Supplementary Data. Supplementary Table S1.

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1 Supplementary Data AFFFs AOPs ARPs CEC ISCO ph pzc SA BET TNTs TSS WWTP VSS Decomposition Mineralization Supplementary Table S1. Abbreviations of General Terms, Definitions, and Equations Aqueous film-forming foams Advanced oxidation processes Advanced reduction processes Cation exchange capacity (cmol/kg) In situ chemical oxidation ph point of zero charge Brunauer Emmett Teller surface area (m 2 /g) Trinitrotoluenes Total suspended solids Wastewater treatment plant Volatile suspended solid C C or C F bond cleavage. In general, PFASs can be reduced to shorter-chain PFASs, fluoride ion, CO 2, sulfate ions, etc., depending on the parent compound. Synonyms include degradation and destruction. Degradation of the target compound to its elemental form, such as fluoride ion, CO 2, and sulfate ions. F - yield Removal efficiency Fluoride ions producedð mg L Þ PFASsð mg 100 ¼ Fluoride ion Yield (%) L Þ 0 19 g mol Y PFASs MW g mol Y = number of fluoride ions in PFASs, where 19 g/mol is the molecular weight of fluoride MW = molecular weight Higher fluoride yields are desired and indicate liberation of F - ions from the target PFAS and into solution. For example, if the target PFAS concentration is below the detection limit after the reaction, but F - yield is about 40%, then 60% F - are theoretically still located in target PFAS metabolites and not in solution. F - mass balance loss has been observed in some PFAS destruction studies, as discussed in the main text, and can also be sequestered by calcium precipitation or other methods. [PFASs] 0 ½PFASsŠ t 100 ¼ % Removal [PFASs] 0 The amount of PFASs removed or degraded over time (t). While several studies described in the main text indicate complete removal of the target PFAS(s), metabolites can include shorter-chain PFASs that still exist in the system. Furthermore, the limit of detection for each study should be taken into consideration.

2 Supplementary Table S2. Abbreviations and Formulas of PFASs Used in the Review APFO Ammonium perfluorooctanoate NH + 4 C 7 F 15 COO - DTFA 1H, 1H, 2H, 2H, 8H, 8H-perfluorododecanol CF 3 (CF 2 ) 3 CH 2 (CF 2 ) 5 CH 2 CH 2 OH Forafac 110 C 6 F 13 C 2 H 4 (OC 2 H 4 ) 11.5 OH FTEO Fluorotelomer ethoxylate F(CF 2 CF 2 ) x (CH 2 CH 2 O) y H FTOH Fluorotelomer alcohol (n:2 FTOH) CF 3 (CF 2 ) n-1 CH 2 CH 2 OH FTSA Fluorotelomer sulfonate (n:2 FTSA) - CF 3 (CF 2 ) n-1 CH 2 CH 2 SO 3 FTUCA Fluorotelomer unsaturated carboxylic acid CF 3 (CF 2 ) n-2 CF = CHCOO - (n:2 FTUCA) CF 3 (CF 2 ) n-1 CH = CHCOO - (n:3 FTUCA) NFDOHA Nonafluoro-3,6-dioxaheptanoic acid CF 3 OC 2 F 4 OCF 2 COOH PFBA Perfluorobutanoic acid C 3 F 7 COOH PFBS Perfluorobutane sulfonic acid C 4 F 9 SO 3 H PFCAs perfluorocarboxylic acids C n F 2n+1 COOH PFDA Perfluorodecanoic acid C 9 F 19 COOH PFHpA Perfluoroheptanoic acid C 6 F 13 COOH PFHxA Perfluorohexanoic acid C 5 F 11 COOH PFHxS Perfluorohexanesulfonic acid C 6 F 13 SO 3 H PFOA Perfluorooctanoic acid C 7 F 15 COOH PFOS Perfluorooctane sulfonic acid C 8 F 17 SO 3 H PFOSF Perfluorooctanesulfonyl fluoride C 8 F 18 O 2 S PFNA Perfluorononanoic acid C 8 F 17 COOH PFPeA Perfluoropentanoic acid C 4 F 9 COOH PFPrA Perfluoropropanoic acid C 2 F 5 COOH PFSAs perfluorosulfonic acids C n F 2n+1 SO 3 H TFA Trifluoroacetic acid CF 3 COO - PFAAs Perfluoroalkyl acids PFASs, perfluoroalkyl and polyfluoroalkyl substances.

3 Supplementary Table S3. Abbreviations of Sorption Terms AC Activated carbon ACF Activated carbon fiber BAC Bamboo-derived AC CNTs Carbon nanotubes ECH Epichlorohydrin E(N)FMs Electrospun (nanofibrous) membranes f OC Organic carbon fraction GAC Granular activated carbon HDTMAB Hexadecyltrimethylammonium bromide ( M)MCN (Magnetic) mesoporous carbon nitride MOFs Metal-organic frameworks Mt Montmorillonite MWCNTs Multiwalled carbon nanotubes PAC Powdered activated carbon PAC-MBR Powdered activated carbon membrane bioreactor PCMAs Permanently confined micelle arrays PLGA Poly(d, l-lactide-co-glycolid) PVA Polyvinyl alcohol TRIA Trimethylolpropane triacrylate

4 Supplementary Table S4. Abbreviations of AOP Terms BDD Boron-doped diamond CB Conduction band CHP Catalyzed H 2 O 2 propagation MWCNTs Multiwalled carbon nanotubes RDE Rotating disk electrode SCE Saturated calomel electrode Titania TiO 2 UNCD Ultrananocrystalline boron-doped conductive diamond VB Valence band (V)UV (Vacuum) ultraviolet light AOPs, advanced oxidation processes.

5 Supplementary Table S5. Abbreviations of ARPs E-beam - e aq I - VOCs ZVI ARPs, advanced reduction processes. Electron beam Aqueous or hydrated electrons Aqueous iodide (from KI) Volatile organic compounds Zero-valent iron powder

6 Supplementary Table S6. Proposed Equations for the Transformations of PFASs Electrochemical oxidation, the PFCA example 1. Radical formation on BDD surface C 7 F 15 COO - /C 7 F 15 COO + e - S1 H 2 O/ OH + H + + e - S2 2. Mineralization C 7 F 15 COO /C 7 F 15 + CO 2 S3 C 7 F 15 + OH/C 7 F 15 OH S4 C 7 F 15 OH/C 6 F 13 COF + H + + F - S5 C 6 F 13 COF + H 2 O/C 6 F 13 COO - + 2H + + F - S6 Repeat Equations (S1) (S6) Electrochemical oxidation, PFSA example 1. Radical formation on BDD surface C 8 F 17 SO - 3 /C 8 F 17 SO 3 + e - S7 2. Mineralization C 8 F 17 SO 3 + H 2 O/C 8 F 17 + SO H + S8 Repeat Equations S4 S6 Proposed photocatalysis mechanisms 1. Radical formation C n F 2n+1 COO - + (1)/C n F 2n+1 + COO - S9a C n F 2n+1 COO - + (2) or (3)/C n F 2n+1 COO S9b 2. Decarboxylation C n F 2n+1 COO /CO 2 + C n F 2n+1 S10 C n F 2n+1 + OH /C n F 2n+1 OH S11 3. HF elimination C n F 2n+1 OH/C n-1 F 2(n-1)+1 COF + HF S12 4. Formation of shorter-chain PFAS C n-1 F 2(n-1)+1 COF + H 2 O/C n-1 F 2(n-1)+1 COOH + HF S13 Proposed iron photocatalysis decomposition mechanism C 7 F 15 COO - + Fe 3+ /[C 7 F 15 COO Fe] 2+ S14 [C 7 F 15 COO Fe] 2+ + hv/fe 2+ + C 7 F 15 COO S15 Fe 2+ + O 2 /Fe O 2 S16 Fe 2+ + OH/Fe 3+ + OH - S17 Proposed iron hydrogen peroxide photocatalysis decomposition mechanism Fe 2+ + H 2 O 2 /Fe 3+ + OH + OH - S18 Fe 2+ + OH/Fe 3+ + OH - S19 Fe 3+ + H 2 O 2 /Fe 2+ + HO 2 + H + S20 Fe 3+ + HO 2 /Fe 2+ + O 2 + H + S21 H 2 O 2 + OH/HO 2 + H 2 O S22 CHP reaction mechanism Fe 3+ + H 2 O 2 /Fe 2+ + HO 2 + H + S23 OH + H 2 O 2 /HO 2 + H 2 O S24 HO 2 4O H + (pk a = 4.8) S25 HO 2 + Fe 2+ /Fe HO 2 S26 H 2 O 2 4HO H + (pk a = 11.8) S27 Proposed persulfate oxidation mechanism 1. Persulfate activation S 2 O hv/2so 4 S28 SO OH - /SO OH S29 2a. Sulfate radical scavenging SO H 2 O/ OH + SO H + S30 SO SO /S 2 O 8 S31 SO S 2 O 2-8 /SO S 2 O 8 S32 2b. Sulfate radical reaction with PFASs SO PFASs/SO PFASs + S33 Proposed advanced reduction of PFAS mechanism - 1. Cleavage of a-position C F bond by e aq C n F 2n+1 COOH + e - aq / C n F 2n COOH + F - S34 C n F 2n COOH + H 2 O/C n F 2n HCOOH + OH S35 C n F 2n HCOOH + e - aq / C n F 2n 1 HCOOH + F - S36 C n F 2n 1 HCOOH + H 2 O/C n F 2n 1 H 2 COOH + OH S37 2. Free radical formation (e.g., via UV irradiation) C n F 2n 1 H 2 COOH/ C n 1 F 2n 1 + :CH 2 + COOH S38 C n 1 F 2n 1 + COOH/C n 1 F 2n 1 COOH S39 3. Carbene reaction : CH 2 + H/ CH 3 S40 CH 3 + COOH/CH 3 COOH S41 Proposed hydrated electron generation and recycle mechanism from iodide ion 1. Formation of caged complex I - + H 2 O + hv (254 nm)/i H 2 O* S42 I H 2 O*/(I,e - ) + H 2 O S43 2. Radical formation (I,e - )/I - + e aq S44 3. Iodide radical reactions I + I - - /I 2 S45 I + I /I 2 S46 2I - 2 /I I 3 S47 4a. e - aq consumption: I 2 or I 3 present I I 2 /I 3 S48 e - - aq + I 2 /I 2 S49 e - aq + I - 3 /I I - S50 4b. e - aq consumption: H + present or low ph e - aq + H 3 O + /H S51 5. I - regeneration (ph >8.5) 3I 2 + 6OH - /5I - + IO H 2 O S52 (continued)

7 Supplementary Table S6. (Continued) Proposed dithionite and sulfite reaction mechanism 1a. Radical formation: dithionite S 2 O 2-4 /2SO - 2 (or H 2 SO 3, HSO - 3,SO 2-3 ) S53 1b. Radical formation: hydrogen sulfide HSO hv/so H S54 1c. Radical formation: sulfite SO hv/so e aq S55 2a. Sulfite radical: oxidant SO e - 2- aq /SO 3 S56 2b. Sulfite radical: reductant SO O 2 /SO 5 S57 2SO SO H 2 O/S 2 O SO H HSO 3 S58 SO SO /S 2 O 6 S59 SO SO H 2 O/SO H HSO 3 S60 Microwave-hydrothermal treatment effects of ph on sulfate radical All phs SO H 2 O/SO OH + H + k < 60 M -1 s -1 S61 Alkaline ph SO OH - /SO OH k = M -1 s -1 S62 Microwave-hydrothermal treatment effects of ZVI on sulfate radical S 2 O Fe 2+ /Fe 3+ + SO SO 4 S63 Electrohydraulic plasma discharge reactor 1. Decarboxylation C n F 2n+1 COO - + M + /C n F 2n+1 COO + M + + e - S64 C n F 2n+1 COO /C n F 2n+1 + CO 2 S65 C n F 2n+1 + 2H 2 O/C n 1 F 2n 1 COO - + 3H + + 2F - + H S66 2. C C cleavage (PFOA example) C 7 F 15 COO - + 2M + /CF 3 + C 6 F 12 + COO - + 2M + S67 CF 3 + COO - /CF 3 COO - S68 C 6 F H 2 O/C 5 F 11 COO - + 2H + + F - + 2H S69 3. PFOS example C 8 F 17 SO M + /C 8 F 17 SO 3 + M + + e - S70 C 8 F 17 SO 3 /C 8 F 17 + SO 3 S71 C 8 F H 2 O/C 7 F 15 COO - + 3H + + 2F - + H S72 SO 3 + H 2 O/2H SO 4 S73 Nonthermal plasma Glidarc H 2 O + e - / OH + H + e - S74 N 2 + e - /N( 4 S) + N( 2 D) + e - S75 N( 2 D) + O 2 /NO + O S76 NO + OH/NO 2 + H S77 NO 2 + HO 2 /HNO 2 + O 2 S78 HNO 2 + 2HO /HNO 3 + H 2 O S79 CHP, catalyzed H 2 O 2 propagation.