Antonio Stocco

David Carriere

Maximilien Cottat

Dominique Langevin

Interfacial behaviour of Catanionic surfactants

Keywords: catanionics, dynamic surface tension, multiple light scattering, foam

We report a dramatic increase of foam stability for catanionic mixtures (myristic acid and cetyl trimethylammonium bromide, CTABr) with respect to pristine CTABr solutions. This increase was related to the low surface tension, high surface concentration and high viscoelastic compression moduli, as measured with rising bubble experiments and ellipsometry. Dialysis of the catanionic mixtures has been used to decrease the concentration of free surfactant ions (CTA + ). The equilibrium surface tension is reached faster for non dialysed samples, due to the presence of these free ions. As a consequence, the foamability of the dialysed solutions is lower. Foam coarsening has been studied using multiple light scattering: it is similar for dialysed and non dialysed samples and much slower than for pure CTABr foams.

Introduction

Aqueous mixtures of anionic and cationic surfactants (catanionic mixtures) show strongly synergetic behaviour due to mutual electrostatic attraction. [START_REF] Khan | Catanionic Surfactants[END_REF] This leads in particular to deviation from ideal mixing, [START_REF] Goldsipe | [END_REF] for instance a dramatic decrease in interfacial tension at peculiar ratios has been reported. 3,4 Additional peculiarities such as a two-dimensional gas/condensed phase transition 5 and an adsorption energy barrier 6 were also observed at the air-water interface. Although some points remain to be elucidated, such behaviours are essentially captured by using or adjusting thermodynamic theories. 7 The hypothesis for thermodynamic equilibrium is essentially met in catanionic systems where at least one of the surfactant molecules is "short", i.e. typically up to 8-12 carbon atoms, and holds even if the other surfactant molecule is significantly longer. 8,9 In such systems, surfactant aggregates, in particular vesicles, form spontaneously, 10 their size distribution arises from a competition between energetic and entropic contributions 11 and they adapt quickly to the outer conditions (ionic strength, temperature, pH if applicable etc.). 12,13 However, some catanionic systems do not achieve equilibrium within an experimental timescale which can reach several months. For instance, mixtures of linear fatty acids and linear cationic surfactants (e.g. myristic acid and cetyl trimethylammonium bromide or hydroxide) form bilayers which are in a quasi-solid state (gel phase) at room temperature. [14][15][16] As a consequence, the aggregates in solution (discs, icosehedra, lamellar phases etc. 17 ) are quenched at room temperature, which is illustrated e.g. by a size distribution of vesicles which is dependent on sample history instead of final composition. 18 This restrained dynamics, combined with strong local electrostatic constraints, 19 probably accounts for the high rigidity of the bilayers at zero frequency, as measured by atomic force microscopy on vesicles. 20 We expect these peculiar dynamic and mechanical properties of the bilayers to provide original interfacial behaviours, and outstanding properties to systems where adsorption processes and monolayer elasticity are critical. In particular, it has been shown before that such catanionic systems stabilize oil-in-water emulsions with no significant coarsening over several months, and it has been suggested that the adsorption of rigid bilayer fragments -a Pickering-like effect -accounts for these properties. 21 Here, we focus on the interfacial properties of air/water interfaces prepared from solutions of rigid catanionic bilayers below the melting point of the surfactant chains (classically referred to as "gel-phase"). With respect to the above-mentioned properties, the most relevant points to investigate are not only the static interfacial properties as determined at large timescales (Sec.

3.2), but also the dynamics of the adsorption process which show very peculiar two-step processes (Sec. 3.3). This allows us to propose a first explanation for both the foamability and the remarkable foam stability that we report on these systems (Sec. 3.4).

Material, preparation and methods

Materials

Myristic acid (C 13 COOH, Fluka; Mw = 228 g mol -1 ) was recrystallized twice from hot acetonitrile, and cetyl trimethylammonium bromide (CTABr, Mw = 364 g mol -1 , cmc = 0.36 gL -1 ) was purchased from Sigma and used as such. Solutions were prepared with MilliQ water.

Solution preparation

The catanionic mixtures have been prepared as described previously: 22 suitable amounts of C 13 COOH and CTABr are mixed with water at a typical weight fraction of surfactant of 1% and heated at 50°C ± 0.1°C for 3 days. The resulting mixture is dialyzed against a 100-fold volume of water (SpectraPor regenerated cellulose membranes, 10 kDa cutoff). In a typical preparation, the dialysis water is changed after 1 hour, 4 hours, 24 hours, 48 hours and 5 days.

The effective composition of the mixtures is controlled by the initial composition and the time of dialysis. 22 The compositions of the various samples investigated here and their conditions of preparation are summarized in table 1.

Foam production

Foam samples were prepared by vigorous hand shaking. We produced foams in cylindrical plastic containers (27 mm internal diameter, 120 mm height) filled with 20 mL of surfactant solution at the bulk concentration c = 1 gL -1 .

Tensiometry

We measured the surface tension  by using the Wilhelmy plate method and the pendant drop/rising bubble tensiometer apparatus (Teclis, France). In the first method, the air-water interface is created in a home-made Teflon circular trough (diameter = 8 cm, depth = 3 cm) and the surface tension is monitored up to a time t = 10 5 s by a pressure transducer (Nima, UK);  always reaches a constant value at long times, called  e afterwards.In the pendant drop/rising bubble method, the surface tension is calculated by image analysis from the shape of the drop or bubble using the Laplace equation. [START_REF] Benjamins | Colloids and Surf[END_REF] Usually, we monitored the change of surface tension during adsorption up to a time t = 10 4 s. Above the latter time, liquid evaporation and non-Laplacian shape may introduce artefacts in the surface tension evaluation. Initial volumes for bubble and drop changed from 6 to 12 µL and no feedback control for volume or area was selected since it perturbed the adsorption kinetics. As a result, bubbles/drops tend to detach as surface tension drops significantly.

Ellipsometry

We performed multiple angle of incidence (MAI) measurements [START_REF] Azzam | Ellipsometry and polarized light[END_REF] using an imaging ellipsometer (Nanofilm, Germany) working with green laser light ( = 532 nm). A fixed compensator (= 45°) and 4-zone averaging nulling scheme were adopted. Solutions were prepared in a circular trough (diameter = 8 cm, depth = 3 cm). We waited from one to four hours (after preparation) before measuring the ellipsometric angles Ψ and Δ (around the Brewster angle  B = 53.1° for the air-water interface). [START_REF] Azzam | Ellipsometry and polarized light[END_REF] Measured ellipsometric angles  and at a given incident angle  are related to the ratio of the Fresnel reflection coefficients r in p and s polarization by r p /r s = tan exp(i. Ψ and Δ were measured from  = 52° to 54.5° in steps of 0.1°. The data were fitted with a single homogeneous layer model, characterized by a refractive index n l and a thickness d, between the air (n Air = 1) and water (n H2O = 1.333) bulk phases (see Supporting Information).

Multiple light scattering

In order to study the foam evolution we measured the multiply scattered light intensity I s during foam aging. This technique is also known as diffusing wave spectroscopy (DWS). [START_REF] Vera | [END_REF]26 In this study we adopted an optical scheme detecting the multiply scattered light in transmission. The source of radiation was a laser (Coherent, Compass 315M-100) working at  = 533 nm. The foam cell was a plastic cylinder of 120 mm height and with an internal diameter of 27 mm. The diffused transmitted light was collected by an optical fibre (Oz Optics) equipped with a focus lens designed to collect a spot size of the same order than the laser speckle. A photomultiplier (Hamamatsu) and a correlator (Correlator.com, Flex2k-12x2) were used together with the software Flex2k. In order to follow the foam evolution in time (usually up to 10 5 s), we performed 10 measurements of duration = 10 s, followed by 10 measurements of 120 s and measurements of 7200 s until the foam bubbles became too large for the validity conditions of the method to be fulfilled.

From the static intensity, we could gain information on the bubble size evolution. In fact, the intensity I s is proportional to l * /L, [START_REF] Vera | [END_REF] where l * is the mean free path of light photons and L is the thickness of the foam sample; l * depends on the mean bubble radius R in the foam and on the foam liquid fraction , i.e. I s ~ R/  Results presented in this article were obtained within 10 days after solution preparation.

The experiments were conducted at room temperature, being 20 ± 2 ºC.

Results and Discussion

Brief summary of the known behaviour of the studied systems

The co-solubilisation of myristic acid (C 13 COOH) and cetyltrimethyl ammonium bromide (CTABr) at 50°C, and the subsequent dialysis have been studied recently by Michina et al. 22 and Kopetzki et al.. 18 Upon association, both amphiphilic molecules form gel phase (solidlike) mixed bilayers of CTA + , C 13 COOH and C 13 COO -and release their counter-ions H + and Br -ions. 15,19 The initial composition and the time of dialysis t d determine their effective composition, the nature of the aggregates (possible presence of mixed micelles in addition to the bilayers), their morphology and their properties. If we define the molar fraction of myristic acid f as:

      CTABr COOH C COOH C f   13 13
, then the general behaviour of these mixtures is summarized as follows:

(i) Upon dialysis, f increases (CTA + is extracted from the mixture) until a value of f ≈ 0.66 is reached (in typically 25 days). No CTA + extraction occurs in mixtures prepared at an initial fraction f 0 = 0.66 and above.

(ii) Mixtures prepared at an initial fraction f 0 < 0.66 form ill-defined aggregates of bilayers.

Mixtures prepared at f 0 = 0.66 form elongated vesicles prior to dialysis, which swell to spherical vesicles upon dialysis (iii) Upon dialysis, H + Br -ions released upon association of both amphiphilic molecules are extracted. The extraction remains incomplete if vesicles are present, as 30% of the ions remain encapsulated (iv) The bilayers coexist with CTA + ions with concentrations in the 10 -4 -10 -2 mol•L -1 range, depending on composition, present either under the form of free ions or micelles. Upon dialysis, the amount of such free CTA + decreases and reaches the minimal value of 10 -4 mol•L -1 as f reaches the maximal value of f = 0.66.

The final pH is 6.5 (MilliQ water) and shows no noticeable dependency on composition.

The effective compositions of the sample investigated here and their conditions of preparations are summarized in table 1 using estimated values from ref. 22 . Once the dialysis is stopped, the samples show little evolution, except the CTA-rich samples (f < 0.5) that tend to phase separate.

f 0 dialysis f [Br -]/[CTA + ] [CTA + ]
We emphasize two characteristics of this system that are particularly relevant to the work presented afterwards : first, the bilayers are in the gel phase, i.e. are solid-like bilayers with slow lateral diffusion and exchange with the outer solution. In addition, these bilayers are in coexistence with small concentrations of "free" CTA + , present either under the form of monomers, or micelles in non-dialyzed samples at f 0 = 0.33. It was shown that the concentration of free CTA + decreases upon dialysis (table 1). This was assigned to an increase in the cohesive energy of the bilayers as the composition approaches the optimum ratio of f = 0.66. The concentration of myristic acid outside the bilayers was below the detection limit (< 10 -5 M). Upon dilution, these concentrations slowly equilibrate again with timescales far above the experimental times investigated here (weeks). We therefore consider that dilution will decrease equally the total bulk concentration and the concentration of free surfactants in solution.

Equilibrium surface tension and interfacial profile

Fig. 1 presents the equilibrium surface tension  e as determined by the Wilhelmy plate method for CTABr (f = 0) and for the six surfactant mixtures. For CTABr, at c = 0.01 gL -1  e begins to deviate significantly from the air-water value (  = ca 72 mN m -1 ) and saturates around 35 mN m -1 , at the solubility limit, in good agreement with the literature data. 28 Using the Gibbs equation before saturation, we determine the surface concentration  in CTABr as a function of the bulk concentration c CTABr (see solid line in Fig. 2):

) (ln 2 1 ) ( CTABr e CTABr c RT c       , ( 1
)
where R is the ideal gas constant is and T is the absolute temperature. This yields values of  that increase with the bulk concentration up to about 1 mg/m² (corresponding to a surface area of 62 Ų per molecule), which is well above the mean surface per molecule in the C 13 COOH/CTABr bilayers (around 20 Ų at f > 0.50). 15,18,22 Contrary to CTABr, no significant differences in  e were observed for catanionic mixtures as the bulk concentration was changed. Typically,  e  25 mN m -1 was found, significantly lower than for CTABr even at the highest concentration studied and comparable to the surface tension of pure myristic acid above the melting point, i.e.,    27.9 mN m -1 at 343 K. [START_REF] Wohlfarth | Surface Tension of Pure Liquids and Binary Liquid Mixtures[END_REF] The small surface tension of the mixtures can be assigned to the strong attractive interaction between polar heads which enhances significantly the surface coverage as compared to CTABr alone (as confirmed by the ellipsometry measurements, see below).

Furthermore, it is worth noting (inset of Fig. 1) the small increase of  e with increasing f, independently on the residual amount of bromide ions.

Fig. 2 shows ellipsometric results for catanionic mixtures in the same range of concentrations. We fitted the thickness d of the layer keeping constant the refractive index n l = 1.45, being close to the refractive index of CTABr and C 13 COOH (see Supporting Information). In a first approximation, this analysis allows to evaluate the surface concentration 30  = d (n l -n H2O )/(n/c), where n/c ( n/c = 0.12 mL g -1 ) is the refractive index increment. A clear increase of  from ca 0.2 to 0.7 mg m -2 (from ca 277 to 87 Ų) was observed for CTABr between 0.01 and 0.1 gL -1 in agreement with the values calculated from

Eq. 1 (see solid line in Fig. 2). For catanionic mixtures, the surface concentrations are higher than for CTABr, and  remains close to 1 mg m -2 . If one assumes that the layer composition is similar to that of the most stable bilayers, i.e. f=0.66, the value of the average area per molecule drops to 45Ų.

Adsorption and surface relaxation

For non ionic surfactant systems a plateau value in the dynamic surface tension curves ( vs. t) is reached after a complete surfactant adsorption onto the interface. Diffusion-limited adsorption shows the following asymptotic behaviours: for short times t~t 1/2 , whereas for long times t~t -1/2 . By contrast, adsorption limited by a energy barrier can be described by simple exponential function t ~ exp(-t/), where  is a characteristic relaxation time. [START_REF] Kralchevsky | Handbook of Surface and Colloid Chemistry (Third Edition)[END_REF] When the adsorption barrier is due to electrostatic effects, Bonfillon et al. [START_REF] Bonfillon | [END_REF] described the adsorption of charged surfactants as a combination of diffusion and adsorption barrier processes. In the first adsorption stage, diffusion brings molecules and charges at the interface creating a repulsive potential, hence depletion and accumulation of surfactant below the interface. However, the latter surfactant can overcome this barrier in a final adsorption stage when the concentration is large enough, leading to t ~ t. [START_REF] Bonfillon | [END_REF] This process has been modelled later by Diamant et al. 33 Dynamic surface tension curves for the catanionic mixtures, are shown in Figs. 3a,3b.

Note that for each tcurve, the experimental data correspond to surface tensions evaluated in a region where the Laplace equation could be safely applied, far before bubble/drops detachment or observation of a non Laplacian shape. The following observations can be made:

i) asymptotic values are in good agreement with the equilibrium surface tensions measured by the Wilhelmy plate method, ii) two distinct relaxations are usually observed, iii) significant differences between the pendant drop and rising bubble data are observed, with relaxations for pendant drop experiments slower than for rising bubble ones, iv) a singularity in the first derivative of tbetween the two relaxations is usually observed, v) within the same method, the relaxation rates increase with the bulk concentration.

At t = 1 s, values for (t) shown in Fig. 3 could be related to the adsorption of free CTABr. This can be clearly observed for ND catanionic mixtures focusing on c = 1 gL -1 at increasing CTABr content (i.e. decreasing f). For f = 0.66, (t) > 60 mN m -1 ; for f = 0.55, (t)

= ca 55 mN m -1 ; and for f = 0.35, (t) = ca 43 mN m -1 . Indeed, it has been shown before that the gel-phase bilayers are in coexistence with free CTABr molecules and with CTABr-rich micelles when f is small enough. The concentration of free monomers decreases as the effective molar fraction of myristic acid f increases, due to the increase in the interaction with CTABr molecules as f approaches f critical = 0.66. 22 If we assume that the adsorption of the amphiphiles forming the bilayers is much slower than the adsorption from the free molecules and micelles, we can explain why the surface tension at short times is larger for larger f. More quantitatively, the dynamic surface tension at t = 1 s, (t=1) (Fig. 3), can be plotted as a function of the concentration c CTABr,FREE of the surfactants which are not inserted in the bilayers estimated from the data of Michina et al. 22 (Figure 6 in reference 22 ) or as a function of the concentration c CTABr,TOTAL considering all CTABr molecules in solution and calculated as:

           f f Mw CTABr Mw c c TOTAL CTABr 1 ) COOH C ( ) ( 1 / 13 , .
In Fig. 4, we present the comparison between (t=1) (data from Fig. 3) vs c CTABr,FREE and c CTABr,TOTAL ) with the equilibrium surface tension  e of pure CTABr solutions (data from Fig. 1). The  e curve lies between the two estimated plots. This comparison confirms the observation that for short times (t < 10 s) adsorption of free CTABraccounts only partially for (t). The free CTABr concentration underestimates the amount of surfactant contributing to adsorption at the surface. This means that there is a small but significant extra contribution due to the dissolution of surfactant from the micelles or the less stable vesicles (with f < 0.66).

In turn, for dialyzed catanionic mixtures, when the amount of free CTABr is reduced, (t) remains larger than 60 mN m -1 for 0 < t < 10 s. This is also observed for ND solutions with f = 0.66, which contain the most stable vesicles.

In order to quantify the observations made in the whole time range studied, we fitted (t) curves considering two time intervals (before and after a singular point) using the empirical function introduced recently by Moorkanikkara and Blankschtein: 34

                            m i n i e t t t t       2 1 ) ( ) ( 0 (2)
where n, m are two adimensional parameters and  i is a characteristic relaxation time. For n = m, Eq. 2 correspond to the function introduced by Rosen and Gao to describe (t) curves of ionic surfactants and their mixtures. 35 We fitted 5 parameters (   e ,  i , n, m) in each time interval where a relaxation was observed (see Supporting Information). In most of the cases, two relaxation times  1 and       are needed to describe experimental (t) curves shown in Fig. 3. For f =0 .55, rising bubble experiments could be fitted by one relaxation. Typical values for n and m are in the 0.1-5 range. In Fig. 5 we plotted the characteristic times  1 and   . In the first interval at low concentrations, fitted   values are in good agreement with the literature value of pure water (ca 72 mN m -1 ); and in the second interval, fitted  e values are in good agreement with the experimental values shown in Fig. 1 (ca 25 mN m -1 ).

Rising bubble and pendant drop experiments clearly differ from each other, especially for the ND samples with f = 0.66. In this case,   which changes from ca 2000 to 200 s is almost ten times higher than for rising bubble experiments. These differences are usually due to the depletion of surfactants form the interface in the case of pendant drops, which is enhanced by electrostatic effects. 36 We will not discuss further these differences and focus afterwards on the rising bubble data.

For non dialyzed catanionic mixtures,  1 decreases by increasing the concentration :   ~ c -1/2 (see Fig. 5a). This is much slower than for diffusion-limited adsorption, for which the asymptotic behaviour of the surface tension is:

31 2 / 1 0 2 4 ) (            t D c RT t e e    , ( 3
)
where R is the gas constant, T is the temperature,  e is the equilibrium surface concentration and D 0 is the diffusion coefficient. This leads to a characteristic time ~ c -2 . However, the scaling predicted by eq. 3 applies to the concentration of free surfactant, or of surfactant rapidly available (in labile aggregates such as mixed micelles). It is very difficult to estimate the actual CTABr concentration contributing to 

. It lies probably between c

CTABr,FREE and c CTABr,TOTAL as discussed above. Moreover, adsorption is slowed down by the charges present at the surfaces, which are progressively screened by increasing bulk concentration. Hence the adsorption rate may appear less dependent on the overall bulk concentration than predicted by equation 3. For dialyzed mixtures,   show the scaling ~ c -1/2 just for f = 0.58, 0.62 (see Fig. 5b). For f = 0.66,   remain approximately constant as the concentration is changed. This indicates that no free surfactant is available in this case, and therefore suggests that the free surfactant molecules detected at this composition (table 1) are encapsulated in the vesicles and can not reach the interface during this initial step. Consistently, this concentration-independent behaviour is only observed when vesicles are present after dialysis. For all mixtures   does not vary much (remaining around ca 3000 s) when c and f are varied.

The relaxation time   could correspond to the time needed to overcome the repulsive interfacial barrier. [START_REF] Bonfillon | [END_REF] In fact, for f = 0.55, 0.58, 0.62 and 0.66(ND) we found n, m = ca. 1, t ~ t, as observed by Bonfillon et al. [START_REF] Bonfillon | [END_REF] However, the model leads as for standard diffusion, to a characteristic time ~ c -2 . It is again possible that the actual free concentration increases very slowly with the overall concentration as discussed above for  1 .  Alternatively,   may account for the dissolution time needed to free additional surfactant molecules from bilayers. 37 Chang et al. model the dynamic adsorption process of surfactants at the air-water interface by: . ) , ( ) , (

2 2 0 q x t x c D t t x c       where the term q = k 1 -k 2 •c
, which is the aggregation dissolution rate, is added to the classical Fickian law for diffusion; k 1 and k 2 are rates for the transfer of free surfactants into the aggregates. Chang et al. found good agreement with experiments on solutions of other catanionic surfactants, using only k 1 , i.e. a concentration independent rate of transfer. This process would account for the limited concentration variation of  2 seen here.

Foam stability and foamability

In Fig. 6, we show the average multiple scattered light intensity I s as a function of foam age. The scattering volume is fixed in space and it lies above the macroscopic interface between the drained liquid and the foam. In the first stages of foam aging, drainage takes place followed by coarsening. 27 I s ~ R/ increases monotonically with foam age for CTABr, whereas for the mixtures, a small decrease can be seen in the first stages of aging. This decrease can be due either to a decrease of the mean bubble size R or to a local increase of the liquid fraction in the scattering volume.

In the first hypothesis, coarsening leads to a decrease of the size of many small bubbles and the increase of size of few large bubbles that in order to expand tend to move upwards. Thus, in the scattering volume an increasing concentration of small bubbles could explain a decrease of I s .

In the second hypothesis, the decrease of I s could be explained by a local increase in the liquid fraction profile (z) of the scattering volume due to drainage. In fact, two boundaries for the liquid fraction profile can be considered. Just after foam production, we can suppose  =   everywhere in the foam independently on the foam height. Whereas, at the equilibrium,

(z) = k (/ R) 2 [p g -p 0 -g(z-z 0 )] -2 ,
where k is a geometrical constant, p g is the gas pressure in the bubble, p 0 is the liquid pressure at the top of the foam (z = z 0 ) and g(z-z 0 ) represents the hydrostatic contribution to the liquid pressure. [START_REF] Weaire | The Physics of Foams[END_REF] Being    0.36, there will be a significant liquid flow from the top to the bottom of the foam during equilibration; and this net flow, passing through the scattering volume, could generate a local increase of  in time affecting I s .

For CTABr, after 10 2 seconds, drainage is almost completed (see Fig. 7) and I s follows a scaling exponent of 1/3 typical of wet foam coarsening ( ≈ 0.12). After 10 3 seconds, the scaling exponent changes to 1/2 as it is expected for dry foam coarsening ( ≈ 0.07). [START_REF] Durian | [END_REF] After a foam age of 10 4 seconds, the bubbles are large as it can be seen by the photographic images in Fig. 7 and the validity conditions of the multiple scattering analysis (I s ~ R) are not fulfilled (R/L > 0.1). 27 Hence the fast time variation of R (faster than t 1/2 ) seen in the figure cannot be regarded any more as the true time variation. Note that due to the very limited variation of R, the agreement with the scaling laws at shorter times can only be considered as indicative.

Foams prepared from catanionic mixtures solutions of 1 gL -1 last much longer than CTABr foams, foam collapse starting only after around 10 5 seconds. Note that when the intensity reaches the value around 10 5 count s -1 , the foam is composed just by a few bubbles that can be stable even for longer time.

For f = 0.35, we observed that the volume of foam produced (= foamability) from non dialyzed solution is as high as for the pure surfactant solutions and much higher than for dialysed solution (see Fig. 7). This difference in foamability is due to the lower concentration of free CTABr in the non dialysed solutions as demonstrated in the previous section. Note also that the foams made with dialysed solutions are wetter (higher  and lower I s ).

For f 0 = 0.55, dialyzed and non dialyzed foams behave similarly and the increase of I s is monotonic in the last stages of aging, with a trend similar to CTABr foam but shifted towards a longer foam age. For f 0 = 0.66, I s shows a minimum around 10 3 seconds followed by an increase up to the foam collapse; as discussed before, the minimum is likely due to a local increase of the liquid fraction because of drainage, more important for these foams which are wetter just after production. From photographic images (Figs 7e, 7f), we noted the formation of a dense foam layer: at the top, the foam is similar to the other foams observed in the other cases; at the bottom layer, an accumulation of closely packed spherical bubbles in the liquid phase is observed. This dense foam layer is also present for the dialysed sample with f 0 =0.55.

Conclusions and Outlook

In conclusion, the dramatic increase of foam stability for catanionic mixtures respect to pure CTABr can be related to the low surface tension and high surface concentration. The tension is low even at very low surfactant concentration and is similar for dialysed and non dialysed samples, ~ 25 mN m -1 . The high surface concentration  should be accompanied by high elastic and viscous compression moduli as confirmed by preliminary oscillating bubble experiments. The equilibrium surface tension is reached in two steps; the first one is related to the presence of CTABr molecules, either free, or contained in labile aggregates. The second step is similar for dialysed and non dialysed samples, and may be controlled either by a repulsive electrostatic barrier or by dissolution of surfactants from bilayers located in the subphase.

Foamability is related to concentration of free surfactants and is higher for non dialysed samples: for solutions with f = 0.35 that contain the largest amount of free CTABr, foamability is comparable to that of pure CTABr solutions. Multiple scattered light intensity I s increases following the scaling laws predicted for wet and dry foam coarsening for f = 0.35 and f 0 = 0.55. For f = 0.66 a minimum is observed at short times and it could be related to a local increase of the liquid fraction due to drainage, the initial liquid fraction in these foams being very large. The rate of coarsening is similar for dialysed and non dialysed samples and much slower than for pure CTABr foams.

Interfacial rheology studies using oscillating bubble experiments and by an interfacial bicone rheometer are currently in progress, together with a confocal microscopy investigation of the surface of the solutions, which may elucidate the role played by aggregates located in the subphase near the air-water interface.

Supporting information:

In this file, we provide 1) ellipsometric data as a function of the angle of incidence for CTABr and a for a catanionic solution, and 2) all parameters of the fits of dynamic surface tension data. This information is available free of charge via the Internet at http://pubs.acs.org/.

Table of Contents Graphic

FiguresFig. 1

 1 Figures

  Equilibrium surface tension  e , measured by Wilhelmy plate method, of pure CTABr (f 0 = 0), non dialyzed ND and dialyzed D catanionic mixtures as a function of bulk concentration. The inset is a plot of  e vs f.

Fig. 2 Thickness

 2 Fig. 2

Fig. 3

 3 Fig. 3Dynamic surface tension curves for non dialyzed (a) and dialyzed (b) catanionic mixtures. Solid lines are fits of the data using Eq. 2.

Fig. 4 Equilibrium

 4 Fig. 4

Fig. 5 Relaxation

 5 Fig. 5

Fig. 6

 6 Fig. 6 Multiply scattered light intensity I s as a function of foam age. Foams were made from non dialyzed (ND) and dialyzed (D) catanionic mixtures at the bulk concentration c = 1 g L -1 . f 0 = 0 corresponds to pure CTABr.

Fig. 7

 7 Fig. 7 Photographic images taken at foam age = 10 2 s (a,d), 10 3 s (b,e), 10 4 s (c,f). Foams were made from non dialyzed (a,b,c) and dialyzed (d,e,f) catanionic mixtures at the bulk concentration c = 1 g L -1 . f 0 = 0 corresponds to pure CTABr.

Table 1 .

 1 Initial and final values of f, dialysis time, final values of [Br -]/[CTA + ] and concentration of [CTA + ] outside the bilayers as estimated by Michina et al.[ref]

	outside
	bilayers

Acknowledgements

We are grateful to Thomas Zemb for discussions on catanionic systems and to Arnaud Saint-Jalmes for sharing his expertise concerning multiple light scattering. Emmanuelle Rio and Wiebke Drenckhan are also gratefully acknowledged for numerous discussions. A.S. has benefited from a post-doctoral Marie Curie fellowship (RTN SOCON).


Claire Arnaud

Maurice Dematteis

Jean-Louis Pepin

Jean-Philippe Baguet

Patrick Lévy

Keywords: Obstructive sleep apnea, immuno-inflammation, and atherosclerosis


Dr Benjamin Erable

Dr Damien Føron

Dr Alain Bergel
email: alain.bergel@ensiacet.fr

Microbial Catalysis of the Oxygen Reduction Reaction for Microbial Fuel Cells: A Review

Keywords: electrochemistry, fuel cells, microbes, oxygen reduction, thin films

Introduction

For approximately one century, [1] microbial fuel cells (MFCs) have been believed to be a promising technology for the production of electrical energy directly by the oxidation of organic matter. Since the discovery, early in the 21 st century, of the capacity of microbial cells [2] and microbial biofilms [3] to catalyse electrochemical reactions, our understanding of microbial electrocatalytic mechanisms on anodes has advanced fast. [4] In comparison, few studies have been devoted to the development of MFC cathodes, even though they constitute a crucial bottleneck. Using oxygen as final electron acceptor would clearly be the most convenient solution to develop MFCs with wide applicability, but the kinetics of the oxygen reduction reaction (ORR) is slow. Different final electron acceptors, such as hexacynoferrate(IV) or permanganate, can give faster reduction kinetics than oxygen, but they would not afford sustainable options. [5] The high value of the standard equilibrium potential of oxygen reduction,

O 2 þ 4 H þ þ 4 e À ! 2 H 2 O ð1Þ
E 0 = 1.229 V measured versus standard hydrogen electrode (SHE) under standard conditions, makes it a ubiquitous final electron acceptor for a very large number of redox processes. Fortunately, the kinetics of ORR is slow and catalysts are rare. [START_REF] Kinoshita | Electrochemical Oxygen Technology[END_REF] If ORR kinetics were fast on materials readily available over the earth's surface, a wide variety of oxidation reactions would occur spontaneously. For example, metallic materials would corrode very rapidly and non-metallic materials might be highly sensitive to oxidative deterioration. The reactive oxygen species resulting from fast oxygen reduction would exert incredibly high oxidative stresses on living organisms, resulting in accelerated ageing and death. The rarity of efficient ORR catalysts on the surface of the earth can be seen as a necessary condition for the protection of living creatures in general and human beings in particular. These few general considerations give an idea of the difficulty of discovering efficient ORR catalysts.

ORR catalysts used in MFCs can be organised into three groups: chemical, enzymatic and microbial. Chemical catalysts have been directly derived from the work on conventional low-temperature fuel cells, notably proton exchange membrane fuel cells (PEMFCs). Platinum offers the highest catalytic performance, but has not allowed PEMFCs to become economically efficient yet. The limited availability of platinum, and therefore its cost, and the strong environmental impact linked to its production are serious drawbacks. Moreover, platinum is inhibited by numerous pollutants and consequently requires very pure fuels. Earlier studies of other chemical compounds for PEMFCs have met little success.

Living organisms have developed efficient oxidoreductases to achieve and control ORR. By taking advantage of these enzymes, mainly laccases and bilirubin oxidases, [START_REF] Cooney | [END_REF] it has been possible to design biofuel cells allowing ORR at potential values close to the E 0 ' value. Associating a microbial anode with a laccase-catalysed cathode has given the highest voltage reported for a MFC that uses oxygen as electron acceptor. [8] The slow kinetics of the electrochemical oxygen reduction reaction (ORR) is a crucial bottleneck in the development of microbial fuel cells (MFCs). This article firstly gives an overview of the particular constraints imposed on ORR by MFC operating conditions: neutral pH, slow oxygen mass transfer, sensitivity to reactive oxygen species, fouling and biofouling. A review of the literature is then proposed to assess how microbial catalysis could afford suitable solutions. Actually, microbial catalysis of ORR occurs spontaneously on the surface of metallic materi-als and is an effective motor of microbial corrosion. In this framework, several mechanisms have been proposed, which are reviewed in the second part of the article. The last part describes the efforts made in the domain of MFCs to determine the microbial ecology of electroactive biofilms and define efficient protocols for the formation of microbial oxygen-reducing cathodes. Although no clear mechanism has been established yet, several promising solutions have been recently proposed.

In this respect, enzymes are likely the best catalytic option. Nevertheless, enzymes are very sensitive to any kind of inhibition, they often require sophisticated chemical operations to be immobilised on electrode surfaces and their lifetimes generally do not exceed a few days in operating conditions. From the current state of the art, it can be thought that enzyme catalysis is more suitable for disposable devices that should be able to deliver high power density immediately and for a short time, whereas microbial catalysis seems more suited to longterm production where a relatively long starting phase is acceptable.

A multi-criteria comparison of the different options of ORR catalysis has been proposed recently. [9] From a general point of view, microbial catalysis may offer very promising advantages [10] because its characteristics and constraints are similar to those of microbial anodes. Moreover, microbial catalysis of ORR is known to occur spontaneously on the surface of metallic materials that are exposed to natural environments, notably seawater. This phenomenon has been identified as the main motor of aerobic corrosion, which is called microbially influenced corrosion (MIC) in this case. The knowledge gained in the domain of MIC may offer a helpful basis for progressing in cathode design for MFCs.

The purpose of this article is to review the advances that have been made in understanding microbial catalysis of ORR in both MIC and MFC domains. Reviews on MIC generally devote a large part to the characterisation of material surfaces and passive layers, [11][12][13] whereas reviews on MFCs generally broaden their scope to abiotic oxygen-reducing cathodes [9,10] or to anaerobic microbial cathodes for synthesis and bioremediation applications. [14][15][16][17] The present article only focuses on ORR microbial catalysis while trying to build bridges between microbial corrosion and MFC thematic areas.

Basics on Oxygen Reduction Reaction in MFC Conditions

The electrochemical reduction of oxygen in an aqueous electrolyte can proceed by two overall pathways as represented in Table 1. Detailed mechanisms are more complex and they can involve many elementary steps with adsorbed species and radicals, which depend strongly on the electrode material. [START_REF] Kinoshita | Electrochemical Oxygen Technology[END_REF] The 4-electron pathway appears to be predominant on noblemetal electrocatalysts, whereas the peroxide pathway is predominant on graphite, gold, oxide-covered metals and most carbon materials.

ORR has been investigated in depth with a view to developing chemical fuel cells, mainly PEMFCs for low temperatures, but MFCs involve different constraints and requirements [5] that are listed below.

Neutral pH value

The abiotic cathodes developed for chemical fuel cells offer only limited performance in MFCs. These cathodes have been optimised to work in contact with a proton exchange membrane at extreme acidic pH values. A quick glance at the reac-tion equations shows that oxygen reduction is favoured by acid conditions, to provide the reaction with protons or to extract the hydroxyl ions produced. However, microbial development most often requires solutions at pH values ranging from 6.0 to 9.0. The common MFC operating conditions are consequently detrimental to ORR thermodynamics and kinetics.

Slow oxygen transfer

Oxygen solubility is low in aqueous solutions. It depends on the temperature and salinity of the solution, being higher at low salinity and low temperature, but it should be borne in mind that oxygen solubility is around 1 mm in pure water, implying that a solution in contact with air contains only around 0.24 mm dissolved oxygen. Diffusion coefficients are within the common range of values for dissolved gases in aqueous solution, that is, 1-3 10 À9 m 2 s À1 . [START_REF] Kinoshita | Electrochemical Oxygen Technology[END_REF] Mass transfer of oxygen to the electrode surface is consequently a slow step in MFCs, which must be considered with considerable care to improve cathode design. Air-breathing cathodes with a side in direct contact with air, a design coming from chemical fuel cell development, offer a relevant solution. Nevertheless, in MFCs the second face of air-breathing cathodes is in contact with the solution. The air-cathodes may be subject to problems of water "crossover", which provokes the decrease of catalytic performance.

Sensitivity of the microbial catalyst to reactive oxygen species

The peroxide pathway leads to hydrogen peroxide, with the possible production of other intermediate reactive oxygen species, such as the superoxide radical ion (O 2 C À ), which results from the mono-electronic reduction of oxygen. The hydroxyl radical (OHC) can also appear, particularly in the presence of iron ions, through the Haber-Weiss reaction and the system can then cycle in the Fenton process. The reactive oxygen species can damage almost all components of living cells, including proteins, lipids and DNA. The overproduction of reactive oxygen species at the cathode can have immediate detrimental effects by killing the microbial catalysts of both cathode and anode. It should be noted that the reactive oxygen species are known to be responsible for similar long-term problems in PEMFCs, for example, deterioration of the proton exchange membrane.

Fe 2þ þ H 2 O 2 ! Fe 3þ þ OHC þ OH À

Fouling due to alkalinisation of the interface and biofouling

The consumption of protons or the production of hydroxyl ions at the cathode surface results in alkalinisation of the interface. This is not a problem for PEMFCs, which use only hydrogen and oxygen. In contrast, MFC solutions contain many compounds and ions that precipitate when the pH value is decreased. Alkalinisation of the cathode interface can thus lead to severe fouling of the cathode surface by precipitation of hydroxides. The value of the interfacial pH depends on the balance between the rates of proton consumption and proton transport to the surface. Mass transport of protons must consequently be increased as much as possible in the vicinity of the cathode surface by stirring or buffering the solution. Nevertheless, it can be predicted that the decrease of the interfacial pH on the cathode surface will dramatically restrict MFC suitability for open environments that contain high ionic concentrations. For example, the presence of calcium ions in seawater results in cathode fouling by precipitation of calcium hydroxides when the current density increases. High current densities could be reached only in media that do not contain species that precipitate at the interfacial pH value. Biofouling should also be noted as a possible cause of decreased performance in open environments. Biofouling can easily be induced by influents that contain organic matter, even at low concentration, causing thickening of the biofilm and a dramatic decrease in the mass transfer rates of ionic species.

History: From MIC to MFC

LaQue [18] and then Nikita and Ulanovskii [19] pointed out that the open circuit potential of stainless steels increased with exposure time in natural seawater. This phenomenon, called "ennoblement of free (corrosion) potential" in the field of corrosion, has considerable economic importance because it shifts the material from passivity to an electrochemical state at which corrosion can occur. Ennoblement of free potential is commonly of the order of + 300 mV and can reach + 500 mV. [START_REF] Fischer | European Federation of Corrosion Publications[END_REF] It has been observed in seawaters from tropical [21] to Antarctic conditions; [START_REF] Alabiso | Dellepiane European Federation of Corrosion Publications[END_REF] in a large diversity of water bodies [13] such as rivers, [START_REF] Dickinson | [END_REF][START_REF] Chen | European Federation of Corrosion Publications[END_REF] estuaries [START_REF] Ishihara | [END_REF] and wastewater plants; [26] and with different metallic materials. [27] In 1976, Mollica and Trevis [START_REF] Mollica | Proceedings of the 4 th Int. Congress on Marine Corrosion and Fouling 1976[END_REF] correlated the free-potential ennoblement to the formation of a microbial biofilm that enhanced the cathodic branch of the exchange currents. From this date, it was widely agreed upon that biofilms formed in aerated waters spontaneously catalysed ORR on metallic surfaces. The biofilm effect [29] or the role of ORR catalysis [START_REF] Dickinson | [END_REF] have sometimes been denied in a few studies, but the great majority of studies have postulated microbial catalysis of ORR. [27,30] Corrosion studies have commonly been carried out in opencircuit conditions with the objective of investigating the effect of ORR catalysis on the free potential. In this type of experiments only the exchange currents are involved, which have very low values. To the best of our knowledge, the first oxygen-reducing microbial cathodes designed with the aim of increasing current densities were reported in parallel by two different groups in 1997. Mollica's group [START_REF] Mollica | European Federation of Corrosion Publications 1997[END_REF] showed that stainless-steel electrodes polarised at À0.2 V versus saturated calomel electrode (SCE) for a few days in seawater provided current densities of around 0.2 A m À2 . The same procedure repeated at eleven different European sea sites, with polarisations of 0.0 V versus SCE, gave current densities from 0.01 to 0.1 A m À2 , whereas less than 10 À5 A m À2 was measured in the absence of a biofilm. [32] In parallel, a similar seawater oxygen-reducing biofilm was developed on a graphite brush and coupled to a magnesium alloy anode in the design of a submarine battery. [START_REF] Hasvold | [END_REF] The seawater microbial cathode was then adapted to a fuel cell, giving current densities of up to 1.89 A m À2 with aerated seawater. [34] As was the case for corrosion, microbial cathodes for fuel cells have now been formed with various inocula (see Table 2). The knowledge gained in the corrosion domain allowed the first pure-strain oxygen-reducing cathode to be designed. [58] Pure cultures still remain poorly explored, although the highest current density has been reported with a pure strain of Acidithiobacillus ferrooxidans grown on a graphite electrode, which gave rise to 5.0 A m À2 at 0.0 V versus SCE working at pH 2.0 under a pure oxygen atmosphere. [54] It appears that a majority of studies devoted to ORR microbial catalysis has now shifted from the domain of corrosion to the MFC area.

Mechanisms of ORR Microbial Catalysis Identified in MIC

Direct catalysis by extracellular enzymes released by microbial cells

Pioneering research in aerobic MIC was aimed at identifying the components of the seawater biofilms that could be linked to microbial ORR catalysis. [59] Potential ennoblement was found to be more closely correlated to the quantity of carbohydrates and proteins contained in the biofilm than to the number of settled bacteria. Moreover, the addition of sodium azide, a strong inhibitor of the enzymes of the respiratory chain, to natural seawater decreased the free potential from + 350 to + 100 mV versus SCE. It has been concluded that ORR microbial catalysis was due to extracellular proteins, such as enzymes, which were adsorbed on the material surface (Scheme 1, reaction 1). Superoxide dismutases, catalases and peroxidases, which respectively catalyse > + 400 [a] 3 [b] 60 [b] months [36] plain granular graphite anaerobic/anoxic sludge continuous (1.3 mL min À1 ) nutrient solution, nitrate 350 days MFC (30 W) 6.5 [b] 34.46 [b] days [37] glassy carbon activated sludge continuous synthetic wastewater MFC (250 W) 60 159 months [38] carbon felt aerobic sludge batch-fed mode phosphate buffer solution IP ( + 0.242 V [a] ) 0.11 [b] 0.85 days [39] graphite fibre brush aerobic activated sludge batch-fed mode nutrient solution MFC (100 W) 0.482 [a] 68.4 [b] 325 [b] h [40] graphite felt membrane electrode assemblies aerobic sludge batch-fed mode phosphate buffer 144 mL MFC (51 W) 16.7 [b] 4.0 [b] days

[41a] plain granular graphite anaerobic/anoxic sludge continuous (13 mL min À1 ) synthetic wastewater nitrate 350 days, oxygen 50 days MFC (30 W) 10.3 [b] 44.2 [b] days

[41b] graphite granules aerobic sludge continuous (0.2 mL min À1 ) anodic effluent MFC 2.55 [b] 20 [b] days [42] granular graphite 6 mm diameter acetate-fed MFC (200 days) origin: activated sludge batch-fed mode synthetic medium recirculation loop (8 L h À1 ) IP (in MFC, À0.3 V [c] ) 0.040 [d] < 1 day [43] rough graphite plates nitrifying biomass (WTP) recirculation 12 mL h À1 IP (in MFC, + 0.150 V [c] ) 313 days [44] MFC (1000 W) 20.1 [b] 24.3 [b] 14.1 [b] 17.1 [b] months [c] 0.600 days [50] graphite plates sediment/water batch-fed mode SMFC-OCP 506 [a, f] 485 [a, g] 0.470 [a, e, f] 0.3a [h] 0.750 [h] days [53] graphite fibre brush and carbon granules topsoil batch-fed mode MFC (500 W) 500 [a] 100 [b] > 400 [b] h

Seawater
Pure culture [47] 32 [b] 28 [b] 79 [b] h

[a] Measured versus SHE. -disproportionation of the superoxide radical ion

2 O 2 C À þ 2 H þ ! O 2 þ H 2 O 2 ð9Þ
-disproportionation of hydrogen peroxide 2 H 2 O 2 ! O 2 þ 2 H 2 O ð10Þ
-and oxidation of several substrates (noted X-H 2 )

2 X-H 2 þ H 2 O 2 ! 2 X-HC þ 2 H 2 O ð11Þ
were guessed to be possible extracellular enzymes able to catalyse ORR. Bioelectrochemical studies have confirmed that catalase and horseradish peroxidase adsorbed on glassy-carbon and pyrolytic-graphite electrodes catalyse ORR by direct electron transfer. [56,60]

Direct catalysis by porphyrins and organometallic compounds entrapped in microbial biofilms

Porphyrins constitute the prosthetic group of catalase and several oxidases. Adsorbed iron porphyrin has been shown to catalyse ORR on glassy-carbon electrodes. [56,61,62] On stainless steel, micro-sized spots of iron porphyrin have induced local catalysis of ORR. [63] It can consequently be thought that the prosthetic group of oxidases, which would remain adsorbed on the electrode surface after enzyme degradation, can play the role of the ORR catalyst inside natural biofilms (Scheme 1, reaction 2). Similarly, organometallic complexes can be formed by complexation of metallic cations by the polysaccharides, which form an important part of the biofilm matrix. [11,64] Such organometallic complexes have been suggested as possible ORR catalysts. [30a, 65,66] However, it has been observed that freepotential ennoblement is decreased by enzymatic inhibitors such as sodium azide, [59] which suggests that functional enzymes are involved in ORR and metallic complexes can only play a secondary role in natural biofilms.

Indirect catalysis mediated by hydrogen peroxide produced by the microorganisms

It has been pointed out that the presence of hydrogen peroxide at the biofilm/electrode interface is a key parameter for free-potential ennoblement. [START_REF] Chandrasekaran | 12 th Int. Corr. Congress[END_REF] It has been postulated that three conditions were required to reproduce potential ennoblement in artificial seawater: The solution must be acidic (pH value around 2.9), partially deoxygenated and must contain hydrogen peroxide (2.4 mm). Hydrogen peroxide can be produced by marine bacteria, [START_REF] Denis | [END_REF] and hydrogen peroxide has often been detected in marine and fresh water biofilms. [69] Concentrations of 0.14-0.73 mm [START_REF] Chandrasekaran | 12 th Int. Corr. Congress[END_REF] and up to 6 mm [70] have been measured in natural marine biofilms. In parallel, an experimental model has been designed using glucose (10 mg L À1 ) and glucose oxidase (GOx, Scheme 1, reaction 3). The GOx-catalysed reduction of oxygen led to hydrogen peroxide:

C 6 H 12 O 6 þ O 2 þ H 2 O ! C 6 H 12 O 7 þ H 2 O 2 ð12Þ
which induced free-potential ennoblement of stainless steels. The model assumes that oxidases are present in wild biofilms and produce hydrogen peroxide by oxidising organic compounds. The same experimental model has been implemented with glucose (1 mg L À1 ) and glucose oxidase in sterilised or synthetic seawater. [71] It has thus been confirmed that acidification, which was ensured by the gluconic acid (C 6 H 12 O 7 ) produced, contributes to the ennoblement effect. A role of the (semi-)conductive properties of the oxide layers has also been evidenced. [71c] The glucose/glucose oxidase model has now been widely used to reproduce ORR microbial catalysis in aerobic MIC studies. [71d] 4.4. Indirect microbial catalysis mediated by manganese or iron oxides

In environments containing manganese or iron ions, ferro/ manganese oxidising bacteria can oxidise these ions to oxides, which are reduced back to ions on metallic surfaces (Scheme 1, reaction 4). Such a cycling of manganese ions by manganese oxidising bacteria (MOBs) results in an electron transfer chain from the material to oxygen, which is the final electron acceptor of MOBs. The system has been widely investigated as a possible mechanism of aerobic MIC. [START_REF] Dickinson | [END_REF]72] In more details, MOBs use oxygen to reduce manganese ions to manganese oxohydroxide (MnOOH), which deposits on the electrode surface and then leads to manganese dioxide (MnO 2 ). On the electrode surface, manganese dioxide is electrochemically Scheme 1. Different mechanisms postulated to explain the microbial catalysis of oxygen reduction by biofilms. 1) Direct catalysis by adsorbed extracellular proteins. 2) Direct catalysis by adsorbed prosthetic groups (porphyrins) or metal-exopolymer compounds. 3) Indirect catalysis by enzymes that reduce oxygen to hydrogen peroxide and organic acid. 4) Indirect catalysis mediated by manganese or iron oxides produced by ferro/manganese bacteria. The bacteria reduce oxygen and oxidise iron or manganese ions to oxihydroxides or oxides, which are reduced back to ions on the electrode surface. 5) Production of hydrogen peroxide by the biofilm improves the oxygen-reducing catalytic properties of the oxide layers of stainless steels. 6) Direct electron transfer from the electrode to the bacterial cell; this mechanism has been postulated by analogy with anaerobic cathodes. [16] reduced back into Mn 2 + ions with MnOOH as an intermediate species. The electrochemistry of manganese is complex, but it has been suggested that the reduction of manganese oxide into oxyhydroxide,

MnO 2 þ H 2 O þ e À Ð MnOOH þ OH À ð13Þ
with a standard equilibrium potential of 0.335 V versus SCE at pH 8.0, should be the key reaction that controls the free potential of the samples. This equation involves only solid deposited species, which can explain why the free potentials of metallic coupons have similar values in all field experiments. For example, the reduction of manganese oxide into manganese ions

MnO 2 þ 2 H 2 O þ 2 e À Ð Mn 2þ þ 4 OH À ð14Þ
has been ruled out because its standard equilibrium potential depends on the manganese ion concentration: 0.235 V versus SCE at pH 8.0 with 0.3 mm Mn 2 + [START_REF] Dickinson | [END_REF] or 0.310 V versus SCE at pH 7.5 with 0.1 mg L À1 Mn 2 + . [73] This reaction would consequently result in ennoblement values fluctuating as a function of the concentration of the Mn 2 + ions in different natural waters.

The model was confirmed by lab experiments with a MOBpure culture. [73] Surface analyses demonstrated that the potential was controlled by the ratio between the amount of MnOOH and MnO 2 deposited on the material surface (Scheme 2). A large experimental campaign demonstrated that the concentration of manganese ions directly influenced the rate of ennoblement, whereas the concentration of dissolved oxygen had no significant effect. [74]

Modification of the catalytic properties of iron oxides by seawater biofilms

The composition of the passive layer of stainless steels depends on the nature of the steel and is significantly affected by the medium in which the material is immerged. Studies of different stainless steels immersed in natural and artificial seawaters [75] have pointed out a thickening and a stratification of the passive layer. Hydrogen peroxide concentrations of 3-8 mm were measured in a two-month-old biofilm, and it has been postulated that hydrogen peroxide partially reduces the surface iron oxides, transforming trivalent iron atoms into divalent ones, which are known to be better ORR catalysts. According to this model, hydrogen peroxide produced by mature biofilms has an indirect effect by improving the catalytic properties of the iron oxides (Scheme 1, reaction 5).

Local acidification inside mature biofilms

Authors do not agree on whether or not marine biofilms can cause a local pH-value decrease on the material surface. Some authors have observed drastic acidification beneath some parts of the biofilm, [76] whereas others have claimed that the buffer power of seawater cannot allow the pH value to decrease significantly even in mature biofilms. [77] It has even been observed that ennoblement could be eliminated at low pH values. [27] The possible (or not) local acidification assumption remains a debated topic.

Influence of light

The possible influence of light on free-potential ennoblement remains uncertain. Some authors have denied any significant role of light, [78] others have shown that, after 4 h exposure to natural sunlight, seawater no longer causes free-potential ennoblement, whereas the amount of hydrogen peroxide produced is approximately doubled. Experiments performed with a Hg-Xe light source have suggested that light may also act on the nature of the oxides of the passive layer of steels. [START_REF]FØron in Microbially influenced corrosion and biodeterioration[END_REF] It may be guessed that some possible effects of light that are not generally controlled during field experiments might be the cause of unexplained discrepancies among the results from different teams.

Microbial Catalysis of ORR in MFC

Ecology of oxygen-reducing microbial cathodes

Since 1997 [START_REF] Mollica | European Federation of Corrosion Publications 1997[END_REF] and with renewed interest [34] due to the emergence of MFCs, the exploitation of microbial biofilms has been proposed as an effective solution for catalysing ORR around neutral pH at room temperature. The first studies have implemented aerobic biofilms formed from seawater on stainless steel electrodes. Now, microbial oxygen-reducing cathodes have been designed from many other sources of inoculum that can be divided into three groups: (i) wastewater and aerobic sludge, [36,37,41,80] (ii) seawater and freshwater [47][48][49] and (iii) Scheme 2. Detailed pathway of the indirect microbial catalysis mediated by manganese compounds. The reaction between the deposited manganese hydroxides and manganese oxide controls the free potential of the electrode. [73] soil. [53] These environments are known to offer broad bacterial diversity. [START_REF] Curtis | Proc. Natl. Acad. Sci[END_REF] In comparison to the work performed in the MIC area, a large amount of work devoted to MFCs has been turned towards the identification and isolation of bacterial species and systematic molecular characterisation of bacterial communities. The large ecological diversity of the ORR-catalysing biofilms is highlighted in Table 3.

Enrichment and isolation of pure strains

A few studies have attempted to isolate pure cultures from wild multi-species biofilms. [47,49] Bacterial isolations were always preceded by a phase of enrichment that promotes the growth of a given type of microorganism selected according to the physicochemical and nutritional conditions of the medium. Techniques that allow access to individual strains introduce a bias inherent in culture-dependent methods in two ways. Depending on the medium and the culture conditions, the growth of some species/genera/families is favoured. Moreover, only a very small proportion of the microorganisms contained in wild environments is cultivable. It has been assessed that only 0.001-0.1 % of the wild bacteria contained in seawater can be cultivated using conventional microbiology tech- niques. [83] The ratio is around 0.25 % for freshwater and sediments and up to 15 % to activated sludge. Rabaey et al. [47] first isolated autotrophic strains from an ORR-catalysing biofilm in 2008. A few isolates (Sphingobacterium sp. and Acinetobacter sp.) showed electroactive properties, but they led to current densities lower than those provided by the wild parental biofilm. A similar behaviour was observed with marine electroactive biofilms. [49,84] Among 30 heterotrophic bacterial strains isolated from wild ORR-catalysing marine biofilms, only two (Winogradskyella johsonii and Acinetobacter poriferorum) proved able to catalyse ORR, giving current densities of only a few percent of the current obtained with the parental wild biofilm. The hypothesis of a synergistic effect between the different microbial species making up the wild biofilm can be put forward. Other possible explanations can be pH change, surface modification or underdeveloped biofilm growth under pure culture conditions. [15]

Molecular phylogeny of wild complex biofilms

Culture-independent techniques are based on the analysis of nucleic acids (genomic DNA or 16S ribosomal RNA). The tools of molecular biology such as cloning and sequencing of 16S rRNA, [36,41,47] fluorescence in situ hybridization (FISH) [53] or denaturing gradient gel electrophoresis (DGGE) [37,49,53] have been largely implemented to analyse the microbial communities of ORR-catalysing biofilms (Table 3).

Analyses of the community structure and composition by molecular ecology techniques have revealed a high phylogenetic diversity of the ORR-catalysing biofilms. Phylogenetic groups detailed from oxygen-reducing microbial cathodes are mainly alpha-, delta-and gamma-Proteabacteria. Less known groups, such as Bacteroidetes and Firmicutes, have also been reported to be associated to these predominant groups (Table 3). These two groups have principally been highlighted in electroactive biofilms obtained from activated or anoxic sludge inocula. [36,41,47] In addition, novel and unculturable bacteria appear to be enriched.

Studies carried out on seawater microbial cathodes have shown no difference between the microbial composition of the biofilms that were able to catalyse ORR and those that were not. [45] In addition, the microbial population of the biofilms and of the surrounding seawater had the same dominant members. [84] It is consequently difficult to draw any firm conclusion, except that it has not yet been possible to establish a correlation between the electroactivity of aerobic biofilms and their microbial composition. [45] 5.2. Implementation in MFCs and performance

Biofilm formation: Polarisation, open circuit, low-resistance-connected MFC

The first phase of biofilm formation plays an important role in the evolution and performance of the cathode in a MFC. The first strategy proposed for forming efficient microbial cathodes consisted of polarising the electrode at a potential value low enough to induce a cathodic behaviour. [31, 20, 32b] A current density of 1.89 A m À2 was thus obtained with stainless steel cathodes in seawater maintained under air-bubbling. [34] These experiments used a three-electrode set-up with a potentiostat controlling the potential of the cathode versus a reference electrode.

Biofilms were then formed under "natural" conditions or, in other words, on electrodes left at open circuit. [46,48,50] In this case, the open circuit potential (OCP) value corresponds to the so-called free potential in the domain of corrosion. Similarly, it was also possible to connect the cathode and the anode of a MFC through a high resistance (R > 1000 W). [51,52,85] The electrode potential remained close to the OCP value, but it was slightly influenced by the potential of the anode. As the microbial anode forms concomitantly with the cathode, the potential of the cathode may vary erratically. In both cases (open circuit or high resistance) the availability of electrons from the cathode is very low and the growth of electroactive species that would use the electrode as electron source is not specifically favoured.

With a view to increasing the availability of electrons at the cathode and thus promoting development of electroactive species, a strategy consists in connecting the anode and cathode through a low resistance (R < 1000 W). [35,37,[39][40][41]47] The cathode potential is thus attracted to that of the anode, generally in the range of À300 to À400 mV versus SCE. Nevertheless, the potential is not controlled and changes depend on the rates of biofilm development on the anode and the cathode. It has been suggested that the control of the electrode potential could play a role in microbial physiology, including changes in cell surface properties, an increase in enzymatic activity and a shortening of the generation time of bacteria. This certainly explains why potential control is widely used in the most recent studies. [38,42,43,45,49,54,56] Nevertheless, it has recently been reported [45] that marine biofilms formed on stainless steel electrodes, either under polarisation or at open circuit, supported a similar ORR performance when they were finally polarised, providing current densities of about 0.6 A m À2 for several weeks. The best strategy for forming efficient oxygen-reducing microbial anodes remains open to debate.

Electrode material

Carbon and graphite materials are used in most studies on oxygen microbial cathodes. A few studies have used flat, smooth electrode structures such as graphite plates, [43,50] glassy carbon [37] or carbon paper, [56] but the majority has implemented three-dimensional (3D) structures, such as the widely-used carbon felts, [35,38,40,47,48,51,54] graphite granules [36,41,57,85] and graphite fibre brush. [START_REF] Hasvold | [END_REF]39] Zhang et al. [53] even combined graphite fibre and granules to create a new generation of graphitefibre-based cathode, in which the brush played the dual role of biofilm support and current collector for granules. Wei et al. [85] compared several carbon-based supports using a mix of aerobic and anaerobic sludge as inoculum. The different carbon-based electrodes offered structures with increasing surface areas: plain graphite, carbon felt, carbon granules and ac-tivated carbon granules. The higher the developed surface area of the carbon support was, the greater was the current density obtained. However, a linear relationship between the surface area available for biofilm growth and the current density was not obtained.

It is difficult to compare performance when it comes to 3D structures. The surface areas really active are clearly increased and consequently the current densities need to be expressed in A m À3 , rather than A m À2 . Moreover, when using volumetric current densities, care should be taken to express the current with respect to the electrode volume and not versus the total reactor volume. The first is relevant for 3D structures, whereas the second would not make sense and would only result in wrong comparisons.

Beyond carbon or graphite electrodes, stainless steel has also often been used as a support electrode. [34,45,46,48,49] There are very few studies comparing electrode materials in strictly identical experimental conditions. Carbon felt cathodes have been reported to give an approximately three times higher performance, with current densities of about 1 A m À2 , than stainless steel. [48] Nevertheless, it should be noted that the specific surface area of the carbon felt can be 10 3 times that of the stainless steel. [14]

Fed-batch versus continuous catholyte flow

For nutrient-poor environments such as seawater or freshwater, the availability of nutrients in the solution can drastically affect the electrode performance and stability. This consideration depends on the "electrode surface area/bulk volume" (A/V) ratio. A current density limited to 20 mA m À2 was provided by a marine biofilm formed in aerated seawater. The current was stable for only six days due to nutrient depletion. In this case, the A/V ratio was rather high, that is, 5 10 À2 cm À1 . [49] In contrast, the same experimental system implemented in continuous mode (60 mL h À1 ) reached 600 mA m À2 with a stability of more than 40 days. Similarly, such nutrient limitations were observed with similar marine cathodes implemented with lower A/V ratios in the range of 1. 2 10 À5[45] to 7.6 10 À3 cm À1 . [48] For richer media (anodic effluent, nutrient-supplemented solution, synthetic wastewater), the feeding mode does not significantly affect the performance of microbial cathodes. Many of the studies carried out with rich media have been performed by means of continuous feeding or at least by using a catholyte recirculation loop. Continuous feeding allowed a maximum concentration of oxygen to be ensured in the catholyte and the thickness of the biofilm to be controlled by hydrodynamic erosion. [43] Other studies have started in fedbatch mode for a few days before switching to continuous mode. [42,44] A study dealing with a Mn II -and Fe II -mediated system did not reveal any difference between fed-batch and continuous-feeding modes. [57] 6. Future for Microbially-Catalysed ORR: Targets and Outlook

About mechanisms

The MIC and MFC domains have developed complementary investigation approaches. The former have put their main efforts into looking for the component(s) and the mechanism(s) responsible for "free (corrosion)-potential ennoblement", whereas the latter have focused on the microbial composition of the biofilms and the isolation of bacterial strains. Nevertheless, no correlation has been evidenced yet between the microbial composition of aerobic biofilms and their capability to catalyse ORR.

No considerable advances have been made in the fundamental understanding of mechanisms in MFCs with respect to the knowledge gained in the MIC domain. The "mediation by manganese oxides" model discussed in MIC (section 4.4) has been confirmed and exploited to design specific cathodes. [35] Biomineralised manganese oxide deposited by a pure bacterial strain (Leptothrix discophora) has been observed on graphite cathodes, which provided currents two orders of magnitude higher than the clean electrode. [58] Cathodes elaborated by impregnating their surface with iron and manganese have also shown an increase in ORR catalysis, which was associated with the presence of ferro/manganese-oxidising bacteria in the biofilm. [57] In addition, studies carried out in pure cultures with collection strains [START_REF] Dickinson | [END_REF] and isolates [62] have confirmed the probable involvement of catalase or porphyrinic compounds in the catalytic pathway (sections 4.1 and 4.2).

A huge number of isolates and collection strains have been tested by cyclic voltammetry. Among 32 bacterial isolates coming from electroactive phototrophic river biofilms, 25 have thus shown their ability to induce transient catalysis of ORR. [START_REF] Lyautey | [END_REF] Several seawater isolates, [62] many collection strains [55,56] and even strains coming from anoxic biofilms [86] have shown similar transient catalysis. The very different phenotypic properties of these strains (gram stain, oxidase, catalase…) tend to confirm the involvement of a ubiquitous compound such as porphyrin. Actually, the voltammetry experiments involved adhered bacterial cells only, and no structured biofilm was formed on the electrode surface during these tests. This transient analytical technique detected a catalytic compound, but it did not prove the presence of a metabolic pathway that could support stationary oxygen reduction. The majority of these cells were not able to form ORR-catalysing biofilms. It must be concluded that the compound detected by voltammetry does not necessarily confer the ability to achieve stable oxygen reduction under constant polarisation. Voltammetry may consequently detect a secondary catalytic pathway, which bypasses the respiratory chain. This pathway may be due to excreted compounds, extracellular porphyrinic enzymes and their prosthetic groups, for example, which are produced to protect the cells against oxidative stress. In this case, other pathway(s) that require live bacteria should exist. [56,62] In the same way, Rosenbaum et al. [16] have suggested that the reduction of oxygen does not necessarily require enzymes, postulating that microbi-al cofactors, such as heme molecules, can be involved. By analogy to anaerobic cathodes, it may be thought that direct electron transfer may occur from the electrode to the bacterial cell [16] (Scheme 1, reaction 6), but this pathway still remains to be demonstrated.

The nature of the electrode material and its surface state are likely to have a significant effect on the performance of microbial cathodes, mainly in the final electron transfer from the biofilm to the electrode surface. Studies investigating this topic remain rare. For example, by using a stainless steel electrode, the electronic state of the surface oxide layer has been highlighted as a significant parameter that affects the current provided by seawater microbial cathodes in both, laboratory tests [71c, 46a] and a marine MFC pilot. [46b] A complex interface elaborated by electrodepositing carbon nanotubes and chitosan nanocomposite on a carbon electrode has been shown to enhance electron transfer between the electrode and the ORRcatalysing biofilm. [87] Increasing research efforts on this aspect would certainly afford significant advances.

Clearly, better understanding of the fundamental mechanisms remains a strong need. In this framework, identifying a pure strain, or a mixed culture if synergetic effects are essential, that could serve as experimental model would constitute a considerable progress.

Applications

The number and diversity of the constraints listed in Section 2 of this article may encourage pessimism. In contrast, the brief review of the studies devoted to oxygen-reducing microbial cathodes shows that clever and multiple tracks have been opened up to solve them.

pH value

The slow ORR kinetics at neutral pH might be solved in different ways. The acidophilic strain Acidithiobacillus ferrooxidans, which produces 5 A m À2 at 0.0 V versus SCE at pH 2.0, is a very promising option. [54] It should be associated with an acidophilic anode-respiring bacterium at the anode or would require a particular MFC design with an acidic cathode chamber. [88] In an MFC, oxidation of the fuel, which is usually acetate for laboratory cells,

CH 3 COO À þ 4 H 2 O ! 2 HCO 3 À þ 9 H þ þ 8 e À ð15Þ
results in acidification of the anode chamber, whereas oxygen reduction causes alkalinisation of the cathode side. This is a general problem for MFCs, which is solved in laboratory conditions by using buffered solutions. It has been proposed that the pH value of the cathode should be controlled by sequentially feeding the cathode with the effluent of the acetate-fed anode. In this way, the protons produced at the anode side are directly introduced into the cathode compartment to enhance ORR. Such an experiment showed a four-fold increase of the current provided by the microbial cathode during nine months of operation. [89] In this framework, the reversible anode concept is also of great interest. Cord-Ruwisch's group demonstrated that a microbial electrode formed from activated sludge and maintained at À0.3 V versus Ag/AgCl was able to repeatedly change from anode to cathode function when the supply alternated between acetate and dissolved oxygen. [80] The protons produced during the anode phase by acetate oxidation were used during the cathode phase for oxygen reduction. In parallel, Buisman's group developed a solar microbial cathode, which showed similar reversibility. [90] The electrode was first inoculated with a nitrifying sludge, which was thereafter illuminated and further inoculated with phototrophic microorganisms. During the dark period, in which the microbial electrode produced an anodic current, the pH value of the bulk solution dropped due to the accumulation of the protons produced. During illumination, the phototrophic biofilm, which contained algae, cyanobacteria and other bacteria, consumed CO 2 and produced oxygen, which was locally reduced by the microbial cathode. In this period, the pH value increased as a result of the consumption of protons by oxygen reduction. The pH value of the reversible electrode thus oscillated between 6.7 and 7.2 without pH control for a period of 22 days. Once again, the protons required for oxygen reduction were provided in situ during the anode period. The concept is interesting, but further research is needed to explore the application of such bidirectional microbial electrodes. [89]

Oxygen transfer

Oxygen transfer can clearly be promoted by stirring the catholyte or increasing the catholyte flow rate in continuous systems. [80] Using an open air cathode [35] is a relevant and perhaps the most effective way to enhance oxygen availability on the cathode surface. In this case, the gas diffusion layer becomes a core component of the cell to promote a uniform access of oxygen to the catalyst [91] and with complex other roles such as removing by-produced vapour and preventing water crossover. Using pure oxygen resulted in high currents. [54] It may be guessed that a too-high oxygen concentration may favour the formation of reactive oxygen species that are detrimental to living cells, but it appears that aerobic biofilms possess an arsenal of enzymes to protect them against oxidative stress. Finally, the solar microbial reversible cathode developed by Buisman's group [90] (see paragraph above) is a very elegant way to solve the problem of slow oxygen transfer by producing oxygen directly on the cathode surface. Current density and Coulombic efficiency related to oxygen consumption were quite low, but the stability of the system (reversible anode and cathode functioned for 63 days) showed that the concept deserves further investigation.

Sensitivity to reactive oxygen species

On this issue, the numerous studies carried out in the field of MIC are reassuring. It seems that aerobic biofilms possess a large diversity of proteins (catalase, superoxide dismutase, peroxidases…) that catalyse the elimination of reactive oxygen species (reactions 9-11). The electroactive biofilms may thus be naturally protected from producing too high concentrations of reactive oxygen species.

Fouling due to alkalinisation of the interface and biofouling

This problem has certainly not been sufficiently considered as yet. Chemical fouling [34,92] and also biofouling due to heterotrophic bacteria encouraged by rich organic feeding [89] have already been observed. Nevertheless, (bio)fouling still seems underestimated in laboratory experiments that use synthetic media. It may become a severe constraint when trying to transfer microbial cathodes to actual environments.

Finally, it can be concluded that investigation of microbial cathodes for ORR catalysis has so far been modest with respect to their great interest. Combined approaches, associating electrochemistry, chemistry, microbiology, biology, ecology, material sciences and engineering, need to be extensively pursued to explore the numerous seminal technologies that have been described and, hopefully, to open up new knowledge-based paths.

  [b] Per m 3 . [c] Measured versus Ag/AgCl. [d] Current in A. [e] 250 mV. [f] Seawater. [g] River. [h] Open circuit voltage.

Table 1 .

 1 ORR overall pathways and standard potentials (from Ref.[6]).

	Condition Equations	Equation	E 0 (vs. SHE)
					number	[V]
	acid	4-electron pathway
	solution	O 2 + 4 H + + 4 e À Q2 H 2 O	1	1.229
		Peroxide pathway
		O 2 + 2 H + + 2 e À QH 2 O 2	2	0.67
		followed by the reduction of peroxide
		H 2 O 2 + 2 H + + 2 e À Q2 H 2 O	3	1.77
		or peroxide disproportionation
		2 H 2 O 2 Q2 H 2 O + O 2	4
	alkaline	4-electron pathway
	solution	O 2 + 2 H 2 O + 4 e À Q4 OH À	5	0.401
		Peroxide pathway	À0.065
		O 2 + H 2 O + 2 e À QHO 2 À + OH À	6
		followed by the reduction of peroxide
		HO 2	À + H 2 O + 2 e À Q3 OH À	7	0.867
		or peroxide disproportionation
		2 HO 2	À Q2 OH À + O 2

Table 2 .

 2 Electrode materials, inoculum sources, operating conditions and performances of oxygen-reducing microbial cathodes.

	Ref. Cathode	Inoculum source	Operating mode	Electrochemistry	Free potential [mV] P	J	Time
					[W m À3 ]	[A m À2 ]
	Waste water
	[35] carbon felt	sludge/sediment mix	continuous (6 L h À1 )	MFC (100 W)
			M9 medium

Table 2 .

 2 (Continued)

	days
	c, e, g]

Table 3 .

 3 Bacterial diversity highlighted from ORR catalysing biofilms.

	Ref. Cathode material	Electrochemistry Film age Inoculum source	Population analysis of biofilms ([%])
	wastewater
	[36] plain granular	MFC (30 W)	40 days	anaerobic/anoxic sludge	proteobacteria (50)
	graphite				bacteroidetes (21.6),
					alphaproteobacteria (9.5),
					chlorobi (8.1),
					deltaproteobacteria (4.1),
					actinobacteria (4.1 %),
					gammaproteobacteria (2.6 %)
	[37] untreated glassy	MFC (250 W)	10 months activated sludge	firmicutes,
	carbon				alphaproteobateria,
					betaproteobacteria,
					gammaproteobacteria,
					bacteroidetes
	[41a] plain granular	MFC (30 W)	400 days anaerobic/anoxic sludge	proteobacteria,
	graphite				bacteroidetes,
					actinobacteria,
					planctomycetes,
					firmicutes,
					uncultured bacteria
	[61b] graphite granules	MFC	180 days aerobic sludge	> predominant: deltaproteobacteria
	seawater/freshwater
	[47] graphite felt		48 days	mixture of environmental samples	bacteroidetes,
				from river-rusted metal	alphaproteobacteria,
					gammaproteobacteria
	[48] carbon felt	OCP-MFC	60 days	aliquots of water from previous biocathodes	pseudomonas
	stainless steel 316L	(500 W)		origin: sediments, soil, river water, sludge,	ralsronia
				MOB	gammaproteobacteria
					cyanobacteria
					> different EA population between carbon and
					SS
	[49] stainless steel 254SMO IP (À200 mV vs.	10-	seawater/wild aerobic marine biofilm	alphaproteobacteria
		Ag/AgCl)	40 days		gammaproteobacteria
					firmicutes
					acitobacteria
					flavobacteriaceae
					> main Gram negative bacteria
	[82] stainless steel	OCP	35 days	river water	actinobacteria
					firmicutes
					bacteroidetes
					alphaproteobacteria
					betaproteobacteria
					gammaproteobacteria
	soil
	[53] graphite fibre brush	MFC (500 W)	400 h	topsoil	Nitrobacter sp.,
	graphite granules				Achromobacter sp.,
					Acinetobacter sp.,
					bacteroidetes
					> chemoautotrophic bacteria

Acknowledgements

The authors gratefully acknowledge the late Dr. Vittoria Scotto and Dr. Alfonso Mollica (CNR Genoa, Italy) for very helpful discussions. The article has benefited greatly from their extensive experience and their great scientific enthusiasm. A part of the article has been written in the framework of the "Agri-Elec (ANR-008-BioE-001)" project, supported by the French ANR.