Chicgoua Noubactep

Sabine Caré

Richard Crane

Nanoscale metallic iron for environmental remediation: prospects and limitations

Keywords: Environmental remediation, Material reactivity, Nanoscale iron, Roll-front, Zerovalent iron

The amendment of the subsurface with nanoscale metallic iron particles (nano-Fe 0 ) has been discussed in the literature as an efficient in-situ technology for groundwater remediation.

However, the introduction of this technology was controversial and its efficiency has never been univocally established. This unsatisfying situation has motivated this communication whose objective was a comprehensive discussion of the intrinsic reactivity of nano-Fe 0 based on the state-of-the art knowledge on the mechanism of contaminant removal by Fe 0 and a mathematical modelling. It is showed that due to limitations of the mass transfer of nano-Fe 0 to contaminants, available concepts can not explain the success of nano-Fe 0 injection for insitu groundwater remediation. It is recommended to test the possibility of introducing nano-Fe 0 to initiate the formation of roll-fronts which propagation would induce the reductive transformation of both dissolved and adsorbed contaminants. Within a roll-front, Fe II from nano-Fe 0 is the reducing agent for contaminants. Fe II is recycled by biotic or abiotic Fe III reduction. While the roll-front concept could explain the success of already implemented reaction zones, more research is needed for a science-based recommendation of nano-Fe 0 for subsurface treatment by roll-fronts.

Introduction

The development of new methods and materials for environmental remediation is a real challenge for the scientific community. Such technologies will only be adopted by industry if they can exhibit marked improvements in efficiency, affordability or eco-compatibility compared to conventional techniques. The use of metallic iron (Fe 0 ) in subsurface reactive permeable barriers has been identified as such a technology [START_REF] Gillham | Enhanced degradation of halogenated aliphatics by zerovalent iron[END_REF][START_REF] Matheson | Reductive dehalogenation of chlorinated methanes by iron metal[END_REF][START_REF] Blowes | In-situ remediation of Cr(VI)-contaminated groundwater using permeable reactive walls: laboratory studies[END_REF][START_REF] O'hannesin | Long-term performance of an in situ "iron wall" for remediation of VOCs[END_REF]. Since this discovery almost 20 years ago, extensive research of Fe 0 /H 2 O system has been performed in an attempt to understand the controlling mechanisms behind the remediation of redox-amenable contaminant species using Fe 0 -based materials [START_REF] Scherer | Chemistry and microbiology of permeable reactive barriers for in situ groundwater clean up[END_REF][START_REF] Henderson | Long-term performance of zero-valent iron permeable reactive barriers: a critical review[END_REF][START_REF] Bartzas | Solid phase studies and geochemical modelling of low-cost permeable reactive barriers[END_REF][START_REF] Li | Evaluation of five strategies to limit the impact of fouling in permeable reactive barriers[END_REF][START_REF] Noubactep | Dimensioning metallic iron beds for efficient contaminant removal[END_REF][START_REF] Kim | Inactivation of escherichia coli by nanoparticulate zerovalent iron and ferrous ion[END_REF][START_REF] Comba | A comparison between field applications of nano-, micro-, and millimetric zero-valent iron for the remediation of contaminated aquifers[END_REF][START_REF] Gheju | Hexavalent chromium reduction with zero-valent iron (ZVI) in aquatic systems[END_REF][START_REF] Jeen | Predictions of long-term performance of granular iron permeable reactive barriers: Field-scale evaluation[END_REF][START_REF] Noubactep | Metallic iron for safe drinking water production[END_REF]. Two different tools are commonly used to optimise the efficiency of Fe 0 for aqueous contaminant removal: (i) reducing the particle size of Fe 0 down to the nanoscale (nano-Fe 0 ) [START_REF] Wang | Synthesizing nanoscale iron particles for rapid and complete dechlorination of TCE and PCBs[END_REF][START_REF] Ponder | Remediation of Cr(VI) and Pb(II) aqueous solutions using supported, nanoscale zero-valent iron[END_REF], and (ii) using bimetallic systems [START_REF] Muftikian | A method for the rapid dechlorination of low molecular weight chlorinated hydrocarbons in water[END_REF][START_REF] Korte | Field application of palladized iron for the dechlorination of trichloroethene[END_REF]. In recent years there has been considerable interest into combining the two methods [START_REF] Schrick | Hydrodechlorination of trichloroethylene to hydrocarbons using bimetallic nickel-iron nanoparticles[END_REF][START_REF] Karn | Nanotechnology and in situ remediation: A review of the benefits and potential risks[END_REF][START_REF] Nagpal | Reductive dechlorination of ?-hexachlorocyclohexane using Fe-Pd bimetallic nanoparticles[END_REF][START_REF] Chen | Renewable hydrogen generation by bimetallic zerovalent iron nanoparticles[END_REF][START_REF] Hosseini | Nitrate reduction by nano-Fe/Cu particles in packed column[END_REF].

Since the original proof of concept study into the application of nano-Fe 0 for water treatment at Lehigh University, USA [START_REF] Wang | Synthesizing nanoscale iron particles for rapid and complete dechlorination of TCE and PCBs[END_REF], research within this field has boomed. On April 23 th 2011, a search at "Science Direct" using key words "nanoscale" and "zerovalent iron" yielded 208 peer-reviewed articles in 6 selected journals (Table 1). The same search at "Environmental Science and Technology" resulted in 157 articles. According to Table 1, [START_REF] Boparai | Kinetics and thermodynamics of cadmium ion removal by adsorption onto nano zerovalent iron particles[END_REF] articles have already been published in the first quarter of 2011 in the 7 selected journals. This clearly demonstrates the interest within academia for this technology.

In recent years, several review articles and critical views on nano-Fe 0 for environmental remediation have been published [START_REF] Karn | Nanotechnology and in situ remediation: A review of the benefits and potential risks[END_REF][START_REF] Zhang | Treatment of chlorinated organic contaminants with nanoscale bimetallic particles[END_REF][START_REF] Gillham ; Evan | Discussion of Papers/Discussion of nano-scale iron for dehalogenation[END_REF][START_REF] Zhang | Nanoscale iron particles for environmental remediation: an overview[END_REF][START_REF] Li | Zero-valent iron nanoparticles for abatement of environmental pollutants: materials and engineering aspects[END_REF][START_REF] Macé | Controlling groundwater VOCs: do nanoscale ZVI particles have any advantages over microscale ZVI or BNP?[END_REF][START_REF] Macé | Nanotechnology and groundwater remediation: A step forward in technology understanding[END_REF][START_REF] Tratnyek | Nanotechnologies for environmental cleanup[END_REF][START_REF] Pradeep | Noble metal nanoparticles for water purification: A critical review[END_REF][START_REF] Agarwal | Environmental sciences application of nanotechnology in the remediation of contaminated groundwater: A short review[END_REF][START_REF] Müller | Nano zero valent iron -THE solution for water and soil remediation?[END_REF][START_REF] Noubactep | On nanoscale metallic iron for groundwater remediation[END_REF][START_REF] Cullen | Assessing the impact of nano-and micro-scale zerovalent iron particles on soil microbial activities: Particle reactivity interferes with assay conditions and interpretation of genuine microbial effects[END_REF][START_REF] Noubactep | Comment on "Reductive dechlorination of g-hexachloro-cyclohexane using Fe-Pd bimetallic nanoparticles[END_REF][START_REF] Peralta-Videa | Nanomaterials and the environment: A review for the biennium 2008-2010[END_REF][START_REF] Shi | Effects of nano zero-valent iron on oxidationreduction potential[END_REF][START_REF] Truex | Injection of zero-valent iron into an unconfined aquifer using shear-thinning fluids[END_REF][START_REF] Truex | Demonstration of combined zero-valent iron and electrical resistance heating for in situ trichloroethene remediation[END_REF]. However, the original discussion on the suitability of nano-Fe 0 for in-situ field applications [START_REF] Gillham ; Evan | Discussion of Papers/Discussion of nano-scale iron for dehalogenation[END_REF] has not been satisfactorily addressed [START_REF] Macé | Controlling groundwater VOCs: do nanoscale ZVI particles have any advantages over microscale ZVI or BNP?[END_REF][START_REF] Noubactep | Comment on "Reductive dechlorination of g-hexachloro-cyclohexane using Fe-Pd bimetallic nanoparticles[END_REF]. Moreover, a recent comparison between field applications of Fe 0 of different particle sizes (nm, µm, and mm) for field applications has clearly demonstrated the superiority of mm-Fe 0 (average efficacy 97 %) [START_REF] Comba | A comparison between field applications of nano-, micro-, and millimetric zero-valent iron for the remediation of contaminated aquifers[END_REF]. The decreasing order of reactivity was mm-Fe 0 (97 %) > µm-Fe 0 (91 %) > nano-Fe 0 (65 %). Expectably, the lower efficiency of nano-Fe 0 is due their high reactivity [START_REF] Gillham ; Evan | Discussion of Papers/Discussion of nano-scale iron for dehalogenation[END_REF][START_REF] Noubactep | On nanoscale metallic iron for groundwater remediation[END_REF]. Therefore, the question arises on the fundamental necessity to further increase the reactivity of nano-Fe 0 by using a noble metal combination.

The problem

Nano-Fe 0 technology for environmental remediation was introduced as an alternative to the conventional Fe 0 walls mostly for inaccessible aquifers [START_REF] Li | Zero-valent iron nanoparticles for abatement of environmental pollutants: materials and engineering aspects[END_REF][START_REF] Masciangioli | Environmental technologies at the Nanoscale[END_REF]. The very small particle size of nano-Fe 0 (1-100 nm) would allow the material to penetrate deep into soil networks [START_REF] Comba | A comparison between field applications of nano-, micro-, and millimetric zero-valent iron for the remediation of contaminated aquifers[END_REF][START_REF] Gheju | Hexavalent chromium reduction with zero-valent iron (ZVI) in aquatic systems[END_REF][START_REF] Karn | Nanotechnology and in situ remediation: A review of the benefits and potential risks[END_REF][START_REF] Truex | Injection of zero-valent iron into an unconfined aquifer using shear-thinning fluids[END_REF][START_REF] Truex | Demonstration of combined zero-valent iron and electrical resistance heating for in situ trichloroethene remediation[END_REF][START_REF] Ghauch | Antibiotic removal from water: Elimination of amoxicillin and ampicillin by microscale and nanoscale iron particles[END_REF].

Due to the exponential relationship between specific surface area (SSA) and radius (R = d/2) of a perfectly spherical object (SSA = 4πR 2 ), as a rule, a decrease in Fe 0 particle size increases the surface area per gram by up to 3 orders of magnitude [START_REF] Chen | Renewable hydrogen generation by bimetallic zerovalent iron nanoparticles[END_REF][START_REF] Macé | Nanotechnology and groundwater remediation: A step forward in technology understanding[END_REF]. In other words, the inverse relationship between Fe 0 particle size and reactivity is due to a greater density of reactive sites on the particle surface at smaller scale. The following three claims have been made with regard to the use of nano-Fe 0 for aqueous contaminant removal (ref. [START_REF] Gheju | Hexavalent chromium reduction with zero-valent iron (ZVI) in aquatic systems[END_REF] and ref. therein): (i) some aqueous contaminant species that have been proven as unsuccessful for remediation using µm-Fe 0 and mm-Fe 0 can be effectively removed using nano-Fe 0 , (ii) nano-Fe 0 can be used for more rapid degradation of contaminants, and (iii) the formation of some undesirable by-products during remediation using µm-Fe 0 and mm-Fe 0 can be avoided by using nano-Fe 0 .

Such processes whilst correct are all linked to the greater reactivity nano-Fe 0 possesses due to its size (reactive surface area). When performed in conditions without a large nano-Fe 0 stoichiometric excess, e.g. a system analogous to the environment, it may prove that such claims will be unfounded [START_REF] Nagpal | Reductive dechlorination of ?-hexachlorocyclohexane using Fe-Pd bimetallic nanoparticles[END_REF][START_REF] Noubactep | On nanoscale metallic iron for groundwater remediation[END_REF][START_REF] Noubactep | Comment on "Reductive dechlorination of g-hexachloro-cyclohexane using Fe-Pd bimetallic nanoparticles[END_REF][START_REF] Sakulchaicharoen | Enhanced stability and dechlorination activity of pre-synthesis stabilized nanoscale FePd particles[END_REF][START_REF] Nagpal | Reply to comment on "Reductive dechlorination of γ-hexachlorocyclohexane using Fe-Pd bimetallic nanoparticles[END_REF]].

An undisputed drawback with regards to the use of nano-Fe 0 for environmental applications is their strong tendency to aggregate and adhere to solid surfaces [START_REF] Comba | A comparison between field applications of nano-, micro-, and millimetric zero-valent iron for the remediation of contaminated aquifers[END_REF][START_REF] Gheju | Hexavalent chromium reduction with zero-valent iron (ZVI) in aquatic systems[END_REF][START_REF] Karn | Nanotechnology and in situ remediation: A review of the benefits and potential risks[END_REF][START_REF] Li | Zero-valent iron nanoparticles for abatement of environmental pollutants: materials and engineering aspects[END_REF][START_REF] Tratnyek | Nanotechnologies for environmental cleanup[END_REF][START_REF] Truex | Injection of zero-valent iron into an unconfined aquifer using shear-thinning fluids[END_REF][START_REF] Truex | Demonstration of combined zero-valent iron and electrical resistance heating for in situ trichloroethene remediation[END_REF][START_REF] Sakulchaicharoen | Enhanced stability and dechlorination activity of pre-synthesis stabilized nanoscale FePd particles[END_REF].

Karn et al. [START_REF] Karn | Nanotechnology and in situ remediation: A review of the benefits and potential risks[END_REF] listed some parameters that influence nano-Fe 0 adsorption onto soil and aquifer materials: (i) the surface chemistry of soil and Fe 0 particles, (ii) the groundwater chemistry (e.g., ionic strength, pH and presence of natural organic matter), and (iii) the hydrodynamic conditions (pore size, porosity, flow velocity and degree of mixing or turbulence). Several methods have been developed for the stabilization of nano-Fe 0 particles over the past decade and proven efficient to sustain the reactivity of nano-Fe 0 [START_REF] Comba | A comparison between field applications of nano-, micro-, and millimetric zero-valent iron for the remediation of contaminated aquifers[END_REF][START_REF] Gheju | Hexavalent chromium reduction with zero-valent iron (ZVI) in aquatic systems[END_REF][START_REF] Karn | Nanotechnology and in situ remediation: A review of the benefits and potential risks[END_REF][START_REF] Sakulchaicharoen | Enhanced stability and dechlorination activity of pre-synthesis stabilized nanoscale FePd particles[END_REF].

One factor that has been overlooked, however, is the impact volumetric expansion has on the mobility of (i) residual Fe 0 , (ii) primary corrosion products (Fe II and H 2 ) and contaminants.

The volume of any corrosion product (Fe hydroxide or oxide) is higher than that of the original metal (Fe 0 ). The ratio between the volume of expansive corrosion product and the volume of iron consumed in the corrosion process is called "rust expansion coefficient" (η) [START_REF] Anstice | Cover cracking as a function of bar corrosion: part Iexperimental test[END_REF][START_REF] Caré | Mechanical properties of the rust layer induced by impressed current method in reinforced mortar[END_REF][START_REF] Zhao | Composition and expansion coefficient of rust based on X-ray diffraction and thermal analysis[END_REF]. Volumetric corrosion products are likely to: (i) contribute to porosity loss, (ii) impact the retention of contaminants and transformation products, and (iii) increase the particle agglomeration.

Another area of heightened research is with regard to the determining the toxicity of nano-Fe 0 , with mixed results reported [START_REF] Gheju | Hexavalent chromium reduction with zero-valent iron (ZVI) in aquatic systems[END_REF][START_REF] Grieger | Environmental benefits and risks of zero-valent iron nanoparticles (nZVI) for in situ remediation: Risk mitigation or trade-off?[END_REF]. For example, Barnes et al. [START_REF] Barnes | The impact of zero-valent iron nanoparticles on a river water bacterial community[END_REF] reported minimal change to the structure of a river water community due to the addition of nano-Fe 0 , while Diao and Yao [START_REF] Diao | Use of zero-valent iron nanoparticles in inactivating microbes[END_REF] reported nano-Fe 0 particles as highly cytotoxic towards both gram-positive and gram-negative bacteria species.

While taking into account all known influencing parameters, the following seven features have to be systematically studied in order to optimise the general applicability of this technique [START_REF] Gheju | Hexavalent chromium reduction with zero-valent iron (ZVI) in aquatic systems[END_REF][START_REF] Karn | Nanotechnology and in situ remediation: A review of the benefits and potential risks[END_REF][START_REF] Tervonen | Risk-based classification system of nanomaterials[END_REF]: (i) mobility changes due to nano-Fe 0 volumetric expansion during corrosion, (ii) the bioavailability of Fe 0 and corrosion products (Fe II /Fe III species, H/H 2 ), (iii) the ecotoxicity of Fe 0 and its corrosion products, (iv) the bioaccumulation of Fe 0 and its corrosion products, (v) the translocation potential of nano-Fe 0 , (vi) the long-term reactivity of nano-Fe 0 particles, and (vii) the speciation, persistence and fate of contaminants and their transformation products. A major contributing factor to the latter point is that little is known (compared to permeable reactive barrier technologies) about the extent contaminants are removed via size exclusion using nano-Fe 0 .

Only when all seven "operational drivers" have been determined can the global community have full faith in the technology.

Objectives of the study

The present communication is focused on the "field persistence" or reactive "life span" of nano-Fe 0 particles. For in-situ applications a keen understanding of nano-Fe 0 reactive fate is essential for effective and prudent site clean-up. The knowledge of which is likely to largely underpin decisions as to the (i) the choice of material selected, (ii) the mechanism of application and, (iii) the strategy (if any) for repeated treatments.

In the current work a multidisciplinary approach is used to analyse the relationship between nano-Fe 0 reactivity and its performance for in-situ field applications. The discussion is based on the contemporary knowledge of the mechanism of aqueous contaminant removal by Fe 0 [START_REF] Noubactep | Processes of contaminant removal in "Fe 0 -H 2 O" systems revisited. The importance of co-precipitation[END_REF][START_REF]Noubactep A critical review on the mechanism of contaminant removal in Fe 0 -H 2 O systems[END_REF][START_REF] Noubactep | The fundamental mechanism of aqueous contaminant removal by metallic iron[END_REF]. Much of the impetus for this work has come from the work of Noubactep and Caré [START_REF] Noubactep | On nanoscale metallic iron for groundwater remediation[END_REF], who have challenged the concept that nano-Fe 0 is a strong reducing agent for contaminant reductive transformation.

Nanoscale metallic iron or environmental remediation

To date, nano-Fe 0 particles have been reported as largely successful for water and soil treatment [START_REF] Comba | A comparison between field applications of nano-, micro-, and millimetric zero-valent iron for the remediation of contaminated aquifers[END_REF][START_REF] Pradeep | Noble metal nanoparticles for water purification: A critical review[END_REF][START_REF] Agarwal | Environmental sciences application of nanotechnology in the remediation of contaminated groundwater: A short review[END_REF][START_REF] Litter | Possible treatments for arsenic removal in Latin American waters for human consumption[END_REF][START_REF] Crane | Magnetite and zero-valent iron nanoparticles for the remediation of uranium contaminated environmental water[END_REF]. A wide variety of redox-amenable organic and inorganic species and non-reducible species (e.g. Cd, Zn) have been efficiently treated. Similar to µm and mm-Fe 0 , adsorption is considered important only for non-reducible species [START_REF] Noubactep | Processes of contaminant removal in "Fe 0 -H 2 O" systems revisited. The importance of co-precipitation[END_REF][START_REF]Noubactep A critical review on the mechanism of contaminant removal in Fe 0 -H 2 O systems[END_REF][START_REF] Noubactep | The fundamental mechanism of aqueous contaminant removal by metallic iron[END_REF][START_REF] Celebi | A radiotracer study of the adsorption behavior of aqueous Ba 2+ ions on nanoparticles of zero-valent iron[END_REF][START_REF] Li | Sequestration of metal cations with zerovalent iron nanoparticles-a study with high resolution X-ray photoelectron spectroscopy (HR-XPS)[END_REF][START_REF] Boparai | Kinetics and thermodynamics of cadmium ion removal by adsorption onto nano zerovalent iron particles[END_REF][START_REF] Xiao | Excellent copper(II) removal using zero-valent iron nanoparticle -immobilized hybrid electrospun polymer nanofibrous mats[END_REF]. For example, Boparai et al. [START_REF] Boparai | Kinetics and thermodynamics of cadmium ion removal by adsorption onto nano zerovalent iron particles[END_REF] reported that heavy metals are either reduced (e.g. Cu 2+ , Ag 2+ ) at, or directly adsorbed (e.g. Zn 2+ , Cd 2+ ) onto the Fe 0 surface. They further argued that "the controlling mechanism is a function of the standard redox potential of the contaminant".

Recent work has however challenged this concept [START_REF] Noubactep | Comment on "Reductive dechlorination of g-hexachloro-cyclohexane using Fe-Pd bimetallic nanoparticles[END_REF][START_REF] Noubactep | The fundamental mechanism of aqueous contaminant removal by metallic iron[END_REF], which is explained below.

Contaminant reduction by nano-Fe 0

The chemical reaction between Fe 0 and redox-amenable aqueous species is considered to involve three steps: (i) direct electron transfer from Fe 0 at the metal surface or through a conductive oxide film on Fe 0 (direct reduction), (ii) catalyzed hydrogenolysis by the H/H 2 (indirect reduction mechanism 1), and (iii) reduction by Fe II species resulting from Fe 0 corrosion (indirect reduction mechanism 2). In this constellation, H 2 is supposed to result from H 2 O reduction during anoxic iron corrosion [START_REF] Chen | Renewable hydrogen generation by bimetallic zerovalent iron nanoparticles[END_REF][START_REF] Reardon | Anaerobic corrosion reaction kinetics of nanosized iron[END_REF]. However, evidence exists in the literature, e.g. Stratmann and Müller [START_REF] Stratmann | The mechanism of the oxygen reduction on rust-covered metal substrates[END_REF], that even under external oxic conditions, Fe 0 is oxidized by H 2 O (or more precisely by H + ) and O 2 by Fe II (Table 2). Despite the significant reaction rate exhibited by nano-Fe 0 due to its high surface area, such processes are considered to occur (discounting any quantum size effects) independent of particle size.

Table 2 summarizes the half reactions for the aqueous oxidation of Fe 0 under both anoxic and oxic conditions. Thermodynamically, the major cathodic reaction depends on the availability of molecular O 2 (E 0 = 0.81 V). In the absence of O 2 , Fe 0 is oxidized by H + (E 0 = 0.00 V). It can therefore be stated that the rate of Fe 0 oxidation is dictated by the concentration of dissolved O 2 , H + and H 2 O in proximity to Fe 0 surfaces. Le Chatelier's principle also states that the consumption of Fe II (via oxidation to Fe III ) will also result in an increase in Fe 0 oxidation.

The electrode potential of the redox couple Fe II /Fe 0 is -0.44 V, a value which is independent of the particle size (nm, µm or mm). The value -0.44 V is considered largely unchanged due to the presence of alloying materials (e.g. low alloy steel, bimetallic systems).

As a consequence, statements including "nano-Fe 0 are more reactive than µm-Fe 0 and mm-Fe 0 " are misleading; as the reactivity of Fe 0 (discounting quantum size effects), is independent of the particle size. Any enhanced reactivity reported is likely to be due to the significantly high surface area of nano-Fe 0 compared to other forms. A second statement "bimetallic nano-Fe 0 is more reactive that monometallic nano-Fe 0 " is also a qualitative statement, as the reactivity of the materials depends on numerous factors associated with the materials synthesis route and varies depending on the chemistry of the chosen alloying metal. Ideally, comparisons should be made versus standard reference materials using established standard experimental protocols [START_REF] Noubactep | Exploring the influence of operational parameters on the reactivity of elemental iron materials[END_REF], which once established, will significantly improve the design of future field applications.

Limitations of the nano-Fe 0 technology

The efficiency of nano-Fe 0 for aqueous contaminant reduction faces some key issues for insitu applications in porous media. These challenges include: (i) the strong tendency of aggregation/agglomeration, (ii) the rapid settlement on subsurface solid phases, (iii) the porosity and permeability loss of porous media [START_REF] Hosseini | Nitrate reduction by nano-Fe/Cu particles in packed column[END_REF][START_REF] Cullen | Assessing the impact of nano-and micro-scale zerovalent iron particles on soil microbial activities: Particle reactivity interferes with assay conditions and interpretation of genuine microbial effects[END_REF][START_REF] Behrens | Charging and aggregation properties of carboxyl latex particles: experiments versus DLVO theory[END_REF][START_REF] Dickinson | The application of zero-valent iron nanoparticles for the remediation of a uranium-contaminated waste effluent[END_REF]. Aggregation and settlement limit nano-Fe 0 transport through porous media. Porosity and permeability loss limit nano-Fe 0 transport to target contaminants. It was demonstrated that nano-Fe 0 may travel only a few centimetres in porous media from the injection position under typical groundwater conditions [START_REF] Comba | A comparison between field applications of nano-, micro-, and millimetric zero-valent iron for the remediation of contaminated aquifers[END_REF][START_REF] Gheju | Hexavalent chromium reduction with zero-valent iron (ZVI) in aquatic systems[END_REF][START_REF] Tratnyek | Nanotechnologies for environmental cleanup[END_REF][START_REF] Johnson | Mineral precipitation upgradient from a zero-valent iron permeable reactive barrier[END_REF]. Accordingly, recent efforts have been made to (i) increase the porosity of porous media, (ii) mechanically increase the distribution of nano-Fe 0 , and/or (iii) chemically modify nano-Fe 0 for improved aqueous mobility in porous networks.

2.3

Improving the efficiency of the nano-Fe 0 systems

Dispersion agents

Methods to improve the aqueous mobility of nano-Fe 0 have received the greatest research interest. It has been determined that the key to improving particle mobility is found in modifying their surface properties such that the nano-Fe 0 have significantly improved colloidal stability and a commensurate reduction in the likelihood of adherence to mineral surfaces. Several synthetic methods are now available to produce more mobile nano-Fe 0 .

Efficiently tested dispersants include anionic surface chargers (e.g. polyacrylic acid), nonionic surfactants, starch, and oil [START_REF] Hosseini | Nitrate reduction by nano-Fe/Cu particles in packed column[END_REF][START_REF] Wu | Chromium (VI) reduction in aqueous solutions by Fe 3 O 4 -stabilized Fe 0 nanoparticles[END_REF][START_REF] Fang | Degradation of the polybrominated diphenyl ethers by nanoscale zero-valent metallic particles prepared from steel pickling waste liquor[END_REF][START_REF] Lvl | Nitrate reduction using nanosized zero-valent iron supported by polystyrene resins: Role of surface functional groups[END_REF][START_REF] Tong | Reduction of nitrobenzene in groundwater by iron nanoparticles immobilized in PEG/nylon membrane[END_REF].

Bimetallic combinations

In recent years, noble metals have been used to increase the reactivity of monometallic nano-Fe 0 [START_REF] Nagpal | Reductive dechlorination of ?-hexachlorocyclohexane using Fe-Pd bimetallic nanoparticles[END_REF][START_REF] Hosseini | Nitrate reduction by nano-Fe/Cu particles in packed column[END_REF][START_REF] Yuan | Surfactant mediated HCB dechlorination in contaminated soils and sediments by micro and nanoscale Cu/Fe Particles[END_REF][START_REF] Zhu | Effective dechlorination of HCB by nanoscale Cu/Fe particles[END_REF][START_REF] Kadu | Efficiency and recycling capability of montmorillonite supported Fe-Ni bimetallic nanocomposites towards hexavalent chromium remediation[END_REF]. As mentioned above, this appears counterintuitive as nano-Fe 0 is already high reactivity due to its size [START_REF] Wang | Synthesizing nanoscale iron particles for rapid and complete dechlorination of TCE and PCBs[END_REF][START_REF] Zhang | Nanoscale iron particles for environmental remediation: an overview[END_REF][START_REF] Macé | Nanotechnology and groundwater remediation: A step forward in technology understanding[END_REF][START_REF] Ghauch | Antibiotic removal from water: Elimination of amoxicillin and ampicillin by microscale and nanoscale iron particles[END_REF] and is unstable during synthesis, storage and application [START_REF] Lvl | Nitrate reduction using nanosized zero-valent iron supported by polystyrene resins: Role of surface functional groups[END_REF]. This chemical instability has been documented as a key reason for the observed lower efficiency exhibited by nano-Fe 0 systems compared to µm and mm-Fe 0 [START_REF] Comba | A comparison between field applications of nano-, micro-, and millimetric zero-valent iron for the remediation of contaminated aquifers[END_REF].

Accordingly, it is questionable whether further enhancing the reactivity of nano-Fe 0 , e.g. by plating with more noble elements, may be of any benefit. The reactivity of nano-Fe 0 will be discussed in the next section on the basis of mathematical modelling.

3 Significance of increased reactivity

The problem

The increased Fe 0 reactivity from mm to nm size should be better characterized. The relative reactivity of four different materials is discussed on the basis of 1 kg Fe 0 : one nm-Fe 0 (d 0 = 25 nm), one µm-Fe 0 (d 0 = 25 µm), and two mm-Fe 0 (d 0 = 250 and 1000 µm). Calculations for the number particles (N) in 1 kg of each material and the number of layers (N') in each particle are made after the Eq. ( 1) and Eq. ( 2) presented in details elsewhere [START_REF] Noubactep | Dimensioning metallic iron beds for efficient contaminant removal[END_REF][START_REF] Noubactep | Extending service life of household water filters by mixing metallic iron with sand[END_REF].

R 0 3 4 M = N 3 Fe . / . π ρ (1) N' = 2.[4/3(πR 0 3 )]/a 3 ( 2
)
where M is the mass of Fe 0 (here 1 kg), Fe ρ is the specific weight of Fe (7,800 kg/m 3 ), R 0 is the initial radius of the Fe particle (d = 2*R 0 ) and a the lattice parameter (a = 2.866 Å).

The results are summarized in Table 3. It can be seen that the number of layers of Fe 0 in individual particles varies from 87.2 for nano-Fe 0 to more than 3*10 6 for mm-Fe 0 (d = 1 mm).

In the meantime, the number of particles in 1 kg decreased from 1.96*10 18 for nano-Fe 0 to only 3.1*10 4 for mm-Fe 0 . The ratio of the number of Fe 0 layers in each particle to the number of Fe 0 layers in nano-Fe 0 varies from 1 to 4*10 4 . This ratio corresponds to the relative time (τ) as defined later (section 3.2). On the other hand, the ratio of the number of particles in 1 kg of nano-Fe 0 to the number of particles in the same mass of each other materials varies from 1 to 6.4*10 13 . These results are summarized in Fig. 1. Instead of the mass of Fe 0 , the number of electrons released by the conversion of Fe 0 to Fe II is used to assess the kinetics of Fe 0 consumption. This is discussed in the next section.

Relative corrosion kinetics of Fe 0 materials

For the discussion in this section, uniform corrosion for spherical particles is assumed.

Individual particles corrode independently until material depletion. It is further assumed for simplicity that individual layers corrode with the same kinetics independent of particle size (d = 2*R 0 ). The latter assumption is conservative as larger particles react slower than smaller [START_REF] Zhang | Treatment of chlorinated organic contaminants with nanoscale bimetallic particles[END_REF][START_REF] Macé | Nanotechnology and groundwater remediation: A step forward in technology understanding[END_REF][START_REF] Reardon | Anaerobic corrosion reaction kinetics of nanosized iron[END_REF]. With these assumptions, a relative time (τ) can be defined while taking the time for the corrosion of the smallest particle (here 87.2 layers of nano-Fe 0 ) or t ∞,nano as unit.

τ = t/t ∞,nano (3)
Accordingly, one unit of time corresponds to the time to nano-Fe 0 depletion. Remember that all 1.96*10 18 particles in the 1 kg of nano-Fe 0 simultaneously corrode with the same kinetics.

The results of the calculations are presented in Fig. 2. From Fig. 2a and Tab. 3 it can be seen that after nano-Fe 0 depletion, the material with 1000 µm (or 1 mm) diameter will still react for more than 3*10 4 times longer than the time necessary for nano-Fe 0 depletion (τ = 4*10 4 , see Tab. 3). Fig. 2b shows that the mm-Fe 0 with 250 µm diameter is depleted after about 10 4 *t ∞,nano .

Based on the assumptions above, the service life of a nano-Fe 0 particle can be estimated.

Table 4 summarizes the results of such estimations while varying the service life of a 1 mm Fe 0 particle from 5 to 40 years. This assumption is based on the fact that conventional Fe 0 walls are supposed to function for several decades (here up to 4 decades). Results show (Tab.

4) that the maximum life-span of a nano-Fe 0 is about 8.8 hours (less than one day). In other words, following approximately 9 hours from subsurface deployment it is suggested that all nano-Fe 0 would be reactively exhausted. The success of this is dependent on three key factors: (i) the hydrodynamic conditions: pore size, porosity, flow velocity and degree of mixing or turbulence, (ii) the water chemistry and the affinity of nano-Fe 0 and its transformation products to the soil materials, and (iii) the reactivity of Fe 0 .

It is certain, that the dynamic process of transformation of concentric layers of Fe 0 atoms to concentric layers of iron (hydr)oxides can not be linear [START_REF] Noubactep | On nanoscale metallic iron for groundwater remediation[END_REF]. In fact, effects similar to "case hardening" for food-and wood-drying will lead to "surface hardened layers" [START_REF] Tarvainen | The effect of drying and storage conditions on case hardening of scots pine and norway spruce timber[END_REF][START_REF] Fernando | A model for constant temperature drying rates of case hardened slices of papaya and garlic[END_REF] leading to differential kinetics/extents of Fe 0 passivation for different particle size ranges. In other words, the extend of restricted corrosion rates through resulting surface hardened layers will be different for nm-, µmand mm-Fe 0 . Bearing this in mine, the very short relative life-span of a nano-Fe 0 estimated above will be used for the discussion in this work. It is certain that "case hardening"-like effects will prolong this hypothetical life-span to some days or weeks.

Extent of iron corrosion from Fe 0 materials

A discussion as to the extent of Fe 0 consumption is limited in the present section to τ = 1 or t ∞,nano . It is considered for simplification that the sole iron corrosion product is Fe 3 O 4 . The corresponding coefficient of volumetric expansion is η Fe3O4 = 2.08 (Eq. 4) [START_REF] Caré | Mechanical properties of the rust layer induced by impressed current method in reinforced mortar[END_REF]. Using ρ = M/V, the volume of Fe corresponding to 1 kg Fe 0 is calculated as 127.0 mL (V 0 ). This is the initial volume of Fe 0 (V 0 ). Following corrosion, this volume is partly or totally consumed.

The volume (∆V) corresponding to the volume of pores occupied by the volumetric expansion of corrosion products can be estimated.

Assuming that the coefficient of volumetric expansion (η) ("rust expansion coefficient" or "specific volume") [START_REF] Anstice | Cover cracking as a function of bar corrosion: part Iexperimental test[END_REF][START_REF] Caré | Mechanical properties of the rust layer induced by impressed current method in reinforced mortar[END_REF][START_REF] Zhao | Composition and expansion coefficient of rust based on X-ray diffraction and thermal analysis[END_REF] of the reaction products is:

η = V oxide /V Fe (4)
where V oxide is the volume of the reaction product and V Fe the volume of the parent Fe 0 .

The volume ∆V characterizing the extent of porosity loss due to volumetric expansion is given by Eq. 5:

∆V = (η -1) * V consumed Fe (5) ∆V = V ∞ -V 0 = ν*(η Fe3O4 -1)*V 0 (5a)
Where V consumed Fe is the volume of consumed Fe 0 at time t ∞ , V 0 is the volume occupied by the initial Fe 0 particles and ν (ν ≤ 1) is the fraction of the initial amount of Fe 0 (1 kg) which has reacted at t ∞,nano . V ∞ is the total volume occupied by residual Fe 0 and in-situ formed corrosion products. t ∞ corresponds to nano-Fe 0 depletion (25 nm in this section). In the discussion on the reactivity at nano-scale, t ∞ corresponds to the depletion of the material with 10 nm diameter (section 4).

V ∞ = η * V consumed Fe + (V 0 -V consumed Fe ) (6) V ∞ = V 0 [1 + ν*(η Fe3O4 -1)] (6a)
The volumetric expansion (∆V, Eq. 5) can be characterized as percent of the initial volume (V 0 ) using Eq. ( 7):

∆V (%) = 100*ν*(η Fe3O4 -1) (7)
Table 5 summarizes the results. It is shown that at τ = 1 (nano-Fe 0 depletion), a volume augmentation of 108 % has occurred in the nano-Fe 0 system, with volume augmentations in all other systems lower than 0.5 %. This clearly shows that the porosity of the subsurface will be significantly influenced by nano-Fe 0 at t ∞ . Remember that 100 % reactive exhaustion of nano-Fe 0 is predicted to occur by approximately 9 hours time. During this same period the porosity loss due to expansive iron corrosion is likely to be negligible for all other Fe Another important aspect of Fe 0 consumption is given by the number of moles of Fe 0 that have been oxidized (Tab. 5). Assuming contaminant reduction, Tab. 5 shows that after τ = 1, 35.71 moles of electrons have been released in the nano-Fe 0 system but less than 0.11 moles in all other systems. In other words, up to 35.71 moles of electrons are available for contaminant reduction per kg nano-Fe 0 within a few hours of reaction (< 9 hours). But what proportion of the electrons produced would reach the contaminant within this period? That is the major question to be answered for the further development of the nano-Fe 0 technology for in-situ applications.

Reactivity of nano-Fe 0 materials

The presentation until now has discussed the reactivity of nano-Fe 0 in comparison to larger scale Fe 0 . Section 4 will focus only on the nanoscale size fraction (d ≤ 100 nm). Equations 1-7

will be used and the particle size will vary from 10 to 100 nm. As stated above t ∞ is for a nano-Fe 0 of 10 nm diameter and the reaction proceeding until 100 % reactive exhaustion has been achieved.

Fe 0 reactivity at nanoscale

Table 6 summarizes the results of calculations for the number of Fe 0 particles and number of layers of Fe 0 in each nano-Fe 0 . It is shown that 1 kg of the material with d = 100 nm contains 1000 times more particles than a material of d = 10 nm.

Table 6 also shows that the maximum value of the relative time (τ) is 10 (or 10 1 ). This is more practical for graphical representations than situations where nano-Fe 0 are compared to larger particles (t ≤ 10 4 ). The physical significance of τ is more important, it means that if a nano-Fe 0 with a diameter of 10 nm depletes after 2 days, the material with a diameter 100 nm will deplete after 20 days. For field applications the selection of the particle size to be used should be dictated by site specific characteristics. Which diameter could quantitatively reach the contaminants before depletion? And what fraction of the material will have already oxidized on the path? What is the impact of this oxidation on the transport of nano-Fe 0 in the porous aquifer? These are some key questions to be answered in order to give this possibly very efficient technology a scientific basis.

Fig. 3 summarizes the evolution of the volumetric expansion in all 5 nano-Fe 0 systems. It can be seen from Fig. 3a that the smallest material (d = 10 nm) experiences the 108 % volumetric expansion within a short time (τ = 1) while the larger materials (d = 100 nm) needs 10 more time for the same expansion. Accordingly, beside the question whether the material will reach the contaminant under site specific conditions, the question has to be answered how the volumetric expansion will impact the aquifer porosity (and permeability).

Fig. 3b compares the variation of the volumetric expansion for two different iron corrosion products, Fe 3 O 4 and FeOOH, which are considered the most likely products in anoxic and oxic aquifers respectively. It also shows that when designing a nano-Fe 0 injection strategy, however, the availability of oxidizing species (e.g. MnO 2 , O 2 ) must also to be taken into account. Fig. 3a shows that under both conditions the trend of porosity loss is similar but the extent is proportional to the coefficient of volumetric expansion (η). In particular, at τ = 1, the system with the material d = 10 nm experiences 250 % volumetric expansion under oxic conditions and only 110 % under anoxic conditions. As a result the kinetics of more rapid Fe 0 corrosion in an oxygen-rich environment must also be considered for an effective treatment strategy.

Fe 0 reactivity of nano-bimetallics

The reactivity of monometallic nano-Fe 0 can be improved by combining it with a noble metal.

Assuming α (α > 1) the coefficient of reactivity enhancement, the relation between the relative time of a bimetallic system (τ Fe/M ) and that of a non plated metal (τ Fe ) is given by Eq.

6:

τ Fe = α * τ Fe/M (8)
To characterize the impact of plating on nano-Fe 0 , the material with the largest size (d = 100 nm) will be plated by three hypothetical metals (M 0 1 , M 0 2 and M 0 3 ) to yield a reactivity factor of 2.5 (for Fe 0 /M 0 1 ), 5 (for Fe 0 /M 0 2 ) and 10 (for Fe 0 /M 0 3 ). The considered α values of (α ≤ 10) are realistic and even conservative. In fact, reported reactivity enhancement is essentially larger [START_REF] Chen | Renewable hydrogen generation by bimetallic zerovalent iron nanoparticles[END_REF][START_REF] Zhuang | Dehalogenation of polybrominated diphenyl ethers and polychlorinated biphenyl by bimetallic, impregnated, and nanoscale zerovalent iron[END_REF]. For example, Zhuang et al. [START_REF] Zhuang | Dehalogenation of polybrominated diphenyl ethers and polychlorinated biphenyl by bimetallic, impregnated, and nanoscale zerovalent iron[END_REF] reported that palladized nano-Fe 0 promoted the dehalogenation kinetics for polybrominated diphenyl ethers by orders of magnitude equal to 2, 3 and 4 (α ≥ 100). The results of the calculations for the four systems (d = 10 nm) are summarized in Fig. 4. The system with d = 10 nm is represented for comparison. It can be seen that system Fe 0 /M 0 3 (d = 100 nm) is as reactive as Fe 0 (d = 10 nm). Given that the reactivity of nano-Fe 0 (d = 100 nm) could already significantly been too high in some situations, the results from Fig. 4 strongly question the suitability of plating at nano-scale.

Accordingly, while the application of bimetallic Fe 0 is definitively useful at µmand mmscale, it usefulness at nano-scale is likely inappropriate. It can also be noted that by increasing the reactivity of the material the rate at which volumetric pore clogging also increases. As a consequence it should be acknowledged that there exists a conceptual play-off between increased reaction rate and increased porosity loss, the impact of which will vary depending on the physiochemical conditions of each contaminated site.

Characterizing the process of reactivity loss

To better characterize the process of porosity loss due to the volumetric expansion of nano-Fe 0 , the evolution of the porosity of a sand column filled with nano-Fe 0 will be discussed as volumetric expansion proceeds. A laboratory column with a height h (h = 75.0 cm) and diameter D (D = 5.0 cm) is composed of spherical sand particles (d = 5.0 mm). The compactness of the column is ideally C = 0.64 [START_REF] Noubactep | Dimensioning metallic iron beds for efficient contaminant removal[END_REF][START_REF] Noubactep | Extending service life of household water filters by mixing metallic iron with sand[END_REF]. The pore volume is given by Eq. 9:

V pore = V * (1 -C) ( 9
)
where V is the apparent volume of the sand column (V = h * π *D 2 /4).

It is supposed that the nano-Fe 0 particles fill the inter-granular porosity of the sand column V pore without modifying the compactness C and the apparent volume V of the sand column.

The residual porosity of the sand column (V' pore ) is given by Eq. 10:

V' pore = V*(1-C) -V 0 [START_REF] Kim | Inactivation of escherichia coli by nanoparticulate zerovalent iron and ferrous ion[END_REF] where V 0 is the volume of the Fe particles.

The evolution of the residual porosity (V' pore ) as nano-Fe 0 particles undergo volumetric expansive corrosion is considered by introducing the specific volume (η) of the reaction products according to Eq. 11:

V' pore = V*(1 -C) -(V 0 -V consumed Fe ) -η * V consumed Fe (11) V' pore = V*(1 -C) -V 0 -(η-1) * V consumed Fe (11a)
where V consumed Fe is the volume of nano-Fe 0 particles which is consumed at a given time.

Equations 9 through 11 are very useful to design reactive zone. However, they are limited to describe the initial (V pore ) and a final conditions (V' pore ) regardless on the nature of iron corrosion products and the kinetics of the process.

Using a sand column comparable to one of those used by Moraci and Calabrò [START_REF] Moraci | Heavy metals removal and hydraulic performance in zerovalent iron/pumice permeable reactive barriers[END_REF] and 1 kg of nano-Fe 0 , the process of pore filling (porosity loss) can be better characterized. For simplicity nano-Fe 0 considered as transported by a biodegradable dispersant which does not significantly contribute to porosity loss. As shown in section 3.3, 1 kg of nano-Fe 0 occupies a volume of 127 mL. The initial pore volume of the sand column calculated after Eq. 9 is 530.36 mL (100 % porosity), i.e. a capacity for approximately 4.17 kg of nano-Fe 0 . Filling the initial pore volume of the sand column (530.36 mL) with 1 kg of nano-Fe 0 (127.00 mL) yields a 23.9 % porosity loss (Tab. 7). This, however, does not take into account the expansive nature of iron during oxidative corrosion.

Using the 8 possible iron corrosion products documented by Caré et al. [START_REF] Caré | Mechanical properties of the rust layer induced by impressed current method in reinforced mortar[END_REF] and their respective coefficient of volumetric expansion (2.08 ≤ η ≤ 6.40), the extent of porosity loss is calculated and summarized in Table 7. The results show that the residual volume of pores (V' pore ) decreases with increasing η values and is zero for Fe(OH) 3 and Fe(OH) 3 .3H 2 O (100 % porosity loss). Ferrihydrite (Fe(OH) 3 .3H 2 O) is the largest known iron corrosion products.

In other words, depending on environmental conditions as little as 1 kg of nano-Fe 0 could clog the tested column. Although this discussion considers the nature of the corrosion products, there are other important factors which must be considered. The negative values (-3.04 and -282.4 mL) corresponds to the mass of Fe 0 which will not oxidized because of lack of space for expansion [START_REF] Noubactep | Dimensioning metallic iron beds for efficient contaminant removal[END_REF][START_REF] Noubactep | Extending service life of household water filters by mixing metallic iron with sand[END_REF].

The extent of porosity loss (∆V in %) given in Tab. 7 assumes uniform distribution of nano-Fe 0 in the whole column. This is, however, not a very good field representation. For example, if 1 kg of nano-Fe 0 (V 0 = 127 mL) is uniformly distributed only in the first third of the column (V 1/3 pore = 176.8 mL), with Fe 3 O 4 as the primary corrosion product (∆V = 137.16 mL) a 78 % porosity loss can be expected. For all other oxide phases it is calculated that complete porosity loss (100 %) will precede nano-Fe 0 reactive exhaustion. However, in the practice a system with 78 % porosity loss is considered as clogged. One possibility to avoid the clogging of the entrance zone of a porous system is to intermittently inject calculated amounts of nano-Fe 0 .

The volume to be injected at each event and the time scale between two injections are necessarily determined by site specific characteristics (e.g. aquifer porosity, water flow rate).

Discussion

A primary reason behind the interest into the use of nano-Fe 0 particles over µm-Fe 0 and mm-Fe 0 particles for water treatment is ascribed to a significant increase the materials efficiency [START_REF] Comba | A comparison between field applications of nano-, micro-, and millimetric zero-valent iron for the remediation of contaminated aquifers[END_REF][START_REF] Gheju | Hexavalent chromium reduction with zero-valent iron (ZVI) in aquatic systems[END_REF]. For example, as reported by Vodyanitskii [START_REF] Vodyanitskii | The role of iron in the fixation of heavy metals and metalloids in soils: a review of publications[END_REF], Kanel et al. [START_REF] Kanel | Arsenic(V) Removal from groundwater using nano scale zero-valent iron as a colloidal reactive barrier material[END_REF] reported near-total remediation of a 1 mg L -1 As V solution within only 10 min by a nano-Fe 0 with a specific surface of 24 m 2 /g, whereas the same goal was achieved by mm-Fe 0 (1-2 m 2 /g) after only 4 days or 5760 min (ratio of time 570; average ratio of surface 16). However, this experimental evidence is highly qualitative as neither the number of atoms directly accessible at the surface nor the intrinsic reactivity of individual materials are considered in both cases [START_REF] Noubactep | On nanoscale metallic iron for groundwater remediation[END_REF]. For a better comparative result, the following three key conditions must be considered: (i) the intrinsic Fe 0 reactivity should be characterized, (ii) the amount of used materials should be based on the reaction stoichiometry, and (iii) the experimental conditions should be relevant for field applications. In particular, the driving force for the transport of contaminants and Fe species should be relevant for field situations: (i) mixing operation (type and intensity) in batch studies, (ii) flow rate and column dimensions in column studies [START_REF] Noubactep | Exploring the influence of operational parameters on the reactivity of elemental iron materials[END_REF].

Transport of nano-Fe 0 to the contaminants

The efficiency of nano-Fe 0 for the in-situ treatment of a contaminated aquifer body is intrinsically linked to the extent of physical contact between Fe 0 and any aqueous contaminant species present. In some circumstances, contaminants could diffuse to the suspended Fe 0 particles and be degraded in the aqueous phase. However, typically the suspended Fe 0 particles must migrate to the contaminants. As Fe 0 particles are transported from the injection zone to the target contaminant plume by natural groundwater, diffusion experiments under relevant groundwater velocity, using site specific aquifer materials are essential in order to effectively assess the suitability of nano-Fe 0 for in-situ applications [START_REF] Antia | Modification of aquifer pore-water by static diffusion using nano-zerovalent metals[END_REF].

Contaminants are typically partitioned between sediment and water phases in a "pseudoequilibrium" state. Therefore, it is likely that Fe 0 particles whilst acting to reduce any soluble contaminants are also likely to promote the dissolution of a range of adsorbed chemical species (Le Chatelier's principle). However, as water is also a redox-amenable species the specific mechanism for nano-Fe 0 reactivity in a range of conditions is difficult to resolve [START_REF] Tratnyek | Nanotechnologies for environmental cleanup[END_REF].

In other words, nano-Fe 0 is readily oxidized by H 2 O during subsurface migration to the target contaminant plume and also competes with any other redox-amenable (including contaminants) present in the groundwater. Additionally, expansive iron corrosion will yield voluminous iron (hydr)oxides (Tab. 7) with limited aqueous mobility due to (i) an increased size and weight, and (ii) a possible increased affinity to aquifer material.

This discussion has intentionally neglected the segregation between parent compounds, the reaction products and their relative affinity to Fe 0 and Fe (hydro)oxides. The fact that the core Fe 0 is always covered by oxide layers is also neglected for simplification. The process of preferential flow which is crucial in predicting mass transfer in the subsurface is also not considered [START_REF] Flury | Brilliant Blue FCF as a dye tracer for solute transport studies. A toxicological review[END_REF][START_REF] Fryar | Hydraulic-conductivity reduction, reaction-front propagation, and preferential flow within a model reactive barrier[END_REF][START_REF] Simunek | Review and comparison of models for describing non-equilibrium and preferential flow and transport in the vadose zone[END_REF]. However, it is clearly shown, that due the acute redox sensitivity of nano-Fe 0 and the subsequent significant formation of highly voluminous oxidative corrosion products it is likely that for environmentally relevant distances (m), a significant proportion of the originally injected nano-Fe 0 will remain "clogged" in pore spaces.

Beside the transport of nano-Fe 0 to contaminants, the possibility of quantitative contaminant desorption and their subsequent transformation by suspended Fe 0 could be considered.

However, it is not likely that concentration-gradient-driven mass transfer could be quantitative at considered distances (m). It should be recalled that the slow kinetics of contaminant desorption form aquifer materials is the major cause of the ineffectiveness of the pump-and-treat technology for groundwater remediation [START_REF] Mcmurty | New approach to in-situ treatment of contaminated groundwaters[END_REF][START_REF] Mackay | Groundwater contamination: Pump-and-treat remediation[END_REF][START_REF] Starr | In situ remediation of contaminated Ground water: The funneland-Gate System[END_REF].

This section has shown that it is likely that the success of nano-Fe 0 for in-situ remediation is seriously limited by the intrinsic formation of voluminous iron corrosion products [START_REF] Comba | A comparison between field applications of nano-, micro-, and millimetric zero-valent iron for the remediation of contaminated aquifers[END_REF][START_REF] Gheju | Hexavalent chromium reduction with zero-valent iron (ZVI) in aquatic systems[END_REF][START_REF] Tratnyek | Nanotechnologies for environmental cleanup[END_REF][START_REF] Truex | Injection of zero-valent iron into an unconfined aquifer using shear-thinning fluids[END_REF][START_REF] Truex | Demonstration of combined zero-valent iron and electrical resistance heating for in situ trichloroethene remediation[END_REF]. Bearing this in mind, the next section suggests an alternative nano-Fe 0 subsurface deployment mechanism that more effectively takes into account the aforementioned nano-Fe 0 hydraulic mobility issues than conventional injection processes: the formation of a nano-Fe 0 "redox-front" injection array system for progressive contaminant reduction. The geochemical process of redox-front migration is a well-documented one [START_REF] Fryar | Hydraulic-conductivity reduction, reaction-front propagation, and preferential flow within a model reactive barrier[END_REF][START_REF] Min | Evidence of uranium biomineralization in sandstonehosted roll-front uranium deposits, northwestern China[END_REF][START_REF] Sidborn | Long term redox evolution in granitic rocks: Modelling the redox front propagation in the rock matrix[END_REF].

5.2

Nano-Fe 0 as source of Fe II for a redox-front?

The concept

The progressive consumption of mm-Fe 0 (Fig. 1; Tab. 3) is the guarantee for the long-term efficiency of reactive barriers [START_REF] Comba | A comparison between field applications of nano-, micro-, and millimetric zero-valent iron for the remediation of contaminated aquifers[END_REF]. In fact, continuously generated small amount of high reactive iron minerals [START_REF] Noubactep | Comment on "Reductive dechlorination of g-hexachloro-cyclohexane using Fe-Pd bimetallic nanoparticles[END_REF][START_REF] Noubactep | Processes of contaminant removal in "Fe 0 -H 2 O" systems revisited. The importance of co-precipitation[END_REF][START_REF]Noubactep A critical review on the mechanism of contaminant removal in Fe 0 -H 2 O systems[END_REF][START_REF] Noubactep | The fundamental mechanism of aqueous contaminant removal by metallic iron[END_REF][START_REF] Gu | Biogeochemical dynamics in zerovalent iron columns: implications for permeable reactive barriers[END_REF][START_REF] Su | Arsenate and arsenite removal by zerovalent iron: kinetics, redox transformation, and implications for in situ groundwater remediation[END_REF][START_REF] Furukawa | Formation of ferrihydrite and associated iron corrosion products in permeable reactive barriers of zerovalent iron[END_REF][START_REF] Kohn | Longevity of granular iron in groundwater treatment processes: corrosion product development[END_REF] are sufficient for the removal of contaminants which are present in trace amounts [START_REF] Palmer | Processes affecting the remediation of chromiumcontaminated sites[END_REF]. As discussed above, for nano-Fe 0 however, (i) Fe 0 reactive exhaustion typically occurs in a relatively short time scale (< 9 hours) and, (ii) it is likely that nano-Fe 0 subsurface mobility is significantly retarded or even prevented due to the volumetric expansive nature of iron corrosion [START_REF] Caré | Mechanical properties of the rust layer induced by impressed current method in reinforced mortar[END_REF]. As a consequence an alternative method of subsurface deployment is suggested in the current work: the deployment of a linear nano-Fe 0 injection array orientated perpendicular to the flow direction of the contaminant plume. The injected nano-Fe 0 can effectively form a redox-front (roll-front) which migrates through the contaminated zone and transforms the contaminants during its migration as illustrated in Fig. 5. The Fe II /Fe III roll-front travels across the contaminated zone with all possible mechanisms (e.g. diffusion, dispersion, convection, preferential flow) and the contaminants are transformed and immobilized during the cycle Fe II ⇔ Fe III . In other words, it is a plume of Fe II /Fe III formed from injected nano-Fe 0 which migrates through the contaminated zone and "sweeps" the contaminants. As a consequence this method considers all nano-Fe 0 mobility issues.

Nano-Fe 0 as Fe II generator

Nano-Fe 0 in the aqueous phase is certainly a Fe II /Fe III producer. Fe II -species are the main reducing agents for contaminants under both anoxic and oxic conditions [START_REF] Stratmann | The mechanism of the oxygen reduction on rust-covered metal substrates[END_REF]. The reducing capacity of Fe II -species nominally depends on the pH value [START_REF] Noubactep | The fundamental mechanism of aqueous contaminant removal by metallic iron[END_REF][START_REF] Zhuang | Dehalogenation of polybrominated diphenyl ethers and polychlorinated biphenyl by bimetallic, impregnated, and nanoscale zerovalent iron[END_REF][START_REF] Nesic | Key issues related to modelling of internal corrosion of oil and gas pipelines -A review[END_REF][START_REF] Kiser | Reduction and immobilization of chromium(VI) by iron(II)-treated faujasite[END_REF]. Microbial activity could regenerate Fe II (bio-corrosion) for more contaminant reduction [START_REF] Vodyanitskii | The role of iron in the fixation of heavy metals and metalloids in soils: a review of publications[END_REF]. In this case, more contaminant is reduced than can be predicted from the reaction stoichiometry. In order words, the operating mode of nano-Fe 0 for contaminant reduction can be summarized as follows: (i) Fe 0 is oxidized to produce Fe II , (ii) Fe II reduces the contaminant and is oxidized to Fe III , and

(iii) a proportion of Fe II is regenerated by the biological reduction of Fe III . Accordingly, before Fe 0 depletion, there are three sources of Fe II : (i) the Fe 0 mediated abiotic oxidation by H 2 O, (ii) the Fe 0 mediated abiotic oxidation by Fe III , and (iii) the biological reduction of Fe III .

After Fe 0 depletion, the only remaining source of Fe II is the biological reduction of Fe III .

Provided that the appropriate micro-organism species are present in the subsurface, this process, however, could conceptually proceed for a significantly long time period [START_REF] Cullen | Assessing the impact of nano-and micro-scale zerovalent iron particles on soil microbial activities: Particle reactivity interferes with assay conditions and interpretation of genuine microbial effects[END_REF].

Evidence suggests that such micro-organism colonies can be sustained by a consistent supply of Fe II , Fe III and molecular hydrogen (H/H 2 ). Another further process that is worth noting is the generation of atomic or molecular hydrogen (H/H 2 ) by Fe 0 mediated hydrolysis reactions, which is likely to aid and the aforementioned biotic processes [START_REF] Cullen | Assessing the impact of nano-and micro-scale zerovalent iron particles on soil microbial activities: Particle reactivity interferes with assay conditions and interpretation of genuine microbial effects[END_REF].

The abiotic conversion of Fe III to Fe II has been successfully utilised in the hydrometallurgy industry, for example Lottering et al. [START_REF] Lottering | Mineralogy and uranium leaching response of low grade South African ores[END_REF] reported on the sustainable use of MnO 2 for the abiotic regeneration of Fe III for U IV oxidation.

The fate of contaminant reduction products is discussed in the next section.

Mechanism of contaminant removal by injected nano-Fe 0

The successful application of nano-Fe 0 injection technology for in-situ remediation is highly dependent on a comprehensive understanding of the fundamental processes governing the processes of contaminant removal. The hitherto discussion has focused on reductive transformations by nano-Fe 0 . However, contaminant reductive transformation is not a guarantee for contaminant removal [START_REF] Noubactep | Processes of contaminant removal in "Fe 0 -H 2 O" systems revisited. The importance of co-precipitation[END_REF][START_REF]Noubactep A critical review on the mechanism of contaminant removal in Fe 0 -H 2 O systems[END_REF][START_REF] Noubactep | The fundamental mechanism of aqueous contaminant removal by metallic iron[END_REF]. Additionally, certain reaction products are more toxic than their parent compounds [START_REF] Jiao | Reductive dechlorination of carbon tetrachloride by zero-valent iron and related iron corrosion[END_REF]. Accordingly, efforts have to be focused on the specific mechanism of aqueous contaminant removal. Relevant removal processes include: (i) adsorption, (ii) chemical precipitation, (iii) co-precipitation, (iv) size exclusion or straining, and (v) volatilization [START_REF] Noubactep | Processes of contaminant removal in "Fe 0 -H 2 O" systems revisited. The importance of co-precipitation[END_REF][START_REF]Noubactep A critical review on the mechanism of contaminant removal in Fe 0 -H 2 O systems[END_REF][START_REF] Noubactep | The fundamental mechanism of aqueous contaminant removal by metallic iron[END_REF][START_REF] Vodyanitskii | The role of iron in the fixation of heavy metals and metalloids in soils: a review of publications[END_REF][START_REF] Crawford | Adsorption and coprecipitation of single heavy metal ions onto the hydrated oxides of iron and chromium[END_REF][START_REF] Crawford | Adsorption and coprecipitation of multiple heavy metal ions onto the hydrated oxides of iron and chromium[END_REF][START_REF] Eusterhues | Fractionation of organic matter due to reaction with ferrihydrite: Coprecipitation versus adsorption[END_REF][START_REF] Johnson | Straining credibility: A general comment regarding common arguments used to infer straining as the mechanism of colloid retention in porous media[END_REF]. Chemical precipitation is a characteristic of inorganic compounds when the solubility limit is exceeded [START_REF] Crawford | Adsorption and coprecipitation of single heavy metal ions onto the hydrated oxides of iron and chromium[END_REF][START_REF] Crawford | Adsorption and coprecipitation of multiple heavy metal ions onto the hydrated oxides of iron and chromium[END_REF][START_REF] Kalin | The removal of uranium from mining waste water using algal/microbial biomass[END_REF]. Volatilization is subsequent to chemical transformation yielding gaseous species like AsH 3 , CH 4 , CO 2 , H 2 , N 2 .

In Fe 0 reactive barrier systems, contaminants are efficiently removed by the combination of adsorption, co-precipitation and size exclusion within the engineered barrier [START_REF] Noubactep | Metallic iron for safe drinking water production[END_REF][START_REF] Noubactep | Metallic iron for safe drinking water worldwide[END_REF]. As a result the current discussion concentrates on such processes.. With Fe 0 (< 1 m 2 /g) first transformed to voluminous hydroxides species (> 100 m 2 /g) and subsequently transformed to oxides (< 40 m 2 /g), contaminant size exclusion (straining) is driven by the dynamic cycle of expansion/compression accompanying the corrosion process [START_REF] Noubactep | Metallic iron for safe drinking water production[END_REF][START_REF] Pokhrel | Arsenic removal in an iron oxide-coated fungal biomass column: Analysis of breakthrough curves[END_REF]. During these cycles contaminants are enmeshed and sequestrated in a "matrix" of iron corrosion products.

For conventional nano-Fe 0 injection arrays, size exclusion may play an important role (i) in proximity for Fe 0 particles, and (ii) by reducing the pore space during expansive corrosion of the materials. However, if roll-fronts are formed as discussed above, the extent of permeability loss in aquifer will be limited. The roll-front could act as a colloidal reactive barrier for the removal of parent contaminants and reaction products. Species are removed or immobilized by colloids and not because they are reduced. More research is needed to test this hypothesis.

Fe II /Fe III redox-front as a colloidal reactive barrier

Aqueous contaminants have been reported to be quantitatively removed both during abiotic and biotic (i) oxidation of Fe II and (ii) reduction of Fe III [START_REF] Pokhrel | Arsenic removal in an iron oxide-coated fungal biomass column: Analysis of breakthrough curves[END_REF][START_REF] Pokhrel | Arsenic contamination of groundwater in the Terai region of Nepal: an overview of health concerns and treatment options[END_REF][START_REF] Pokhrel | Biological filtration for removal of arsenic from drinking water[END_REF]. On the other hand, injection of Fe III salts for adsorptive contaminant removal has been reported [START_REF] Morrison | Chemical barriers for controlling groundwater contamination[END_REF][START_REF] Morrison | Subsurface injection of dissolved ferric chloride to form a chemical barrier: Laboratory investigations[END_REF].

Accordingly, the migration of the Fe II /Fe III -redox-front may be coupled to quantitative contaminant removal by adsorption and co-precipitation.

The primary reason for contaminant removal during these redox reactions is the colloidal nature of in-situ generated Fe species [Fe(OH) 2 , Fe(OH) 3 ] [START_REF] Hanna | Sorption of two naphthoic acids to goethite surface under flow through conditions[END_REF], which necessarily experience volumetric contraction to form oxides (of Fe II or Fe III ). Contaminants are first adsorbed by highly reactive colloids and are co-precipitated during transformation to amorphous and crystalline oxides [START_REF] Vodyanitskii | The role of iron in the fixation of heavy metals and metalloids in soils: a review of publications[END_REF][START_REF] Ghauch | Bdeir Aqueous removal of diclofenac by plated elemental iron: Bimetallic systems[END_REF] 6

Concluding remarks

Constructed geochemical barriers of metallic iron (Fe 0 ) have been used for groundwater remediation since 1996 [START_REF] Gillham | Enhanced degradation of halogenated aliphatics by zerovalent iron[END_REF][START_REF] Scherer | Chemistry and microbiology of permeable reactive barriers for in situ groundwater clean up[END_REF][START_REF] Henderson | Long-term performance of zero-valent iron permeable reactive barriers: a critical review[END_REF][START_REF] Vodyanitskii | The role of iron in the fixation of heavy metals and metalloids in soils: a review of publications[END_REF][START_REF] Noubactep | Aqueous contaminant removal by metallic iron: Is the paradigm shifting?[END_REF]. In recent years, however, nano-Fe 0 has received proclaim as a new tool for water treatment due to (i) improvements in reactivity and associated aqueous contaminant removal performance compared to conventional materials, and (ii) the option of subsurface deployment via injection for targeted in-situ treatment of contaminant plumes [START_REF] Comba | A comparison between field applications of nano-, micro-, and millimetric zero-valent iron for the remediation of contaminated aquifers[END_REF][START_REF] Gheju | Hexavalent chromium reduction with zero-valent iron (ZVI) in aquatic systems[END_REF].

Considering reactivity first, the current work has highlighted the need for prudent use of terminology. Discounting any quantum size effects, which are only prevalent for Fe 0 less than approximately 10 nm in diameter, the reactivity of nano-Fe 0 as a function of surface area is no more reactive than larger forms. Nano-Fe 0 only exhibits such high reactivity due to it significantly high surface area as a function of mass/volume. Despite this, a recent trend in research has been the development of bimetallic nano-Fe 0 wherein the combination of a noble metal acts to further increase the reactivity of nano-Fe 0 . It is argued in the current work that as reactive exhaustion is already achieved by monometallic nano-Fe 0 in the order of minutes this seems counterintuitive for the majority of environmental applications.

Considering the nano-Fe 0 subsurface injection procedure, in the current work it has been highlighted that the hydraulic mobility of the particles is likely to be significantly retarded by voluminous expansion due to particle corrosion. An alternative nano-Fe 0 injection procedure has been suggested herein. The injected nano-Fe 0 effectively forms an in-situ migrating front which possibly reductively transforms contaminant and removes reduced species by adsorption and co-precipitation.

It is also outlined in the current work that a number of studies with experiments "proclaimed" as analogous to environmental systems are largely overlooked a range of operational drivers including changes in nano-Fe 0 (i) reactivity, and (ii) voluminous as a function of time. It is hoped that the huge literature on redox-front migration [START_REF] Reynolds | Origin of a south Texas roll-type uranium deposit: I. Alteration of iron-titanium oxide minerals[END_REF][START_REF] Posey-Dowty | Dissolution rate of uraninite and uranium roll-front ores[END_REF][START_REF] Romero | Movement of the redox front at the Osamu Utsumi uranium mine, Poços de Caldas, Brazil[END_REF][START_REF] Read | Uranium migration through intact sandstone cores[END_REF] and the cycle of iron in the hydrosphere ( [START_REF] Vodyanitskii | The role of iron in the fixation of heavy metals and metalloids in soils: a review of publications[END_REF] and ref. therein) will now be used for the further development of nano-Fe 0 injection technology.

  0 particle size fractions. Calculations for Akageneite β-FeOOH (η FeOOH = 3.48) as sole corrosion products shows that V ∞,nano = 448.7 mL, ∆V = 320.5 mL or 250.4 %. The examples of Fe 3 O 4 (anoxic) and FeOOH (oxic) demonstrate the crucial importance of the nature of formed corrosion products for the discussion of the extent of porosity loss.

Figure 1 :

 1 Figure 1

Figure 2 :

 2 Figure 2: Kinetics of the process of Fe 0 exhaustion at nano-, micro-and millimetre scale as for: (a) d ≤ 1000 µm, and (b) d ≤ 200 µm.

Figure 3 :

 3 Figure 3: Kinetics of the process of porosity loss at nano-scale as characterized by: (a) the

Figure 4 :

 4 Figure 4: Calculated extent of Fe 0 exhaustion as a function of the relative time (τ) for three

Figure 5 :

 5 Figure 5: Schematic diagram of the flow process of the U-shaped redox-front through a

Table 1 :

 1 Results of a web-search in 7 selected relevant journals demonstrating the current interest within academia for the nano-Fe 0 technology.

	Journal	Impact Issues	Search's results
		Factor (year -1 )	Period	Total 2011
	Environ. Sci. Technol.	4.630	24	1995 to 2011 157 13
	J. Hazard. Mater.	4.144	33	2004 to 2011	86	15
	Chemosphere	3.253	44	2000 to 2011	49	5
	Water Res.	4.355	20	2005 to 2011	31	9
	Chem. Eng. J.	2.816	30	2008 to 2011	15	6
	Desalination	2.034	48	2008 to 2011	12	9
	Environ. Pollut.	3.426	12	2007 to 2011	12	1
	Appl. Catal. B	5.252	32	2009 to 2011	3	1
				Total	365 59

Table 2 :

 2 Relevant redox couples for the process of aqueous Fe 0 dissolution and oxide scale formation in a passive remediation Fe 0 /H 2 O system. These processes are thermodynamically the same for all Fe 0 particle sizes. Observed differences are due to kinetics aspects.

	Electrode reactions

Table 3 :

 3 Summary of the values of the number of particles contained in 1 kg of each material, the number of layer making up each particle and estimation of the relative time (τ).The life span of nano-Fe 0 is operationally considered as the unit of time while assuming uniform corrosion. τ coincides with the ratio of the number of layers of Fe in each particle to that of nano-Fe 0 . The ratio of the number of particles in individual systems is also given.

	Size	d	n particles	n layers n layers /n nano n nano /n particles	τ
		(µm)	(-)	(-)	(-)	(-)	(-)
	Nano-Fe 0 25*10 -3 1.96*10 18	87.2	1.0	1.0	1.0
	µm-Fe 0	25	1.96*10 9 87.2*10 3	10 3	10 9	10 3
	mm-Fe 0	250 1.96*10 6 87.2*10 4	10 4	10 12	10 4
	mm-Fe 0 1000 3.06*10 4 3.49*10 5	4*10 4	6.4*10 13	4*10 4

Table 4 :

 4 Estimation of the value of the life span (t ∞ ) of a nano-Fe 0 particle with 25 nm diameter for barrier life spans (t) from 10 to 40 years. The considered conventional reactive wall contains granular Fe 0 with a diameter of 1 mm. For comparison the relative life span (in days and years) of the micrometric particles is given.

	t	(years)	5	10	15	20	25	30	35	40
	t µm (days) 45.7	91.3	137.0	182.6	228.3	273.9	319.6	365.3
	t µm (years)	0.2	0.3	0.5	0.7	0.9	1.0	1.2	1.4
	t ∞ (hours) 1.1	2.2	3.3	4.4	5.5	6.6	7.7	8.8

Table 5 :

 5 Estimation of the extent of porosity loss (∆V) due to the volumetric expansion of iron corrosion for Fe 0 particles of different sizes. The operational unit of time is arbitrarily the time to nano-Fe 0 depletion (t ∞ ). V 0 is the volume occupied by the initial Fe 0 particles; V ∞ is the volume occupied by residual Fe 0 and in-situ formed corrosion products. ∆V corresponds to the volume of pore occupied by the volumetric expansion of corrosion products. m consumed = mass of Fe 0 consumed; ν = percent of Fe 0 depletion, n Fe(II) = number of moles of corroded Fe 0 ; n Fe3O4 = number of moles of generated iron corrosion products, n electrons = 2*n Fe(II) = number of electrons released by corroded iron; and n nano /n electrons is the ratio of the number of electrons produced in by nano-Fe 0 to n electrons .

	Size	m consumed	ν	V ∞	∆V	∆V	n Fe(II)	n Fe3O4 n electrons n nano /n electrons
		(kg)	(%)	(mL)	(mL)	(%) (moles) (moles) (moles)	(-)
	nm-Fe 0	10 0	100.00 264.16 137.16 108.00 17.857 5.9524 35.714	1
	µm-Fe 0 3*10 -3	0.30 127.41 0.41	0.32	0.053	0.0178 0.107	335
	mm-Fe 0 3*10 -4	0.03 127.04 0.04	0.03	0.005	0.0018 0.011	3342
	mm-Fe 0 7.5*10 -5 0.01 127.01 0.01	0.01	0.001	0.0004 0.003	13369

Table 6 :

 6 Summary of the values of the number of particles contained in 1 kg of each nano-Fe 0 , the number of layer making up each particle and estimation of the relative time (τ). The life span of the material with the smallest particle site (d = 10 nm) is operationally considered as the unit of time while assuming uniform corrosion. The ratio of the number of particles in 1 kg of d = 10 nm to that of other d values is also given.

	d	n particles	n layers	n layers /n 10 n 10 /n particles	τ
	(nm)	(-)	(-)	(-)	(-)	(-)
	10	3.06*10 19	34.9	1.0	1.0	1.0
	25	1.96*10 18	87.2	2.5	16	2.5
	50	2.45*10 11	174.5	5.0	125	5.0
	75	7.25*10 16	261.7	7.5	422	7.5
	100	3.06*10 16	348.9	10.0	1000	10.0

Table 7 :

 7 Summary of the extent of porosity loss (∆V pore in %) as 1 kg of nano-Fe 0 (V 0 = 127 mL) is corroded to various iron oxides. V ∞ is the volume of iron oxide at Fe 0 exhaustion. The initial volume of pore (V pore ) is 530.4 mL and V' pore is the residual pore volume at Fe 0 exhaustion. The absolute value of negative values for V' pore corresponds to the mass of nano-Fe 0 which can not oxidize because of lack of space for volumetric expansion.

	Fe species	η	V ∞	∆V	V' pore	∆V pore
		(-)	(mL)	(mL)	(mL)	(%)
	Fe 0	1	127	0	403.4	23.9
	Fe 3 O 4	2.08	264.2	137.2	266.2	49.8
	Fe 2 O 3	2.12	269.2	142.3	261.1	50.8
	α-FeOOH	2.91	369.6	242.6	160.8	69.7
	γ-FeOOH	3.03	384.8	258.0	145.6	72.6
	β-FeOOH	3.48	442.0	315.0	88.4	83.3
	Fe(OH) 2	3.75	476.3	349.3	54.1	89.8
	Fe(OH) 3	4.2	533.4	406.4	-3.0	100.0
	Fe(OH) 3 .3H 2 O	6.4	812.8	685.8	-282.4	100.0

Acknowledgments


Adrian Leip

Marco Follador

Stefano Tarantola

Mirko Busto

Sensitivity of the process-based model DNDC on microbiological parameters

come   L'archive ouverte pluridisciplinaire

Sensitivity of the process-based model DNDC on microbiological parameters

Leip A. 1 , Follador M. 1 , Tarantola S. 2 , Busto M. 1 , Villa-Vialaneix N.

Overview

Process-based model such as DNDC rely on a large numbers of parameters which were defined by the model developer on the basis of existing references. Subsequently, some values have been changed to improve model performance for specific applications, often without adequate documentation. Many of these parameters are thus estimates of the real values appropriate for local conditions introducing approximation errors for applications at larger scales. Spatially explicit datasets might be required for some parameters for which model output is highly sensitive. We will present a sensitivity analysis of 38 mainly micro-biological internal parameter of DNDC-EUROPE.

Methods

We test 38 mostly, currently internal, soil microbiological parameters required to simulate rates of nitrification, denitrification, and soil organic matter turnover on its sensitivity to estimated rates of N 2 O fluxes and nitrate leaching. The selected parameter include microbiological parameters describing population dynamics of denitrifying and nitrifying organisms as well as the characterization of soil carbon pools and their mineralization rates. The shape of the probability density functions was assumed to be triangular, when the range of a parameter could be obtained from literature data. In such cases, the default value was set as the mode and the maximum and minimum values of the rages were set as the extremes of the distribution. When no information on the range was available, we opted for a normal distribution with a CV of 20% around the nominal values. Input data for simulations of N 2

First, a list of sample points from the marginal pdfs of the k input parameters using a quasi-Monte Carlo generator [START_REF] Sobol | Distribution of points in a cube and approximate evaluation of integrals[END_REF]) is generated. It consists of blocks of with k+2 rows, where the first two rows are the coordinates of two independent realizations A and B and the subsequent k rows represent points having in turn all coordinates from A but one that is from B. In order to achieve convergence we generated 166 blocks resulting in 6640 simulations to be carried out at each simulation unit.

O and N-leaching with the DNDC-EUROPE model model set-up are described in detail elsewhere [START_REF] Follador | Assessing the Cross-Compliance effects on European agricultural environment with DNDC-EUROPE[END_REF][START_REF] Leip | Linking an economic model for European agriculture with a mechanistic model to estimate nitrogen and carbon losses from arable soils in Europe[END_REF].

Second, we apply both a machine learning, a random forest meta-model [START_REF] Villa-Vialaneix | Metamodels comparison for the simulation of N2O fluxes and N leaching from corn crops[END_REF], and the method of Sobol' as improved by [START_REF] Saltelli | Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index[END_REF]. Here we focus on the random-forest approach.

Sensitivity of DNDC to the internal parameters was tested indirectly by (i) developing a R-metamodel based on the first 200 simulations carried out at 997 randomly selected HSMUs from the training set as described in [START_REF] Follador | Assessing the Cross-Compliance effects on European agricultural environment with DNDC-EUROPE[END_REF]. The importance of the variables is then as the increase in the mean square error (MSE) when the variable's values in the out-of-sample observations (OOB) for each tree are randomly permuted before running the simulation. A decrease in the goodness of prediction, compared to the performance obtained with the original variable's value, defines the score of importance. As this assessment is based on OOB, it does not depend on the learning process and on the way the regression is built.

Results

Figure 1 shows the ranking of the importance for the tested parameters for the simulation of N 2 O fluxes and N-leaching with the random-forest model. Most important parameters for both fluxes are parameters related to denitrification, i.e. the ratio of denitrifiers to total microbial biomass and the maintenance coefficient of denitrifiers on NO. N 2 O fluxes were not sensitive on tested "soil parameters", but C/N ratio of humads and biomass was important for N-leaching. The tested nitrification parameter played a minor role for both N-fluxes. Parameters controlling soil carbon dynamics are particularly important for N 2

Fig. 1 .

 1 Fig. 1. Ranking of importance of tested microbiological parameters