Daniel Bouchard

Patrick Hӧhener

Didier Gori

Daniel Hunkeler

Tim Buscheck

Chemosphere

Stable carbon and hydrogen isotope fractionation of volatile organic compounds caused by vapor-liquid equilibrium

Keywords: Stable isotopes, carbon isotope, hydrogen isotope, VOC volatilization, organic liquid vaporization, isotope fractionation

Several types of laboratory experiments were conducted to evaluate isotope fractionation caused by phase transfer process for a selection of common environmental contaminants. Carbon and hydrogen isotope fractionation caused by vaporization of non-aqueous phase liquid (NAPL), by volatilization from water and by dissolution into an organic solvent (tetraethylene glycol dimethylether or TGDE) was investigated under closed system experimental setups to isolate the airliquid partitioning process. A selection of aromatic, aliphatic and chlorinated compounds along with one fuel oxygenate (methyl tert-butyl ether or MTBE) were evaluated to determine isotope the enrichment factor related to respective phase transfer process. During NAPL vaporization, the residual mass of aromatic compounds, aliphatic compounds and MTBE became progressively depleted in heavy carbon and hydrogen isotopes. In contrast, during volatilization from water, the residual mass of aromatic compounds and MTBE dissolved in the water became progressively enriched in heavy hydrogen isotopes, whereas no significant change in carbon isotope was observed, except for MTBE showing a significant depletion. For the air-TGDE partitioning process, most of the aromatic compounds tested led to no significant carbon (except ethylbenzene) or hydrogen (except toluene and o-xylene) isotope fractionation. In contrast, significant carbon isotope fractionation was observed for aliphatic and chlorinated compounds and hydrogen isotope fractionation for aliphatic compounds, and are comparable to progressive NAPL vaporization in direction and magnitude. The isotope fractionation factors determined in this study are key for interpreting the change in isotope ratios when assessing the fate of gas-phase VOCs present in the soil air or when gas-phase VOCs are sampled using TGDE as the sink matrix. The results of this study contribute to expand the list of common environmental contaminants that can be assessed by the compound-specific isotope analysis (CSIA) method deployed in the frame of gas-phase studies.

Introduction

Volatile organic compounds (VOCs) represent an important class of subsurface environmental contaminants, among which chlorinated solvents and petroleum hydrocarbons are commonly encountered. In general, these contaminants have penetrated into the subsurface as non-aqueous phase liquids (NAPL) due to accidental releases above ground or improper storage tank containment in the subsurface. During downward migration through the unsaturated zone, portions of the moving NAPL become immobilized in the soil pores, resulting in a residual saturation ranging from 2 to 20% of the soil pore volume [START_REF] Boulding | Practical handbook of soil, vadose zone, and ground-water contamination. Assessment, prevention, and remediation[END_REF]. Due to their high vapor pressure, VOCs are expected to volatilize from the immobilized NAPL and migrate by gas-phase diffusion through the soil porosity, thus forming gas-phase plumes. potentially posing threats to human health if entering buildings (so called vapor intrusion process) [START_REF] Johnson | Heuristic model for predicting the intrusion rate of contaminant vapors into buildings[END_REF][START_REF] Verginelli | Role of the source to building lateral separation distance in petroleum vapor intrusion[END_REF] or contaminating sub laying groundwater resources [START_REF] Grathwohl | Guideline for groundwater risk assessment at contaminated sites (GRACOS). Recommendations for the assessment of a potential risk of groundwater pollution originating from a soil contamination in the unsaturated zone[END_REF]. Biodegradation and chemical oxidation are naturally occurring attenuation processes limiting gas-phase plume expansion by transforming VOCs into less harmful compounds (see [START_REF] Rivett | Review of unsaturated-zone transport and attenuation of volatile organic compound (VOC) plumes leached from shallow source zones[END_REF] for an extensive review of processes).

Aerobic biodegradation of VOCs during migration can be expected to readily occur for petroleum hydrocarbons under field conditions [START_REF] Lahvis | Quantification of aerobic biodegradation and volatilization rates of gasoline hydrocarbons near the water table under natural attenuation conditions[END_REF][START_REF] Baker | Estimation of hydrocarbon biodegradation rates in gasoline-contaminated sediment from measured respiration rates[END_REF][START_REF] Christophersen | Transport of hydrocarbons from an emplaced fuel source experiment in the vadose zone at Airbase V ae rlose, Denmark[END_REF][START_REF] Davis | Measurement and Modeling of Temporal Variations in Hydrocarbon Vapor Behavior in a Layered Soil Profile[END_REF][START_REF] Höhener | Biodegradation of hydrocarbons vapors: Comparison of laboratory studies and field investigations in the vadose zone at the emplaced fuel source experiment, Airbase Vaerløse, Denmark[END_REF][START_REF] Molins | Vadose zone attenuation of organic compounds at a crude oil spill site -interactions between biogeochemical reactions and multicomponent gas transport[END_REF][START_REF] Sihota | Seasonal Variability in Vadose Zone Biodegradation at a Crude Oil Pipeline Rupture Site[END_REF]. Aerobic biodegradation of chlorinated compounds in the unsaturated zone may also naturally occur, with biodegradation of cis-DCE and VC being commonly reported [START_REF] Kirtland | Isotopic and geochemical assessment of in situ biodegradation of chlorinated hydrocarbons[END_REF][START_REF] Patterson | Multiple lines of evidence to demonstrate vinyl chloride aerobic biodegradation in the vadose zone, and factors controlling rates[END_REF][START_REF] Kurt | Biodegradation of cis-dichloroethene and vinyl chloride in the capillary fringe[END_REF]. The literature remains scarce regarding aerobic biodegradation of TCE. While shown to occur in aqueous media [START_REF] Barth | Carbon isotope fractionation during aerobic biodegradation of trichloroethene by Burkholderia cepacia G4: a tool to map degradation mechanisms[END_REF][START_REF] Chu | Stable carbon isotope fractionation during aerobic biodegradation of chlorinated ethenes[END_REF][START_REF] Clingenpeel | Stable carbon isotope fractionation in chlorinated ethene degradation by bacteria expressing three toluene oxygenases[END_REF], occurrence during gas-phase transport in unsaturated soil remains to be demonstrated. Similarly, chemical oxidation of TCE under oxic conditions was shown to occur in aqueous media [START_REF] Pham | Trichloroethylene Transformation by Natural Mineral Pyrite: The Deciding Role of Oxygen[END_REF][START_REF] Schaefer | Mechanisms for Abiotic Dechlorination of Trichloroethene by Ferrous Minerals under Oxic and Anoxic Conditions in Natural Sediments[END_REF], but occurrence during gas-phase transport in unsaturated soil also remains to be validated. Finally, anoxic environments favorable to anaerobic biodegradation can also be developed at sites where the oxygen is consumed at higher rates than supplying rates [START_REF] Molins | Vadose zone attenuation of organic compounds at a crude oil spill site -interactions between biogeochemical reactions and multicomponent gas transport[END_REF], which was also shown to contribute limiting petroleum hydrocarbon plume expenditure.

Natural source zone depletion (NSZD) by physical and reactive processes has been presented as a viable site management strategy [START_REF] Johnson | Assessment of the Natural Attenuation of NAPL Source Zones and Post-Treatment NAPL Source Zone Residuals[END_REF]. Relying on natural attenuation processes as a site management strategy is acceptable when one can scientifically document the occurrence and contribution of attenuation processes along with quantification of contaminant mass reduction rates, while posing no risk to nearby population or natural resources. Quantification of mass reduction rates associated with a source zone located in the unsaturated zone is generally carried out by evaluating concentration changes for each targeted VOC in the soil gas over time [START_REF] Cozzarelli | Progression of natural attenuation processes at a crude-oil spill site: I. Geochemical evolution of the plume[END_REF][START_REF] Lundegard | Source Zone Natural Attenuation at Petroleum Hydrocarbon Spill Sites-II: Application to a Former Oil Field[END_REF]. However, understanding the VOC mass-transfer dynamics of a multiple-component NAPL is critical to accurately assess fate and contaminant transport, and yet represents a challenge to predict [START_REF] Wang | Volatile Organic Compounds Volatilization from Multicomponent Organic Liquids and Diffusion in Unsaturated Porous Media[END_REF][START_REF] Broholm | Compositional evolution of the emplaced fuel source in the vadose zone field experiment at airbase Vaerlose, Denmark[END_REF][START_REF] Mccoll | Evaporative mass transfer behavior of a complex immiscible liquid[END_REF]. In addition, while VOC concentrations are dependent on many environmental factors (for instance seasonal temperature variation, recharge water or groundwater level fluctuation), representative concentrations over space and time remain a limiting factor in quantifying accurate NSZD rates [START_REF] Ponsin | Documentation of time-scales for onset of natural attenuation in an aquifer treated by a crude-oil recovery system[END_REF][START_REF] Sihota | Seasonal Variability in Vadose Zone Biodegradation at a Crude Oil Pipeline Rupture Site[END_REF]. When remediation actions on the source are required, some engineered systems will take advantage of the high vapor pressure of the contaminants to accelerate source mass reduction. Soil vapor extraction (SVE) systems were shown to be an effective method for removing VOCs from the unsaturated zone, and thus became a common technology deployed by remediation engineers. Over prolonged treatment duration, the treatment efficiency tends to decrease indicated by reduced mass-removal rates and concentration tailings. This efficiency loss is caused by different physical, chemical, and biological factors influencing contaminant transport [START_REF] Mccoll | Evaporative mass transfer behavior of a complex immiscible liquid[END_REF], from which emerges the question whether or not the treatment efficiency reached its limitations and should thus be ended. To confidently determine proper NSZD rates in the unsaturated zones or to appropriately evaluate the efficiency of remediation systems applied to unsaturated zones, field practitioners therefore need assessment tools that are suitable for gasphase investigations.

Compound-Specific Isotope Analysis (CSIA) is a process-specific assessment tool increasingly used in gas-phase studies. CSIA was shown to be an appropriate assessment tool to evaluate NSZD in the unsaturated zone (Bouchard et al., 2008b;Höhener et al., 2008;[START_REF] Bouchard | Analytical modelling of stable isotope fractionation of volatile organic compounds in the unsaturated zone[END_REF], to assess for vapor intrusion [START_REF] Mchugh | Application of CSIA to Distinguish Between Vapor Intrusion and Indoor Sources of VOCs[END_REF][START_REF] Jeannottat | Can Soil Gas VOCs be Related to Groundwater Plumes Based on Their Isotope Signature[END_REF][START_REF] Beckley | Utility of Compound-Specific Isotope Analysis for Vapor Intrusion Investigations[END_REF] and to evaluate the performance of remediation systems (Bouchard et al., 2017a;Bouchard et al., 2018b;[START_REF] Zamane | Multistep partitioning causes significant stable carbon and hydrogen isotope effects during volatilization of toluene and propan-2-ol from unsaturated sandy aquifer sediment[END_REF]. Basically, the CSIA method aims at tracking the isotope ratio evolution of an element ( 13 C/ 12 C, 2 H/ 1 H, 37 Cl/ 35 Cl) for selected VOC with time (and/or distance) to demonstrate VOC biodegradation (Aelion et al., 2010) or to identify the dominant attenuation process [START_REF] Kuder | Effects of Volatilization on Carbon and Hydrogen Isotope Ratios of MTBE[END_REF]Bouchard et al., 2018a). The impact of biodegradation on the isotopic composition of VOC is well understood and leads to an accumulation of heavy isotopes (i.e. isotope enrichment) in the remaining pool of VOCs due to slower reaction kinetics of molecules including a heavy isotope.

However, it was shown that some physical attenuation processes, which had been neglected when applying CSIA for VOCs in saturated soil conditions (i.e. groundwater), must be considered in unsaturated soil conditions as causing significant isotope fractionation. For instance, vaporization of organic liquid, air-water partitioning and gaseous diffusion are physical processes known to change the isotopic composition of gas-phase VOCs (Bouchard et al., 2008b;[START_REF] Kuder | Effects of Volatilization on Carbon and Hydrogen Isotope Ratios of MTBE[END_REF]. These processes are hence expected to impact the isotopic signature of the VOCs during the course of passive vaporization (such as during natural source zone depletion) or during an active engineered remediation treatment. The direction (i.e. enrichment or depletion in heavy isotopes) and the magnitude of the isotope fractionation is, however, dependent on the conditions under which the processes are occurring. For equilibrium conditions in a closed system (i.e. static conditions), an isotope fractionation is expected due to different vapor pressure properties for isotopically different molecules (and called isotopologues) [START_REF] Van Hook | Condensed matter isotope effect[END_REF][START_REF] Wolfsberg | Condensed Phase Isotope Effect: Isotope Effects[END_REF]. In contrast, for non-equilibrium conditions in an open system (i.e. dynamic conditions), isotope fractionation due to kinetic processes such as gaseous and aqueous diffusion is occurring, and the observed isotopic change reflecting the processes interplay (vapor pressure and diffusion) is explained by the Craig-Gordon model [START_REF] Kuder | Effects of Volatilization on Carbon and Hydrogen Isotope Ratios of MTBE[END_REF][START_REF] Jeannottat | Chlorine and Carbon Isotopes Fractionation during Volatilization and Diffusive Transport of Trichloroethene in the Unsaturated Zone[END_REF]Julien et al., 2015b;[START_REF] Kopinke | Comment on Vapor Pressure Isotope Effects in Halogenated Organic Compounds and Alcohols Dissolved in Water[END_REF]. Currently, the direction and the magnitude of the isotope fractionation caused by vaporization and air-water partitioning process (under equilibrium conditions) are known for only few VOCs and elements, which limits the number of VOCs that can be assessed on field sites.

Lastly, application of CSIA in gas-phase studies is still largely limited due to lack of appropriate sampling devices specific to isotope measurements. A simple and robust solvent-based method specifically developed to facilitate isotope measurement on collected gas-phase VOCs has been recently documented as an alternative sampling method (Bouchard et al., submitted). The method uses tetraethylene glycol dimethylether (TGDE) as a liquid sink matrix to accumulate the gaseous VOCs. TGDE was selected among other potential solvents due to its lower vapor pressure property, increased affinity with polar and apolar compounds, and lastly due to absence of interference with the analytes during the analytical measurements (Bouchard et al., 2017b). During the sampling process, dissolution of gas-phase VOC into TGDE is controlled by the air-solvent partitioning process. This air-solvent partitioning process potentially leads to an isotope fractionation during the sampling process, which warrants further evaluations.

This study has two objectives, both focusing on isotope fractionation caused by phase transfer processes. First, carbon and hydrogen isotope fractionation factors related to vaporization from organic liquid and air-water partitioning under equilibrium conditions were determined for a selection of aromatic, aliphatic and fuel oxygenate compounds. A large subset of hydrocarbons was tested to evaluate the isotope fractionation variability related to different molecular structure, and in view to expand the CSIA application in soil gas studies to additional common contaminants observed at contaminated sites. Second, with the aim to support the development of the solvent-based sampling method specific to CSIA, carbon and hydrogen isotope fractionation related to air-TGDE partitioning was evaluated for a selection of aromatic, aliphatic, fuel oxygenate and chlorinated compounds. An isotope-specific analytical simulation was subsequently conducted reproducing the progressive accumulation of VOCs into TGDE during a sampling event. The analytical simulation was performed with the purpose of gaining comprehensive insights on the isotope fractionation caused by air-TGDE partitioning process during transient and steady state conditions.

Material & methods

Laboratory experiments

Stepwise NAPL vaporization in closed system

Multi stepwise NAPL vaporization experiments were carried out as previously performed for chlorinated ethenes by [START_REF] Jeannottat | Chlorine and Carbon Isotopes Fractionation during Volatilization and Diffusive Transport of Trichloroethene in the Unsaturated Zone[END_REF] to quantify carbon and hydrogen isotope fractionation factor for benzene (B), toluene (T), o-xylene (o-X), cyclopentane, n-octane, 2,2,4trimethylpentane (isooctane) and methyl tert-butyl ether (MTBE) (99% purity, various suppliers). The experimental setup consisted of two 5 mL air-tight syringes (Hamilton -model 1005 RN SYR for screw RN nut end tip) connected using a custom-designed screwing metal connector and maintained in vertical position during the experiment. A small 25 L metal receptacle was welded on the lower syringe plunger to contain the NAPL. Once spiked in the receptacle, the NAPL was allowed to equilibrate (20 minutes) with a fixed volume of air inside the lower syringe only by keeping the lock closed. The selected air volume was the smaller, the higher the VOC vapor pressure. The lock was reopened, and the headspace of the lower syringe was then transferred into the upper syringe. Once the syringes disconnected, clean air was reintroduced in the lower syringe whereas isotope analysis for the gas-phase compound contained in the upper syringe was performed. The VOC mass removed per step was related to the syringe volume and the vapor pressure of the compound at the experimental temperature (25°C). The mass removal evolution was tracked by using the total integrated peak area obtained during each isotopic analysis (see further explanation in Supplementary material). Repeated equilibration and dispense steps were performed until >95% of the NAPL mass was depleted, except for MTBE (>88%). Each compound was individually tested. For each VOC, carbon and hydrogen isotopes were evaluated separately respectively in duplicate and in triplicate experiments.

Stepwise air-water partitioning in closed system

Multi stepwise air-water partitioning experiments were carried out as previously performed for chlorinated ethenes by [START_REF] Jeannottat | Chlorine and Carbon Isotopes Fractionation during Volatilization and Diffusive Transport of Trichloroethene in the Unsaturated Zone[END_REF] to quantify carbon and hydrogen isotope fractionation factor for BTo-X and MBTE. An aqueous solution of 10 mg/L was separately prepared for each VOC in a 250 mL glass vial. Ten (10) mL of the solution was introduced into a 25 mL gas-tight glass syringe with the plunger fully extended to the 25 mL mark, hence leaving 15 mL of headspace.

The syringe was closed and was slightly shaken (200 rpm) for at least 20 minutes to reach the airwater equilibrium. The headspace was dispensed in a fume hood and followed by the introduction of 15 mL of ambient air in the syringe. The equilibration-dispense step was repeated until a defined mass proportion was removed based on Henry's law (at room temperature). The relative VOC mass decrease over time was validated by concentration analysis carried out on each aqueous sample.

One experimental series involved six (6) independently produced water samples with increasing number of equilibration steps. Three series were conducted for each compound (individually tested), except for MTBE (2 series). Isotope analyses were performed on the water samples in duplicates.

Air-TGDE partitioning in closed system

Single step air-TGDE partitioning experiments were carried out to quantify carbon and hydrogen isotope fractionation factor for a selection of aromatic compounds (BTo-X, ethylbenzene (E) and m,pxylene (m,p-X)), aliphatic compounds (cyclopentane, n-hexane and n-octane) and one fuel oxygenate compound (MTBE). In addition, a selection of chlorinated compounds including perchloroethene (PCE), trichloroethene (TCE), 1,1,2-trichloroethane (1,1,2-TCA), cis 1,2-dichloroethene (cis-DCE) and 1,2-dichloroethane (1,2-DCA) were evaluated to quantify carbon isotope fractionation factor. TGDE was obtained from Sigma-Aldrich (>99% purity) whereas the chlorinated compounds were obtained from various suppliers (all > 99 %). One (1) mL of TGDE was pipetted into a 20 mL glass vial. A defined volume of one pure compound was pipetted into the vial containing TGDE and then closed with teflon-lined septa using screw caps. The volumes were chosen according to the air-tetraglyme partitioning constant to produce about equal concentrations of each element C or H in the headspace. Additional vials without TGDE and reduced NAPL volume were prepared to measure the isotope ratio of the neat material (Table 1), again adjusting the amount of C and H to about equal vapor concentrations. These concentrations produced peaks within the IRMS linear range calibration, with amplitudes equal to reference gas peaks. For each VOC, a set of 5 vials with and without TGDE was prepared and left to equilibrate for 24 hours at 30°C. Carbon and hydrogen isotopes were evaluated in separate experiments.

- 0.5 -- PCE 80 -- 1.2 -- TCE 101 -- 1.4 -- 1,1,2-TCA 695 -- 1.4 -- cis-DCE 150 -- 1 -- 1,2-DCA 180 -- 1 --

Analytical methods and data treatment

. The methods for concentration and for carbon and hydrogen isotope analysis are described in the Supplementary Material.

For all cases, isotope ratios are reported in the delta ( notation [START_REF] Coplen | Guidelines and recommended terms for expression of stable-isotope-ratio and gas-ratio measurement results[END_REF]:

eq. 1

where R and R std are the isotope ratio of the sample and the international reference standard, respectively (VPDB for carbon and SMOW for hydrogen). The δ value obtained was then multiplied by 1000 to conveniently express it in units of per mil (‰).

For single step equilibrium conditions, the isotope fractionation caused by phase partitioning (between the gas and liquid) was quantified using: eq. 2

Where  is the isotope fractionation factor, and where δ gas and δ liquid are the isotope values for the VOC in gas phase and in the liquid phase, respectively. For convenience, the isotope fractionation factor is further transformed into an isotope enrichment factor (ε) using:

eq. 3

An ANOVA test was carried out to evaluate difference between δ gas and δ liquid measurements, and the standard deviation reported for ε is the sum of the two standard deviations of the mean for each sample.

For multi stepwise equilibrium conditions, the general equation to quantify the isotope fractionation factor for NAPL-vapor equilibration and air-water partitioning was developed in Jeannottat and Hunkeler (2012):

eq. 4

Where is the isotopic shift measured in the liquid, and is the fraction of the VOC in the liquid. Since the latter expression was shown to provide equivalent results to the Rayleigh approach, the air-NAPL (ε air-NAPL ) and the air-water (ε air-water ) enrichment factor for each compound was quantified using the Rayleigh equation: eq. 5

Where δ i is the initial isotopic composition of the compound, δ is the isotopic composition of the compound at the remaining fraction f.

For each compound, ε (for C and H) was determined by plotting as function of lnf, where ε is the slope of the linear regression. A slope was determined for each replicate and also by regrouping triplicate experiments as a whole to report the bulk slope. The slope was not forced through the origin, as suggested by [START_REF] Scott | Optimal methods for estimating kinetic isotope effects from different forms of the Rayleigh distillation equation[END_REF]. A Student-T test for regression method (to validate a slope different than zero) and a 95% confidence interval (for slope uncertainty) were calculated using the Statistics module from Grapher-Golden software®.

Finally, the relationship Ʌ = H-ε air-NAPL / C-ε air-NAPL was applied to report Ʌvalues as H-ε air-NAPL and C-ε air- NAPL were determined in separate experiments. The Ʌ values contribute to enlarge the dataset used in the frame of 2D-CSIA approach to assess the dominant contaminant mass removal process during remediation treatment (Bouchard et al., 2018a).

Isotope modeling

A simple analytical simulation was performed describing the increasing VOC concentration into a solvent when an air stream loaded with gaseous VOCs is forced through. The analytical simulation incorporates isotope fractionation during dissolution process to investigate for potential isotope fractionation effect. The mathematical solution applied was previously described in Huybrechts et al.

(2001):

eq. 6

Where C L is the VOC concentration in the liquid at time t, C g is the VOC concentration in the gas phase, K is the air-solvent partitioning constant for the VOC, F is the air flow rate passing through the solvent and V is the total volume of air injected. At infinite time (leading to VOC concentration equilibrium between gas and solvent), equation 6 simplifies to: eq. 7

To evaluate the isotope composition evolution of TCE used as the modeled compound, TCE molecules including a 13 C ( 13 C-TCE) or without ( 12 C-TCE) were distinguished (forming 2 isotopologues) and modeled as two different contaminants. Different initial concentrations and air-solvent partitioning coefficients were attributed to each isotopologue, which were determinedas follow:

initial concentrations: For a given initial TCE concentration (C TCE ) in the gas stream and isotopic composition (δ 13 C), initial concentrations for 13 C-TCE (C 13C-TCE ) and 12 C-TCE (C 12C-TCE ) were determined using:

eq. 8 eq. 9

air-solvent partitioning constants: To account for isotope fractionation during dissolution, the air-TGDE isotope fractionation factor ( air-TGDE ) for TCE determined in this study was used. The literature air-TGDE partitioning constant (K) was attributed to 12 C-TCE (K L ) and the K value for 13 C-TCE(K H ) was determined by: eq. 10

The two isotopologues were independently treated to evaluate their respective accumulation in the solvent during a simulated sampling event. Forgiven periodicities, the simulated quantities of the two isotopologues were combined to calculate the δ 13 C. See [START_REF] Bouchard | Analytical modelling of stable isotope fractionation of volatile organic compounds in the unsaturated zone[END_REF] for further explanation on the isotopic modeling approach.

Finally, a second simulation was performed to reproduce the isotope change measured during a multi step air-water equilibrium experiment. The equation 4 was expanded to include the number of equilibrium steps (n) as follow:

eq. 11 with eq.12 where C n and C 0 are respectively the concentration in aqueous phase after n equilibration steps and Initial concentration in aqueous phase.

Results

NAPL vaporization

During stepwise NAPL vaporization of VOCs conducted in closed systems, the residual VOC mass became progressively depleted in heavy carbon and hydrogen isotopes for all tested VOCs (Figure 1 and 2). The depletion trends indicate that molecules with heavy isotopes are more volatile than those with light isotopes only. For carbon, the magnitude of isotope fractionation is small, but was consistently reproduced over triplicate experiments. The carbon enrichment factors (C-ε air-NAPL ) obtained for the bulk slope of the triplicates range between 0.14 ± 0.04 ‰ (cyclopentane) and 0.38 ± 0.05 ‰ (MTBE) (Table 2). The enrichment factors for aromatic compounds are within the same range as aliphatic compounds, whereas the oxygenate compound (MTBE) provided a larger factor. For hydrogen, the isotope enrichment factors (H-ε air-NAPL ) determined were at least an order of magnitude larger than for carbon, and ranged between 2 ± 1‰ (MTBE) and 12 ± 2‰ (n-octane)

(Table 3). The hydrogen enrichment factors for aromatic compounds are smaller than for aliphatic compounds, whereas the oxygenate compound (MTBE) provided a significantly smaller factor compared to the two other groups. The variation of enrichment factors (C and H) among all tested

VOCs is best visualized when plotting H-ε air-NAPL values as function of C-ε air-NAPL , where the resulting Ʌ values (H-ε air-NAPL /C-ε air-NAPL ) allowed dissociating the 3 main compounds groups (Figure 3). The fuel oxygenate (MTBE) provided the lowest Ʌ value (Ʌ=5), whereas the aliphatic compounds (n-octane, cyclopentane and isooctane) provided the largest values (Ʌ ranging from 35 to 59), and with the aromatic compounds (BTo-X) positioning in between (Ʌ ranging from 20 to 26). [START_REF] Barth | Carbon isotope fractionation during aerobic biodegradation of trichloroethene by Burkholderia cepacia G4: a tool to map degradation mechanisms[END_REF].

Table 3: Hydrogen enrichment factors (H-ε air-NAPL ) related to stepwise NAPL vaporization and airwater partitioning process in closed system experimental setups (measured in the current study) and related to gas-phase diffusion and biodegradation (literature data) for selected aromatic, aliphatic, oxygenate and chlorinated compounds.

Compound

Air-NAPL partitioning

Air-water partitioning

Gas-phase diffusion

* Aerobic biodegradation** ε (‰) Benzene 4 ± 1 -5 ± 1 -1.71 -11 to -17 Toluene 6 ± 1 -5 ± 2 -1.28 -8.6 to-159 Ethylbenzene -- -- -1.00 +4 to -28 a m,p-Xylene -- -- -1.00 -- o-xylene 6 ± 1 -9 ± 4 -1.00 -- n-octane 12 ± 2 -- -0.88 -- cyclopentane 9 ± 2 -- -2.05 -- isooctane 6 ± 1 -- -0.88 -- MTBE 2 ± 1 -9 ± 3 -1.42 -29 to -66 PCE -- -- -0.45 -- TCE -- -- -0.69 -- 1,1,2-TCA -- -- -0.66 -- * calculated

Air-water partitioning

During stepwise air-water partitioning of MTBE in closed systems, the remaining MTBE in the water became progressively depleted in heavy carbon isotopes, indicating that MTBE molecules with a heavy carbon isotope are more volatile than those including light carbon isotopes only (Figure 4). Significant change occurred for MTBE in both duplicate experiments, from which a carbon enrichment factor (C-ε air-water ) of 0.22 ± 0.06‰ was calculated based on the bulk slope of the two repetitions (Table 2). For benzene and toluene (with mass removed proportion  97%), only one repetition of each VOC showed a significant depletion trend (respectively C-ε air-water of 0.09 ± 0.05‰ and 0.17 ± 0.09‰), whereas the other two repetitions and the bulk slope of the three repetitions indicated no significant change (Figure 4). Finally, no significant carbon isotope enrichment was observed for o-xylene in all three repetitions, for a mass removed proportion 97% (Figure 4). For hydrogen, in contrast, the residual VOC in water became progressively enriched in heavy hydrogen isotopes for every repetition of all four tested compounds (Figure 5), hence indicating that molecules with a heavy hydrogen isotope are less volatile than those with light hydrogen isotopes only. The bulk slope for BTo-X compounds respectively provided hydrogen enrichment factors (H-ε air-water ) of -5 ± 1‰, -5 ± 2‰ and -9 ± 4‰, whereas the oxygenate MTBE compound provided H-ε air-water = -9 ± 3‰ (Table 3).

Air-TGDE partitioning

Petroleum hydrocarbons: During single step air-TGDE partitioning in closed systems, the carbon isotope composition of gas phase aliphatic compounds (cyclopentane, n-hexane and n-octane) became enriched in heavy carbon isotopes, indicating that molecules with a heavy carbon isotope are less soluble in TGDE than molecules with light isotopes only (inverse isotope effect). The carbon enrichment factors (C-ε air-TGDE ) determined for the three aliphatic compounds tested were uniform and averaged 0.4 ± 0.2 ‰) (Table 4). For the aromatic compounds, in contrast, no significant isotopic change compared to the initial NAPL composition was measured for benzene, toluene, m,p-xylene and o-xylene (Table 4), with the exception of ethylbenzene. The isotopic composition of gas phase ethylbenzene became depleted in heavy carbon isotopes, indicating a normal isotope effect (C-ε air- TGDE = -0.6  0.2‰). For hydrogen, the isotope composition measured for benzene and ethylbenzene in the gas-phase showed no significant change compared to the initial NAPL value, whereas the isotope composition of gas-phase toluene (H-ε air-TGDE = 6  4 ‰) and o-xylene (H-ε air-TGDE = 28  2 ‰) became enriched in heavy hydrogen isotopes (Table 4). Accordingly, molecules with a heavy hydrogen isotope are less soluble in TGDE than those with light isotopes only (inverse isotope effect).

For the aliphatic compounds, no significant isotope composition change was observed for n-hexane and n-octane, whereas the isotope composition of gas phase cyclopentane (H-ε air-TGDE = 6  1 ‰) became enriched in heavy hydrogen isotopes (Table 4).

Chlorinated compounds: gas-phase composition of all five chlorinated compounds tested (PCE, TCE, 1,1,2-TCA, cis-DCE and 1,2-DCA) became enriched in heavy carbon isotopes, indicating that molecules with a heavy carbon isotope are less soluble in TGDE than molecules with light isotopes only (inverse isotope effect) (Table 4). The C-ε air-TGDE determined for the chlorinated compounds ranged from 0.3 ± 0.2 ‰ (cis-DCE) to 1.1 ± 0.3 ‰ (1,1,2-TCA) (Table 4), which are generally larger than those determined for petroleum hydrocarbons.

.4 ± 0.2 -- -- -- -- -- TCE -25.8 0.1 -24.8 0.1 1.0 ± 0.2 0.7 a -- -- -- -- -- 1,1,2-TCA -33.6 0.2 -32.5 0.1 1.1 ± 0.3 -- -- -- -- -- cis-DCE -22.9 0.1 -22.6 0.1 0.3 ± 0.2 -- -- -- -- -- 1,2-DCA -28.0 0.1 -27.1 0.1 0.9 ± 0.2 -- -- -- -- --
n.s.= not significant. a Bouchard et al. (2017b). Italic font indicates no significant change.

Discussion

Phase transfer isotope effect

The distribution of isotopologues between the gas phase and liquid phase upon equilibrium in closed systems is controlled by quantum mechanics, which accounts for the free energy involved for molecule translation, rotation and vibration in the system. The energy difference between the two isotopologues results in a vapor pressure isotope effect (VPIE) [START_REF] Bigeleisen | Theoretical Basis of Isotope Effects from an Autobiographical Prespective[END_REF]. The chemical environment provided by each phase will impact the energy distribution involved in the system. The chemical environment in the gas phase is governed by the intramolecular (vibrational) forces, while the chemical environment in the liquid phase is governed by the intermolecular forces (rotation and translation) and the intramolecular forces [START_REF] Bigeleisen | Theoretical Basis of Isotope Effects from an Autobiographical Prespective[END_REF]. Therefore, the different chemical environment provided by the NAPL compared to water is expected to influence the direction (inverse or normal isotope effect) and the magnitude of the isotope fractionation. For partitioning systems where the solute is dissolved into water, the isotope effect related to a different solubility property (i.e. the Henry constant) of each isotopologue can be evaluated using the same theoretical considerations (i.e. translation, rotation and vibration energy) as for the NAPL system described above [START_REF] Jancso | Interpretation of isotope effects on the solubility of gases[END_REF].The discussion below will first treat results involving NAPL vaporization, and will be followed by results obtained when VOC is a solute in water.

Isotope fractionation during stepwise NAPL vaporization

The results of all experiments evaluating NAPL vaporization for a selection of petroleum hydrocarbons and one fuel oxygenate consistently underlined a higher volatility for molecules with a heavy isotope (either a 13 C or 2 H), hence producing an inverse isotope fractionation effect. This inverse direction of the isotope fractionation observed for hydrocarbons was expected as previously discussed by [START_REF] Van Hook | Condensed matter isotope effect[END_REF] and reflects the interaction of intramolecular and intermolecular molecular forces in the NAPL. An inverse isotope effect is generated when the effect of intramolecular forces associated with vaporization becomes larger than the effect of intermolecular forces in the NAPL. For hydrocarbons, the reduction of the vibrational frequencies of molecules in the NAPL relatively to the air-phase due to interactions among the molecules creates this inverse isotope effect [START_REF] Jancso | Condensed phase isotope effects (Especially vapor-pressure isotope effects)[END_REF]. The reduced vibrational frequencies for hydrocarbons was empirically rationalized by [START_REF] Bartell | Isotope Effects on Molar Volume and Surface Tension: Simple Theoretical Model and Experimental Data for Hydrocarbons[END_REF]to be caused by longer C-H bonds compared to C-D bonds, which leads to a preferential retention of light isotopes in the NAPL. However, this empirical molar vapor isotope effect (MVIE) does not consider the temperature effect, and only applies to liquids near the melting point [START_REF] Van Hook | Condensed matter isotope effect[END_REF]. Furthermore, theoretical calculations performed by [START_REF] Lacks | Origins of molar volume isotope effects in hydrocarbon systems[END_REF] underlined the necessity to consider additional intermolecular effects (intermolecular separations) to more accurately foresee MVIE.

The magnitude of ε air-NAPL values determined in this study compare well to the very few values available in the literature determined using similar closed system experimental setups. For carbon, similar depletion magnitudes of heavy isotopes in the NAPL caused by vaporization were observed for benzene and for toluene (Table S-1 in Supplementary Material). For hydrogen, larger H-ε air-NAPL were expected compared to carbon as the isotope effects in general depend on the masses of the isotopic atoms involved and the force constants bonding 2 atoms in the molecule [START_REF] Van Hook | Condensed matter isotope effect[END_REF].

The H-ε air-NAPL determined for benzene and toluene in this current study are also in good agreement with older literature (Table S The results of the current study for closed systems revealed smaller carbon isotope fractionation for petroleum hydrocarbons (carbon atoms number ranging from 5 to 8) compared to fuel oxygenate (5 carbon atoms) (Table 2) and also compared to chlorinated compounds (2 carbon atoms) (Table S-1).

It must be considered that the C-ε air-NAPL values reported are "bulk" isotope effect, contrasting with the concept of specific reactive position as considered for kinetic isotope fractionation during biodegradation [START_REF] Elsner | A new concept linking observable stable isotope fractionation to transformation pathways of organic pollutants[END_REF]. For thermodynamic isotope fractionation at equilibrium conditions, the molecular structure and the positioning of the heavy isotope were shown to be of importance [START_REF] Van Hook | Condensed matter isotope effect[END_REF]. While all positions are considered reactive, the positioning of the heavy isotope at the terminal position of a molecule is expected to lead to larger isotope fractionation [START_REF] Bigeleisen | Application of finite orthogonal polynomials to the thermal functions of harmonic oscillators. V. Isotope chemistry and molecular structure. Simplified theory of end atom isotope effects[END_REF]. This terminal-position specific impact for carbon was addressed for heptane by Julien et al. (2015a), but the difference in isotope fractionation compared to the other position was very small. The latter study additionally showed minor position-specific isotope fractionation for toluene. For hydrogen, isotope fractionation of monodeuterated benzene (C 6 H 5 D) was shown to be equivalent to 1/6 of the isotope fractionation of perdeuterated benzene (C 6 D 6 ) [START_REF] Jakli | Vapor pressure isotope effects in the benzene (B)cyclohexane (C) system from 5 to 80 °C. I. The pure liquids B-d0,B-d1,ortho-,meta-, and para-B-d2, B-d6,C-d0, and C-d12. II. Excess free energies and isotope effects on excess free energies in the solutions B-h6/B-d6, C-h12/C-d12, B-h6/C-h12, B-d6/C-h12, and B-h6/C-d12[END_REF], thus also suggesting no significant reactive position for hydrogen as well for petroleum hydrocarbons. Our results agree with this lack of reactive-position isotope fractionation,

showing no clear trend between isotope enrichment factors obtained for petroleum hydrocarbons and increasing number of C or H atoms (Table 2). Therefore, the larger C-ε air-NAPL values for MTBE and TCE are more likely related to the presence of the oxygen or chlorine atoms in the molecule, respectively, impacting more significantly the vibrational frequencies of molecules in the NAPL phase compared to petroleum hydrocarbons. Furthermore, the molecular structure and H-saturation extent of petroleum hydrocarbon seems to be a distinctive aspect for H-ε air-NAPL values, as discernible on Figure 3 where Λ values distinguish the aromatic compounds from aliphatic and fuel oxygenate compounds. Distinction is mainly due to the various magnitudes of H-ε air-NAPL values. While the molecular structure impacts differently the motion (rotation and translation) of molecules in the NAPL phase, hydrogen bonds and different polarization potential of molecules also contribute to the isotope fractionation [START_REF] Lacks | Origins of molar volume isotope effects in hydrocarbon systems[END_REF][START_REF] Wade | Deuterium isotope effect on noncovalent interactions between molecules[END_REF]. In our case, the electrical configuration of aliphatic compounds (involving H-saturation) suggests a stronger polarization impact on the H-ε air-NAPL values compared to aromatic rings (involving π electrons) and MTBE. This polarization impact trend on the H-ε air-NAPL values for the three different groups respect the polarizability potential expressed by each group, with aliphatics having the least polarizability potential and MTBE having the largest [START_REF] Reichardt | Empirical Parameters of Solvent Polarity[END_REF]. However, this polarizability potential impact trend is not respected when considering chlorinated solvents. A H-ε air-NAPL value for TCE larger than for petroleum hydrocarbons was reported in the literature (Table S-2) while the polarizability potential would predict a smaller value, hence suggesting additional chemical interactions contributing to isotope fractionation for chlorinated solvents.

Isotope fractionation caused by stepwise air-water partitioning

The air-water partitioning experiments conducted in this study indicated that the partitioning of BTo-X compounds between the air and water (polar protic solvent) does not create significant carbon isotope fractionation (not significant in 2 out of 3experiments). Our results for toluene agree with the published work investigating this process using a closed system experimental setup (Table S-1). This absence of a systematic carbon isotope fractionation for BTo-X is contrasting with the systematic, yet small, observed carbon isotope fractionation caused by NAPL vaporization (Table 2). While for MTBE the air-water partitioning process created a significant inverse carbon isotope fractionation (C-ε air-water = 0.220.06 ‰), the latter process also created a smaller isotope fractionation compared to air-NAPL vaporization (C-ε air-NAPL = 0.38 0.05 ‰), which is in agreement with MTBE values reported by previous works using similar experimental setups (Table S-1). Based on different isotope fractionation magnitude obtained for the two liquids, the intermolecular forces applied by the water on aromatic compounds and MBTE seem to generate a smaller difference in free energy between heavy and light isotopes than the NAPL phase, which is leading to smaller isotope fractionation. This trend for larger carbon isotope fractionation caused by air-NAPL vaporization compared to air-water partitioning was also observed for TCE by [START_REF] Jeannottat | Chlorine and Carbon Isotopes Fractionation during Volatilization and Diffusive Transport of Trichloroethene in the Unsaturated Zone[END_REF] and Horst and Lacrampe-Couloume (2020) (Table S-1). The reported C-ε air-water values for TCE are larger compared to BTo-X and MTBE determined herein. In this case, the presence of chlorine atoms in the molecules and the different molecular structure of chlorinated compounds compared to aromatic compounds are likely impacting differently the intermolecular forces with water. As mentioned above, values derived from open system experimental setups cannot be compared to our values but are summarized in Table S1 and S-2 respectively for carbon and hydrogen.

For hydrogen, the normal isotope fractionation observed during air-water partitioning is contrasting with the inverse hydrogen isotope fractionation observed for air-NAPL vaporization, as predicted when changing the chemical environment from a nonpolar to a hydrogen bonded liquid [START_REF] Wolfsberg | Condensed Phase Isotope Effect: Isotope Effects[END_REF]. In this case, the motion forces (rotation and translation) exerted by water molecules surrounding BTX and MTBE compounds outweigh the vibrational forces, generating higher volatility for molecules including a heavy hydrogen isotope in the molecular structure. The motion forces seem more impactful for o-xylene and MTBE compared to benzene and toluene, generating a smaller H-ε air- water value for the latter two compounds (Table 3). For MBTE, the polar nature of the compound likely initiating stronger interactions with water molecules would explain the larger H-ε air-water value compared to benzene and toluene. However, the forces leading to larger H-ε air-water value for o-xylene compared to benzene and toluene requires more detailed investigations. In addition, the normal isotope fractionation for TCE (H-ε air-water = 5.2 2.6 ‰) and for trichloromethane recently reported by

Horst and Lacrampe-Couloume ( 2020) and contrasting with the inverse isotope fractionation obtained herein for aromatic compounds and MTBE would also require more detailed investigations.

Significance for gas-phase VOC assessments

Extending the application of CSIA to soil gas studies will significantly improve assessment strategies relying on VOC concentration measurements such as NSZD monitoring or remediation treatments like SVE or air-sparging systems. The enrichment factors determined in this study during volatilization of common subsurface contaminants contributes to increase the number of VOC candidates for CSIAbased assessments. However, ε values for CSIA data interpretation should be cautiously selected.

Whilst our study focused on closed system experiment setups (i.e. equilibrium conditions) to determine isotope fractionation strictly related with the phase partitioning process, several other studies have reported values determined using open system experiment setups (i.e. non-equilibrium conditions). In the latter case, the gas-phase volume above the liquid is constantly renewed at an experiment-specific rate, hence involving additional physical isotope fractionation process such as gas-phase diffusion. Table S-1 and S-2 (in Supplementary Material) compiles respectively carbon and hydrogen isotope fractionation factors determined using open system experiment setups for VOC volatilization from NAPL or water. One can note a wider ε value range for open system experimental setups, even observing opposite fractionation direction in the case for carbon, thus confirming the contribution of one or several other isotope fractionation processes. For a porous system with very slow air renewal rate, one can assume quasi-equilibrium conditions to control the isotope fractionation evolution in the soil air immediately surrounding the residual NAPL. In contrast, nonequilibrium conditions would control the isotope fractionation evolution during forced air flow circulation applied by specific remediation treatment systems. Therefore, the interplay of physical processes (i.e. phase transfer and diffusion) must be properly considered to correctly interpret CSIA field data. For instance, during NSZD of trapped NAPL in the unsaturated zone, NAPL vaporization leads to VOC mass input into soil gas and pore water. With small C-ε air-NAPL and insignificant C-ε air-water determined for BTX, progressive NAPL vaporization will not create significant change in isotope composition of gas-phase VOCs over time as long as the gas-phase VOC concentration in soil air remains in equilibrium with the NAPL (i.e. steady state condition) (Bouchard et al., 2008a;[START_REF] Bouchard | Analytical modelling of stable isotope fractionation of volatile organic compounds in the unsaturated zone[END_REF]. This can also be assumed although the occurrence of biodegradation as the kinetic rate of VOC mass input at the NAPL fringe may overwhelm the biodegradation rate, hence masking the isotopic effect of the latter as commonly observed for groundwater assessments within source zone areas. However, once the VOC mass in the NAPL has significantly decreased and equilibrium conditions can no longer be maintained, hence initiating a transient state condition, gas-phase diffusion process will lead isotope composition towards enriched values. For all petroleum hydrocarbons tested herein, the larger carbon isotope fractionation related to gas-phase diffusion (Table 2) will dominate over air-NAPL partitioning. This evolution from constant to gradually enriched isotope composition appears to be a more reliable metric than concentration analysis to support source vanishing. Given the small and narrow range of C-ε air-NAPL values determined for petroleum hydrocarbons herein, similar enrichment trends can be expected for other petroleum hydrocarbons such as ethylbenzene and trimethylbenzene, hence allowing additional compounds to be assessed.

For hydrogen, with inverse H-ε air-NAPL and normal H-ε air-water values determined for BTX (Table 3), the interplay between air-NAPL, air-water and gas-phase diffusion during steady and transient state conditions should be further investigated to confidently predict the direction and the magnitude of the isotope change.

For remediation techniques focusing on physical mass removal process such as SVE systems, the airliquid isotope effects can be exploited to monitor the progress and the limitations of the treatment.

Contrasting with NSZD, the isotope composition in this case will evolve as for an open system (i.e.

non-equilibrium conditions). During non-equilibrium conditions, not only that the diffusive isotope effect is additive to air-liquid isotope effect, but a number of studies have previously described that the expression of the diffusive isotope effect is impacted by the air volume renewal rate (Bouchard et al., 2008a;Bouchard et al., 2008b;Höhener et al., 2008;[START_REF] Kuder | Effects of Volatilization on Carbon and Hydrogen Isotope Ratios of MTBE[END_REF]Julien et al., 2015b;Bouchard et al., 2017a;[START_REF] Zamane | Multistep partitioning causes significant stable carbon and hydrogen isotope effects during volatilization of toluene and propan-2-ol from unsaturated sandy aquifer sediment[END_REF]. In cases where biodegradation occurs during the VOC transit through the unsaturated soil (as for petroleum hydrocarbons), this third process will also need to be considered to appropriately interpret isotopic trends. Due to those many uncertainties, the mass removal process is best characterized with the use of two elements (i.e. dual-isotope assessment) [START_REF] Kuder | Effects of Volatilization on Carbon and Hydrogen Isotope Ratios of MTBE[END_REF]Bouchard et al., 2017a). To appreciate the additive isotope effects on VOCs studied herein, enrichment factors related to gas-phase diffusion and biodegradation under aerobic conditions are reported in Table 2 and3, respectively for carbon and hydrogen. For carbon, the diffusion effect will systematically mask both the air-NAPL and air-water partitioning effects for every petroleum hydrocarbon tested, leading to carbon isotope enrichment (as biodegradation does). For hydrogen in contrast, the air-NAPL partitioning is the only process leading to significant hydrogen isotope depletion. Thorough combined interpretation of the carbon and hydrogen isotope evolution pattern over time will therefore indicate the controlling mass-removal process.

TGDE and isotope fractionation

Isotope fractionationcaused by air-TGDE partitioning

Despite a single equilibration step, C-ε air-TGDE values determined for air-TGDE partitioning (Table 4) can be directly compared to ε values derived by multistep equilibration experiments based on equation 4.Accordingly, the lack of significant carbon isotope fractionation observed for benzene, toluene and both xylenes during air-TGDE partitioning is akin to inconsistent carbon isotope fractionation observed for the same compounds during air-water partitioning and also to the lack of significant carbon isotope fractionation previously reported for benzene during similar testing with TGDE (Bouchard et al., 2017b). These non-significant carbon isotope fractionations observed for BTX compounds during air-TGDE partitioning underline minor impact for phase transfer process, and where the prevailing partitioning forces would be more comparable to water than neat compounds.

The significant fractionation obtained for ethylbenzene, in contradiction to the other 4 aromatic compounds tested, are counter intuitive. Additional evaluations are needed to understand this distinctive behavior. In contrast to aromatic compounds, the phase transfer process involving aliphatic and chlorinated compounds generated significant isotope fractionation. The global set of chlorinated compounds showed isotope fractionation generally of larger magnitude, with chlorinated ethane compounds more likely to generate larger fractionation compared to chlorinated ethene compounds (Table 4). The lack of available works assessing isotope fractionation of aliphatic and chlorinated compounds during air-water and air-NAPL partitioning, however, limits the comparison and previously reported (0.7 ‰) (Bouchard et al., 2017b) are in the range of reported C-ε air-NAPL values (ranging from 0.4 to 1.0 ‰), and slightly larger than the reported C-ε air-water range values (0.4 to 0.7 ‰) (Table S-1 in Supplementary Material). The result comparison for different compounds outlines some partitioning specificities. Overall, this polar aprotic solvent with multiple ether oxygen atom functional groups generates inverse carbon isotope effect as for water and NAPL, with magnitude of isotope fractionation being larger for chlorinated compounds compared to aromatic and aliphatic compounds. Once more, the degree of H saturation of the molecules and the presence of chlorine atoms in chlorinated compounds seem to be responsible for the various isotope fractionation magnitudes observed for those three different types of compounds.

For hydrogen, no clear molecular structural trend can be outlined when comparing compounds expressing no isotope fractionation (benzene, ethylbenzene, m,p-xylene, n-hexane and n-octane) with those undergoing isotope fractionation (toluene, o-xylene and cyclopentane) during air-TGDE partitioning. Nonetheless, the inverse isotope fractionation observed for aromatic and aliphatic compounds during air-TGDE partitioning, when significant, is analogous to air-NAPL vaporization, and is contrasting with the normal isotope fractionation observed for air-water partitioning. The magnitude of H-ε air-TGDE values determined for toluene and cyclopentane are relatively in the same range or lower than for NAPL vaporization, hence suggesting that the vibrational forces out weighting the motion forces in TGDE are similar to the air-NAPL system, and that functional groups of TGDE act on those compounds differently than do water molecules. In this regard, influence of different functional groups causing isotope fractionation was recently investigated using benzene and toluene as tested compounds [START_REF] Imfeld | Carbon and hydrogen isotope fractionation of benzene and toluene during hydrophobic sorption in multistep batch experiments[END_REF]. The latter study demonstrated the occurrence of isotope fractionation for specific functional groups represented by a subset of different organic solvents. For instance, 1-octanol (hydroxyl functional group with hydrogen-bridging interaction) led to significant inverse carbon and hydrogen isotope fractionation for benzene. However, as their experimental setup involved solute partitioning into two liquids (solvent and water), the additional hydrophobic factor impacting the isotope fractionation impedes direct ε comparison with our study. Finally, the larger H-ε air-TGDE value determined for o-xylene compared to the other aromatic compounds is prominent. Additional evaluations are needed to understand this distinctive behavior.

TGDE and gas-phase VOC sampling

Gas-phase sampling process: an innovative solvent-based method has been recently developed to perform CSIA on VOCs collected in the gas-phase [START_REF] Bouchard | δ 13 C and δ 37 Cl on Gas-Phase TCE for Source Identification Investigation -Innovative Solvent-Based Sampling Method[END_REF]. The sampling method consists in pulling the ambient air through a solvent via an adapted sampling device, hence relying on the VOC affinity with the solvent to accumulate (by dissolution) during the sampling process. To evaluate TCE dissolution efficiency and the potential for isotope fractionation during the process, a gas-phase sampling event was mimicked at the laboratory scale (see Bouchard et al. (2017b) for further experimental details). While the measured dissolved TCE concentrations in TGDE over time followed the theoretical expectation (equation 6), no δ 13 C evolution simulation was attempted to reproduce the measured isotope values. The equation 6 and C-ε air-TGDE were used herein to scrutinize the potential carbon isotope fractionation caused during the sampling process and to reproduce the isotope values measured over the 3 mimicked gas-phase sampling events. The calculations made use of two TCE isotopologues ( 13 C-TCE and 12 C-TCE) as described in section 2.4. Both C-ε air-TGDE values available (0.7 ‰ and 1.0 ‰) were sequentially implemented to evaluate the sensitivity of the parameter. Table 5 summarizes the values used for 13 C-TCE and 12 C-TCE isotopologues for the calculations, as well as the fixed parameters. The simulated dissolved concentration and δ 13 C results obtained for three different gas-phase TCE concentrations (21, 79 and 167 μg/m 3 ) over a sampling duration of t = 50h are presented on Figure 6.

The simulated concentrations indicate a non-linear TCE increase in TGDE during the sampling process. The steady state is reached (i.e. saturation condition) within 10h for the smallest gas-phase concentration (figure 6a, 21 μg/m 3 ), while a quasi-steady state is reached around t = 50h for gasphase concentration of 79 μg/m 3 (figure 6b), and a transient state is still observed at t=50h for the gas-phase concentration of 167 μg/m 3 (Figure 6c). Note that the difference in concentration evolution is due to different sampling flow rates used (Table 5), and not the gas-phase concentration.

During the sampling event, the isotopic composition of dissolved TCE evolved from -30.30 ‰ (equivalent to the gas-phase TCE composition) to a maximum depleted value of -30.98 ‰ (using Cε air-TGDE = 0.7 ‰) and -31.25 ‰ (using C-ε air-TGDE = 1.0 ‰) when saturation conditions are reached (Figure 6A). At early sampling phase, the higher solubility of 12 C-TCE is not yet apparent, hence the dissolved TCE isotope composition was reflecting the gaseous TCE isotope composition. With time, the higher solubility of 12 C-TCE eventually disrupts the initial 13 C-TCE / 12 C-TCE mass proportion, which leads to a gradual depleting isotope trend. The shift of 0.68 ‰ and 0.95 ‰ observed at saturation conditions compared to the source signal (Figure 6A) is respectively equivalent to the Cε air-TGDE of 0.7‰ and 1.0 ‰ experimentally determined (Table 4). Moreover, this slight isotopic depletion trend provided by the analytical solution was able to reproduce the measured laboratory values, validating the impact of different solubility coefficient for the two distinct TCE isotopologues.

While laboratory results for gas-phase TCE at 21 μg/m 3 (Figure 6A) and 167 μg/m 3 (Figure 6C) are mostly contained within the variation expressed by the two different C-ε air-TGDE values, the laboratory results for gas-phase TCE at 79 μg/m 3 (Figure 6B) showed good fit only at later time (quasi-steady state). This can perhaps be related to a gas leak in the system delivering less TCE than expected.

According to these isotopic simulations, sampling gas phase VOCs using TGDE (or any other solvent)

will create an isotopic shift that can be predicted by the ε air-TGDE value. Based on ε air-TGDE values reported in Table 4 for the tested VOCs, no significant carbon isotope shift is expected for BTX, aliphatic compounds (n-octane, n-hexane, cyclopentane), MTBE, PCE and cis-DCE, no significant hydrogen isotope shift is expected for B, E, m,p-X, n-hexane and n-octane, and lastly no significant chlorine isotopic shift for TCE, as respective ε air-TGDE value is either not detectable or within the common analytical uncertainty of 0.5 ‰ (for C and Cl) and 5 ‰ (for H). However, carbon isotope measurements for ethylbenzene, TCE, 1,1,2-TCA and 1,2-DCA, and hydrogen isotope measurement for toluene, o-xylene and cyclopentane will request an adjustment for sampling conducted until the saturation condition is reached. In this case, the equivalence of the ε air-TGDE value has to be added to provide a more positive final δ 13 C composition (or more negative in the case of ethylbenzene).

Post sampling event: An additional simulation was further carried out to evaluate the impact of repeated headspace volume exchange potentially occurring during sample handling and storage on the isotope composition of the dissolved VOCs. This evaluation made use of equation 11 to calculate the related hydrogen isotopic shift caused by multi equilibrium steps using either TGDE or water as solvent. Between each equilibrium step, a complete headspace renewal with fresh air was considered. For the evaluation purpose, toluene was the modeled compounds as results of the airwater and air-TGDE partitioning experiments performed in the laboratory led to significant hydrogen isotope fractionation. In addition, the dataset collected during the air-water partitioning experiment can be used as reference to validate the calculations. Table 6 summarizes the parameters and coefficients used for those two air-liquid partitioning evaluations. Changes in hydrogen isotope composition of dissolved toluene caused by 12 equilibrium steps with water or TGDE are shown on Figure 7. For the air-water partitioning simulation, the equation reproduced well the isotopic trend observed with the laboratory experiment, to ultimately predict a significant hydrogen shift of 11.8 ‰ after 12 equilibration steps. For the air-TGDE partitioning simulation, a shift of 0.03 ‰ can be expected for the hydrogen isotope composition of dissolved toluene dissolved after proceeding to 12 equilibration steps. Compared to a common uncertainty error of 5 ‰ for hydrogen analysis, this shift remains not significant. This negligible isotopic impact is explained by the strong affinity of toluene with TGDE, providing a very small air-TGDE partitioning coefficient (Table 6). Upon equilibrium, a mass fraction of 99.97% of toluene is expected to be in TGDE, thus leaving a small 0.03% mass fraction in the gas-phase. This very small mass fraction of gaseous toluene lost by each equilibrium step is not sufficient to significantly impact the isotope signature of toluene dissolved in TGDE, although several multiple equilibrium steps are carried out.

This is in agreement with [START_REF] Bouchard | δ 13 C and δ 37 Cl on Gas-Phase TCE for Source Identification Investigation -Innovative Solvent-Based Sampling Method[END_REF] reporting no significant change in the carbon isotope composition of TCE after 12 months of storage in methanol. Therefore, although carbon and hydrogen isotope fractionation have been observed for diverse VOCs during the air-TGDE partitioning process, no further impacts on the isotopic signature of dissolved VOCs is expected once the sampling process is ended. This can be assumed for every compound with similar low range of air-TGDE partitioning coefficients than toluene.

Conclusion

Several types of laboratory experiments were conducted in the present study to evaluate isotope fractionation caused by phase transfer process for a selection of common environmental contaminants, with the general objective being to contribute in expanding the use of CSIA as an assessment tool for gas-phase studies. For this purpose, the occurrence of isotope fractionation related to NAPL vaporization and VOC volatilization from different liquids (water or TGDE) was investigated through closed system experimental setups. In contrast to open system, conducting stepwise VOC mass removal from a closed system setup insures the isolation of the partitioning process from other potential physical process. A selection of aromatic, aliphatic, fuel oxygenate and chlorinated compounds was evaluated for carbon and hydrogen isotope fractionation. NAPL vaporization consistently indicated a preferential volatility for molecules including a heavy isotope, either 13 C or 2 H isotope, for all tested VOCs. The magnitude of the carbon isotope enrichment was small and relatively uniform among the selected petroleum hydrocarbons, and globally smaller compared to chlorinated compounds. The magnitude of the hydrogen isotope enrichment was more substantial and distinctive among petroleum hydrocarbons, but still globally smaller compared to chlorinated compounds. The carbon and hydrogen isotope fractionation pattern, evaluated through the Λ value, was found to differ between aromatic, aliphatic and fuel oxygenate compounds.

Furthermore, during VOC volatilization from the water, the partitioning process led to no significant carbon isotope fractionation for aromatic compounds. These observations for aromatic compounds contrast with significant fractionation observed for MTBE and the reported isotope fractionation for chlorinated compounds (PCE and TCE), underlying for the latter three compounds a higher volatility for molecules including a heavy carbon isotope. In contrast, for hydrogen, volatilization of BTX compounds from water consistently created a normal isotope fractionation, translating into a preferential solubility for molecules including the heavy hydrogen isotope. The numerous isotope enrichment factors derived in this study relative to NAPL vaporization and air-water partitioning process provide the possibility to expand the application of CSIA to a broader range of common environmental contaminants in view to assess their fate in the unsaturated zone, either passively attenuating (for instance, to document a natural source zone depletion in the unsaturated zone) or actively removed (for instance, to assess the performance of a remediation treatment). The second goal of this study was also achieved by quantifying carbon and hydrogen isotope enrichment factors related to air-TGDE partitioning for a subset of VOCs. For carbon, most of the aromatic compounds tested led to no significant isotope fractionation (except ethylbenzene), whereas MTBE, aliphatic and chlorinated compounds led to significant enrichment, underlying potential for higher volatility of molecules including a heavy isotope similarly to progressive NAPL vaporization. The carbon isotope composition of chlorinated compounds was found to be more affected than petroleum hydrocarbons by air-TGDE partitioning. For hydrogen, selected aromatic and aliphatic compounds showed no significant enrichment, except for toluene, o-xylene and cyclopentane, which showed significant enrichment. When significant, both isotopes underlined the potential for higher volatility of molecules including a heavy isotope similarly to progressive NAPL vaporization. The impact of isotope fractionation related to air-TGDE partitioning during a sampling event using TGDE as a sink matrix to

  as described in Aelion et al. (2010), using 28,8 g/mol for air mass. ** In Aelion et al. (2010), if not specified. a Dorer et al. (2014).

  with air-TGDE. For PCE, the C-ε air-TGDE value determined (0.4  0.2 ‰) is in the range of the C-ε air-water value reported by Jeannottat and Hunkeler (2013) (0.46  0.04 ‰), although no air-NAPL partitioning values for PCE are available for comparison. For TCE, the C-ε air-TGDE values determined (1.0  0.2 ‰)

Figure 1 :

 1 Figure 1: Carbon isotope fractionation during stepwise air-NAPL vaporization for selected compounds. The change in carbon isotope ratio is plotted as function of the remaining mass (m/m0) in the Ln scale. The bulk slope and the 95% confidence interval (ci) were determined using all plotted data (triplicate experiments). NAPL designates the neat liquid of each compound.

Figure 3 :

 3 Figure 3: Plot of H-ε air-NAPL as function of C-ε air-NAPL measured for monoaromatic (BTo-X) aliphatic (noctane, isooctane and cyclopentane) and fuel oxygenate (MTBE) compounds caused by air-NAPL vaporization. The Λ values reported represent H-ε / C-ε ratios.

Figure 4 :

 4 Figure4: Carbon isotope fractionation during stepwise air-water partitioning for selected compounds. The change in carbon isotope ratio is plotted as function of the remaining mass (m/m0) in the Ln scale. The bulk slope (black line) and the 95 % confidence interval (ci) were determined using all plotted data (triplicate experiments), except for MTBE (duplicate experiments). Replicatespecific slope is represented by a red line. ns: not significant.

Figure 5 :

 5 Figure 5: Hydrogen isotope fractionation during stepwise air-water partitioning for selected compounds. The change in hydrogen isotope ratio is plotted as function of the remaining mass (m/m0) in the Ln scale. The bulk slope and the 95 % confidence interval (ci) were determined using all plotted data (triplicate experiments), except for MTBE (duplicate experiments).

Figure 6 :

 6 Figure6: Evolution of concentrations (black line) and δ 13 C composition (blue and red lines, considering different isotope enrichment factors ε air-TGDE ) for TCE dissolved in TGDE during 3 simulated gas-phase sampling events using TCE gas-phase concentration of 21 μg/m 3 (A), 79 μg/m 3 (B), and 167 μg/m 3 (C), and respective gas flow rate of 800, 400 and 200 mL/minute. Laboratory data fromBouchard et al. (2017b)

Table 1 : Volume of NAPL added per 20 mL vial containing TGDE (1 000 L) or without TGDE, for each VOC tested. Compound With TGDE (L) Without TGDE (L) For 13 C analysis For 2 H analysis For 13 C analysis For 2 H analysis

 1

	Benzene	20	158	0.5	0.5
	Toluene	34	269	0.5	0.5
	Ethylbenzene	115	462	1	1
	m,p-xylene	230	230	0.5	0.5
	o-xylene	115	400	0.5	2
	cyclopentane	4	7	0.7	1
	n-hexane	5	7	0.6	1
	n-octane	40	8	0.6	1
	MTBE	230	-

Table 2 :

 2 Carbon enrichment factors (C-ε air-NAPL ) related to stepwise NAPL vaporization and air-water partitioning process in closed system experimental setups (measured in the current study) and related to gas-phase diffusion and biodegradation (literature data) for selected aromatic, aliphatic, oxygenate and chlorinated compounds.

		Air-NAPL	Air-water	Gas-phase	Aerobic
	Compound	partitioning	partitioning	diffusion*	biodegradation**
			ε (‰)
	Benzene	0.18 ± 0.03	n.s. to 0.09 ± 0.05	-1.71	-0.5 to-3.65
	Toluene	0.22 ±0.04	n.s. to 0.17 ± 0.09	-1.28	n.d.to -3.3
	Ethylbenzene	--	--	-1.00	-0.4 to -0.6 a
	m,p-Xylene	--	--	-1.00	-0.6 to-1.7 (m-X)
	o-xylene	0.24 ± 0.04	n.s.	-1.00	--
	n-octane	0.21 ± 0.03	--	-0.88	-0.7 to -1.1
	cyclopentane	0.14 ± 0.04	--	-2.05	--
	isooctane	0.17 ± 0.02	--	-0.88	--
	MTBE	0.38 ± 0.05	0.22 ± 0.06	-1.42	-1.5 to-2.4
	PCE	--	--	-0.45	--
	TCE	--	--	-0.69	-11.6±4.1 b to -18.2 c
	1,1,2-TCA	--	--	-0.66	--
	n.s.= not significant. * calculated as described in Aelion et al. (2010), using 28,8 g/mol for air mass. **
	In Aelion et al. (2010), if not specified.

a Dorer et al. (2014), b Clingenpeel et al. (2012), c

Table 4 :

 4 C and H enrichment factors (ε air-TGDE ) related to air-TGDE partitioning process for selected aromatic, aliphatic, oxygenate and chlorinated compounds.

						Carbon						Hydrogen
	Compound			13 C (‰)		ε (‰)					2 H (‰)	ε (‰)
		pure	std with TGDE std	Thiswork literature pure std with TGDE std Thiswork
	Benzene	-24.3	0.2	-24.1	0.1 0.2 ± 0.2	n.s.	a	-52	1	-50	2	2 ± 3
	Toluene	-26.4	0.2	-26.3	0.1 0.1 ± 0.3			-28	2	-22	2	6 ± 4
	Ethylbenzene	-27.0	0.1	-27.6	0.1 -0.6 ± 02			-13	2	-9	2	4 ± 4
	m,p-Xylene	-25.1	0.2	-25.2	0.1 -0.1 ± 0.3			-49	1	-47	1	2 ± 2
	o-xylene	-29.2	0.1	-29.1	0.1 0.1 ± 0.2			-138	1	-114	1	24 ± 2
	n-octane	-49.6	0.1	-49.3	0.1 0.3 ± 0.2			-213	3	-212	2	1 ± 6
	n-hexane	-27.0	0.2	-26.6	0.1 0.4 ± 0.2			-101	2	-99	1	2 ± 3
	cyclopentane	-22.6	0.1	-22.2	0.1 0.4 ± 0.2			-22	1	-16	1	6 ± 2
	MTBE	-27.3	0.1	-27.7	0.1 0.4 ± 0.2			--	--	--	--	--
	PCE	-26.5	0.1	-26.1	0.10 0

Table 5 :

 5 Initial gas phase concentration (Cg) and air-TGDE partitioning coefficient (K) specific to 13 C-TCE and 12 C-TCE isotopologues, TCE initial isotopic composition (δ 13 C), air flow rate (F) and volume of solvent (V) used for the analytical simulation.

			Simulation 1	Simulation 2	Simulation 3
	Parameter	12 C-TCE		13 C-TCE	12 C-TCE		13 C-TCE	12 C-TCE		13 C-TCE
	Cg (ug/m3)	20.7736		0.2264	78.1484		0.8516	165.1999		1.8001
	K (unitless)	0.0003400	a	0.0003402	0.0003400	a	0.0003402	0.0003400	a	0.0003402
	with ε air-TGDE = 0.7‰ K (unitless)	0.0003400	a	0.0003403	0.0003400	a	0.0003403	0.0003400	a	0.0003403
	with ε air-TGDE =1.0‰
	F (mL/minute)		800			200			100
	V (mL)			35			35			35
	Initial δ	13 C (‰)		-30.3		-30.3			-30.3
	a(Bouchard et al., 2017b)

Table 6 :

 6 Parameters used to calculate the hydrogen isotope shift expected for toluene caused by multistep air-water or air-TGDE partitioning process (equilibrium conditions).

	Parameter	Coefficient	Unit
	H-ε air-TGDE	6*	‰
	H-ε air-water	-5**	‰
	C 0	1	g/L
	Air-water partitioning (Henry coefficient, at 25 °C)	0.244 a	unitless
	Air-TGDE partitioning (K, at 25 °C)	0.000344 b	unitless
	Vial volume	40	mL
	Liquid volume	35	mL

*This study. ** Value obtained for replicate 2, Figure

5

.

a

[START_REF] Mackay | Handbook of Physical-Chemical Properties and Environmental Fate for Organic Chemicals[END_REF]

.

b

[START_REF] Huybrechts | Evaluation of tetraglyme for the enrichment and analysis of volatile organic compounds in air[END_REF]

Acknowledgments

The authors are grateful to the former Chevron Energy Technology Company (now Chevron Technical Center) for the financial support needed to conduct laboratory experiments related to the air-NAPL and air-water partitioning investigation.

collect gas-phase VOCs was further addressed by means of analytical simulations. The simulation results indicated an isotopic shift equivalent to the enrichment factors, once the VOC concentration equilibrium between the air and TGDE is reached. Therefore, the need for an isotopic correction post sampling event only applies to VOCs having an enrichment factor larger than the GC-IRMS analytical uncertainty. The quantification of enrichment factors by the current investigations and the knowledge gained through analytical simulations support the field application of the solvent-based sampling method specific to CSIA. Although a broad range of common environmental contaminants were evaluated for carbon and hydrogen isotopes, potential for chlorine isotope fractionation remains to be evaluated for chlorinated compounds. S1+S2, Is available.

Supplementary Material: Description of analytical techniques, Tables

Figure 2: Hydrogen isotope fractionation during stepwise air-NAPL vaporization for selected compounds. The change in hydrogen isotope ratio is plotted as function of the remaining mass (m/m0) in the Ln scale. The bulk slope and the 95% confidence interval (ci) were determined using all plotted data (triplicate experiments). NAPL designates the neat liquid of each compound.