T Förster

I Kraft

I Sheikin

A D Bianchi

J Wosnitza

H Rosner

Fermi surface of LaFe 2 P 2 -a detailed density functional study

Angular-dependent de Haas-van Alphen measurements allow to map Fermi surfaces in great detail with high accuracy. Density functional electronicstructure calculations can be carried out with high precision, but depend crucially on the used structural information and the applied calculational approximations. We report in a detailed study about the sensitivity of the calculated electronic band structure of the 122 compound LaFe 2 P 2 on (i) the exact P position in the unit cell, parametrized by a so-called z parameter, and on (ii) the treatment of the La 4f states. Depending on the chosen exchange and correlation-potential approximation, the calculated z parameter varies slightly and corresponding small but distinctive differences in the calculated band structure and Fermi-surface topology appear. Similarly, topology changes appear when the energy of the mostly unoccupied La 4f states is corrected regarding their experimentally observed position. The calculated results are compared to experimental de Haas-van Alphen data. Our findings show a high sensitivity of the calculated band structure on the pnictide z position and the need for an accurate experimental determination of this parameter at low temperatures, and in particular the need of a sophisticated treatment of the La 4f states. Thus, this is not only crucial for the special case of LaFe 2 P 2 studied here, but of importance for the precise determination of the band structure of related 122 materials and La containing compounds in general.

Introduction

The comprehensive and detailed knowledge of the electronic band structure is a necessary ingredient for the fundamental understanding of the physical properties of solids. To date, a number of powerful state-of-the-art software packages are on the market that allow to calculate the band structures and Fermi surfaces of metals with high precision and give essentially the same result. But the unknown part of the interaction energy, the exchange-correlation functional and its specific implementation in the codes, gives rise to small differences in the result of these complex numerical problems [1]. So, only the experiment can decide on the validity of the outcome of such calculations. One of the most powerful bulk methods to experimentally determine Fermi-surface parameters is to measure magnetic-field-induced quantum oscillations in, for instance, the magnetization [de Haas-van Alphen (dHvA) effect] and the resistance [Shubnikov-de Haas (SdH) effect] [START_REF] Shoenberg | Magnetic Oscillations in Metals[END_REF]. These techniques provide not only very accurate values for the extremal Fermi-surface cross sections, but also the corresponding renormalized effective masses and quasiparticle scattering rates.

Soon after the discovery of superconductivity in quaternary oxypnictides [START_REF] Kamihara | [END_REF]4] and the iron-pnictides [5] first band-structure calculations appeared [6,7,8,9,10,11]. The predicted peculiar Fermi-surface topology, in turn, stimulated a number of theories on the nature of superconducting pairing in these materials [10,11,12,13,14,15,16,17]. These theories are based on the nesting between the electron and hole bands of the quasi-two-dimensional Fermi-surface sheets. Unconventional superconductivity might result from interband scattering leading to an extended s-wave pairing, with the superconducting gap changing signs between the hole and electron Fermi surfaces.

Experimental support for the bandstructure calculations was first given by angular resolved photoemission spectroscopy (ARPES) [18,19] and later by dHvA or SdH studies [20,21,22,25,26,27,29,28]. In the latter experiments, besides some oxypnictides [20,21,22], mainly 122 iron pnictides (XFe 2 As 2 and XFe 2 P 2 , with X = Sr, Ca, Ba) were investigated (see Refs. [23,24] for reviews). All these data are in reasonable agreement with the predicted band structure.

Most importantly, two electron and two hole quasi-two-dimensional Fermi-surface sheets can be assigned in the superconducting LaFePO [20,21]. This supports the already mentioned notion of Cooper pairing due to interband scattering. There are, however, some examples where deviations from the band-structure predictions were observed in experiments, which are thought to be important for understanding the nature of the electronic properties in these materials, i.e., for the occurrence and stability of either superconductivity, or magnetic order. Such an example is SrFe 2 P 2 , a non-superconducting phosphide analogue of the 122 iron-arsenide materials, for which some discrepancies between experiment and calculation were reported [29]. Also here, two hole and two electron sheets can be resolved.

The corrugation of the Fermisurface cylinders is, as generally found for the 122 materials, much more pronounced than for the superconducting oxypnictides. Thus, the Fermi-surface sheets in SrFe 2 P 2 do not fulfill a nesting condition. Indeed, neither superconductivity nor magnetic order has been observed in SrFe 2 P 2 .

Here, we report on comprehensive bandstructure calculations for the isostructural 122 iron phosphide LaFe 2 P 2 , replacing the divalent Sr by the trivalent rare-earth metal La. LaFe 2 P 2 shows no signs of magnetic or superconducting order down to 20 mK [30]. When comparing the calculated extremal Fermi-surface orbits with experimental data, we realized a high sensitivity of the computed results on the exact P position within the tetragonal crystal structure (Fig. 1). The calculated Fermi surface and the density of states at the Fermi energy change significantly when allowing the P position (reflected by the distance z of the P atom from the basal plane) to relax and depending on the used exchange and correlation potential V xc . This holds true for other 122 compounds as well.

Indeed, in the 122 systems the Fe-pnictide interlayer distance is smaller than in other pnictides making the interlayer-interaction strongly depended on the c lattice parameter and the internal z position. This results in a strong dependence of the electronic structure near the Fermi level on the interlayer coupling and can lead to isostructural phase transitions under applied hydrostatic pressure such as the tetragonal collapsed phase in CaFe 2 As 2 [31] or SrFe 2 As 2 [32].

Method

The band structure was calculated using the full potential local-orbital (fplo 9.01-35) [33] code on a well-converged 24 × 24 × 24 k mesh. Exchange and correlation potentials were estimated using either the local density approximation (LDA) [34] or generalized gradient approximation (GGA) [35]. Treatments of the La 4f states, which in LDA lie too close to the Fermi energy, (upper panel) Experimentally determined z = 0.3557 [36], (middle panel) optimized applying GGA (z = 0.3505), and (lower panel) optimized applying LDA (z = 0.3477). Some of the dHvA orbits are depicted by solid lines and labeled (see Fig. 4).

E F , will be discussed below. As a starting point, we used the structural data obtained at room temperature by [36]: a = 3.8382(9) Å c = 11.006(6) Å and z = 0.3557.

We compare our results with experimental dHvA data measured by use of torque magnetometers [30]. For that, we used CuBe capacitive cantilevers fixed on platforms that could be rotated in situ around one axis. Placing the sample on these cantilevers, the dHvA effect is measured as field-dependent oscillations of the capacitance. The measurements were performed at the Dresden High Magnetic Field Laboratory (HLD) in a superconducting 20-T magnet and at the Grenoble High Magnetic Field Laboratory (LNCMI-Grenoble) using a resistive magnet in fields up to 34 T [30].

Results and discussion

We first consider the high sensitivity of the band structure and the density of states (DOS) on the position z of the P atom. Figure 2 shows the calculated band structure and DOS close to the Fermi level for LaFe 2 P 2 . Starting with the experimentally determined room-temperature P position, with z = 0.3557 as the relative caxis unit-cell parameter, and using LDA the blue curves are calculated (Fig. 2). When using instead GGA potentials with the same fixed z, virtually the same band structure is obtained (data not shown). Indeed, for any fixed z LDA and GGA result in practically identical band structures.

Although the z position at room temper-ature is well defined, it may change upon cooling. We, therefore, allowed the P to relax to its optimum position by minimizing the total energy within the used potential approximation. Interestingly, clearly different z resulted when using either GGA (z = 0.3505) or LDA (z = 0.3477), with the clear trend towards somewhat smaller z positions, i.e., 1 -2 % smaller than the experimental value. It is worth to note that this difference is several times larger than the difference in z observed by cooling SrCo 2 P 2 from room temperature down to 10 K [37]. The reduction of z also reduces the distance between Fe and P by 0.04 Å. This leads to substantial modifications of the band structure and the DOS (Fig. 2). The largest changes appear at the Z point of the Brillouin zone, where some bands below E F shift down by up to 0.3 eV and another band is pushed below E F when z is smallest (red curve for LDA opt).

In consequence, this leads to a considerable reduction of the DOS at E F [(Fig. 2(b)] and even to a change of the Fermi-surface topology (Fig. 3). For large z, i.e., for the experimental P position, two Fermi-surface sheets appear around Z, one pillow-like (shown in red in Fig. 3) and one small spherical sheet (purple). With decreasing z, the spherical sheet first becomes tiny (for GGA opt) and eventually vanishes for LDA opt. At the same time, the pillow develops a hole around Z leading to a donut-like shape. The other two sheets (green and blue sheets in Fig. 3) only change their sizes but keep their topologies.

For a comparison with the experimental dHvA data we need to determine the extremal Fermi-surface cross sections perpendicular to the applied magnetic fields. Such extremal orbits for fields along [001] and [100] are marked by solid lines in Fig. 3 and labeled by different Greek letters for the different Fermi-surface sheets. Calculating these orbits for various angles within the main rotation planes, we can compare the result with our dHvA data, as shown in Fig. 4. The overall agreement between the calculations and experiment is very good, but there are some modifications appearing for the different approximations and z parameters. For the α (blue) and β (green) orbits, the absolute numbers of the calculated dHvA frequencies change somewhat for the different z, being off from the experimental data for all three approximations, but the angular dependences are robust and agree with experiment. These two Fermi surfaces account for most of the experimentally observed dHvA data.

Further, there are clear dHvA signals for small angles (close to [001]) observed (see Ref. [30] for original data) that can nicely be attributed to the γ (red) or δ (purple) sheets. Clearly, the dHvA frequencies γ 1 at around 10 kT can only be attributed to the outer circumference of the pillow or donut. The low frequencies at about 370 T, however, may either be caused by the small spherical (purple) sheet with orbit δ or by the hole of the (red) donut-like sheet for small z with orbit γ 4 . These low frequencies, however, are detected only for a narrow angular range that would not be expected for the spherical Fermi surface (δ) orbit. A closed γ 4 orbit, on the other hand, exists only close to [001]. Consequently, our data agree best with the calculations using LDA with optimized z.

In a next step, we now consider the influence of the La 4f states on the calculated band-structure results. It is known that DFT calculations overestimate the hybridization of the 4f states due to the underestimated Coulomb repulsion in the rather localized 4f orbitals, resulting in an energy too low for the unoccupied 4f states shifting them too 4. Angular dependence of the measured (symbols) and calculated (lines) dHvA frequencies estimated with different z parameters as explained in Fig. 2. The colors of the lines correspond to the colors of the Fermi surfaces shown in Fig. 3.

close to the Fermi energy. Experimentally, the unoccupied La 4f peak is centered around 5 eV [38,39], about 2.5 eV higher than in our calculation (see Fig. 5b).

Therefore we performed a so-called opencore calculation (ocore) where modifying the basis set of La manually moves the 4f states into the core states [START_REF]The used base for La is for the core: 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f and for the valence electrons: 5s 5p 6s 5d 6p. The remaining basis set was not modified[END_REF] to study possible effects on the band structure and DOS. The result of this calculation is shown for the band structure and DOS in Fig. 5.

For the following calculations we fixed the P position to the optimum value using LDA, namely z = 0.3477 [41]. For this approximation, discussed above, ∼ 3.5 % of the DOS at E F originates from the La 4f states.

Although the DOS at E F changes only slightly, some noticeable modifications of the band structure occur [Fig. 5(a)]. These are rather pronounced between Γ and X, where the bands shift downward with decreasing 4fstate fraction, whereas the bands shift upward around Z and close to E F . Removing the 4f states from the valence states, therefore, does not correspond to a rigid band shift of the Fermi energy.

The band shifts at Z are small, only up to about 0.1 eV. Nevertheless, this is sufficient to change the Fermi-surface topology of the (red) donut-like sheet (Fig. 6). As observed before for the optimum z (Fig. 3), the green and blue Fermi-surface sheets change only their sizes but not their topologies. The red sheet, however, is modified considerably. For the open-core approximation, the hole vanishes leading to the reappearance of the pillow-like sheet and the fourth band of spherical shape. This as well leads to the vanishing of the γ 4 and the appearance of the δ orbit (Fig. 6).

When comparing the calculated extremal orbits with the dHvA results (Fig. 7), reasonable agreements for all treatments are found.

However, best agreement appears to be obtained for the LDA open-core calculation. For all experimental dHvA data, this approximation gives, besides the correct angular dependences, almost perfectly fitting absolute values for the dHvA frequencies.

However, this calculation predicts as well a δ frequency from a small sphere around Z that should be visible for all angles. Very close to the δ another, β 1 , frequency from the green Fermi-surface sheet is predicted. This latter orbit (Fig. 6) fits well with the experimentally observed data. It remains then, however, a puzzle why no signs of the δ orbit are found in experiment. Possible reasons for that might be a high scattering rate (and Dingle temperature) for this orbit or an unfavorable curvature factor. In addition, the torque method is not very sensitive to such an isotropic, especially spherical Fermi surface. Further, since the orbit is just on the verge of existence, the "real" frequency might by somewhat smaller leading to a very slow dHvA oscillation that would be difficult to detect in the magnetization background. Anyway, besides these unsolved details of the possible existence of a fourth Fermi-surface sheet and the corresponding pillow or donut shape of the (red) sheet the quasi-two-dimensional (blue) and multiconnected (green) Fermi surfaces are nicely confirmed experimentally.

Conclusion

We studied in detail the influence of the chosen exchange and correlation-potential, V xc , approximations as well as the treatment of the 4f states on the calculated band structure and z parameter in LaFe 2 P 2 and compared the results to experimental dHvA data. Since this compound shows no magnetic order it is well suited for such an investigation. Using the same structural input with different V xc results, within the error bars, in the same Fermi-surface cross sections. In contrast, we found significant changes of the calculated z parameter when using different V xc . This is observed as well for other 122 compounds, however, not always with such clear topology changes of the Fermi surface. For example, for BaIr 2 P 2 the Fermi surface changes only marginally [START_REF] Förster | [END_REF]. Although the calculated DOS at E F has only about 3.5% 4f contribution in LDA removing the states leads to topological changes of the Fermi surface further improving the calculated result to a very good agreement with the experiment. In conclusion, our study shows that reliable low-temperature structure data and a proper treatment of the formally unoccupied La 4f states is essential in order to have good agreement with experiment.

Figure 1 .

 1 Figure 1. Crystal structure of LaFe 2 P 2 (space group I4/mmm). The black arrow marks the only degree of freedom, the z parameter of the P (4e) position.

Figure 2 .

 2 Figure 2. Band structure (a) and density of states (b) of LaFe 2 P 2 . The colors depict calculations with different z parameter of the P (4e) position: (blue) experimentally determined z = 0.3557 [36], (green) optimized applying GGA yielding z = 0.3505, and (red) alternatively optimized applying LDA resulting in z = 0.3477. The inset in (a) shows the Brillouin zone with some symmetry points.

b 1 Figure 3 .

 13 Figure 3. Calculated Fermi surfaces of LaFe 2 P 2 estimated with different z parameters as explained in Fig. 2.(upper panel) Experimentally determined z = 0.3557[36], (middle panel) optimized applying GGA (z = 0.3505), and (lower panel) optimized applying LDA (z = 0.3477). Some of the dHvA orbits are depicted by solid lines and labeled (see Fig.4).

4

 4

Figure 5 .

 5 Figure 5. Band structure (a) and density of states (b) of LaFe 2 P 2 . The colors depict calculations using different treatments of the La 4f states starting with the optimized LDA result (red) as shown already in Fig. 2. The open-core approximation calculation is shown in blue. The inset in (b) shows an enlargement of the density of states close to E F = 0.

LDA opt ocore b 1 Figure 6 .

 16 Figure 6. Calculated Fermi surfaces of LaFe 2 P 2 estimated by use of different treatments of the La 4f states as explained in Fig.5. Some of the dHvA orbits are depicted by solid lines and labeled (see Fig.7).

  Figure 6. Calculated Fermi surfaces of LaFe 2 P 2 estimated by use of different treatments of the La 4f states as explained in Fig.5. Some of the dHvA orbits are depicted by solid lines and labeled (see Fig.7).

  Figure 6. Calculated Fermi surfaces of LaFe 2 P 2 estimated by use of different treatments of the La 4f states as explained in Fig.5. Some of the dHvA orbits are depicted by solid lines and labeled (see Fig.7).

Figure 7 .

 7 Figure 7. Angular dependence of the measured (symbols) and calculated (lines) dHvA frequencies estimated by use of different treatments of the La 4f states as explained in Fig. 5 and in the text.

Acknowledgments

We acknowledge support from HLD at HZDR and LNCMI at CNRS, members of the European Magnetic Field Laboratory (EMFL), the Deutsche Forschungsgemeinschaft (SPP 1458) and the ANR-DFG grant Fermi-NESt


Nico Steinki

David Schroeter

Niels Wächter

Dirk Menzel

Hans Werner Schumacher

Ilya Sheikin

Stefan Süllow

Electronic transport in high magnetic fields of thin film MnSi

We present a study of the magnetoresistivity of thin film MnSi in high magnetic fields. We establish that the magnetoresistivity can be understood in terms of spin fluctuation theory, allowing us to compare our data to studies of bulk material. Despite of a close qualitative resemblance of bulk and thin film data, there are clear quantitative differences. We propose that these reflect a difference of the spin fluctuation spectra in thin film and bulk material MnSi.

I. INTRODUCTION

The cubic helimagnet MnSi has intrigued researchers in the field of solid state magnetism for over half a century [1][2][3]. The material, belonging to the class of B20 compounds, was originally studied in the context of spin fluctuation theory [4,[START_REF] Moriya | Spin Fluctuations in Itinerant Electron Magnetism[END_REF]. Later, the pressure induced suppression of helical magnetic order (T N = 29 K at ambient pressure) became the focus of studies in the context of quantum criticality in itinerant d-metals [3,[START_REF] Thompson | [END_REF]. Finally, it was noted that the early-reported field-induced A-phase in MnSi [4] does represent a skyrmion lattice phase [7], this way establishing the material as a model compound for studies of skyrmion physics.

Especially in the latter context of skyrmionics, in recent years various efforts have been undertaken to grow MnSi thin films. Conceptually, the idea is based on the notion that skyrmionic phases should be energetically favored in two-dimensional structures. Hence, in order to study skyrmionic properties in solid state materials, thin film MnSi has been a prominent candidate to perform corresponding studies . Surprisingly, while these studies brought various insights into the relationship of the properties of thin film MnSi and the corresponding bulk behavior, there are also a few quite striking differences.

First of all, in comparison to bulk material, thin film MnSi undergoes a transition into a helical magnetic phase below T N ∼ 45 K . This enhanced T N is attributed to the tensile strain in the MnSi film, exerted by the mismatch of the lattice parameters of MnSi and the underlying Si substrate. Effectively, it leads to a state of negative pressure in thin film material, with the bulk T N recovered if the films are pressurized [20].

Moreover, the structural anisotropy induced by the tensile strain affects the in-field properties, leading for instance to an increased critical field B C into the magnetically polarized state [16]. Most strikingly, as yet there is no direct experimental evidence for a skyrmion lattice phase for the so-called out-of-plane geometry in thin film MnSi. As well, there is no final consensus if this "non-observation" of a skyrmion lattice is an intrinsic or extrinsic property. On the one hand, it was argued that the effective negative pressure and pressure induced anisotropy drives thin film MnSi into a parameter range where a skyrmion lattice would not be stable anymore [10]. On the other hand, the thin films -even if grown epitaxially -arise from island growth on the Si substrate. This results in merohedrally twinned thin films, i.e., the films contain left-and right-handed crystallites. In this situation, the corresponding skyrmions would have opposite sense of rotation, and would annihilate upon meeting. Here, of course, the lack of observation of a skyrmion lattice would be extrinsic, as it results from the non-monochiral character of the films.

The difference in behavior of thin film and bulk MnSi begs the question if they can be related to fundamental material properties. Bulk MnSi is a prime example of a system, where spin fluctuation theory has been invoked to quantitatively describe the material properties. Here, an analogous study of thin film MnSi seems worthwhile, with issues such as the influence of residual disorder in the films, structural low-(two)-dimensionality or the effectively negative pressure possibly becoming relevant. Therefore, we have set out to perform a high field magnetoresistivity study of thin film MnSi. In our approach, we closely follow in procedure and compare our data to a seminal study of the magnetoresistive properties of bulk single crystalline MnSi [4]. Based on the comparison, we discuss the electronic properties of thin film MnSi in terms of spin fluctuation theory.

II. EXPERIMENTAL

For the high magnetic field studies, two two epitaxial grown MnSi thin films (thickness sample #1: 10 nm; sample #2: 30 nm) were synthesized by molecular beam epitaxy on [111] Si-substrate as described previously [29]. To enable a direct comparison between MnSi thin films and MnSi bulk material regarding the magnetotransport properties the MnSi thin film samples were micro-structured by electron beam lithography (see Ref. [29]). This allows resistance measurements with a conventional four point AC-method in the same geometry as for bulk material. The structures are 50 µm wide and 0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 1 the voltage leads have a distance of 70 µm.

1 0 1 0 0 1 0 0 0 ρ ( µ Ωc m ) T ( K ) # 1 # 3 # 5 # 2 # 4
The high magnetic field measurements were performed on the thin film samples at the Laboratoire National des Champs Magnétiques Intenses in Grenoble, France. The magnetoresistivity was measured at various temperatures in a range between 3 and 100 K in an external magnetic field B up to 24 T. For both samples the external magnetic field was applied perpendicular and parallel to the sample current I (B ⊥ I and B I). In the former configuration, the field was applied out-of-plane, in the latter in-plane.

For direct comparison to the results from Ref. [4], we also studied MnSi bulk crystals synthesized by the Czochralski tri-arc method. The single crystals have been characterized with respect to their essential physical properties as described below. The transverse magnetoresistivity (B ⊥ I) of the bulk samples was determined in a temperature range between 2 and 100 K in an external magnetic field up to 8 T. In addition the zero field resistivity of all samples was measured in a temperature range between 2 and 300 K.

III. RESULTS

In Fig. 1 we plot the zero field resistivities of our bulk and thin film samples. Qualitatively, the overall behavior is similar to that reported previously for single-crystalline and thin film material. For both types of systems, overall there is a metallic temperature dependence, with an anomaly at the transition at T N into the helical state, a T 2 -like behavior below T N and some rounding of the resistivity above T N attributed to spin fluctuations on top of the phononic resistivity. In detail, however, there are a few issues to be noted.

First, while all single crystals MnSi have the same transition temperature into the helimagnetic state at T N = 29 K (which was also verified by susceptibility measurements, not shown) and exhibit a similar temperature dependence of the resistivity ρ, absolute values of ρ vary by more than an order of magnitude. It suggests that the determination of the absolute value of ρ is affected by cracks in the single crystalline samples. Then, in terms of characterizing the crystalline quality of our bulk samples, instead of the residual resistivity ρ 0 the best measure is the residual resistivity ratio (RRR) here defined as ρ 300K /ρ 2K . We find values RRR for sample #3: RRR = 15, #4: RRR = 42 and #5: RRR = 104. We thus conclude that sample #5 has the highest crystalline quality, even though the room temperature resistivity is nonphysically high with 1700 µΩcm. For comparison, from the experimental data published in Ref. [4] we estimate a value RRR for the crystal studied in that work of the order of 60. Nowadays, for MnSi, in general a RRR of the order of 100 is taken to signal a "good sample quality" [30].

Second, for the thin film samples we find transition temperatures into the helimagnetic state at T N = 45 K, consistent with previous reports . Only, at high temperatures both film samples exhibit a downturn of ρ, different from the single crystal behavior. As we have demonstrated in Ref. [29], the downturn arises from a breakdown of a Schottky barrier between thin film MnSi and the Si substrate. In result, at high temperatures the MnSi film is shortcut by the substrate, leading to the downturn in ρ. We note that -while we need to keep aware of these experimental artifacts -they will not affect the magnetoresistive behavior reported below, as we can use normalized representations of the magnetoresistive behavior and we discuss only low-temperature data not affected by the shortcut.

Subsequently, we have carried out an extensive run of magnetoresistivity measurements. As an example, in Fig. 2 we plot the magnetoresistivity M R defined as M R = (ρ(B, T ) -ρ(B = 0, T )) /ρ(B = 0, T ) in transverse magnetic fields B up to 24 T at temperatures between 3 and 100 K for the 30 nm thick sample MnSi. Qualitatively and semiquantitatively, as will be documented below, the general behavior reported here for the 30 nm sample in transverse geometry is similarly seen for the 10 nm sample and the second field alignment.

For low temperatures, the magnetoresistivity exhibits an inverted S-shaped behavior which is easily saturated in a few T. As temperature is increased up to T N , the M R increases as well and the inverted S-shaped behavior broadens without reaching saturation. Finally, above T N only the downward curvature of the M R ∝ B 2 remains from the inverted S-shaped character, with the overall size of the M R being reduced again relative to the signal close to T N in the field range covered.

From the data presented in Fig. 2, for comparison with Ref. [4] we construct the temperature dependence of ρ in transverse magnetic fields up to 24 T for the 30 nm thick sample MnSi, which we plot in Fig. 3. Qualitatively, the behavior is similar to that reported in Ref. [4] (see Fig. 6 therein), with a suppression of the resistivity in magnetic fields over a wide temperature range and the largest effect close to T N . We note that the critical field of the helical phase of MnSi is about 1 T, accounting for the observed disappearance of the kink in the resistivity in the magnetic fields plotted here. Of course, the qualitative similarity in behavior of single crystal and thin film material holds as well for the measurements of the 10 nm sample and the second field alignment (not shown).

T ( K ) 0 T 1 1 T 1 8 T 2 2 T 1 T 1 2 T 1 9 T 2 3 T 2 T 1 3 T 2 0 T 2 4 . 9 T 3 T 1 4 T 2 1 T 4 T 1 5 T 5 T 1 6 T 6 T 1
The interpretation of the magnetoresistivity of MnSi has invoked the suppression of spin fluctuations in magnetic fields. These spin fluctuations are present over a very wide temperature range. A different approach to illustrate this effect is to present the data in form of contour plots, as we do in Fig. 4 for the data from Fig. 2. In this representation, the color coding reflects the size of the magnetoresistivity, which nicely illustrates the most pronounced negative magnetoresistivity to occur close to T N . Interestingly, the contour plot demonstrates that there is some asymmetry in the magnetoresistivity. The magnetoresistivity is somewhat stronger at temperatures T < T N than at T > T N . Within a view of the M R as just reflecting the suppression of spin fluctuations, one would naively argue that magnetic order already removes some of the spin fluctuations, as it is indicated by the downturn of the zero field resistivity at T N . Then, for a normalized quantity as the M R this should show up as a comparatively smaller signal, if compared to a situation were no spin fluctuations have been removed in zero magnetic field. Therefore, the asymmetry would be expected to appear as a stronger M R above T N , and as it has been shown for instance for the itinerant weak ferromagnet NbFe 2 [31].

In fact, corresponding magnetoresistivity measurements on single crystalline MnSi (now up to only 8 T) seem to be more in line with the observations made for single crystalline NbFe 2 . This is illustrated in Fig. 5, where we display a contour plot of the M R of sample #5 in the same fashion as the thin film data. Here, the asymmetry in the magnetoresistivity is clearly tilted towards temperatures T > T N , reflecting a stronger suppression of spin fluctuations in the paramagnetic phase. Altogether, as a qualitative interpretation, while the overall magnetoresistive behavior of bulk and thin film material exhibits a strong resemblance, there seem to be residual subtle differences in some aspects. If these subtle differences are extrinsic or intrinsic is not entirely clear. It seems conceivable that a distribution of transition temperatures in the films causes a smearing of the magnetoresistive features towards lower temperatures, and thus would be the result of a somewhat larger structural inhomogeneity in films than in single crystals. Finally, to illustrate the similar behavior seen for both our samples and both field geometries, in the Figs. 678we plot the contour plots of the magnetoresistivity for the remaining data sets. Overall, there is a close similarity for all data sets, be it that the magnetoresistive effects are somewhat weaker for the 10 nm sample compared to the 30 nm film. Likely, it simply reflects the larger zero field resistivity of the 10 nm sample, which will reduce the overall signal size of the M R (see Fig. 1).

IV. DISCUSSION

So far, experimentally we have demonstrated two points: a.) There is basically no difference in the magnetoresistive response of films MnSi with different thickness and for different field directions. Thus, structurally the films are still in a 3D-limit, consistent with the argument that size effects induced by the film thickness only occur below ∼ 10 nm thickness [13]. As well, the negligible difference between longitudinal and transverse magnetoresistivity likely reflects the morphology of our films, i.e., epitaxial growth of MnSi islands with a typical diameter of ∼ 50 nm [29]. A significant scattering contribution will thus arise from the grain boundaries and surfaces, which are present for both experimental geometries. Conversely, effects such as the existence of skyrmions, domains, Fermi surface anisotropies etc. that might lead to a difference of longitudinal and transverse magnetoresistivity will only have a secondary relevance. b.) On a qualitative and semi-quantitative level there is a close resemblance of the magnetoresistivity of thin film MnSi to that of single crystalline material. We thus can proceed and carry out a data analysis as has been put forth by Sakakibara et al. [4]. We start by noting that for weakly and nearly ferromagnetic metals the in-field dependence of the lowtemperature magnetoresistivity can be expressed as [32]

R(T, B) = R 0 + R 2 (B)T 2 .
R 0 is the residual resistance at 0 K, while the second term reflects the spin fluctuation effect of an itinerant weakly or nearly ferromagnetic material. The factor R 2 (B) of the spin fluctuation term can be determined from the M R data by plotting R(T, B) -R 0 over T 2 . For T < T N and in high magnetic fields, in this representation the quantity R(T, B) -R 0 results in straight lines vs. T 2 , were the slope corresponds to R 2 (B). In Fig. 9 we plot the experimental data for the 10 nm film in this representation, verifying that our approach to analyze the data properly reproduces our experimental findings.

With respect to this type of analysis, since the residual resistivity R T,B=0 has a temperature dependence because of phonon scattering, strictly speaking we should plot R(T, B) -R(T, B = 0) ∝ T 2 . In fact, as a first approximation, allowing R 0 as a free fitting parameter to vary by about 10 % slightly improves the fitting, but it does not affect the fundamental outcome of the data analysis, i.e., the field dependence R 2 (B).

Next, we follow the argumentation set out in Ref. [4] and plot the normalized field dependence of the resistive coefficient R 2 (B)/R 2 (B = 0) in Fig. 10. Here, we include the data from our two thin film samples for both field geometries, from the single crystals measured as references, and the data published in Ref. [4]. By plotting a normalized quantity, we get around the uncertainties in the determination of absolute resistivity values.

From the plot, it is immediately clear that overall thin film and single crystal samples exhibit a qualitatively similar behavior, while quantitatively there are clear differences. First, for single crystalline material, and even under consideration of the limited field range for the crystals measured here, our data sets essentially reproduce those from Sakakibara et al. [4] on single crystalline samples. With the residual resistivity ratios for the crystals used for this plot varying by almost an order of magnitude, we conclude that disorder does not significantly affect the magnetoresistive behavior, although there might be some effect hidden in the data.

Next, it was pointed out that in high fields the magnetoresistive behavior of a weakly or nearly ferromagnetic metal such as MnSi should have a field dependence evolving like R 2 (B)/R 2 (B = 0) ∝ B -1/3 [4,32]. The solid lines in Fig. 10 visualize such a field dependence, which to good approximation is fulfilled both for single crystal and thin film MnSi in a similar high field range. Consequently, the magnetoresistive response of thin film MnSi can essentially be understood within what is nowadays labeled the self-consistent renormalization (SCR) theory of spin fluctuations [START_REF] Moriya | Spin Fluctuations in Itinerant Electron Magnetism[END_REF]. Conversely, the quantitative difference between thin films and single crystals must reflect a difference of the microscopic parameters used within SCR theory to describe the spin fluctuations. In detail, by writing out the expressions for the high field magnetoresistivity given in Ref. [32], one finds that R 2 (B)/R 2 (B = 0) is a complex function of variables introduced in SCR theory to parametrize the spin fluctu-ations: R 2 (B)/R 2 (B = 0) ∝ χ0 χL 1/3 B -1/3 , with χ 0 the susceptibility of the non-interacting system, χ the susceptibility of the interacting system, and L an expansion coefficient of the magnetic free energy.

Evidently, we cannot extract unique values for these parameters from our experiment. However, comparing the experimental results for single crystalline and thin film material MnSi, the quantitative differences imply that the spin fluctuation spectrum in our thin films is different from the single crystals. At this point, it is not clear if this just reflects the effective negative pressure in the thin films. Alternatively, the uni-axial anisotropy induced in the films, which was argued to substantially affect film properties [10,19], might cause modifications of the spin fluctuation spectra. One way to test these notions would be -for instance -corresponding magnetoresistivity measurements under pressure on thin film MnSi. If the pressure scenario holds, we would expect a gradual transition of the magnetoresistive behavior of the films towards the bulk behavior with applied pressure. Altogether, while in terms of spin fluctuations thin film and bulk (single crystal) MnSi can be understood within the same SCR theoretical framework, our findings imply that thin films are in a different spin fluctuation parameter range than bulk (single crystalline) material.

FIG. 2 .

 2 FIG. 2. (Color online)Magnetoresistivity in transverse magnetic fields up to 24 T for a 30 nm thin film MnSi; for details see text.

FIG. 3 .

 3 FIG. 3. (Color online) Resistivity in transverse magnetic fields up to 24 T for a 30 nm thin film MnSi; for details see text.

  FIG. 4. (Color online) Contour plot of the magnetoresistivity M R in transverse magnetic fields up to 24 T for a 30 nm thin film MnSi; for details see text.

8 (FIG. 5 .

 85 FIG. 5. (Color online) Contour plot of the magnetoresistivity M R in transverse magnetic fields up to 8 T for a single crystal MnSi, sample #5; for details see text.

(BFIG. 6 .

 6 FIG. 6. (Color online) Contour plot of the magnetoresistivity M R in parallel magnetic fields up to 24 T for a 30 nm thin film MnSi; for details see text.

(FIG. 7 .

 7 FIG. 7. (Color online) Contour plot of the magnetoresistivity M R in transverse magnetic fields up to 24 T for a 10 nm thin film MnSi; for details see text.

FIG. 8 .

 8 FIG. 8. (Color online) Contour plot of the magnetoresistivity M R in parallel magnetic fields up to 24 T for a 10 nm thin film MnSi; for details see text.

FIG. 9 .

 9 FIG. 9. (Color online)Plot for data analysis of the magnetoresistivity M R in parallel magnetic fields up to 24 T for a 10 nm thin film MnSi; for details see text.

FIG. 10 .

 10 FIG. 10. (Color online) Field dependence of the magnetoresistive coefficient R2(B)/R2(B = 0) of bulk and thin film MnSi (#1: thin film 10 nm thickness, #2: thin film 30 nm thickness, #3: bulk with RRR of 15, #4: bulk with RRR of 42, #5: bulk with RRR of 104); for details see text.

ACKNOWLEDGMENTS

We acknowledge the support of the LNCMI-CNRS, member of the European Magnetic Field Laboratory (EMFL). We gratefully acknowledge support by the Braunschweig International Graduate School of Metrology B-IGSM and the DFG Research Training Group GrK1952/1 "Metrology for Complex Nanosystems".


Ahmed Hamdani
email: a_hamdani04@hotmail.com

Abdeltif Amrane
email: abdeltif.amrane@univ-rennes1.fr

Imane Kader

Mohammed Mountadar
email: mounta_dar@yahoo.fr

Omar Assobhei
email: assobhei1@yahoo.fr

Sidi Mohamed Ben

Carbon and nitrogen removal from a synthetic dairy effluent in a vertical-flow fixed bed bioreactor

Keywords: biological treatment, COD, fixed-bed bioreactor, heterotrophic flora, nitrogen, wastewater

In this study, a synthetic dairy effluent (SDE) containing high levels of COD and nitrogen was treated in a fixed-bed bioreactor (FBBR) under the influence of the variations in residence time, aeration conditions and temperature. The tests performed continuously in a single step and the same reaction vessel allowed to define a 96h cycle comprising two anoxic/aerobic phases of 48h each.

Sequential anoxic and aerobic conditions improved the removal of TKN and NH 4 + by a factor of 2.5, whereas low temperature significantly decreased the nitrogen and COD removal rate. Overall, outcomes showed a successful growth of the biomass that reached (5.8 ± 0.31) × 10 6 CFU/mL, and high removal efficiency of COD (93.5 ± 8.1%), NO 3 -(99.2 ± 19%), TKN (87.5 ± 16.1%), and NH 4 + (55.8 ± 8.3%), and hence complied with Moroccan standards. The FBBR system, therefore, can be applied successfully to remove COD and nitrogen from wastewater.

Introduction

Today, most Human activities whether domestic, industrial, agricultural, or touristic have not only enhanced the life quality, but also resulted in the release of wastewater pollutants on the environment and the public health. Human health risk associated with polluted water is one of the major challenges that humanity will face in the twenty-first century because of the diversity and hazardous nature of water-polluting components. There are several categories of water pollutants, i.e. nutrients (Carbon C, nitrogen N, phosphorus P), micropollutants (heavy metals, pesticides, synthetic hormones…), but also microbiological (bacteria: Fecal coliforms, fecal Streptococci, Salmonella, Vibrio cholera…; viruses: hepatitis virus…; parasites: Ascaris, Taenia…; protozoa: Giardia intestinalis, Entamoeba histolytica…) and physical (thermal pollution, suspended solids, radioactivity…). Special attention is given to the various compounds contained in liquid effluents, which are a substantial pollution source to the aquatic environment [START_REF] Chen | Biological Wastewater Treatment: principles, modeling and design[END_REF]Metcalf & Eddy, 2013).

The dairy industry is one of the most important activities causing water pollution due to its high demand for the resources, particularly for water: about 90 % of milk is made of water. Owing to the used raw material and the large amount of water consumed, the dairy factories negatively affect the environment by rejecting great quantities of liquid effluents with a high level of C, N, and P (Hamdani et al., 2018;[START_REF] Porwal | Biodegradation of dairy effluent by using microbial Isolates obtained from activated sludge[END_REF]. These three substances exist naturally at relatively low levels in aquatic environments, once released in large quantities via point source effluents they can have a negative impact on the quality of the receiving environment (malodor, asphyxia, eutrophication...), as well as on people's health and economy [START_REF] Oms | La planification de la gestion de la sécurité sanitaire de l'assainissement : Manual for Safe Use and Disposal of Wastewater, Greywater and Excreta[END_REF]. To avoid these nuisances, the presence of organic matter, nitrogen, and phosphorus in raw wastewater has been regulated and their levels must be reduced to limit values established by this legislation. Organic matter removal can be provided by physico-chemical processes (oxidation, filtration, flocculation-decantation, photo-catalytic reduction...); however, this kind of treatment has a certain number of disadvantages, including a high cost, excessive sludge production, the use of chemicals agents, secondary pollutants generation, physico-chemical monitoring of the effluent (pH) and above all, only partial treatment [START_REF] Crini | Advantages and disadvantages of techniques used for wastewater treatment[END_REF]Hamdani et al., 2005;[START_REF] Porwal | Biodegradation of dairy effluent by using microbial Isolates obtained from activated sludge[END_REF]. As an indication, the costs of chemicals used in wastewater treatment plant are between 5-15% of the total project cost (Anand et al., 2012), while the typical water treatment plant produces from 0.4 to 0.8 mg of chemical sludge per mg of used coagulant (Guimaraes et al., 2016). Hamdani et al., (2005) reported that a cubic meter of dairy effluent treated by using three coagulants generates a sludge in the range of 0.98-1.38 mg of suspended matter per liter of dairy effluent depending on the chemical reagents, and require a cost from 0.01 to 0.25 USD. [START_REF] Van Dongen | The SHARON anammox process for treatment of ammonium rich wastewater[END_REF] reported that the nitrogen conversion process by using biological way is estimated at 1.12 to 1.68 USD/kg N removed compared to 5.6 to 14 USD/Kg N removal for a physico-chemical method. These limitations make the biological processes profitable and alternative for wastewater treatment.

Compared to physical and chemical treatment processes, biological methods are considered more attractive, economical and the best adapted alternative for removing biodegradable pollutants, because (i) their principle of treatment is similar to the natural phenomena of water self-purification, (ii) their support on a significant number of microbial species with high biodegradability of organic matter and nutrients (iii) their best pollution abatement rate, (iv) their capacity for generating much high-value-added product, i.e. water, energy, fertilizers, nutrients, and (v) their moderate cost… [START_REF] Batstone | Platforms for energy and nutrient recovery from domestic wastewater: A review[END_REF][START_REF] Crini | Advantages and disadvantages of techniques used for wastewater treatment[END_REF]Kehrein et al., 2020;[START_REF] Samer | Chapter: Biological and chemical wastewater treatment[END_REF]. In biological wastewater treatment, soluble and colloidal substances in the effluent are decomposed by the action of a variety of living organisms, i.e. plants (microalgae, aquatic vegetation…), animals (protozoa, invertebrates…), and especially purifying microorganisms which remain by far the main actors involved in the wastewater purification. The purifying microorganisms use their specific metabolism to convert carbonaceous and nitrogenous matter (C, N, P) in the liquid effluents to water, new cells, carbon dioxide, and other stables and harmless end products [START_REF] Samer | Chapter: Biological and chemical wastewater treatment[END_REF]. This mechanism can be explained by the following global equation (1) (Wentzel et al., 2003).

Bacteria n 1 (Organic matter) + n 2 (NH 4 + ) + n 3 (O 2 ) + n 4 (PO 4 3-) → n 5 (New cells) + n 6 (CO 2 ) + n 7 (H 2 O) (1)
Organic matter degradation involves heterotrophic bacteria, such as Acinetobacter, Achromobacter, Alcaligenes, Bacillus, Flavobacterium, Micrococcus, Pseudomonas…), which use biodegradable carbon and nutrients as a source of food and energy (Metcalf & Eddy, 2013;[START_REF] Samer | Chapter: Biological and chemical wastewater treatment[END_REF]. Based on oxygen availability, two processes can be envisaged: in the presence of oxygen, microorganisms decompose organic matter to meet their needs and produce new living cells. In the absence of oxygen, microbial growth happens when using other final electron acceptors than molecular oxygen like oxygenated mineral compounds [START_REF] Batstone | Platforms for energy and nutrient recovery from domestic wastewater: A review[END_REF]Kehrein et al., 2020;Mauffrey, 2016;[START_REF] Russell | Practical Wastewater Treatment[END_REF]. This is the case with biodenitrification, which is an anoxic process where heterotrophic bacteria will be forced to use the oxygen contained in the nitrates (nitrate and nitrite respiration) as the final acceptors of electrons during oxidation reactions of organic substances (Hamdani et al., 2018).

For the biological treatment of organic and nitrogen compounds, many studies have focused on the use of suspended biomass systems such as activated sludge and sequencing batch reactors. These systems, although commonly used for big communes, have some disadvantages: problems related to multiple ponds, recirculation of effluent and biomass, water-sludge separation, sensitivity to the load variations, high costs, maintenance… (Gurtekin, 2014;[START_REF] Nancharaiah | Aerobic granular sludge process: A fast growing biological treatment for sustainable wastewater treatment[END_REF].

Other researchers studied the application of different configurations of fixed culture reactors in the removal of organic matters and/or nutrient during wastewater treatment, i.e. fixed bed membrane bioreactor (Subtil et aI., 2014), ozone fixed bed bioreactor (Liu et al., 2017), Up flow fixed bed bioreactor (Hamdani et al, 2018), immersed bacterial bed reactor [START_REF] Sylla | Denitrification of wastewater treatment plant effluent using anaerobic bacterial bed reactor immersed: operating performance[END_REF], hybrid moving fixed bed biofilm reactor [START_REF] Di Bella | Intermittent Aeration in a Hybrid Moving Bed Biofilm Reactor for Carbon and Nutrient Biological Removal[END_REF], submerged fixed bed biofilm reactor [START_REF] Schlegel | Wastewater treatment with submerged fixed bed biofilm reactor systems -design rules, operating experiences and ongoing developments[END_REF]. In all studies, a mean removal efficiencies for COD and total nitrogen in the range of 70-99% and 20-92%, respectively, were obtained at hydraulic retention times in the range of 36 h to 6 months.

In Morocco, -which is experiencing a considerable delay in liquid sanitation-, activated sludge, lagoons, settlers-digesters and infiltration-percolation represent around 80% of all wastewater treatment plants; while bacterial beds are very little represented [START_REF] Belloulid | National Program of Sanitation and Wastewater Treatment in Morocco: Objectives, Achievements and Challenges[END_REF]. Despite the abundance of studies on the subject, only very few investigations focused on environmental impact of Moroccan dairy industry where approximately 4.5 × 10 9 L of processed milk are produced annually in 2020, and 1500L of water is needed to obtain 1 kg of milk (FAO, 2011). The large majority of the water consumed is returned to the receiving environment in the form of raw effluent high in biological and chemical pollutants.

Hence the objective of this study was to assess the performance of an immobilized biomass bed reactor to remove COD and different forms of nitrogen such as NO 3 -, TKN, and NH 4 + from SDE in a single step and in the same reaction chamber, and under the effect of residence time (24, 48, 72, 96 h), aeration conditions (anoxic, aerobic, anoxic/anaerobic, anoxic/aerobic modes) and temperature (10, 15, 20, 30 °C).

A c c e p t e d M a n u s c r i p t

Materials and Methods

Pilot description and operating conditions

Laboratory tests were conducted in a fixed-bed bioreactor, which was a rectangular stainless-steel column with dimension in cm Length × Width × Height = 250 × 250 × 950 (Fig. 1). The bioreactor was filled with food-grade plastic support used as a carrier to biomass immobilization and operated in continuous vertical flow mode. The effective liquid volume of the continuous bioreactor was approximately 60 liters while the apparent volume occupied by the carrier was 51 L with a vacuum of 44.5 L, which is equivalent to 87% of porosity. The bioreactor was equipped with a peristaltic pump "Percom N-M" for influent feeding, an aeration system ON/OFF, a valve sampling, and a pipe of 1.5 cm in diameter for the biogas outlet. To remove undesirable microbes, the column was sterilized with alcohol and then rinsed repeatedly with sterile distilled water, while the carrier was autoclaved at 105°C for 30 minutes. The main characteristics of the support material are shown in Table 1. Values in parenthesis indicate standard error of the mean SEM (a mean of three determinations)

1-Bioreactor

Pilot inoculum, feeding and aeration

The bioreactor was inoculated properly with a bacterial laboratory suspension at approximately (2.6 ± 0.13) x 10 7 CFU/mL. These bacteria were isolated from sediments and soil sample collected in a decantation pits and storage ponds of effluents produced by a dairy industry located in El Jadida City (Morocco), purified and selected in the BIOMARE laboratory, based on their ability to remove carbon and nitrogen.

The bacterial biomass was left to grow gradually on the inert support in the presence of culture medium enriched in nitrate and organic matter, which was renewed every 48h. After four weeks, the biofilm had become visible, and a mucilaginous layer appeared on the surface of the garnishing.

This duration represents the preculture time required to achieve a steady-state.

An adjustable flow rate peristaltic pump provided the bioreactor with SDE based on milk powder manufactured by Dairy industry unit located in El Jadida City (Morocco) that transited in up-flow through the plastic support previously colonized by the acclimated biomass. The recipe of the reconstituted influent was inspired by those proposed by [START_REF] Nopens | Stability analysis of a synthetic municipal wastewater[END_REF] with some modifications to obtain appropriate COD/TKN/TP and COD/NO 3 -initial ratios. This model solution whose composition is presented in the Table 3 was prepared with distilled water and had a pH of 7 ± 0.2. The choice of a model effluent simulating real dairy effluent was justified by the willingness to work with a water of stable of composition, controllable and totally biodegradable, unlike in the case of actual raw dairy effluent, which is characterized by high variability of hourly daytime measurement for flow, temperature, pH, salinity and the pollution load. But also, to avoid technical problems related to the difficulties in taking, transporting and storing samples especially since one of the objectives was to validate the results obtained in previous work (Hamdani et al., 2018). In addition, taking into account the optimal residence time obtained during our previous work (Hamdani et al., 2018), three cycles (short, medium and long) were tested with the aim of allowing the SHF to simultaneously reduce COD and NO 3 by biodenitrification, which is an anoxic process. However, the abatement of the other forms of nitrogen (TKN and NH 4 + ) was researched through the creation of an aeration phase. The oxygen supply was ensured by injecting filtered air in fine bubbles from the base of the reactor to prevent detachment of biofilm and maintain de-aeration in the rest of the bioreactor. The FBBR aeration mode was controlled via the ON/OFF method, i.e. a continuous anoxic mode (OFF) and alternating cycle anoxic/aeration (ON).

The tests were performed at temperatures lower than 30°C to be close to the real conditions in the El Jadida city, where the study took place, which is characterized, -according to the climate data of the provincial meteorological Center, -by a semi-arid climate with an average temperature of 13-25°C.

Analytical and microbiological techniques

The physicochemical and microbiological analyses were determined according to the Standard Methods for the Examination of Water and Wastewater APHA (2012).

Physical and chemical analyses were carried out on the influent and the effluent with the following parameters: Temperature, pH, COD, NO 3 -, NO 2 -, NH 4 + and NTK. While, the bacteriological analysis was performed on water samples taken from only the treated effluent and focused on a qualitative and quantitative evaluation of the biomass.

Four groups of flora were searched using a basal media, e. i. Heterotrophic plate count agar -HPCA-(Difco Laboratories, USA) which contains: 3g peptone, 0.5g soluble casein, 0.2g dipotassium hydrogen phosphate, 0.05 magnesium sulphate, 0.001g ferric chloride, and 15g agar per liter of distilled water. The media was adjusted to pH 7.2 ± 0.2, incubated at 30°C for 96 to 168h depending on the targeted bacterial groups, and customized by adding selective components or modifying the cultural and incubation characteristics to select each microbial group and restrict a possible contamination by non-targeted microorganisms (Table 4). (i) Indirect enumeration of only living cells cultivated on agar media: For the AMF, the aerobic heterotrophic flora and anaerobic heterotrophic flora, the results were expressed in number of colony-forming units (CFU) per mL of sample, and only the petri dishes whose number of colonies was between 30 and 300 were counted. However, the denitrifying flora was counted according to the Most Probable Number (MPN) method.

(ii) Direct method using epifluorescence microscope, after staining bacteria with acridine orange, which considers both living and dead cells, unlike the indirect counting method. A sample previously prepared according to the method described by Hobbie et al. (1977) is placed between a slide and a coverslip, then observed under a microscope (Olympus C×41) at ×100 and ×400 magnification.

(iii) Optical determination of total biomass concentration: The biomass specific growth rate was estimated by monitoring the absorbance (OD) periodically at 620nm. One liter of sterile nutrient broth (Difco Laboratories, Detroit, Mich.) was prepared and specifically, two media were used: uninoculated sterile media designed to blank the spectrophotometer, and the other inoculated with bacteria cells. A sample of 2 mL was taken from the bacterial culture in suspension and transferred into a clean cuvette.

Then, changes in the turbidity of the second medium were recorded against the first uninoculated sterile media as the blank. For the total biomass, an absorbance of 1 was equivalent to 5.8 ×10 6 CFU/mL.

In order to estimate the bioactivity of the SHF in the FBBR, exogenous respirations of heterotrophic bacteria were monitored over time after adding three sources of biodegradable carbon (Milk powder, Starch, Yeast extract). The dissolved oxygen consumption rate due to the removal of biodegradable substrate was continuously measured in the bioreactor with a WTW Oxi 315i oxygen meter (Weilheim, Germany).

The SDE treatment efficiency was evaluated on grab samples collected from the bioreactor outflow, by measuring the above cited parameters. The biological treatment experiments were achieved when a steady state was almost reached, and the efficiency was analytically appreciated by monitoring the concentration evolution of the already mentioned parameters at the input or untreated effluent (C i ) and at the output or treated effluent (C 0 ) of the bioreactor. The abatement effectiveness (A) of these parameters (x) expressed in percentage (%) was calculated according to the equation 2.

A (%) = [1 - C 0 (x) C i (x)
] × 100 (2)

Statistical analysis

The experimental data were analyzed and expressed as the standard error of the mean (SEM).

A c c e p t e d M a n u s c r i p t

To assess the dependence between operating parameters (residence time, temperature, aeration mode) and various parameters to be removed (COD, TKN, NO 3 -, NH 4 + ), statistical calculations according to the paired t-test method were carried out by using statistical software for Microsoft Excel XLSTAT 2020.4.1.1026.

Results and Discussion

Composition of the synthetic dairy effluent

The physical and chemical composition of the SDE used to feed the bioreactor is given in Table 3.

In addition to milk powder, the reconstituted dairy effluent contained the main elements necessary for bacterial growth, notably a carbonaceous fraction (starch and yeast extract) leading according to the theoretical calculation to a COD of approximately 1500 mg/L, a mineral fraction composed of a phosphate solution, a solution of trace elements and nitrate. From this, the initial amounts of TKN, NH 4 + , NO 3 -and TP were 184.6; 160.6; 306.6 and 15 mg/L, respectively. The respective COD/TKN/TP and COD/NO 3 -ratios, close to 100/12/1 and 5, were in favor of a satisfactory biological and denitrifying activity of the influent. The ratios were linked to COD instead of BOD 5 because the COD was almost totally biodegradable owing to the biodegradability of the constitutive components (milk powder, starch and yeast extract). Before the biological treatment, the SDE color was milky white, but after treatment it was apparently clear and clean. This change in color might be related to the organic matter break down by the action of SHF. Similar finding was reported by [START_REF] Porwal | Biodegradation of dairy effluent by using microbial Isolates obtained from activated sludge[END_REF].

Effect of the residence time on bioreactor performance

Operating in continuous anoxic mode and fed by applying loads of 0.536 ± 0.09 and 2.62 ± 0.36 Kg/m 3 .J in NO 3 -and COD respectively, the bioprocess provides the results shown on Fig. 2.

Fig. 2a indicates that after 24 h of treatment, the nitrate concentration in the effluent equal to 63 mg/L was higher than 45 mg/L, value recommended by the CCME (2012) related to the marine aquatic life protection against the direct toxic effects of nitrate. Biodenitrification occurred to reach its optimum (99.99%) after 48 h (Fig. 2b); it was accompanied by the reduction of COD from 1500 to 800 mg/L (24 h), 214 mg/L (48 h) and 102 mg/L (96 h). Thus, to achieve complete biodenitrification, it was necessary to maintain contact between the nitrates, the carbon substrate and the biomass for 48h; at this moment the COD removal rate was 85.7%. It reached its maximum (93.2%) after 96h of treatment (Fig. 2c), thus meeting both the national and the international standards (120 mg/L) (BORM, 2013;Council Directive, 1991). The residence time A c c e p t e d M a n u s c r i p t considered (96h) was higher than that described by [START_REF] Casellas | Stratégies d'élimination de l'azote d'un effluent urbain dans un réacteur discontinu séquentiel (SBR)[END_REF], who indicated that a duration of 36h is largely sufficient to guarantee a good treatment of organic and nitrogen pollution of urban wastewater.

The recorded performances appear to be comparable to those achieved for the treatment of a raw dairy waste in an anaerobic-aerobic (80:20) immersed bacterial bed: total denitrification in 72h coupled with 92% of COD removal (Hamdani et al., 2018). However, they were slightly above the results reported by Di Bella and Mannina (2020) who obtained a removal of 90% of nitrates and 93% of COD during the treatment of synthetic wastewater in a hybrid moving bed biofilm reactor with intermittent aeration. Furthermore, they were noticeably better than those obtained by [START_REF] Sylla | Denitrification of wastewater treatment plant effluent using anaerobic bacterial bed reactor immersed: operating performance[END_REF], showing reduction of 82.2% nitrates and 71.5% COD contained in dairy effluent treated by a submerged bacterial bed, despite the longest period of treatment (42 days).

The high removal efficiencies obtained in this study suggest a high capacity to reduce nitrates and organic matter which is probably favored by:

(i) The selection of natural microbial consortia collected from dairy sludge, and well adapted to grow at the expense of the dairy influent as substrate, especially COD and N. Similar result was found by [START_REF] Porwal | Biodegradation of dairy effluent by using microbial Isolates obtained from activated sludge[END_REF] who reported that the isolation of a mixed culture from dairy sludge is a key parameter to remove efficiently COD, and other parameters effectively from dairy effluent.

(ii) The use of inert carrier that offers the possibility to create a wider contact surface between the biofilm and the influent substrate It is helpful for bacterial development and allows their clinging owing to the mucilaginous substance they secrete.

Founding from recent research demonstrated that the application of fixed cell systems offers multiple advantages in wastewater treatment overusing them in their suspended forms: higher mechanical strength, easier biomass/water separation, large increase in volumetric reaction rate, reduction in the size of reactors [START_REF] Bayat | Immobilization of Microbes for Bioremediation of Crude Oil Polluted Environments: A Mini Review[END_REF]Martynenko and Gracheva 2003;[START_REF] Velkova | Immobilized microbial biosorbents for heavy metals removal[END_REF]. Also, [START_REF] Schlegel | Wastewater treatment with submerged fixed bed biofilm reactor systems -design rules, operating experiences and ongoing developments[END_REF] ) showed satisfactory removal in COD (96%), total nitrogen (73%), and ammonia (98%) from domestic effluent with only 1/3 of the biomass.

Moreover, the immobilized biomass resists better against toxic compounds (acids, metals…), stress conditions (organic solvent, salinity, inhibiting elements, osmotic pressure, dehydration, self-destruction), and changes in physicochemical parameters (pH, temperature, O 2 …) [START_REF] Camargo | Treatment of low-strength wastewater using immobilized biomass in a sequencing batch external loop reactor: influence of the medium superficial velocity on the stability and performance[END_REF][START_REF] Muhamad | Comparison of the efficiencies of attached-versus suspended-growth SBR systems in the treatment of recycled paper mill wastewater[END_REF][START_REF] Velkova | Immobilized microbial biosorbents for heavy metals removal[END_REF]. This is important particularly in favor of wastewater purifying bacteria known for their sensitivity to pH, temperature, oxygen…, that consequently can achieve higher yields. ) is considered to be twice as faster, and more efficient than endogenous one (0.8 mg

N-NO3-mgMVS -1 .h -1
) for the same operating cycle (Casillas et al., 2002) and it can be up to five times according to Metcalf and Eddy (2013). On the other hand, the biodegradation of organic matter is slower if the available carbon is less rapidly biodegradable [START_REF] Deronzier | Traitement de l'azote dans les stations d'épuration biologique des petites collectivités[END_REF]. These results are in accordance with those cited by [START_REF] Sylla | Denitrification of wastewater treatment plant effluent using anaerobic bacterial bed reactor immersed: operating performance[END_REF] and [START_REF] Wang | Biological nitrate removal from water and wastewater by solid-phase denitrification process[END_REF], showing that biodenitrification is always coupled with the degradation of organic matter and depends on the denitrifying capacities of the bacteria, the nature of the carbonaceous substrate and the residence time.

Besides, the denitrification was concomitant with the progressive formation of nitrite, which reached a maximum between 8.7 and 23.8 mg/L depending on the operating cycle (Figures 3a,3b,3c).

However, this formation remained transient since the formed nitrite was completely consumed thereafter. This is in agreement with the results obtained by [START_REF] Pan | Effects of pH on N 2 O reduction and accumulation during denitrification by methanol utilizing denitrifiers[END_REF] who reported that the total elimination of nitrates at pH 6.5 and 7.5 is a guarantee of the absence of the nitrites accumulation in the treated water. Furthermore, the pH values recorded in this study (between 6.5 and 9) were most likely in favor of a total elimination of the nitrite formed during the denitrification process (see Fig. 2, paragraph 3.2), reflecting a high nitrite reductase activity. [START_REF] Albina | Influence of Hydrogen Electron Donor, Alkaline pH, and High Nitrate Concentrations on Microbial Denitrification: A Review[END_REF] reported that the optimal pH range for complete denitrification without nitrite accumulation is between 7.5 and 9.5. According to [START_REF] Cao | Effects of pH on nitrite accumulation during wastewater denitrification[END_REF], increasing pH during the denitrification process is a good sign of the reduction of nitrites because the denitritation produces alkalinity. Furthermore, Hamdani et al. ( 2018) indicated that a temperature of 30 °C promotes a quick and complete nitrite reduction.

Based on these results, only the operating cycle time of 96 h was therefore considered thereafter.

Temperature and pH evolution on an anoxic 96 h cycle

Temperature and pH are two factors that affect the activity of microorganisms and their living environment.

In this research, the inlet temperature was 30 ± 5 °C. Fig. 3a shows that the temperature measured at the bioreactor output remained relatively stable, around a value of 28  2 °C. At the beginning of the treatment, the temperature was supposed to increase because the bacterial growth linked to the degradation of the nutrient substrate is exothermic [START_REF] Chen | Biological Wastewater Treatment: principles, modeling and design[END_REF]. So, this parameter seems to be more impacted by the climate than by endothermic or exothermic reactions Fig. 3b shows that the pH, initially neutral underwent a slight decline to 6.6 during the first 18h of treatment, and then tended to increase slightly until reaching 9 at the end of biodenitrification. The acidification noted at the start of denitrification was also noted by Hamdani et al. (2018). It was probably due to the accumulation of CO 2 in the reaction medium. Concerning the increase in pH, it comes from the consumption of H + during the biodenitrification reactions (3) [START_REF] Powers | Quantifying cradle-to-farm gate life-cycle impacts associated with fertilizer used for corn, soybean, and stover production[END_REF]:

Denitrifying enzymes 4NO 3 -+ 5(CH 2 O) + 4H + → 2N 2 + 5CO 2 + 7H 2 O (3)
Overall, the pH oscillated between 6.5, value located in the pH range required by the Moroccan standard (5.5-8.5), and 9, which slightly exceeds the maximum standard set at 8.5 (BORM, 2013). The measured pH values were compatible with a good activity of SHF.

Effect of the aeration mode on the bioreactor performances

Fig. 4a shows that the COD removal rate depends on the aeration conditions. Compared to the aerobic or anoxic treatment trials where the respective abatement rates were 78 ± 6.9% and 82.1 ± 7.2%, the best yields were observed in alternating anoxia either with anaerobic (94.4 ± 11%) or aerobic (93.5 ± 8.1%) modes. COD removal was marked by a drastic decrease, from 1500 ± 370 mg/L at the inlet to 84 ± 26 mg/L during the anoxic/anaerobic mode and 98.1 ± 32 mg/L during the anoxic/aerobic period at the bioreactor outlet, respectively. As shown in Fig. 4b, the pilot bioprocess exposed to total anoxia during 96h of operation, allowed the removal of 99.9 ± 24% of NO 3 -; while low abatements were observed for TKN and NH 4 + , only 35.4 ± 6.4% and 20.3 ± 4.1% respectively. However, the implementation within the bioreactor of aeration at a rate of 50% alternating over time with anoxia significantly enhanced the elimination of these forms of nitrogen, in addition to a total removal of nitrate: fairly low concentrations of TKN (23 ± 0.37 mg/L) and NH 4 + (71 ± 12.2 mg/L) were recorded for the purified water. The TKN output concentration was below the Moroccan standards (40 mg/L), but slightly higher than the European Communities Directive 91/271/EEC (Council Directive, 1991) (10 to 15 mg/L). According to [START_REF] Sawadogo | Traitement des eaux usées industrielles par des procédés membranaires sous climat sahélien : cas des eaux usées de brasserie au Burkina Faso[END_REF], the integration of anaerobic and aerobic zones inside the same bioreactor promotes an intensive form of biodegradation of organic and nitrogen pollution

The remaining modes (aerobic, anoxic/anaerobic) led to less interesting results in terms of performance: in aerobic, the abatement rate of nitrogen was found relatively high for TKN (85.4 ± 17.3 mg/L) and NH 4 + (67.6 ± 5.1 mg/L), but very low for NO 3 -(18 ± 3.1 mg/L). This shows significant aerobic nitrification and a slight denitrifying activity in the bioreactor. In anoxic/anaerobic mode, the nitrification, which is an aerobic process remained insufficient (44.6 ± 6.9 mg/L).

Effect of the temperature on the bioreactor performances

Fig. 5a and Fig. 5b show the COD and nitrogen concentrations (TKN, NH 4 + and NO 3 -) measured at the input and output of the bioreactor operated in anoxic/aeration mode, at different temperatures, as well as their associated reduction rates. As observed in Fig. 5a, the average removal efficiencies of COD decreased as the temperature decreased from 30 °C to 10 °C. The lowest COD abatement rate (78 ± 10%) corresponded to the lowest temperature (10 °C), while the highest (94.4 ± 14.7%) was recorded at 30 °C and these high performances were almost kept at 20 °C (93.5 ± 12.9%), and even at 15 °C (92.1 ± 13.1%). At 10 °C, the effluent COD content was equal to 332 ± 42.6 mg/L, exceeding the national and international standard recommended for this parameter (120 mg/L). This result is similar and even better than that found by Lew et al. (2011) who reported 82%, 72%, 68%, and 38% COD removal at 28 °C, 20 °C, 14 °C, and 10 °C respectively. Similar trend was observed regarding nitrogen removal (Fig. 5b), since the best performances were obtained both at 30 and 20°C for nitrates (> 99%) and TKN (> 85%) and only at 30 °C for NH 4 + (67.6 ± 5.1%), while these yields dropped to 35.0 ± 4.6%; 20.3 ± 4.1% and 18.0 ± 2.9% for TKN, NH 4 + , and NO 3 -, respectively when the FBBR operated at 10 °C. efficiency which decreased from 99.9 ± 2.9% to 18.0 ± 2.9% for NO 3 -, 67.6 ± 5.1% to 20.3 ± 4.1% for NH 4 + , from 87.5 ± 4.6% to 35.0 ± 4.6% for TKN, and from 94.4 ± 14.7% to 78 ± 10% for COD. This represents a decrease of 82%, 70%, 60%, and 18% for NO 3 -, NH 4 + , TKN, and COD respectively. This influence can be explained by a decrease in the metabolic activity of the purifying biomass at low temperature considered damaging for enzymes and cells, which can destabilize the reaction process (Fields, 2001). Hence, it is necessary to maintain an adequate temperature in the bioreactor. However, these results do not agree with those of [START_REF] Arevalo | Effect of temperature on membrane bioreactor performance working with high hydraulic and sludge retention time[END_REF] who demonstrated that variation in temperature has no significant influence on the efficiency of a pilot bioreactor intended to remove COD and the nitrogen contained in domestic wastewater.

Correlative statistical analysis

The results of the statistical analysis presented in Table 5 showed that the efficiency of COD and NO 3 -removal was significantly influenced by the residence time: there was a significant difference in the removal efficiencies obtained at 24 h, 48 h, and 96 h (p < 0.05 and observed value > critical value). Also, the efficiency of COD, TKN, NO 3 -and NH 4 + removal in the effluent depended on the temperature because the average values of removal obtained at 10 °C were different from those obtained at 15 °C, 20 °C, and 30 °C (p < 0.05 and observed value > critical value). However, except for the reduction of nitrate, the aeration mode had an influence on the removal of COD, TKN, and NH 4 + (p < 0.05 and observed value > critical value). Overall, statistical conclusions seem to be consistent with the experimental results obtained in the present study (Fig. 2a,2b,2c;Fig. 4a,4b;Fig. 5a,5b).

Biomass characteristics

Biomass composition

The examination of the treated water leaving the bioreactor revealed that the biomass was composed of four physiological groups; their respective number and percentage are presented in Table 6. Values in parenthesis indicate standard error of the mean SEM (a mean of three determinations)

In terms of abundance, the results show that the average concentrations of the various bacterial populations measured by direct counting with an epifluorescence microscope were in the range (6.4 ± 0.32) × 10 6 (aerobic mesophilic flora) to (17.6 ± 0.78) × 10 6 CFU/mL (anaerobic heterotrophic flora).

Therefore, they were about an order of magnitude 20 times greater than those counted after cultivation on selective media which varied between (2.8 ± 0.15) × 10 5 and (8.1 ± 0.39) × 10 5 CFU/mL (Table 6).

This difference between the results given by the two techniques should be most likely related to the fact that the direct methods detect all bacteria present, either alive or dead; while indirect methods underestimate the number of bacteria for two major reasons. First, they count only viable cells, and secondly, they consider that a colony comes from a single cell, which is not always true.

A c c e p t e d M a n u s c r i p t Qualitatively, the most remarkable observation was the dominance of the anaerobic heterotrophic flora, which represented approximately 40.5% of the total active biomass colonizing the fixing support. In addition, the density of the aerobic heterotrophic flora was low compared to the anaerobic one. The majority of anaerobic or aerobic heterotrophic bacteria are capable of reducing nitrates to nitrites or nitrogen gas (Mauffrey, 2016). The denitrifying heterotrophic flora, characterized by its ability to use nitrate and other oxygenated mineral nitrogen compounds as the final electron acceptor, was abundant (25.5% of the total biomass). In this work, after inoculation under already favorable operating conditions of temperature, pH, C/N ratio, and hydraulic residence time, the heterogenous bacterial culture (anaerobic, aerobic, heterotrophic, denitrifiyer…) colonized the carrier, rapidly acclimated, proliferated and developed an immobilized biofilm because they were collected from natural sites of dairy effluent and highly adapted and specialized to grow at the expense of the organic matter and nitrogen. This seems play in favour of a better biodegradation of carbon and nitrogen pollution present in the SDE.

Hall-Stoodley et al. ( 2004) and Mauffrey (2016) reported that bacterial populations organized in biofilm lifestyle benefit from multiple advantages: stable development, proximity to cells, effective protection against aggressions from the living environment, and finally the emergence of new subpopulations said "persistent" more resistant than regular populations. This results in an increase in their metabolic performance, which promotes the consumption of organic and mineral substrates and improves the yield of the bioreactor. However, further bacterial analysis is needed to identify the species constituting the different groups of bacteria on the carrier media.

Bioactivity and growth rate determination

Fig. 6a indicates that the average biodegradation rates of organic substrate in the bioreactor were 76 ± 11.64%, 53.2 ± 7.86%, and 47.6 ± 6.76% for starch, milk powder, and yeast extract respectively. It is, therefore, preferable to use starch as a source of exogenous organic carbon, since its degradation is rapid by bacteria able to excrete specific enzymes responsible for carbon breakdown. The degradation of milk powder and yeast extract should then take place. Highly specialized bacteria play a key role in converting organic pollutants into new cells and simple end substances, and thereby producing clean water. Kargi and Pamukoglu, (2003) suggested that in the absence of purifying micro-organisms, the organic COD in wastewater must increase.

Conclusion

The FBBR anoxic-aerobic bioprocess produced a good quality effluent, which respects the recommended standards. The intermittent aeration was the key to achieve high COD and nitrogen removal efficiency from SDE. This investigation developed in one operating cycle and a single laboratory-scale reactor chamber constitutes the most innovative features of this work for future extrapolation on an industrial scale. This would offer a promising solution in the field of bioremediation, especially for agri-food professionals and small municipality officials in developing countries that suffer from released-raw effluents, limited financial means, lack of qualified human resources, and high-cost land.  High and fast growth yields of the biomass were obtained.

Fields

 Anoxic treatment removed 99.9 ± 24% of nitrate, and 82.1 ± 7.2% of COD.

 Anoxic/aerobic mode improved both the reduction of TKN and NH 4 + by 2.5 times.

A c c e p t e d M a n u s c r i p t

Fig. 1 .

 1 Fig. 1. Experimental system: (a) photography taken in the laboratory and (b) its schematic representation

  extract Incubation at 30°C for 144h in strict aerobic Three methods were used to estimate the number of bacteria:

Fig. 2 .

 2 Fig. 2. Variation of nitrate and COD removal efficiency during a (a) 24 h, (b) 48 h and (c) 96 h cycle

  supply of exogenous carbon, in sufficient quantity (COD/NO 3 -≃ 5), easily and completely biodegradable (reconstituted and water soluble). The rate of exogenous biodenitrification (2 mg N

Fig. 3 .

 3 Fig. 3. Evolution over time of (a) the temperature and (b) the pH at the bioreactor outlet

  metabolism in the reaction medium. The experiments were carried out in El Jadida city (Morocco) during the summer period when the temperature is between 25 and 30 °C, and a natural equilibrium is established between the temperature of the input water and the ambient temperature of the outside environment. Operating at room ambient temperature have the benefit to save energy consumption. The obtained values were very close to the limiting value required by the Moroccan standard (30 °C) (BORM, 2013) and considered compatible with a good biological activity.[START_REF] Tejaswini | Effect of temperature on effluent quality in a biological wastewater treatment process[END_REF] reported that the most operated temperature range in a WWTP varies in the range of 25-30 °C.

Fig. 4 .

 4 Fig. 4. (a) COD and (b) nitrogen (TKN, NO 3 -, NH 4 + ) evolution and removal efficiency over the aeration mode

Fig. 5 .

 5 Fig. 5. (a) COD and (b) nitrogen (TKN, NO 3 -, NH 4 + ) evolution and removal efficiency over the temperature

  If compared to the other related studies, the present findings generally agree with those cited by Lotti et al. (2014) who obtained about 85% bio-denitrification in a laboratory bioreactor operated at 25 °C, which decreased below 20 °C; whileHu et al. (2013) observed 90% denitrification at 12 °C. These results clearly show that the decrease of temperature from 30 °C to 10 °C affected the biological removal

Fig. 6 .

 6 Fig. 6. Changes in (a) starch, milk powder and yeast extract removal rate, and (b) starch concentration, cell growth and respiration rate over the time at 30 ± 5 °C and pH of 7 ± 0.5 As shown in Fig 6b, the oxidation of the biodegradable substrate (starch) by heterotrophic biomasswas accompanied by cell growth and respiratory activity, expressed in terms of absorbance at 620 nm and oxygen consumption respectively. After 12h of continuous cultivation, the bacterial growth was unrestricted, after which it appeared to be linear from 12h to 48h, and reached its maximum after 60h

Fig. 6b also

  Fig.6balso showed that the use in this work of starch as an energy and carbon source satisfies both maximal cellular growth and respiration rates (90 mg O 2 /L.h). Degradation of organic matter and nutrient by bacteria needs dissolved oxygen as a final electron acceptor in case of aerobic treatment.When water completely devoid of oxygen (anoxic), bacteria is forced to use the oxygen contained in the nitrates (nitrate respiration). Generally, these processes can be summarized by the aerobic reaction (4) and anoxic reaction (5)(Russel, 2019). Organics + Bacteria + Nutrients + O 2 → New cells + CO 2 + H 2 O + Residual Organics + Inorganics (4) Organics + Bacteria → New cells + Residual organics + NH 3 + N 2 + CO 2 + H 2 S + Inorganics (5)

  , P.A., 2001. Protein function at thermal extremes: balancing stability and flexibility. Comp. Biochem. Physiol. A Mol. Integr. Physiol., 129 (2/3), 417-431.

  The Handbook of Water and Wastewater Microbiology. Part 1: Basic microbiology, section 9: Fundamentals of biological behaviour and wastewater strength tests. Edited by Ducan Mra and Nigel Horan, 145-173. Declaration of interest statement Title of paper: Carbon and nitrogen removal from a synthetic dairy effluent in a vertical-flow fixed bed reactor Authors: Ahmed Hamdani, Abdeltif Amrane, Imane Kader Yettefti, Mohammed Mountadar, Omar Assobhei☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

  Title of paper: Carbon and nitrogen removal from a synthetic dairy effluent in a vertical-flow fixed bed bioreactor. Ref. N°: BITEB-D-20-00388. Authors: Ahmed Hamdani, Abdeltif Amrane, Imane Kader Yettefti, Mohammed Mountadar, Omar Assobhei Article Highlights  Fixed-bed bioreactor was developed for biological carbon and nitrogen removal.  Treatment was conducted in one operating cycle and in a single reactor compartment.

Table 1 .

 1 Support material specifications in the bioreactor

				M a n u s c r i p t
	A c c e p t e d
	Support material	Shape	Color	Diameter (mm)	Height (mm)	Apparent volume (L)	Vacuum (L)	Specific surface (m 2 /m 3 )	Porosity (%)
	Plastic	Ring	White	16 x 2	15 ± 1	51	44.5	190	87

Table 2 .

 2 Bioreactor operating parameters

	Parameter

Table 3 .

 3 Composition of the reconstituted dairy effluent

Table 6 .

 6 Distribution of the bacterial populations in the effluent according to the counting method

	Used method	Indirect counting method	Direct counting method
	Type of flora	CFU/mL	%	Bacteria/mL	%
	Anaerobic heterotrophic flora	[8.1 (± 0.39)] × 10 5	40.5 (± 5.3)	[17.6 (± 0.78)] × 10 6	41.9 ± 4.1
	Heterotrophic denitrifying flora	[5.1 (± 0.24)] × 10 5	25.5 (± 2.1)	[9.8 (± 0.41)] × 10 6	23.3 ± 2.7
	Aerobic heterotrophic flora	[4 (± 0.29)] × 10 5	20 (± 4.6)	[8.2 (± 0.45)] × 10 6	19.8 ± 3.8
	Aerobic mesophilic flora	[2.8 (± 0.15)] × 10 5	14 (± 1.7)	[6.4 (± 0.32)] × 10 6	15 ± 1.2

Table 5 .

 5 Results of statistical analysis (paired two-samples t-test)

		CV= 4.303;		DF= 2;	α=0.05			CV=2.571; DF=5; α=0.05		CV=2.201;	DF=11;	α=0.05
	Variable 1		Temperature			Aeration mode					Residence time
											24h cycle			48 cycle			96h cycle
	Variable 2	COD	TKN	NH 4 +	NO 3 -	COD	TKN	NH 4 +	NO 3 -	COD	NO 3 -	NO 2 -	COD	NO 3 -	NO 2 -	COD	NO 3	-	NO 2 -
	Observed value |OV|	141.949	11.889	8.419	463.429	16.521	11.889	8.419	2.654	3.958	3.928	2.740	5.663	6.709	3.180	5.626	9.290		3.080
	p-value	<0.0001	0.007	0.014	<0.0001	0.004	0.007	0.014	0.117	0.011	0.011	0.041	0.000	<0.0001	0.009	0.000	<0.0001	0.010
	OV/CV	OV>CV OV>CV OV>CV OV>CV OV>CV OV>CV OV>CV OV<CV OV>CV OV>CV OV>CV OV>CV OV>CV OV>CV OV>CV OV>CV OV>CV
	CV: critical value; DF: degree of freedom; α: alpha coefficient

  /mL, indicating that a high bioreactor biomass concentration was attained. This is normal because the selected organic substrate (starch) is readily biodegradable by most heterotrophic populations and injected in abundance (1000 mg/L), which explains the increase of biomass concentration and the respiratory activity. This result remains less than 84h reported byHamdani et al. (2018) who worked with a real dairy effluent rich in an organic matter less easily biodegradable if compared to reconstituted synthetic effluent containing starch, milk powder, and yeast extract.

	M a n u s c r i p t
	A c c e p t e d	Starch	Time (h) Absorbance	Respiration rate	b

CFU

OD 620 ≃ 1), which corresponds according to a calibration curve to approximately (5.8 ± 0.31) × 10

Acknowledgments

The pilot process is part of the "ENVIRONMENT MAROC, FSP RMIE 02/014" project financed by the FSP/SCAC (France) and the CNRST (Morocco). Special thanks to Professor Abdelmajid KHASSIB, English Teacher in Regional Academy of Education and Training Casablaca-Settat (Morocco) for his elaborative language revision on the paper.

We sincerely thank the anonymous reviewers for their time and useful comments towards the improvement of the manuscript.

CRediT authorship contribution statement

Conflicts of Interest

The authors declare that there is no conflict of interest whatsoever for this paper.

Food and