Nicolas Mézières
email: nicolas.mezieres@univ-rennes1.fr

Laurent Le Coq

Senior Member, IEEE Benjamin Fuchs

Spherical Phaseless Antenna Measurements Experimental Validation of a Two Antenna Positions Procedure

Keywords: Antenna measurements, near field, phaseless measurement, phase retrieval, spherical waves

The phaseless characterization of antennas enables to reduce the cost and to ease the measurement of radiating systems, especially at high frequencies. The complex near field is retrieved from the acquisition of the antenna radiated field magnitude only thanks to appropriate phase retrieval algorithms. Thus, a two scan approach combined to a Gerchberg-Saxton algorithm has proven to lead to accurate phase retrievals. However, instead of measuring the field on two spherical surfaces of different radii as conventionally performed, we propose to measure the magnitude of the field on a single sphere but for two antenna positions. This new strategy is easier to implement in a number of measurement setups. Numerical and experimental validations in a commercial, arch-based, measurement system are shown and discussed.

I. INTRODUCTION

S PHERICAL Near-Field (NF) antenna measurement is a standard, accurate and mature technique for antenna characterization [START_REF] Hald | Spherical Near Field Antenna Measurements[END_REF]- [START_REF] Breinbjerg | Spherical near-field antenna measurements -the most accurate antenna measurement technique[END_REF]. However, the phase of the radiated field might be cumbersome and costly to be acquired accurately. Phaseless, or magnitude-only, antenna measurements are an attractive solution to relax the demanding constraints (probe positioning, cable bending, temperature stability, ...) required to ensure reliable phase measurements and consequently reduce the cost of such characterization. The price to pay is the increased number of required sampling points and the significant and notorious numerical difficulties of phase retrieval problems.

In phaseless NF antenna measurements, the complex radiation pattern is retrieved from magnitude only measurements. Among the categories of phaseless antenna measurements, the two scans technique is arguably the most commonly used as well explained in [START_REF] Breinbjerg | Phaseless near-field antenna measurement techniques -an overview[END_REF]. The magnitude of the field radiated by the Antenna Under Test (AUT) is measured over two surfaces that must be sufficiently separated in order to mitigate the otherwise inevitable ambiguities arising in phase retrieval problems. This strategy has proven to provide excellent results in the case of phaseless spherical NF antenna measurements, as recently investigated thoroughly in [START_REF] Varela | Numerical and experimental investigation of phaseless spherical near-field antenna measurements[END_REF]. The magnitude of the field is sampled on two concentric spheres and the influence of their radii is investigated. The Gerchberg-Saxton (GS) algorithm [START_REF] Gerchberg | A practical algorithm for the determination of phase from image and diffraction plane pictures[END_REF] is used to solve the phase retrieval problem and reconstruct the complex NF over one sphere in order to derive the Far Field (FF) radiated by the AUT.

Among the many recent phase retrieval algorithms, including convex methods [START_REF] Candès | Phase retrieval via matrix completion[END_REF], [START_REF] Goldstein | Phasemax: Convex phase retrieval via basis pursuit[END_REF] and non-convex techniques [START_REF] Candès | Phase retrieval via wirtinger flow: Theory and algorithms[END_REF], the pioneer alternating projection algorithm of GS, turns out to perform very well under appropriate conditions of field sampling (e.g. sampling density and sphere radii), as shown in [START_REF] Varela | Numerical and experimental investigation of phaseless spherical near-field antenna measurements[END_REF].

This letter proposes and validates experimentally a different phaseless spherical NF antenna measurement procedure, where the two scans are performed over a single measurement sphere for two positions of the antenna. The shift of the AUT inside the measurement sphere enables to generate the two independent magnitude measurement datasets required in any phaseless measurement procedure. This scenario, first mentioned in [START_REF] Breinbjerg | Mathematical formulation of phase retrieval for phaseless spherical near-field antenna measurements with probe correction[END_REF], has been recently numerically investigated in [START_REF] Alvarez | Phase retrieval for spherical near-field measurements using two antenna positions[END_REF]. An experimental validation of such a phaseless antenna measurement is shown and discussed here for the first time to our best knowledge. Moreover, the present algorithm is more efficient as it avoids working in the FF domain in order to translate the field. Consequently, our approach does not requires a higher truncation order for the modal expansion of the shifted antenna. Also the proposed strategy is not restricted to constant angular step distributions.

The phaseless measurement over a single sphere for two antenna positions is easier to implement in a number of relevant measurement setups, such as arch-based systems. The usual two scan configuration for spherical phaseless measurement and the new one investigated in this letter are represented in Fig. 1. The link between the measurement settings (field sampling, antenna positions) and the accuracy of the phase retrieval is investigated to better understand the conditions of a successful phaseless measurement procedure.

The letter is organized as follows. In Section II, the spherical wave expansion and the standard two scan technique are recalled, the proposed two antenna position for phaseless pro-cedure is also described. The proposed approach is validated on a numerical example in Section III with a discussion on the phase retrieval accuracy and experimental cases are shown in Sections IV. Finally, conclusions are drawn in Section V.

II. PHASELESS ANTENNA SPHERICAL MEASUREMENT A. Spherical Wave Expansion

The electric field E radiated from sources can be expanded outside the minimal sphere using Spherical Waves (SW) F smn as follows [START_REF] Hald | Spherical Near Field Antenna Measurements[END_REF]

E(r, θ, ϕ) = k √ η smn Q smn F smn (r, θ, ϕ) (1)
where k is the wavenumber, η the admittance of the propagation medium and (r, θ, ϕ) the spherical coordinates. The quantities Q smn are the complex spherical coefficients to be determined. The SW are indexed by s ∈ {1, 2} the propagation mode, n the degree and |m| ≤ n the order. The series ( 1) is truncated to n ≤ N according to the rule N = ka +n 1 where a is radius of the minimal sphere, x the floor function and n 1 an integer [START_REF] Hald | Spherical Near Field Antenna Measurements[END_REF], often fixed to 10 [START_REF] Jensen | On the number of modes in spherical wave expansions[END_REF].

If the electric field radiated by the AUT is measured at M sampling positions over a sphere of radius R, the SW expansion of the field (1) can be rewritten as a linear system of equations

y = Ax (2)
where the vector y of size 2M gathers the complex measured field (two polarizations), A is the matrix containing the discretization of the SW, F smn , at the sampling positions and x stores the spherical coefficients Q smn . The SW matrix A is modified according to the transmission formula for NF measurements to compensate for the probe radiation pattern as detailed from p. 61 in [START_REF] Hald | Spherical Near Field Antenna Measurements[END_REF].

B. Phase Retrieval Formulation and Resolution Methods

Only the magnitude of the field i.e. |y|, is measured. However the phase is necessary to perform the Near-Field to Far-Field (NF2FF) transformation. Therefore a phase retrieval procedure, a GS like algorithm, is considered in this letter.

It has also been shown that sampling strategies have an influence on the accuracy achieved by phaseless measurements [START_REF] Bangun | Signal recovery from phaseless measurements of spherical harmonics expansion[END_REF]. More specifically, uniformly distributed sampling are more efficient. Consequently, the igloo sampling [START_REF] Fuchs | Fast antenna far field characterization via sparse spherical harmonic expansion[END_REF], providing such property, is used throughout this letter. A first accuracy assessment based on the orthogonality of the SW for each position of the AUT is also demonstrated.

C. Gerchberg-Saxton for two Spheres

The standard GS algorithm for spherical antenna measurements propagates the retrieved complex field back and forth between the two spheres of different radii until convergence. Indeed, the fields over each sphere must share the same spherical coefficients Q smn . The coefficients identified over one sphere are used to perform a back or forward propagation to the other one. At each propagation to the other measurement sphere, the magnitude is replaced by the measured one and the process goes on until some stopping criterion is satisfied [START_REF] Varela | Numerical and experimental investigation of phaseless spherical near-field antenna measurements[END_REF].

D. Gerchberg-Saxton for two Antenna Positions

The two concentric sphere procedure can be easily adapted to a single measurement sphere for two antenna positions provided that the expansion of the radiated field leads to the same spherical coefficients. This is achieved by an analytical transformation of the SW basis [START_REF] Hald | Spherical Near Field Antenna Measurements[END_REF]. In particular, the radiated field of a shifted antenna, as in Fig. 1, has exactly the same spectrum as before if the shift is also applied to the SW basis. It can also be interpreted as measurements over two non-concentric spheres in the same AUT coordinate system.

Let y, y T the measured fields for the antenna default and shifted away positions respectively, A the SW matrix as in (2) and A T the matrix containing the translated SW. Therefore the following equations hold: Ax = y, A T x = y T . The modified GS algorithm for two antenna positions is given in Algorithm 1. As indicated in the introduction, a similar algorithm was given in [START_REF] Alvarez | Phase retrieval for spherical near-field measurements using two antenna positions[END_REF]. However, the present version avoids the FF propagation step along the reference point method and uses a matrix-vector formulation approach (2). In this paper, a constant phase initialization, φ (0) = 0 is used, as in [START_REF] Varela | Numerical and experimental investigation of phaseless spherical near-field antenna measurements[END_REF]. This simple start is good enough to show the feasibility of our phaseless configuration but other starting points should be considered to improve the convergence. The resolutions of the linear systems are performed in a regularized least square sense. It boils down to a multiplication of the data vector by the pseudo-inverse of the low-rank approximation of the SW matrices, A + and A + T . It enables a computationally fast and efficient algorithm once the matrices have been computed offline.

III. NUMERICAL VALIDATIONS A. Reconstruction Metric

The success of the phaseless characterization is evaluated by comparing the retrieved FF in y to the reference one, y. This comparison is achieved point-wise using the error signal defined by The mean of this error signal defines the Equivalent Noise Level (ENL) and both are given on a dB scale in the sequel. In this letter, only the FF magnitudes are compared because they provide a simple indicator of a coherent retrieved phase from NF measurements.

Error(y, y) = ||y| -| y|| max i |y i | . ( 3
)

B. Simulated Horn Antenna at 10 GHz

Let us consider the numerical model of the standard gain horn in X-band shown in Fig. 4.(a). The field is derived where needed by reference spherical coefficients coming from a very dense simulation data set. The two antenna positions procedure is tested for two configurations, denoted as Cfg. 1 and Cfg. 2. A shift on the z axis is applied to provide the two positions in both cases. These translations have a length of 30 mm for Cfg. 1 and 60 mm for Cfg. 2 (1 and 2λ). The NF samplings are generated on a sphere of 260 mm with respect to the origin (20 % of the Rayleigh FF distance) with 2744 samples for 1248 unknowns, corresponding to a truncation order of the SW expansion of N = 24. The reconstruction of the FF in the co-polarization plane is shown in Fig. 2. The ENL for reconstructions from Cfg. 1 and Cfg. 2 on the whole sphere are -41.7 dB and -43.8 dB respectively. It demonstrates the numerical reliability of the proposed phase retrieval strategy and algorithm.

C. Correlation and Phase Retrieval Accuracy

Phase ambiguities emerge more often when the measurement matrix A possesses redundancies, as showcased in [START_REF] Bangun | Signal recovery from phaseless measurements of spherical harmonics expansion[END_REF]. Consequently, the correlation between the modes stored in matrices A and A T provides an indicator of the expected phase retrieval accuracy. The correlation between two discretized modes is the modulus of complex inner product between the two corresponding normalized columns in the SW matrices. The higher the redundancy, the higher the correlation. The histograms of correlations between the SW matrices for Cfg. 1 and Cfg. 2 are shown in Fig. 3. As expected, the Cfg. 2, leading to better FF reconstruction, uses matrices showing less redundancies. Numerous tests for various shift distances on the z-axis have been led to confirm this behaviour and are not shown here for conciseness and readability. For a given

A. Horn Antenna at 10 GHz

The NF data are made of 3088 measurements along an igloo sampling for 1350 unknowns (truncation order N = 25, sampling ratio ≈ 2.3 per AUT position). The applied shift between the two positions is of 3λ = 9 cm. FF reconstructions of the co and cross-polarizations in the main cutting plane are shown in Fig. 5. The ENL of the reconstruction over the whole sphere is -39.9 dB.

B. Metasurface Antenna at 17 GHz

The NF data are made of 13876 measurements along an igloo sampling for 6493 unknowns (truncation order N = 56, sampling ratio ≈ 2.2 per AUT position). The applied shift is of 2λ ≈ 3.5 cm. FF reconstructions of E θ and E ϕ polarizations in the main cutting plane are shown in Fig. 6. The ENL of the reconstruction over the whole sphere is -34.9 dB. This quite high value is explained by a higher magnitude mean of the radiation pattern itself, as hinted by the cuts in Fig. 6.

V. CONCLUSION

A phaseless spherical antenna measurement strategy has been investigated and experimentally validated. The approach consists in the radiated field magnitude on a single near field sphere for two antenna positions. This phaseless measurement configuration is suitable for arch-based measurement systems and is complementary to the commonly used two sphere approach. In addition, the measurement settings of this two antenna position approach to ensure a proper phase retrieval and mitigate the phase ambiguities have been investigated from the computation of the correlation between the two measurement matrices. These first promising experimental results show that the proposed antenna phaseless measurement procedure could be an interesting alternative to the widely spread and accurate two sphere approach.

Fig. 1 .

 1 Fig. 1. Illustration of two configurations of phaseless spherical NF antenna measurements. The intensity of the NF is measured (left) on two concentric spheres and (right) on a single sphere for two antenna positions.

Algorithm 1

 1 Modified Gerchberg-Saxton for phaseless measurements with two AUT positions Require: |y|, |y T | the measured magnitude and A, A T the SW matrices for the two AUT positions, φ (0) a starting phase guess. 1: Initialization 2: y ← |y|e iφ (0) 3: while Stopping criterion not met do 4: x ← A + y #Solving for the coefficients 5: y T ← A T x #Apply translation 6: φ T ← Phase( y T ) #Store the retrieved phase 7: y T ← |y T |e iφ T #Magnitude correction

Fig. 2 .

 2 Fig. 2. Simulated horn: FF reconstruction of the field from the phaseless spherical NF measurements in the main polarization plane.

Fig. 3 .Fig. 4 .

 34 Fig. 3. Correlation histograms between the columns of the SW matrices for two antenna shift configurations (1 and 2 λ). The histogram displays the number of spherical mode couples distribution with respect to their correlations.

Fig. 5 .

 5 Fig. 5. Measured horn: FF reconstruction of the field from the phaseless spherical NF measurements.

Fig. 6 .

 6 Fig. 6. Measured metasurface: FF reconstruction of the field from the phaseless spherical NF measurements.

ACKNOWLEDGMENT

The authors thank Jérôme Sol for his help in measuring the antennas.

This work was carried out in the frame of a CNES and LNE grant and is supported in part by the European Union through the European Regional Development Fund (ERDF), and by the french region of Brittany, Ministry of Higher Education and Research, Rennes Métropole and Conseil Départemental 35, through the CPER Project SOPHIE / & STIC Ondes.


Guanhong Liu

Jiahao Qian

Yu Zhang

Kuangfei Lin
email: kflin@ecust.edu.cn

Fuwen Liu

Thermal assisted heterogeneous activation of peroxymonosulfate by activated carbon to degrade perfluorooctanoic acid in soil

Keywords: Thermal activation, Activated carbon, PFOA, Soil organic carbon, DFT calculation

The chemical degradation of perfluorooctanoic acid (PFOA), an environmentally persistent contaminant, has recently attracted much attention. Still, very few reports have focused on the degradation of PFOA in soil due to the process's non-liquid, complex system and uneasy operation. In this study, thermal treatment was applied in the remediation of PFOA contaminated soil. Complementary to thermal activation of peroxymonosulfate (PMS), fresh activated carbon (FAC) and modified activated carbon (NAC), which were used as heterogeneous catalysts, were incorporated into the system to promote the production of sulfate radicals (SO 4

•-) and the diminution of PFOA in soil. Two portions of soils, both homogenous but one with and the other without natural organic carbon (OC), were provided to study the impact of OC on the elimination of PFOA in soil. The J o u r n a l P r e -p r o o f degradation of PFOA was initiated using the combined methods in cohesion with heat activation. During the process, the effect of temperature, the dosing amount of catalyst and oxidant, the reaction time and the volume ratio between soil and solution on the degradation of PFOA in soil were fully studied and optimized. The results showed that over a 12 h period, a PFOA (1.0 mg/kg) removal of 76% and 70% by using FAC/PMS and NAC/PMS respectively could be achieved at 60 °C. Furthermore, density functional theory (DFT)

calculations were combined with experimental data and verify that the adsorption ability of both FAC and NAC for PFOA are 3 times stronger than that of soil grain. This greater adsorption can attract PFOA molecules from within soil and provide opportunities for interactions with oxidative radicals. This work sheds light on a much over-looked aspect of advanced oxidation of PFOA in soil systems, which might provide a potential option for the in-situ remediation of PFOA contaminated soil in the future.

Introduction

Perfluorooctanoic acid, which is used extensively in both industrial production and consumer consumption [START_REF] Giesy | Global distribution of perfluorooctane sulfonate in wildlife[END_REF][START_REF] Kannan | Perfluorooctanesulfonate and related fluorochemicals in human blood from several countries[END_REF][START_REF] Jensen | Emerging endocrine disrupters: perfluoroalkylated substances[END_REF], has the ability to remain stable, for great periods of time, in the natural environment and proves difficult to be degraded even under highly extreme conditions due to the high-energy C-F bonds [START_REF] Qu | Photo-reductive defluorination of J o u r n a l P r e -p r o o f perfluorooctanoic acid in water[END_REF][START_REF] Kennedy | The toxicology of perfluorooctanoate[END_REF]. The vast dispersal of PFOA which is regarded as a likely carcinogen, along with its high solubility and migration advantages, makes it a substantial risk to ecological security [START_REF] Lyu | Adsorption of PFOA at the air-water interface during transport in unsaturated porous media[END_REF][START_REF] Murakami | Groundwater pollution by perfluorinated surfactants in Tokyo[END_REF]. Although it has been banned in production and utilization in accordance with the Stockholm convention of 2015 [START_REF] Sorengård | Electrodialytic per-and polyfluoroalkyl substances (PFASs) removal mechanism for contaminated soil[END_REF], there still remains a large remnant in underground water and soil systems. Due to its extensive use, PFOA can be found in both soil and water J o u r n a l P r e -p r o o f environments with high concentrations having been detected especially in particular fields.

For example, Sinclair et al [START_REF] Sinclair | Mass loading and fate of perfluoroalkyl surfactants in wastewater treatment plants[END_REF]] reported that PFOA ranged from 18 to 241 ng/g dry weight in sludge from wastewater treatment plants in New York, USA. In Japan, Ahrens et al [START_REF] Ahrens | Distribution of polyfluoroalkyl compounds in water, suspended particulate matter and sediment from Tokyo Bay, Japan[END_REF]] detected that ∑PFCAs (Perfluorocarboxylic Acids) ranged from 0.29 to 0.36 ng/g dry weight in surface sediment and groundwater within landfill leachate from Tokyo, among which plume-L-PFOA recorded 1.8 μg/L. In China, Yan et al [START_REF] Yan | Short-and long-chain perfluorinated acids in sewage sludge from Shanghai, China[END_REF]] found that PFOA ranged from 23.2 to 298 ng/g dry weight in sewage sludge in Shanghai, and Gan et al [Gan et al. 2010] reported that concentrations of Σ PFCAs in soils, that were greatly dominated by PFOA, ranged from 0.508 to 6.83 ng/g, with an average of 2.81 ng/g in agriculture areas in Sichuan.

Soil is what links the atmosphere and the hydrosphere, and holds a major role in the conversion and build-up of contaminants in both land-based and aquatic environments. The effective and timely removal of soil pollutants can prevent their penetration into groundwater, stop their release into the atmosphere, and/or minimize the dangerous threat they pose to the safety of living organisms [START_REF] He | Natural soil mineral nanoparticles are novel sorbents for pentachlorophenol and phenanthrene removal[END_REF], Liu et al., 2021].Although a good deal of studies to date have been conducted to explore and strengthen the removal of PFOA in aqueous media [START_REF] Yang | Persulfate-based degradation of perfluorooctanoic acid (PFOA) and perfluorooctane sulfonate (PFOS) in aqueous solution: review on influences, mechanisms and prospective[END_REF][START_REF] Turner | Novel remediation of per-and polyfluoroalkyl substances (PFASs) from contaminated groundwater using cannabis sativa L. (hemp) protein powder[END_REF], however only a few approaches have been developed for the degradation of PFOA in soil [Liu et al., 2021[START_REF] Sammut | Perflfluoroalkyl substances in the Maltese environment -(II) sediments, soils and groundwater[END_REF][START_REF] Turner | Mechanochemical remediation of perfluorooctanesulfonic acid (PFOS) and perfluorooctanoic acid (PFOA) amended sand and aqueous film-forming foam (AFFF) impacted soil by planetary ball milling[END_REF].

Based on previous reports, the amendment of PFOA contaminated sites with carbonaceous materials (CMs) was considered advantageous as it combined carbon sequestration with pollutant immobilization. Although it is true that CMs can reduce the leachability of PFOA J o u r n a l P r e -p r o o f and stabilize the solid material [START_REF] Sørmo | Stabilization of PFAS-contaminated soil with activated biochar[END_REF], however, the contamination in these studies were not degraded and remained present in soil; the desorption of pollutants can further cause secondary pollution [START_REF] Du | Adsorption behavior and mechanism of perfluorinated compounds on various adsorbents-a review[END_REF].

The synergistic behavior between granular-sized activated carbon (AC) and appropriate oxidant has been proven to be an effective method to degrade PFOA [Peng et al., 2017[START_REF] Liu | Efficient mineralization of perfluorooctanoate by electro-Fenton with H 2 O 2 electro-generated on hierarchically porous carbon[END_REF]. In situ chemical oxidation (ISCO), which has been gaining greater attention due to its effective and relatively convenient trait for the treatment of organic contaminated soil [START_REF] Devi | In-situ chemical oxidation: principle and applications of peroxide and persulfate treatments in wastewater systems[END_REF][START_REF] Khalil | Decomposition of H 2 O 2 on activated carbon obtained from olive stones[END_REF], also demonstrates great potential to remediate the PFOA-contaminated soil. Moreover, peroxymonosulfate (PMS, HSO 5 -) which is characterized by a high redox potential, as well as good stability under normal conditions, has been gradually adopted for use in ISCO [START_REF] Yun | Oxidation of organic pollutants by peroxymonosulfate activated with low temperature-modified nanodiamonds: understanding the reaction kinetics and mechanism[END_REF][START_REF] Wang | Activation of persulfate (PS) and peroxymonosulfate (PMS) and application for the degradation of emerging contaminants[END_REF]. Therefore, further exploration on whether the combination of AC and PMS methods can be applied in the degradation of PFOA in soil, and how to improve the degradation performance of the combined methods was continued.

In addition, Sulfate radicals (SO

Materials and methods

Chemicals and reagents

PFOA was acquired from Aladdin reagent Co.

Soil sample preparation

Uncontaminated soil was collected from a depth of 0.25-0.35 m at a site in East China University of Science and Technology in Shanghai, China. The soil was air-dried at room temperature, large stones and plant residues were removed, and then passed through a 2 mm sieve. The soil was characterized as follows: 6.1% clay, 28% silt and 65.9% sand, pH 6.5, 3.42% organic matter. For the experiments, a set of spiked soil samples was prepared according to our previous method [Peng et al., 2017]. Clean soil and spiked soil (with 20 mg/L of PFOA stock solution) at a volume ratio of 1:1 were placed in a 1000 mL beaker. The combined soil was then stirred vigorously with a glass rod to promote homogeneous distribution of PFOA, after which the spiked soil was placed in a fume hood. Finally, the soil was aged for 1 month in darkness at room temperature (20 °C) before any treatment in the J o u r n a l P r e -p r o o f laboratory. In order to study the function of organic carbon in soil during the in situ remediation, soil was heated in a muffle oven at 600 °C for 6 h to remove the OC and labeled as soil-600 as a contrast.

Soil sample extraction

To extract the PFOA from the solids, a previously reported method was used as a base and modified accordingly [START_REF] Chen | Perfluorinated compounds in soil, surface water, and groundwater from rural areas in eastern China[END_REF]. 1.0 g of soil sample was weighed and placed into a 50 ml polypropylene centrifuge tube. To the tube, 5 mL methanol was added, vortexed for 1 min, and allowed to stand for 10 min. After standing, the tube was ultrasonicated at 40 °C for 20 mins, then centrifuged at 3500 r/min for 10 mins, the produced supernatant was then placed in a new centrifuge tube. The above extraction process was repeated two more times, collecting a total of 15 mL of supernatant. Afterwards, the supernatant was blown under a gentle flow of high-purity nitrogen to achieve a 1-2 mL concentrated extract which was then diluted with 50 mL ultrapure water.

Before the extract was injected into the WAX column for purification and extraction, the column was activated using a mixed solution (4 mL methanol, 4 mL 0.1% ammonia in methanol and 4 mL ultrapure water), and the effluent discarded. 50 mL of the extract was then added into the activated cartridge. After the solution was allowed to flow out, the cartridge was washed with a mixture of 10 mL of ultrapure water and 4 mL of 25 mM ammonium acetate (sodium acetate). All solutions were not preserved. Finally, the cartridge was eluted with 4 mL methanol and 4 mL 0.1% ammonia methanol solution. The 8 mL of eluate was collected using a 15 mL polypropylene tube, blown to near dryness under a gentle high-purity J o u r n a l P r e -p r o o f nitrogen stream, re-diluted to 2 mL methanol, vortexed for 30 s, and passed through a 0.22 μm membrane before being tested. The extraction efficiency of PFOA in soil was put in Table S1.

Procedures of degradation experiments

PFOA degradation tests were conducted in 250 mL conical flask reactors and were settled in a digital water bath oscillator at the desired temperature. Three sets of systems in which AC, PMS, AC/PMS were separately added to the reactor with contaminated soil were conducted and compared. At the beginning of the preliminary experiment, 1 g contaminated soil was added to the reactor followed by 10 mM PMS and 4 g/L AC, the reaction was then initiated by heat. After the optimization of the dosage of catalysts and oxidant, a given amount of 1 g soil, AC (8 g/L) and PMS (15 mM) were set with the ratio of soil/solution at 1.0 g/1.0 mL. The effects of pH, impact factor and the solid/solution ratio were then investigated by varying the solution pH [START_REF] Jensen | Emerging endocrine disrupters: perfluoroalkylated substances[END_REF][START_REF] Qu | Photo-reductive defluorination of J o u r n a l P r e -p r o o f perfluorooctanoic acid in water[END_REF][START_REF] Kennedy | The toxicology of perfluorooctanoate[END_REF][START_REF] Lyu | Adsorption of PFOA at the air-water interface during transport in unsaturated porous media[END_REF][START_REF] Murakami | Groundwater pollution by perfluorinated surfactants in Tokyo[END_REF][START_REF] Sorengård | Electrodialytic per-and polyfluoroalkyl substances (PFASs) removal mechanism for contaminated soil[END_REF][START_REF] Sinclair | Mass loading and fate of perfluoroalkyl surfactants in wastewater treatment plants[END_REF][START_REF] Ahrens | Distribution of polyfluoroalkyl compounds in water, suspended particulate matter and sediment from Tokyo Bay, Japan[END_REF][START_REF] Yan | Short-and long-chain perfluorinated acids in sewage sludge from Shanghai, China[END_REF], ion concentrations (1 and 10 mM) and the solution volume (1, 2 and 3 mL), respectively. At each designated time interval, extractions were taken from the soil samples and filtered through 0.22 µm membranes, then transferred into auto-sampler vials for quantitative analysis. The system pH was left unadjusted in all tests except when investigating the influence of the initial soil pH. Replicate runs were carried out twice for each test, and the relative standard deviations were determined to be less than 8.0%. The removal efficiency of PFOA (R PFOA ) was calculated from Eq 1, where C 0 and Ct are concentrations of PFOA at initial and fixed reaction times, respectively.

(

J o u r n a l P r e -p r o o f

Analytical methods

During the catalytic oxidation process, the concentrations of PFOA and its degradation products were determined by high-performance liquid chromatography combined with tandem mass spectrometry (HPLC-MS/MS) as demonstrated by Liu et al [Liu et al., 2021].

The limit of detection (LOD) of PFOA is 9 µg/L. The LOD of short-chained PFCAs and more detailed information are summarized in Table S2.

The quantitative analyses of fluorine anion (F -) was performed by ion chromatography (ELCD ICS-1000, USA). The injection volume was 10 µL and a flow rate of 1 mL/min was used for the anion separation. The mobile phase was 9.0 mM Na 2 CO 3 and the flow rate was 1.0 mL/min [START_REF] Köster | Monitoring of the total carbon and nitrogen balance during the mineralization of nitrogen containing compounds by heat activated persulfate[END_REF]. By calculation, the LOD of F -is 1.113 ppb at a signal-to-noise (S/N) ratio of 3, the specific measurement can be found in SI.

Computational Details

DFT calculations were performed using the DMol 3 program package in Materials Studio, in which a double numerical polarization (DNP) basis set was used [Delley, 2020]. The Perde-Burke-Ernzerhof (PBE) functional within the generalized gradient approximation (GGA) [START_REF] Hammer | Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals[END_REF] was applied to describe the electron exchange-correlation function. The total energy, maximum displacement, and maximum force tolerances were converged at 2×10 -5 hartree (Ha), 5×10 -3 Å, and 4 × 10 -3 Ha/Å, respectively. The Methfessel-Paxton method [START_REF] Methfessel | High-precision sampling for Brillouin-zone integration in metals[END_REF]] was adopted in the calculations with a Fermi smearing width of 0.001 Ha and the total energies were extrapolated to 0 K. The Brillouin zone was sampled by a 3×3×1 Monkhorst-Pack k-point mesh [START_REF] Chadi | Special points for Brillouin-zone integrations[END_REF]. The adsorption energy Eads is defined as Eq 2:

J o u r n a l P r e -p r o o f

where E adsorbate/slab represents the total energy of adsorbate and slab, E adsorbate refers to the energy of PFOA, E slab means the energy of clean surface, respectively. The distance between surfaces and adsorbed PFOA molecule was also measured after the structural optimization.

Results and discussion

Degradation optimization

Effect of temperature

Though heat is an effective way to activate PMS [START_REF] Hori | Efficient decomposition of perfluorocarboxylic acids and alternative fluorochemical surfactants in hot water[END_REF], however, there was a notable limitation for sole PMS on the removal of PFOA at elevated temperatures (Fig. S1).

Therefore, the influence of temperature as a crucial activation factor on the removal of PFOA by the combination of FAC/PMS or NAC/PMS was investigated through heterogeneous catalytic reactions in soil. Fig. 1 illustrates a 18% and 34% removal of PFOA by FAC/PMS and NAC/PMS at room temperature, respectively. By raising the temperature, the removal efficiency of PFOA was improved to 33% and 47.5% by FAC/PMS and NAC/PMS at 60 °C.

The results prove that a higher reaction temperature not only has a strong influence on PMS decomposition, but can also improve the diffusion rate of the catalytic molecules across the external boundary layer and within the pores [START_REF] Forouzesh | Transformation of persulfate to free sulfate radical over granular activated carbon: effect of acidic oxygen functional groups[END_REF]. However, when the reaction temperature was increased to 80 °C, no significant enhancement of PFOA removal could be seen. In view of the minimal improvement affected by temperatures beyond 60 °C, it can be surmised that elevated temperatures (> 60 °C) can only enhance the removal rate of PFOA to a small degree in soil as a result of heat loss due to heat transfer between further distances. In addition, the higher temperatures may also alter many soil properties such as J o u r n a l P r e -p r o o f water content which can affect the capacity of certain soil functions (Table S3). Besides, for soil remediation, the increase of temperature can limit the transport of PS in soil, thereby affecting the removal of organic pollutants [START_REF] Tsitonaki | In situ chemical oxidation of contaminated soil and groundwater using PS: a review[END_REF]. Hence, 60 °C was chosen as the optimum temperature to carry out all experiments in our study. This may also reduce the activation energy of the reaction due to the particles adsorbing some portion of heat, resulting in the transference of less energy.

Effect of PMS concentration

PMS + heat → SO 4 •- (3)
SO 4 •-+ H 2 O → SO 4 2-+ •OH + H + (4) SO 4 •-+ OH -→ SO 4 2-+ •OH (5)

Removal of PFOA by FAC and NAC

The PFOA removal capacity of both FAC and NAC were determined using heat without the addition of PMS. As shown in Figure 2b and 2c, a noteworthy advance in the removal rate of PFOA with the rising addition of FAC or NAC in soil is observed. Although the surface area of FAC is twice that of NAC (Table. S4), there was no obvious difference in their capability to adsorb PFOA. The removal rates of PFOA were increased from 30% to 45% and from 33% to 37% with the addition of FAC and NAC from 4 g/L to 12 g/L, respectively. The adsorption amounts of PFOA from soil were 4.28, 5.06 and 6.13 mg/g with the addition of 4, 8 and 12 g/L FAC, and were 4.50, 4.75, 4.73 mg/g with the same quantities of NAC. The adsorption ability of FAC was 0.0052 mg/m 2 , which was five times higher than NAC. In the meantime, for soil-600, an obvious increase in PFOA removal, from 30% to 47% and from 30% to 39%, could be seen after the addition of FAC and NAC from 4 g/L to 12 g/L, respectively.

As observed in Fig. 2d, adsorption did not immediately occur after the injection of FAC or NAC. During the first 1-3 hrs, there was little PFOA removed from the contaminated soil, J o u r n a l P r e -p r o o f however after 5 hrs of reaction a noticeable diminishment of PFOA in soil could be detected, indicating that contact between the PFOA from soil particles and the catalysts requires some time and the contact between FAC or NAC and PFOA in soil is a rate-limited and crucial step.

Meanwhile, with the extending reaction time, the PFOA removal rate was higher in soil-600 than in soil as a result of the loss of the OC in soil Organic carbon can provide more adsorption sites for PFOA in soil through hydrophobic interaction, ligand bridging and electrostatic interactions. Without OC, the binding strength between PFOA and soil-600 was not as strong as that of PFOA and soil, indicating that PFOA-contaminated soils with less OC content can be more readily repaired by adsorbents. Afterwards, the experiments were carried out at a constant dosage of PFOA (1.0 mg/kg), PMS (15.0 mM), FAC or NAC (8.0 g/L) with a reaction time of 6 h in the initial soil system.

Fig. 2.

Evaluation of catalytic oxidation performance

Effect of reagent volume

Contamination in low-permeability soil poses a significant technical challenge to in-situ remediation efforts, primarily due to poor accessibility to the contaminants and difficulty in uniform delivery of treatment reagents. In order to increase the contact area between pollution in soil and chemical reagent so as to achieve a better degradation effect, the soil and solution volume ratio was adjusted and compared. As the volume ratio increased from 1 mL to 3 mL with 1.0 g soil (Fig. 3a), the increased solution volume failed to improve the removal rate of PFOA. This may have been caused by more water molecules dispersing the catalyst and J o u r n a l P r e -p r o o f oxidant in aqueous states instead of promoting them within the soil medium.

Effect of reaction time

As discussed in 3.1.3, a prolonged reaction time could provide more opportunity to create better contact between PFOA and catalysts, hence the reaction time was further extended to investigate the removal rate of PFOA in soil using the combined method. As shown in Fig. 3b, the degradation efficiency of PFOA continuously increased with increasing reaction time. After 12 h, the degradation rate of PFOA reached as high as 70% and 76% for soil/FAC/PMS and soil-600/FAC/PMS, and 60% and 79% for soil/NAC/PMS and soil-600/NAC/PMS, respectively. For the advanced systems of both FAC/PMS and NAC/PMS, the degradation of PFOA was better in soil-600 than in soil. This performance difference can be ascribed to the absence of OC in soil-600 which lowered PMS consumption, and allowed more SO 4

•-and •OH to directly attack PFOA during the remediation process. The results also indicate that a prolonged time did indeed enhance the contact between contaminant and materials in soil.

Fig. 3.

Effect of systematic pH

The effect of pH on PFOA removal in soil based on AC/PMS was conducted using various pH values. In Fig. 4, for FAC/PMS, PFOA is shown to be preferably removed when under acidic conditions rather than alkaline, and can be ascribed to the transformation of SO 4

•-to •OH (Eq. ( 5)) under alkaline conditions. However, there was no significant difference in PFOA removal in soil in the presence of NAC/PMS among various pH values, indicating J o u r n a l P r e -p r o o f that the NAC/PMS system was less affected by pH. Unlike in aqueous solution systems, there was approximately a 20% difference between the degradation of PFOA by AC/PMS under acidic conditions and in alkaline solution [START_REF] Liu | Enhanced thermal activation of peroxymonosulfate by activated carbon for efficient removal of perfluorooctanoic acid[END_REF], however, no obvious distinction (<10%) of PFOA removal could be observed by the advanced oxidation methods in soil systems. For PMS-based AOPs, PMS inevitably acidifies the treated water matrix (Eq. ( 4)), while the structure of the aggregated soil can contain a certain amount of weak organic acids, both of which can act as a good balance to the pH. Therefore, the pH of the soil system was not immediately changed when the PMS solution was initially injected into the reactor, thereby having no significant effect on further generation of SO 4 •-. And, in turn, may also counteract any rate decrease due to PFOA protonation. Hence, this remediation method can be easily implemented under a variety of soil pH conditions.

Effect of co-existing matter

Several matters including chloride anion (Cl -), bicarbonate anion (HCO 3 -), nitrate anion (NO 3 -), sulfate ion (SO 4 2-) and phosphate anion (PO 4 3-), and humic acid (HA) that exist in natural ground water and soil may affect the reactivity of AC and PMS in PFOA removal. The effects of these compositions on PFOA transformation are presented in Fig. 5a and Fig. 5b.

The results illustrate that the presence of SO 4 2-and Cl -had a relatively slight influence on the decomposition efficiency of PFOA by AC/PMS. In contrast, with increasing ionic concentration, the presence of HA had the most prominent, negative impact on PFOA elimination for both FAC/PMS and NAC/PMS. The inhibitory effect of HA on PFOA J o u r n a l P r e -p r o o f degradation can be attributed to the scavenging effect (Eq. ( 8)) and the competition of reactive

HCO 3 -+ •HO → CO 3 •-+ H 2 O K = 8.5×10 6 M -1 S -1 (10) COOH -+ CO 3 •-→ HCO 3 -+ CO 2 •- K = 1.5×10 5 M -1 S -1 (11) CO 2 •-+ POP 2+ → •POP + + CO 2 K = 6.4×10 9 M -1 S -1 (12) SO 4 •-+ PO 4 3-→ SO 4 2-+ PO 4 •- (13)
Fig. 5.

J o u r n a l P r e -p r o o f

The defluorination of PFOA

Along with PFOA degradation, the defluorination of PFOA in the FAC/PMS and the NAC/PMS processes were crucial points for experimental analysis. The F -could be detected in both the reaction solution and the soil extraction solution after the degradation of PFOA. As depicted in Fig. 6a, in each system, the F -concentration increased continuously over time, implying that mineralization and defluorination were significant sources of decomposition for PFOA in the two systems. According to the obtained F -concentration in soil and in liquid, the defluorination rates of PFOA accounted for 24.29% and 30% after the 12 h time period.

Significantly, in terms of PFOA defluorination, FAC/PMS which had a better removal performance, was inferior to NAC/PMS. This may be a result of the surface of NAC containing more defects which allows for greater electron transfer between NAC and PMS during the decontamination process. This phenomenon is consistent with FAC and NAC degradation performance in aqueous systems.

Furthermore, based on the interpretation of HPLC-MS/MS (Fig. S3), C As for soil-600, even though the removal rates were higher than those in soil no matter for FAC/PMS or NAC/PMS system with the prolonged time, the defluorination efficiencies in soil-600 were lower than the values achieved in soil. Due to OC being converted into CO 2 during the burning process, soil-600 may have adsorbed more PFOA during the removal process, thereby causing difficulty for radicals and electrons to attack the protected interior PFOA molecules. In comparison, the negatively-charged PFOA can adsorb onto the surface of soil due to electrostatic attraction with positively-charged OC. Because of more exterior PFOA being prone to attraction in soil, this can lead to a higher defluorination efficiency during the adsorption process.

Fig. 6.

Possible mechanism on PFOA removal

The FTIR and HPLC-MS/MS information of PFOA degradation in AC/PMS processes

The FTIR spectra and LC-MS/MS interpretation were joined to properly analyze the PMS/AC/PFOA interactions. Take FAC for example, the primitive FAC and soil were tested and compared with the solids (the mixed soil with FAC) after reaction. In Fig. decreased after the reaction, implying that PFOA might also be partially bound to Si-O of soil.

In addition, the weakened peak at 3450 cm -1 in NS/FAC indicates that the -OH groups on the surface of FAC and soil act as the main hydrogen bond donors to attract PFOA. Furthermore, with the emergence of C-F bonding at 1000-1400 cm -1 and a new peak observed at 1723 cm -1 , attributed to the carboxyl group of PFOA, it reveals that most PFOA molecules existed in the form of carboxylic acid and were bonded in the solid. In the meantime, the deprotonation of PFOA could cause the dissociation of hydrogen bonding between PFOA and PMS, leading to the appearance of the symmetric stretching (νs) peak of SO 3-shown at 1108 cm -1 . Thus, it could also be postulated that FAC can anchor the PFOA and PMS in ternary mixtures and the whole interaction mode can be carried out harmoniously.

Fig. 7.

Furthermore, the decomposition of PFOA by catalytic oxidation took place in the presence of AC and PMS upon heating. According to the data obtained from HPLC-MS/MS (Fig. S3), it was presumed that C 7 F 15 COOH may be destructed to C 7 F 15 COO • and then C 7 F 15

• , with the attack of SO 4

•-produced from PMS decomposition catalyzed by AC main pathway,

•OH accompanied with SO 4

•-also played a vital role for the formation of C 7 F 15 OH. A series of intramolecular rearrangements proceed and C 6 F 13 COO -was generated through hydrolysis.

The same reactions between C 6 F 13 COO -and SO 4

•-occurred as those of C 7 F 15 COO -and J o u r n a l P r e -p r o o f converted to shorter chain PFCAs. The C n F 2n+1 COO • was unstable and could be readily decomposed to C n-1 F 2n-1 • and CO 2 , and to release H + for a decrease in pH. This subsequently produced shorter-chain PFCAs which followed the same CF 2 unzipping cycle with sufficient oxidant until they were mineralized, allowing AC/PMS to complete the defluorination of PFOA.

Computation of PFOA elimination.

The degradation of PFOA by AC/PMS in soil is a complex process involving several reaction steps. The most important step during the process of PFOA remediation in soil is that AC could efficiently attract and concentrate PFOA molecules present in contaminated soil, which would be beneficial for the next catalytic oxidation. However, the adsorption ability of soil, activated carbon and modified activated carbon have not been verified because the degradation path of adsorbed substances at different interfaces is vastly complex and rarely reported on. DFT calculations were employed to examine the reliability of the proposed pathway systematically and identify the adsorption effect.

The results obtained for the optimized structures of SiO 2 , graphene and graphene with amino groups are reported in Fig. 8, which represent the soil, FAC and NAC and provided The DFT calculations indicated that no matter the form of AC, the adsorption strength of all are much stronger than SiO 2 , and the relative adsorption strengths of PFOA were FAC>NAC>SiO 2 . The combining energy between SiO 2 and PFOA was -8.5 kcal/mol, while the average value of FAC and NAC was -22.2 kcal/mol and -24.65 kcal/mol, respectively, which was 3 times higher than the values obtained from soil and PFOA. It implies that AC could strongly adsorb PFOA even in solid media and PFOA would not be easily released into soil again once it was bonded onto the surface of AC. The results were in line with the above experimental phenomena.

Besides, the distances between FAC and PFOA were smaller than those for NAC and SiO 2 , which provided an advantage to attract PFOA. It is well known that the molecular size of PFOA is 11.7×3.95×3.7 Å, and a media with a higher micropore and a lower mesopore volume will supply the available pores for PFOA removal. Therefore, the transformation from micropores to mesopores after the HNO 3 treatment lead to a further distance between NAC and PFOA. However, the obtained amino group of NAC preferentially reacted with the carboxylic acids of PFOA where the distance between the two was around 2.34 Å, which compensated for the decline of micropore volume of NAC. Furthermore, according to the comparison of the distance, we deduced that, the most appropriate adsorption sites between

Conclusions

The primary benefit of thermal treatment in soil is the speed at which remediation can be controlled, allowing for radicals to be generated from PMS in a sustainable release. PMS dissociation by heat to generate SO 4 •-, in combination with these AC varieties, was anticipated to fully degrade and defluorinate PFOA. For the degradation of PFOA in soil, fewer remakable observations of PFOA diminution using oxidant alone were noted. Although, in the sole presence of activated carbon, very limited PFOA removal could be detected due to the concentration effect though a longer contact time was required. Such results were attributed to the refractory property of PFOA and poor contact between the pollutants and reagents in soil. Compared with the removal rates of PFOA in aqueous systems, although the degradation efficiency in soil was obviously slower and lower, the addition of both catalyst and oxidant and the prolonged reaction time still enhanced the degradation performance when using FAC/PMS or NAC/PMS. The variability of organic carbon contents in soils from different regions also demonstrated a certain influence on PFOA degradation in soil. High OC is likely to immobilize the PFOA but will result in a lower PFOA elimination by the consumption of SO 4

•-during the treatment process. However, the aggregate soil structure J o u r n a l P r e -p r o o f exhibited a distinct advantage where it presents buffering properties against significant variation of temperature and pH during the degradation of PFOA by FAC/PMS or NAC/PMS.

To this end, DFT calculations were used to verify the proposed assumption and provided useful insights into the adsorption effect, which was also a rate-limiting step during the degradation process of PFOA. The FAC and NAC can concentrate the PFOA in soil which proves helpful for the proceeding catalytic oxidation. Therefore, thermally-activated PMS coupled with FAC/NAC can be a promising decomposition technique with significant potential for the in-situ remediation of PFOA-contaminated sites. Table S1. Detailed information of the detected short-chained PFCAs compound.

Table S3. The effect of temperature on moisture content in soil.

Table. S4

Textural properties of FAC and NAC. J o u r n a l P r e -p r o o f

J o u r

  n a l P r e -p r o o f of contaminants or even turn contaminants into less toxic byproducts[START_REF] Peter | Thermal remediation alters soil properties -a review[END_REF][START_REF] Antoniou | Degradation of microcystin-LR using sulfate radicals generated through photolysis, thermolysis and e-transfer mechanisms[END_REF], Wang et al., 2017]. Therefore, thermal activation was adopted in this study and anticipated to enhance the oxidation efficiency on our refractory target pollutant.The fresh activated carbon (FAC) and nitric acid modified activated carbon (NAC) which characterized by better adsorption ability and facilitate electron transfer[START_REF] Liu | Enhanced thermal activation of peroxymonosulfate by activated carbon for efficient removal of perfluorooctanoic acid[END_REF], are respectively used as catalysts in this study. The possible mechanisms for the thermal-assisted AC/PMS methodology are as follows: utilizing thermodynamics for transporting pollution from soil to adsorbent and activating PMS to produce radicals which in turn attack the contaminant. The optimum usage of the catalysts and the oxidant, along with the influence factors of the reaction, were then considered. As the main component of soil, the effects of organic carbon (OC) on PFOA degradation, a rarely discussed topic in soil remediation, were also investigated in this study. Finally, the density functional theory (DFT) calculations were conducted based on the experimental data to verify the elimination mechanisms of PFOA in soil by using FAC/PMS and NAC/PMS. The obtained research conclusions can provide useful information for the chemical oxidation remediation of PFOA contaminated soil and provide a feasible method in practical application.

Fig. 1 .

 1 Fig. 1.

  Firstly, the degradation of PFOA in soil was conducted in the presence of PMS alone which was anticipated to produce strong oxydic radicals. As depicted in Fig2a, the highest removal efficiency of PFOA in soil was 15% when the dosage of PMS was 10 mM. With the increasing concentration of PMS from 10 to 40 mM, however, there was no remarkable improvement or reduction seen during the degradation of PFOA in soil. The removal efficiency of PFOA reached just 7% even though the PMS concentration was raised to four times its initial volume. It was assumed that a higher PMS dosage would lead to a larger generation rate of both SO 4•-and •OH in solution (Eqs. (3-5)) which would in turn improve PFOA removal (Fig.S2)[START_REF] Qi | Oxidation of flumequine in aqueous solution by UV-activated peroxymonosulfate: Kinetics, water matrix J o u r n a l P r e -p r o o f effects, degradation products and reaction pathways[END_REF][START_REF] Duan | Roles of structure defect, oxygen groups and heteroatom doping on carbon in nonradical oxidation of water contaminants[END_REF], however in this experiment that proved not to be the case. Unlike in aqueous solution, the excess SO 4•-produced by aggregation in soil could not be consumed by attacking PFOA, this lead to a mutual quench phenomenon during the degradation of PFOA and resulted in a notable decrease in PFOA removal efficiency despite the increased PMS concentration. For soil-600, the degradation rate of PFOA was increased slightly from the initial 8% to 16% with the addition of more PMS. This may be the result of absent OC from the soil providing more spaces for radicals to J o u r n a l P r e -p r o o f occupy and a smaller consumption of PMS. Nevertheless, the obtained results imply that the dispensed PMS was unable to oxidize the pollutant due to blocking from the soil particles.

Fig. 4 .

 4 Fig. 4.

  6 F 13 COOH (PFHpA), C 5 F 11 COOH (PFHxA), C 4 F 9 COOH (PFPeA) and C 3 F 7 COOH (PFBA) were the main detectable daughter products during the degradation of PFOA. Their total concentration shown in Fig. 6b, increased at the beginning as a result of the breakdown of PFOA and then decreased as the degradation proceeded. The concentration of these products finally amounted to 0.071 mg/L and 0.108 mg/L in the FAC/PMS and NAC/PMS systems respectively, after 12 h. Then, according to the mass balance equation (n F -+ n undegraded PFOA + n short-chained PFOA ), the mass balances of F acquired in 12 h were 42.8 % and 58.3 % for FAC/PMS and NAC/PMS, J o u r n a l P r e -p r o o f respectively. It was noteworthy that the obtained total mass balance of F contains the target values both in soils and in liquids, because the decomposed compounds from soils were likely to dissolve in liquids. The corresponding, remaining percentage 57.2% and 41.7% could roughly represent the PFOA absorbed on soil and AC, respectively.

  7, after exposure to PFOA, due to the electron withdrawing effect of the fluorinated tail on the carbon double bond, the bands of CH 3 and CH 2 of FAC which appear at 2930 and 2857 cm -1 were J o u r n a l P r e -p r o o f weakened. The association with AC was possibly caused by electrophilic character along the C-F bonds and nucleophilic behavior perpendicular to these C-H stretching vibrations bonds [Wang et al., 2019]. The characteristic absorption peaks of soil at 1080 and 800 cm -1

  three different adsorption scenarios with PFOA [Yu an et al., 2020;[START_REF] Zhang | New Insights into the Degradation Mechanism of Perfluorooctanoic Acid by Persulfate from Density Functional Theory and Experimental Data[END_REF]. For the structures of soil, silica as a main component was chosen to simulate soil and the lattice plane of 011 was selected in the calculation according to the XRD result (Fig.S4). The molecular structures of NAC owning planar conformation with amino groups were based on the FTIR information. Two conformations of PFOA were presented on each surface in order to get more J o u r n a l P r e -p r o o f comprehensive information, and the values in parentheses were determined in soil medium.

  PFOA and AC were the carboxyl group of PFOA with the carbon surface of FAC or NAC and with -NH 2 of NAC. As for SiO 2 , the C-F bond expressed tendency to bond with the Si-O-Si of soil. The deduced outcomes based on the DFT calculations corroborate with the FTIR J o u r n a l P r e -p r o o f results. These outcomes elucidate that FAC and NAC could efficiently adsorb PFOA from soil due to the stronger adsorption energy and more stable combination. Finally, the shorter distance and less bonding energy were also beneficial for electron transport between the adsorbent and pollutant during the mineralization of PFOA by FAC/PMS and NAC/PMS.

Fig. 8 .

 8 Fig. 8.

Fig. 1 .

 1 Fig. 1. PFOA degradation performance in the presence of FAC/PMS or NAC/PMS in thermal activated oxidation process in soils, where temperature ranges from 25 -80 °C. ([PFOA] 0 = 1.0 mg/kg, [PMS] = 5.0 mM, [FAC] = [NAC] = 4.0 g/L).

Fig. 2 .

 2 Fig. 2. (a) The influence of PMS dosage on the PFOA removal in soil at 60 °C ([PFOA] 0 = 0.7 mg/kg, soil: PMS solution = 1.0 g/1 mL, 5 h). Effects of FAC (b) and NAC (c) on the PFOA removal in soil, where the

Fig. 3 .

 3 Fig. 3. (a) The relationship between PFOA removal efficiency and the same chemical agent dissolved in different solution volumes. ([PFOA] 0 = 0.7 mg/kg, soil = 1.0 g, AC = 8 g/L, 60 °C). (b) The degradation of PFOA in soils by using FAC/PMS or NAC/PMS as the function of time ([PFOA] 0 = 0.5 mg/kg, PMS = 15 mM, AC = 8 g/L, the ratio of soil and solution = 1.0 g/ 1 mL, 60 °C).

Fig. 4 .Fig. 5 .Fig. 6 .Fig. 7 .Fig. 8 .

 45678 Fig. 4. PFOA degradation over a pH range of 3.0 -9.0 in the presence of FAC/PMS or NAC/PMS in soil. ([PFOA] 0 = 1.0 mg/kg, PMS = 15 mM, AC = 8 g/L, the ratio of soil and solution = 1.0 g/ 1 mL, 60 °C) Fig. 5. Effects of coexisting ions and organic matter on PFOA degradation efficiency of FAC/PMS (a) and NAC/PMS (b) in soil. ([PFOA] 0 = 1.0 mg/kg, PMS = 15 mM, AC = 8 g/L, the ratio of soil and solution = 1.0 g/ 1 mL, 60 °C, reaction time: 6 h) Fig. 6. (a) F -as a function of time and (b) Mass balance of F -during catalytic-oxidation degradation of PFOA at 60 °C. (a and b: [PFOA] 0 = 1.0 mg/kg and the pH was not buffered. The columns from left to right are FAC/PMS and NAC/PMS in soil, and FAC/PMS and NAC/PMS in soil-600 in 1 h and 12 h. The grey, orange and cyan sections respectively represent undegraded PFOA, remained short-chain PFOA and produced F ions.) Fig. 7. FTIR spectra of primary FAC, soil and the mixture of NS/FAC after reaction.Fig. 8. Solid phase molecule configurations of a) FAC, b) NAC and c) SiO 2 bonded with PFOA. (The red, white, grey, blue, cyan, and yellow spheres indicate O, H, C, N, F and Si atom, respectively.)

Fig. S1 .

 S1 Fig.S1. PFOA degradation performance in the presence of PMS alone in thermal activated oxidation

Fig. S2 .

 S2 Fig.S2. (a) Effect of radical scavenger (methanol) on PFOA degradation in soil. (b) EPR spectra of sulfate radicals and hydroxyl radicals in different scenarios. ([PFOA] 0 = 1.0 mg/kg, PMS = 15 mM, FAC/NAC = 8 mg/L, V PFOA /V MeOH = 1:1, T = 60 °C.) Fig. S3 HPLC-MS/MS identified intermediates products of PFOA yielded after thermal activated AC/PMS.

Fig. S4

 S4 Fig. S4The XRD pattern of the SiO 2 in soil.

Fig. 1 .

 1 Fig. 1.

Fig. 1 .

 1 Fig.1. PFOA degradation performance in the presence of FAC/PMS or NAC/PMS in thermal activated

Fig. 2 .

 2 Fig. 2.

Fig. 2 .Fig. 3 .

 23 Fig. 2. (a) The influence of PMS dosage on the PFOA removal in soil at 60 °C ([PFOA] 0 = 0.7 mg/kg, soil:

Fig. 3 .

 3 Fig. 3. (a) The relationship between PFOA removal efficiency and the same chemical agent dissolved in

Fig. 4 .

 4 Fig. 4.

Fig. 4 .Fig. 5 .Fig. 5 .Fig. 6 .

 4556 Fig. 4. PFOA degradation over a pH range of 3.0-9.0 in the presence of FAC/PMS or NAC/PMS in soil.

Fig. 6 .Fig. 7 .Fig. 7 .

 677 Fig. 6. (a) F -as a function of time and (b) Mass balance of F -during catalytic-oxidation degradation of

Fig. 8 .Fig. 8 .

 88 Fig. 8.

  [START_REF] Qu | Photo-reductive defluorination of J o u r n a l P r e -p r o o f perfluorooctanoic acid in water[END_REF]

  [START_REF] Qu | Photo-reductive defluorination of J o u r n a l P r e -p r o o f perfluorooctanoic acid in water[END_REF]

Acknowledgements

This research was supported by National Key Research and Development Program of China (No. 2019YFC1803701), National Natural Science Foundation of China (No. 51708223) and we acknowledge the Chinese Scholarship Council of PR China for providing financial support for Guanhong Liu to stay at the ENSCR.

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Highlights

 Thermal assisted heterogeneous activation of PMS by AC was applied in PFOA contaminated soil remediation.  Soil structure has buffering properties against external factors which in turn reduces removal efficiency.  PFOA contaminated soil with lower OC consumes less adsorbent and oxidant during the remediation.  DFT calculations revealed that adsorption strength of AC on PFOA was 3.5 times higher than soil's.