$ (13)

RESULTS & DISCUSSION

Alumina Characterization.

The SSA of alumina is low (1.5 ± 0.3 m² g⁻¹; n = 8), the pH point of zero charge (pH_PZC) is 8.5,²⁵ and the XRD patterns were consistent with the diffraction patterns found in the library of available mineral (Supporting Information S.2, Figure S.2). ICP–OES analysis indicated low concentrations of total Fe (19 mg kg⁻¹; n = 3), and total Mn and other metals detected were below quantitation limits (8.0 mg kg⁻¹; n = 3).

Summary of Controls.

Control experiments were conducted to evaluate potential fate mechanisms for RhB, PS, and SO₄^•− and confirmed that oxidative SO₄^•− was the only significant fate mechanism (Supporting Information S.3, Figures S.3–S.6). The PS decomposition rate was similar between the base case alumina-free homogeneous and the alumina-amended systems in both UV-APS and T-APS. This indicated that UV irradiation or elevated temperature were the only activators of PS, and that light scattering did not play a role in PS activation. The pseudo-first-order degradation rate of PS (k_PS) in alumina-amended reactors was 2.47(±0.21) × 10⁻⁵ s⁻¹ (n = 4) and 2.02(±0.45) × 10⁻⁵ s⁻¹ (n = 4) in UV-APS and T-APS, respectively. In the mineral-free, homogeneous base case system, k_PS was 2.59(±0.36) × 10⁻⁵ s⁻¹ (n = 2) and 1.80(±0.11) × 10⁻⁵ s⁻¹ (n = 2), for UV-APS and T-APS, respectively. As k_PS was not statistically distinguishable between alumina-free and alumina-amended reactors, the rates of SO₄^•− production $(P_{{{\text{SO}}_4}^{•-}})$ were determined to be approximately equal in these treatment systems (Table S.1). Concentrations of Cl⁻ and Br⁻ in the control reactor amended with alumina were measured and were below the method detection limit (i.e., 0.574 mg L⁻¹ for Cl⁻, and 0.048 mg L⁻¹ for Br⁻). This indicated that SO₄^•− scavenging in the treatment system was because of solid surfaces and not because of dissolved constituents derived from the alumina.

Impact of Alumina on RhB Oxidation.

semi-log plots of RhB concentration versus time were linear for both the UV-APS and T-APS systems (Supporting Information S.4, Figure S.7a,b), indicating that RhB degradation was pseudo-first-order and that the SO₄^•− concentration was at steady-state ([SO₄^•−]_SS) (i.e., the quasi-steady-state assumption is valid). In the alumina-amended UV-APS and T-APS reaction systems, RhB oxidative losses were inversely proportional to alumina solids, and k_RhB declined with increasing alumina concentration (Table 2), indicating that alumina was competing with RhB for SO₄^•−. k₅ was determined to be 3.02(±0.03) × 10⁸ M⁻¹ s⁻¹ (Supporting Information S.5, Figure S.8) and used in conjunction with k_RhB to estimate the [SO₄^•−]_SS (eq 10) (Table 2). Previously, a second-order rate constant for SO₄^•− and methylene blue dye reaction was determined and ranged from 0.34 × 10⁸ to 2.20 × 10⁸ M⁻¹ s⁻¹, depending on the reaction conditions.²⁹ Methylene blue and RhB exhibit similar molecular characteristics that suggest similar reaction mechanisms of SO₄^•− attack (e.g., electron-rich aromatic ring(s) for initial e⁻ transfer or methyl/ethyl groups for hydrogen abstraction). Consequently, similar values in the approximated rate constant were anticipated.

Table 2.

Estimates of the Surface SO₄^•− Scavenging Rate Constant (k_≡S) for Alumina Derived from UV-APS and T-APS Treatment Systems

[alumina] (g L−1)	kRhBa (s−1)	${\left[{{\text{SO}}_4}^{•-}\right]}_{\text{SS}}$a (M)	k≡S (m−2 s−1)
UV-APSb
0 (n = 3)	4.67 × 10−4	1.55 × 10−12
1 (n = 3)	3.22 × 10−4	1.07 × 10−12	5.27 × 105
5 (n = 2)	2.52 × 10−4	8.35 × 10−13	2.04 × 104
10 (n = 4)	1.88 × 10−4	6.25 × 10−13	1.81 × 104
30 (n = 2)	1.55 × 10−4	5.14 × 10−13	8.14 × 10a
50 (n = 2)	7.08 × 10−5	2.35 × 10−13	1.35 × 104
			avg. 2.42 × 104
T-APSc
0 (n = 3)	9.92 × 10−5	3.50 × 10−13
1 (n = 2)	8.17 × 10−5	2.88 × 10−13	2.52 × 104
5 (n = 3)	5.89 × 10−5	2.08 × 10−13	1.63 × 104
10 (n = 3)	3.72 × 10−5	1.31 × 10−13	2.12 × 104
			avg. 2.03 × 104

^aAverage k_RhB and [SO₄^•−]_SS for alumina concentrations 0–50 g L⁻¹; k_RhB in the UV-APS system 0.92 ≤ r² ≤ 0.99; k_RhB in the T-APS system 0.94 ≤ r² ≤ 0.99.

^bUV-APS system: average k_≡S (n = 13) using 1–50 g L⁻¹ alumina (95% C.I. = 1.57 × 10⁴ to 3.27 × 10⁴ m⁻² s⁻¹).

^cT-APS system: average k_≡S (n = 8) using 1–10 g L⁻¹ alumina (95% C.I. = 1.58 × 10⁴ to 2.48 × 10⁴ m⁻² s⁻¹).

k_S, the sum of products of individual aqueous phase scavengers [S_i] and respective SO₄^•− reaction rate constants (k_i) (eq 7), was estimated as k₇ × [PS] (R7, Table 1), as SO₄^•− reaction with PS was significantly greater than all other aqueous phase scavenging reactions. A negligible contribution of OH⁻ (R8; Table 1) was determined, as k₈ × [OH⁻] at pH_start 6 and pH_final 4.5 was 3 and 4 orders of magnitude lower, respectively, than k₇ × [PS]. Further, an overall critical analysis of the potential role of ^•OH indicated that ^•OH did not play a role in the oxidative transformation of RhB or MTBE in this study (Supporting Information S.6, Figure S.9).

In semicontinuous oxidation mode, the solution was decanted and the remaining alumina (10 g L⁻¹, n = 2) was re-amended with fresh RhB and PS for a total of three sequential oxidations of the RhB. Upon treatment with UVAPS, the rate of RhB transformation increased by approximately 30% in the second and third cycles. In comparison to the base case homogeneous reaction system (k_RhB = 0.0280 min⁻¹), k_RhB resulting from the first, second, and third oxidations was 0.011, 0.016, and 0.0165 min⁻¹, respectively. The total amount of PS applied to the alumina (three applications; 50 g PS kg⁻¹ alumina; total 150 g PS kg⁻¹ alumina) would be considered a very high dosage in ISCO deployment. This outcome indicated that alumina scavenging of SO₄^•− continued to play an important role in limiting RhB transformation and that this source of treatment inefficiency is not easily eliminated after multiple treatment cycles (Supporting Information S.7, Figure S.10).

Estimated Surface Scavenging Rate Constant.

k_≡S was calculated by contrasting laboratory-derived kinetic parameters between the base case, alumina-free, homogenous system, and the alumina-amended heterogeneous systems (eq 13). The average values of k_≡S for alumina derived from the UV-APS and T-APS treatment systems were similar, 2.42 × 10⁴ m⁻² s⁻¹ (n = 13) and 2.03 × 10⁴ m⁻² s⁻¹ (n = 8), respectively (Table 2). The initial rates of SO₄^•− reaction with RhB, PS, and alumina (eqs 4, 7, and 9, respectively) represent the relative fate of SO₄^•− in the reaction system (Figure 1). UV activation of PS resulted in the formation of SO₄^•− in the aqueous phase. In the complete-mix, alumina-amended test reactors, the reaction of SO₄^•− can occur with species in the aqueous phase or on the surface of the alumina solids. At low [alumina] (1–5 g L⁻¹), RhB was the predominant reactant. At [alumina] >5 g L⁻¹, alumina became the major reactant with SO₄^•− in the system. Overall, these results indicate that alumina mineral surfaces scavenge SO₄^•− and play a significant role in the fate of SO₄^•−, and that the surface scavenging represents a major source of treatment inefficiency in PS-based treatment systems.

Figure 1.

Initial SO₄^•− reaction rates with RhB (5 mg L⁻¹; 0.01 mM), PS (500 mg L⁻¹; 2.94 mM), and alumina (0–50 mg L⁻¹), pH_start = 6.0, pH_end = 4.5.

Treatment Efficiency.

The impact of radical scavenging by aqueous and solid phase surfaces can be examined in the context of treatment efficiency (η). The efficiency (E₁) (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 3), and the rate of PS reaction (i.e., k_PS × [PS]). The efficiency (E₂) (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 3). The product of E₁ and E₂ simplifies to the ratio of the rate of probe oxidation and the rate of PS reaction. Experimentally determined rates of RhB (Table 2) and PS (Table S.2) reaction were used to quantify η (eqs 16 and 17).

$$\begin{gathered} E_1= \\ \frac{[{{\text{SO}}_4}^{•-}]k_{{{\text{SO}}_4}^{•-},P}[P]+([{{\text{SO}}_4}^{•-}]\sum _{i=1}^n{k}_i[S_i])+([{{\text{SO}}_4}^{•-}]\sum _{i=1}^n{k}_{\equiv ,i}[S_{\equiv ,i}])}{k_{\text{PS}}[\text{PS}]} \end{gathered}$$ (14)

$$\begin{gathered} E_2= \\ \frac{[{{\text{SO}}_4}^{•-}]k_{{{\text{SO}}_4}^{•-},P}[P]}{[{{\text{SO}}_4}^{•-}]k_{{{\text{SO}}_4}^{•-},P}[P]+\left([{{\text{SO}}_4}^{•-}]{\sum }_{i=1}^n{k}_i[S_i]\right)+\left([{{\text{SO}}_4}^{•-}]{{\sum }_{i=1}^{n}k}_{\equiv ,i}[S_{\equiv ,i}]\right)} \end{gathered}$$ (15)

$$\eta =E_1\times E_2=[{{\text{SO}}_4}^{•-}]\times k_{{{\text{SO}}_4}^{•-},P}\times [P]/k_{\text{PS}}\times [\text{PS}]$$ (16)

$$\eta =k_P\times [P]/k_{\text{PS}}/[\text{PS}]$$ (17)

where k_PS is the experimentally determined pseudo-first-order degradation rate of PS (s⁻¹) and k_P is the experimentally determined pseudo-first-order degradation rate of RhB (s⁻¹).

Results indicate that the role of E₁, and therefore NPR remains generally constant (0.13) with increasing alumina concentration (Supporting Information S.8, Figure S.11). The reaction between PS and alumina was negligible (Supporting Information S.3, Figure S.4), indicating that the source of NPRs cannot be attributed to this reaction. A minor source of NPRs in the system was due to the reaction between SO₄^•− and PS (R7, Table 1). Specifically, the rate of PS reaction attributed to SO₄^•− scavenging (i.e., rate of SO₄^•− scavenging by PS) was small relative to the overall reaction rate of PS (i.e., k₇ × [PS] × [SO₄^•−]_SS/k_PS × [PS] ≈ 0.037–0.006; 0–50 g L⁻¹ alumina, respectively). It is also noted that the rate of SO₄^•− scavenging by PS, relative to the overall rate of SO₄^•− consumption (eq 3), was significant (0.29–0.04; 0–50 g L⁻¹ alumina, respectively). This indicates that whereas PS may be a significant scavenger of SO₄^•−, the impact of SO₄^•− on the PS reaction rate was limited and did not constitute a major source of NPRs. Other sources of NPRs played a role and are presently undifferentiated. The efficiency of SO₄^•− reaction with RhB (E₂) declined significantly and was correlated with an increase in the concentration of alumina amended to the test systems (Supporting Information S.8, Figure S.11). Under ideal conditions, that is, in the absence of NPR and SO₄^•− scavenging, the ideal efficiency would be 2.0 for both UV-APS and T-APS oxidative treatment systems, where 2 mol SO₄^•− are formed/mol PS (i.e., R1 and R2, Table 1). On this basis, the overall ideal efficiency (η_ideal), defined as E₁ × E₂/2 = (k_RhB × [RhB]/k_PS × [PS]/2), ranged from 0.044 to 0.007 (0–50 g L⁻¹ alumina, respectively) (Supporting Information S.8, Figure S.11). In natural soil systems where PS reacts directly with reduced aquifer solids and does not form SO₄^•−, NPRs would play a greater role and the range in η_ideal is projected to be lower. It is evident that the reduction in treatment efficiency as a result of alumina amendment to the oxidative treatment system underscores the role of solid surfaces in scavenging radicals in PS-based oxidation treatment systems.

The mechanism of surface scavenging is beyond the scope of this study; however, some speculation is warranted. The alumina mineral (α-phase) used here was highly crystalline (calcined at T ≈ 1000 °C) and is considered to be less catalytically active than low-temperature calcined alumina and exhibited low surface area.²⁵ The dehydration step during calcination causes formation of surface defects^25,30 that may be responsible for SO₄^•− scavenging. Also, the (protonated) hydroxyl groups (OH) on the surface of alumina are known reactants with ^•OH³¹ (1.2 × 10¹⁰ M⁻¹ s⁻¹)³² and could serve as potential H donors to form HSO₄⁻. It is not proposed that Al ion in alumina (Al₂O₃) specifically scavenges SO₄^•−, as it occurs at its highest oxidation state.

Environmental Implications.

In subsurface systems, the solids to water ratio is much greater than in the dilute suspensions used during the laboratory testing in this study. This suggests that the rate of SO₄^•− scavenging by mineral surfaces could be much greater in aquifer and soil systems during ISCO deployment than in dilute solid suspensions. To explore this further, SO₄^•− scavenging rates were calculated using the experimentally derived value of k_≡S for alumina (Table 2) and contrasted with SO₄^•− reaction rates with aqueous phase species. In this simplified analysis, assumed conditions and parameter values included an ideal representative volume of unconsolidated porous media (1 m³) containing 7 wt % of alumina, 1 pore volume mixture of 1,4-dioxane (1.13 × 10⁻⁵ M; 1 mg L⁻¹), and PS (4.2 × 10⁻² M; 10 g L⁻¹) with instantaneous mixing, no 1,4-dioxane sorption or NPR, and [SO₄^•−]_SS = 5 × 10⁻¹² M. The rate of SO₄^•− reaction with alumina surfaces (t = 0 h) dominated the fate of SO₄^•− by approximately 5 and 7 orders of magnitude over PS and 1,4-dioxane, respectively (Figure 2). These results emphasize the dominant role of SO₄^•− scavenging by mineral surfaces during PS-driven oxidative treatment in aquifer and soil systems.

Figure 2.

Calculated SO₄^•− reaction and scavenging rates in aquifer material where k_≡s was derived from this study; aquifer and reaction parameters: total volume = 1 m³, ρ_bulk = 1.6 g cm⁻³, porosity (η) = 0.3, [alumina] = 7 wt %, k_≡s = 4.42 × 10⁴ m⁻² × s⁻¹, [PS]₀ = 4.2 × 10⁻² M, k₆ = 6.1 × 10⁵ M⁻¹ s⁻¹, [1,4-dioxane]₀ = 1.13 × 10⁻⁵ M, k_{SO4^•−,1,4-dioxane} = 4.1 × 10⁷ M⁻¹ s⁻¹,¹⁰ [SO₄^•−]_SS = 5 × 10⁻¹² M (assumed).

Previously, perchloroethylene (PCE) oxidation was evaluated using heat-activated PS in the presence of 10 different solids including clays, sands, and a field soil.³³ In batch systems containing illite or montmorillonite, approximately the same amount of PS was reacted as in the solids-free system, but rates of PCE oxidation were significantly diminished in comparison to the solids-free system. This suggests that the reduction in treatment efficiency outcome was predominantly attributed to surface scavenging (i.e., E₂). Further, the PCE loss was greater in illite than montmorillonite, which suggests that the role of k_≡S is mineral-specific.

The kinetic analysis method developed in this study involved the quasi-steady-state assumption where d[SO₄^•−]/dt ≈ 0 and $C_{{{\text{SO}}_4}^{•-}}\approx P_{{{\text{SO}}_4}^{•-}}$ (eq 2), in conjunction with the condition that $P_{{{\text{SO}}_4}^{•-}}$ was similar between the solids-free and solids-amended systems. Alumina was found to be unreactive with the PS (Supporting Information S.3, Figure S.4), making it an ideal mineral solid to test in these experiments. Given the identical test conditions used for the solids-free and solids-amended systems, and that the pseudo-first-order degradation rate constant for PS (k_PS (s⁻¹)), and the ΔPS (M) were found to be approximately equal, the time-dependent differences in [RhB] were attributed to surface scavenging allowing k_≡S,alumina to be estimated.

Under the condition where the solid phase media reacts with PS and does not produce SO₄^•− (i.e., NPR), the kinetic analysis method presented here would yield an estimate of k_≡S that represents a maximum value (i.e., eq 13) and therefore must be reported with a qualifier (i.e., k_≡S ≤). Under the condition where solid phase media react with PS and produce SO₄^•−, as is most often the case (i.e., natural activation), the kinetic analysis method developed here becomes unstable because P_SO4^•− cannot be equated between the solids-free and solids-amended systems which served as the basis for eq 13. For example, in studies involving PS reaction in soil and mineral oxidative treatment systems, contaminant transformation rates were contrasted between solids-free and solids-amended (i.e., Fe- and Mn-based minerals, including goethite, birnessite, soils, and aquifer materials) to assess PS activation.³⁴ The PS reacted with the solid phase media and consequently, results could not be used to definitively assess whether the changes in probe oxidation rates were attributed to (1) changes in PS activation efficiency (E₁) where SO₄^•− production $(P_{{{\text{SO}}_4}^{•-}})$ changed (i.e., the mineral species is a better/worse activator), (2) NPR, or (3) SO₄^•− oxidation efficiency (E₂) where there was a change in the SO₄^•− scavenging rate by the solids amended to the treatment system, or perhaps by the soluble constituents imparted by the solids. Conversely, where illite–smectite was amended to a thermally activated PS treatment system, a decrease in the PCE degradation rate was measured relative to the solids-free, base-case system, despite similar rates of PS reaction.³³ This result suggested proof of concept that solid surfaces were responsible for scavenging radicals and reducing PCE degradation.

The total oxidant demand test was developed as a diagnostic tool to generally measure the mass of oxidant needed to significantly reduce background soil oxidant demand, improve contaminant oxidation, and to quantify how much oxidant is needed for ISCO design purposes.^35,36 Others have reported that repeated persulfate treatments did not improve the rate of contaminant oxidation in some soils and minerals.³³ One possible explanation for these seemingly opposing results may lie in the role of radical scavenging. Solid phase radical scavenging occurs during and after persulfate treatments, where significant reductions in background oxidant demand and NPR may be achieved. Specifically, elimination of the background oxidant demand does not preclude aggressive surface radical scavenging by some solid phase media, including alumina. Results from our study indicate that repeated and aggressive persulfate 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, suggesting that this source of treatment inefficiency is not easily eliminated for some solid phase media. Rather, these results suggest that surface radical scavenging extends beyond the depletion of oxidant demand, and contaminant transformation is controlled by competing SO₄^•− reactions between the target contaminant(s) and nontarget species, including aqueous species and solid phase surfaces as per eq 15.

In this study, kinetic analysis and laboratory methods were developed to account for the reaction of SO₄^•− in both the aqueous and solid phases for the first time. By accounting for the significant reaction of SO₄^•− at solid surfaces, it is evident that SO₄^•− production is likely much greater than currently being credited in PS-driven ISCO systems, and possibly advanced oxidation technology water treatment systems. Given the predominant role of SO₄^•− scavenging by solid surfaces in environmental oxidative treatment systems, it is evident that methods to mitigate this form of scavenging would have a high potential to improve the treatment efficiency.