Member, IEEE Christophe Finot
email: christophe.finot@u-bourgogne.fr

Student Member, IEEE Hammani Kamal
email: kamal.hammni@u-bour-gogne.fr

Julien Fatome
email: julien.fatome@u-bourgogne.fr

Senior Member, IEEE John M Dudley
email: john.dudley@univ-fcomte.fr

Guy Millot
email: guy.millot@u-bourgogne.fr

K Hammani

Selection of Extreme Events Generated in Raman Fiber Amplifiers Through Spectral Offset Filtering

Keywords: Extreme events, nonlinear optics, Raman fiber amplifiers

In this work, we discuss the emergence of rare and intense events in a Raman fiber amplifier. The temporal and spectral evolutions of continuous and pulsed signals are investigated, and approaches based on spectral slicing of the broadened spectra are proposed in order to isolate the rarest events. Numerical simulations are confirmed by experimental results.

I. INTRODUCTION

F OR more than three decades, optical fibers have been rec- ognized as a versatile and highly effective testbed to investigate a very wide range of nonlinear concepts, ranging from modulation instability, in scalar [START_REF] Tai | Observation of modulational instability in optical fibers[END_REF] or vectorial [START_REF] Seve | Modulational instability and critical regime in a highly birefringent fiber[END_REF] configurations, generated by coherent [START_REF] Tai | Observation of modulational instability in optical fibers[END_REF] or incoherent [START_REF] Sauter | Incoherent modulation instability in instantaneous nonlinear Kerr media[END_REF] pumping waves, to the propagation of optical solitons [START_REF] Mollenauer | Experimental observation of picosecond pulse narrowing and solitons in optical fibers[END_REF] or similaritons [START_REF] Dudley | Self-similarity in ultrafast nonlinear optics[END_REF]. More recently, it has also been demonstrated that the evolution of picosecond pulses or continuous waves in a highly nonlinear optical fiber can be characterized by "extreme value" statistics that deviate strongly from more usual Gaussian statistics [START_REF] Solli | Optical rogue waves[END_REF]- [START_REF] Mussot | Convective instabilities and optical rogue waves in fibers with CW pumping[END_REF]. A suggested analogy with hydrodynamics has led to the use of the term "optical rogue wave" as a description of such rare but intense events occurring during supercontinuum generation.

Other recent studies have shown that such extreme statistics are not restricted to soliton-supporting systems. Indeed, similar heavy tailed statistics can also be observed in other widespread fiber-based configurations such as Raman amplifiers at telecommunication wavelengths [START_REF] Hammani | Optical roguewave fluctuations in fiber Raman amplifiers[END_REF] or optical waveguides [START_REF] Borlaug | Extreme value statistics in silicon photonics[END_REF]. In fact, under the influence of the quasi-instantaneous Raman gain under conditions of low group velocity mismatch, fluctuations of a partially incoherent pump can be exponentially transferred on the amplified signal. Similar trends have also been demonstrated in parametric amplifiers driven by a partially incoherent pump [START_REF] Hammani | Emergence of extreme events in fiber-based parametric processes driven by a partially incoherent wave[END_REF]. In such a context, in order to study and explain the appearance dynamic of these rare events, it becomes of primary importance to find a way to control and isolate the rarest and most intense events. In the framework of supercontinuum generation, it has been demonstrated that appropriately-implemented spectral filtering by means of a off-centered optical band pass filter (OBPF) could efficiently isolate the optical rogue structures [START_REF] Solli | Optical rogue waves[END_REF], [START_REF] Dudley | Harnessing and control of optical rogue waves in supercontinuum generation[END_REF], [START_REF] Lafargue | Direct detection of optical rogue wave energy statistics in supercontinuum generation[END_REF]. Basically, ultrashort pulses generated from the nonlinear dynamic fission/recompression of an initial pumping pulse are indeed strongly affected by the intrapulse Raman response of fused silica which progressively shifts their central frequency towards higher wavelengths. Consequently, recompressed pulses with the highest peak power then leads to the most frequency shifted pulses which can therefore be easily isolated.

In the context of extreme event appearance in Raman amplifiers from a continuous seed, it has been shown that the impact of cross-phase modulation (XPM) induced by a partially incoherent pump on the continuous wave leads to a spectral expansion of the amplified signal. It has also been experimentally suggested that slicing of this broadened spectrum could allow efficient isolation of these rare events [START_REF] Hammani | Optical roguewave fluctuations in fiber Raman amplifiers[END_REF].

In this paper, we further detail how these rare structures can be controlled in a Raman amplifier and how it is possible to discriminate the small-scale fluctuations from the giant structures. We highlight a clear distinction between the behavior affecting a continuous seed and the evolution of an initial ultrashort pulse train. The physical phenomena implied in the rare-event control can indeed significantly vary. Our paper is thus organized as follows. We first present the numerical model we developed as well as a simplified model that enables us to achieve some clear physical understanding of the underlying nonlinear physics. We then investigate the amplification of a continuous wave as well as a pulse train in the Raman amplifier. The numerical conclusions are finally compared to experimental results in the last part of our manuscript.

II. NUMERICAL MODEL

During its evolution in a single mode optical fiber, the slowlyvarying envelope of the electrical field of an optical wave can be described by the extended nonlinear Schrödinger equation [START_REF]Nonlinear Fiber Optics[END_REF]: [START_REF] Tai | Observation of modulational instability in optical fibers[END_REF] with and describing the chromatic dispersive properties of the optical fiber, the Kerr nonlinear coefficient, the optical losses, the silica response, which includes both the instantaneous and the delayed Raman response. and are the propagation distance and the temporal coordinate in a reference frame moving at the group velocity of the wave.

is the initial field made of the temporal superposition of the pump wave and the signal which is shifted by THz with respect to the pump wavelength and therefore leads to the maximum gain response:

. As no additional frequency is generated by nonlinear frequency mixing, it is possible to isolate the evolution of the pump from the evolution of the signal . We can also consider that the Raman gain experienced by the signal is constant over the spectral range under investigation and that the Raman intrapulse effect and resulting soliton self-frequency shift are not significant in the normal dispersion regime. Moreover, due to the propagation length under consideration (typically half a kilometer), the consequences of the fiber linear losses are low and can therefore be neglected. Given all these justified assumptions, (1) can be reduced to the set of two coupled nonlinear Schrödinger equations [START_REF] Headley | Raman Amplification in Fiber Optical Communications[END_REF] shown in equation ( 2) at the bottom of the page, with the walk-off parameter defined as the difference between the group velocities and of the signal and the pump respectively. and are the second order dispersion of the signal and pump respectively. Note that compared to [START_REF] Hammani | Optical roguewave fluctuations in fiber Raman amplifiers[END_REF], we have here taken into account the effects of second order dispersion in order to better describe the pulsed signal dynamics. Let us also notice that compared to the widely used models for Raman amplification which rely on a power analysis [START_REF] Headley | Raman Amplification in Fiber Optical Communications[END_REF]- [START_REF] Betlej | Increased stokes pulse energy variation from amplified classical noise in a fiber Raman generator[END_REF], the model we implement here is based on the evolution of the scalar electrical field. This model will then enable us to describe the dynamics, both in the temporal and spectral domains, which is necessary in order to understand our proposed spectral filtering method.

A crucial point here is that the pump used in our study is a partially incoherent pump that we modeled in the spectral domain by a Gaussian intensity field having a stochastic spectral phase with a uniform distribution between and [START_REF] Vanholsbeeck | The role of pump incoherence in continuous-wvae supercontinuum generation[END_REF], [START_REF] Barviau | Spectral broadening of a multimode continuous-wave optical field propagation in the normal dispersion regime of a fiber[END_REF]:

(3)
is the spectral full-width at half maximum (FWHM) of the pump, GHz, which corresponds in the temporal domain to intensity fluctuations having a minimum temporal FWHM of 25 ps. We will consider an average pump power of 175 mW, leading to an average gain of 3 dB.

Regarding the properties of the initial signals, two kinds of signals will be investigated. First, we will study the evolution of a continuous wave with an average power of 0.5 mW. Then, we will focus on the evolution of a Gaussian pulse train having a 2.5 ps FWHM and an initial pulse energy of 1 pJ.

Our Raman amplifier is based on a 500-meter highly nonlinear fiber, with a second order dispersion 1.3 ps and 2.2 ps at signal and pump wavelengths respectively. The nonlinearity is and the walk-off coefficient is ps , which leads to an integrated walk-off of 50 ps between the pump and the signal. Our fiber is normally dispersive, which enables us to ignore modulation instability [START_REF] Tai | Observation of modulational instability in optical fibers[END_REF] as well as solitonic recompression [START_REF] Mollenauer | Experimental observation of picosecond pulse narrowing and solitons in optical fibers[END_REF].

III. NUMERICAL RESULTS FOR A CONTINUOUS SEED

We first investigate the evolution of a continuous signal. We have outlined in a previous work [START_REF] Hammani | Optical roguewave fluctuations in fiber Raman amplifiers[END_REF] that a continuous signal evolving in a Raman fiber amplifier exhibiting low walk-off between pump and signal will experience an incoherence transfer of noise from the pump to the signal leading to the generation of rare and intense spikes.

A. Simulations Based on a Simplified Model

In order to better understand the physics behind the origin of the formation of those spikes, we propose to consider as a first qualitative approach a simplified model. In this approach, the pump, amplifying the considered continuous seed, is reduced to a single Gaussian pulse with a temporal width of 25 ps corresponding to the shortest temporal width possible in the incoherent pump structure.

We have plotted in Fig. 1(a) the initial pump (a1) and signal (a2) as well as the resulting amplified output signal (a3). As expected, the continuous seed has been amplified and a replica of the pump profile can be observed on the output signal (Fig. 1(a3) plotted on a semi-logarithmic scale). Fig. 1(b) outlines that the amplification undergone by the signal varies exponentially with the pump peak-power, confirming that the process is not affected by any depletion. Simply stated, we can expect any fluctuation of the initial pump to be exponentially transferred on the signal. It should be also noted that due to the walk-off value which is superior to the finite temporal width of the pump pulse, the amplification is much lower than the value in absence of walk-off: [START_REF] Osborne | Raman pulse walk-off in single-mode fibers: An exact analysis[END_REF]. If we now get concerned with the spectral intensity profile of the amplified signal (see Fig. 1(c)), we can note a significant spectral expansion of the initial continuous signal. Such a broadening is caused by the XPM of the pump on the signal [START_REF] Alfano | Induced spectral broadening of a wek picosecond pulse in glass produced by an intense picosecond pulse[END_REF], [START_REF] Martinelli | Inlfuence of polarization on pump-signal RIN tranfer and cross-phase modulation in copumped Raman amplifiers[END_REF]. It is then possible to slice the broadened spectrum by using a frequency offset OBPF in order to remove the central (2) continuous part of the signal [START_REF] Olsson | A simple and robust 40-Gb/s wavelength converter using fiber cross-phase modulation and optical filtering[END_REF]. The principle of such a technique has already been successfully demonstrated in the field of wavelength conversion of high bit-rate optical telecommunication signals [START_REF] Galili | Optical wavelength conversion by cross-phase modulation of data signals up to 640 Gps[END_REF]: the intensity information of the most powerful wave (the pump) is converted on the continuous seed via XPM.

Peak powers of pump and sliced signal are therefore linked via a function that is usually called transfer function. The shape of this function depends critically on the spectral offset of the OBPF. In order to illustrate this point, we have used a Gaussian filter with a spectral FWHM of 9 GHz. We can see from Fig. 1(d) that for higher detuning values , it becomes possible to efficiently reject the low pump powers: the frequency filter as an efficient intensity discriminator whose threshold be continuously tuned according to . Let us point out that previous experimental configurations have also taken advantage of Raman amplification [START_REF] Galili | Optical wavelength conversion by cross-phase modulation of data signals up to 640 Gps[END_REF], [START_REF] Wang | Raman-enhanced regenerative ultrafast all-optical fiber XPM wavelength converter[END_REF]. But using an external counterpropagating Raman pump enables them to avoid any influence of this additional wave on the expected wavelength conversion process. Our scheme here is more complex as the copropagating Raman pump and the XPM pump are intrinsically a single wave and consequently induce simultaneously correlated intensity and phase changes on the signal.

We can also compare our approach to spectral selection process used in the framework of supercontinuum generation [START_REF] Solli | Optical rogue waves[END_REF], [START_REF] Dudley | Harnessing and control of optical rogue waves in supercontinuum generation[END_REF], [START_REF] Lafargue | Direct detection of optical rogue wave energy statistics in supercontinuum generation[END_REF], which essentially relies on the intensity-dependant self-frequency shift undergone by ultrashort soliton pulses. In this context, spectral filtering is only possible at longer wavelength edge and the associated frequency shift is usually of the order of several tens of THz. In our approach, as the spectral expansion of the amplified signal induced by XPM is close from being symmetric (Fig. 1(c)) and does not rely on the intrapulse Raman response, filtering is possible both at shorter and longer wavelengths [START_REF] Hammani | Optical roguewave fluctuations in fiber Raman amplifiers[END_REF]. However, a drawback is that a significant part of the signal structure is lost during the filtering process.

B. Simulations Based on an Initial Incoherent Wave

In order to check the validity of the qualitative conclusions obtained based on our previous simplified model, we have run intensive numerical simulations based on a partially incoherent pump as described by [START_REF] Sauter | Incoherent modulation instability in instantaneous nonlinear Kerr media[END_REF]. Fig. 2(a1) illustrates the initial pump intensity profile plotted on a 50 ns range. We have also computed the statistical distribution of the peak-powers present in this pump (calculating these statistics required a temporal window of 20 s). The results plotted in Fig. 2(b1) illustrate that peak powers deviating significantly from the average pump power can exist. It is indeed possible to observe a structure having a peak-power more than 15 times the average power (which justifies a posteriori the study in part A of Gaussian pulses with initial peak powers as high as 2.5 W). Compared to previous studies dealing with fluctuations of a few tens of percents of the peak-power of pulses delivered by nanosecond -switched laser pumps [START_REF] Borlaug | Extreme value statistics in silicon photonics[END_REF], [START_REF] Betlej | Increased stokes pulse energy variation from amplified classical noise in a fiber Raman generator[END_REF], [START_REF] Garcia | Influence of classical pump noise on long-pulse multiorder stimulated Raman scattering in optical fiber[END_REF], [START_REF] Landahl | A simple analytic model for noise shaping by an optical fiber Raman generator[END_REF], the partially incoherent pump under investigation shows here much larger deviations.

The amplified signal (Fig. 2(a2)) exhibits significant peaks resulting from the instantaneous exponential amplification of the pump initial fluctuations. As expected from our simplified model, we can see from this figure as well as from Fig. 2(b2) that the fluctuation amplitude in the amplified signal is much larger than those present in the initial pump. From the 2 peaks recorded on a temporal window of 20 s, several giant peaks have been found to have peak intensity more than 100 times the average value of the signal. We also note that the probability distribution obtained for the amplified signal (Fig. 2(b2)) is in clear agreement with a linear function when plotted on a log-log scale, consistent with the characteristic power law nature of extreme events. We can also compare the resulting distribution to the distribution one can expect if we consider the incoherent pump as a succession of isolated 25-ps Gaussian identical pulses (such as the simplified model developed in part IIIA) having a peak power distribution following the results of Fig. 2(b1) and an instantaneous gain as Fig. 1(b). We see that this model is qualitatively correct in retrieving a heavily tailed distribution, but fails in quantitatively predicting the values of the maximum peak powers that can be achieved: our simplified model underestimates the peak power value of the giant structures. This is linked to the fact that in this model, we consider a single isolated pump pulse of fixed temporal width whereas in the initial incoherent wave, due to the walk-off effect, the signal can be subject to amplification by several adjacent substructures, which increases the resulting amplification.

The spectrum of the amplified wave (Fig. 2(c)) also exhibits a noticeable reshaping. As discussed above, the initial Dirac spectrum has been significantly broadened under the effect of XPM of the pump on the signal [START_REF] Martinelli | Inlfuence of polarization on pump-signal RIN tranfer and cross-phase modulation in copumped Raman amplifiers[END_REF], [START_REF] Ravet | Spectral broadening in Raman fiber amplifier pumped by partially coherent wave[END_REF], [START_REF] Manassah | Induced phase modulation by noisy fields[END_REF]. Finally, we have checked that offset spectral filtering enables us to efficiently isolate the highest peak-power structures. As shown in Fig. 2(d), higher frequency detunings lead to higher intensity discrimination: it is therefore possible to isolate a single rare event generated by the partially incoherent pump.

IV. NUMERICAL RESULTS BASED ON A PULSED SIGNAL

Let us now investigate the evolution of an initial pulsed signal with a temporal width below the coherence time of the pump.

A. Simplified Model

As in the previous part, we can first study a simplified approach to obtain some physical insights about the pump to signal interactions. In the context of a pulsed signal, it is necessary to take into account an additional parameter, namely, the initial temporal delay (noted ) between the pump pulse and the signal pulse. Indeed, if in the context of a continuous seed, maximum of the amplified pulse and pump were synchronized, in the context of pulsed signal, this is not a priori always the case. The impact of this initial delay can be seen in Fig. 3(a) where we have plotted the amplified signal for different values of . From our simulations, we have made out that an initial delay of ps leads to the rise of higher peak powers. In other words, if in the continuous wave, the pump amplitude was the single parameter influencing the amplitude of the resulting pulse, in the pulsed case, we will have two parameters that will influence the final state: the amplitude of the initial state and the temporal delay between the pump and signal.

In Fig. 3(b), we have plotted the temporal intensity profiles of the initial and final pump and signal. The temporal intensity profile of the pulse propagating in the normally dispersive amplifier progressively evolves towards a parabolic state [START_REF] Dudley | Self-similarity in ultrafast nonlinear optics[END_REF], [START_REF] Finot | Beneficial impact of wave-breaking or coherent continuum formation in normally dispersive nonlinear fibers[END_REF]. Some temporal asymmetry can however be seen due to the temporal walk-off and the depletion effects of the pump during the propagation [START_REF] Finot | Experimental generation of parabolic pulses via Raman amplification in optical fiber[END_REF]. The consequences of the strong temporal depletion experienced by the pump (Fig. 3(b)) [START_REF] Weiner | Self-phase modulation and optical pulse compression influenced by stimulated Raman scattering in fibers[END_REF] can also be seen on the gain evolution according to the pump power plotted in Fig. 3(c) which deviates from the usual linear trends and we can anticipate that the statistical properties of the amplifier will be impacted [START_REF] Mermelstein | RIN transfer analysis in pump depletion regime for Raman fibre amplifiers[END_REF]. Note that compared to the previous part, we are much more affected by depletion effects here because the initial peak power is much higher than in the continuous case (we have here an initial peak power of 175 mW instead of 0.5 mW). Furthermore, we stress that some negative gain could be observed, which is mainly due to the dispersion-induced temporal broadening of the signal pulse which consequently undergoes a peak power reduction.

Regarding the optical spectrum, noticeable broadening can be noticed as well as some spectral asymmetry which is a consequence of the pump-signal walk-off [START_REF] Weiner | Self-phase modulation and optical pulse compression influenced by stimulated Raman scattering in fibers[END_REF], [START_REF] Schadt | Frequency chirp and spectra due to self-phase modulation and stimulated Raman scattering influenced by pulse walk-off in optical fibers[END_REF]. We have numer- ically checked that the spectral expansion originates not from cross phase modulation but rather from self-phase modulation (SPM) [START_REF]Nonlinear Fiber Optics[END_REF]. Note that the optical broadened spectra here are much larger those obtained from a continuous wave, because of a broader initial spectrum and also because the effects of SPM cannot be neglected with the much higher initial peak power As in the preceding part, we can use an offset OBPF to isolate the structures with the highest peak powers. We have therefore plotted in Fig. 3(e) the transfer function obtained for the optimum delay for various values of the spectral offset of a Gaussian OBPF having a spectral FWHM of 100 GHz. Similarly to the previous case, increasing the spectral offset can continuously change the threshold of the transfer function. Such a method based on SPM in an amplifier has already been demonstrated in the telecommunication field with a continuous Raman pumping [START_REF] Finot | Regenerative 40-Gb/s wavelength converter based on similariton generation[END_REF]. It can also be seen as an extension of the well-known signal regeneration technique proposed by Mamyshev [START_REF] Mamyshev | All-optical data regeneration based on self-phase modulation effect[END_REF], [START_REF] Matsumoto | Performance analysis and comparison of optical 3R regenerators utilizing self-phase modulation in fibers[END_REF] and the fact that the extinction level increases with the offset is fully consistent with the previous theoretical analysis [START_REF] Provost | Design scaling rules for 2R-Optical self-phase modulation-based regenerators 2R regeneration[END_REF].

B. Simulations With an Initial Incoherent Wave

In order to confirm our qualitative results, we have performed simulations including an incoherent pump such as described by [START_REF] Sauter | Incoherent modulation instability in instantaneous nonlinear Kerr media[END_REF]. We have run more than 12 000 simulations and the resulting shot-to-shot statistics of the peak powers, plotted in Fig. 4(a), black squares, using a log-log scale, exhibits the linear tail characteristic of extreme phenomena.

We have also plotted in Fig. 4(b) the spectrogram of the output amplified signal (i.e., a spectro-temporal representation) where a pronounced event with a behavior deviating strongly from the average behavior can be noticed. The presence of this extreme shot confirms that pulses amplified to the highest peak power also exhibit the most broadened spectrum.

By recording the number of pulses after spectral slicing, we obtain the resulting statistics described in Fig. 4(c), which clearly reflects that for a low spectral offset (below 0.4 THz), the proportion of pulses recovered after slicing is constant to 1. A statistical analysis of the peak powers of the filtered pulse train (Fig. 4(a), grey diamonds) reveals that filtering at the central frequency behaves as a beneficial instantaneous optical power limiter [START_REF] Kouloumentas | Packet clock recovery using a bismuth oxide fiber-based optical power limiter[END_REF], [START_REF] Asobe | Noise reduction of 20 Gbit/s pulse train using spectrally filtered optical solitons[END_REF]. Indeed, the peak power fluctuations have been divided by more than 2 and we can also make out a statistical distribution reshaping. For further increase of the spectral offset , the number of pulses recovered after spectral filtering drops rapidly down to a very low value. We have finally found empirically that the rate of this decrease versus the frequency offset could be well approximated by an exponential decreasing law (a linear function when plotted on a semi logarithmic scale).

V. E XPERIMENTAL VALIDATION

A. Experimental setup

In order to confirm our numerical model, we have implemented the experimental setup illustrated in Fig. 5(a). The Raman pump is delivered by a fiber Raman laser with an initial average power of 350 mW at an initial wavelength of 1455 nm. As the pump is not polarized, this average pump power of 350 mW corresponds in our scalar numerical model to a value of 175 mW [START_REF] Headley | Raman Amplification in Fiber Optical Communications[END_REF]. Such a power experimentally leads to an average experimental gain of 3 dB. With such reduced pump power and gain, we have not observed any spontaneous Raman emission so that we can neglect this effect in the modeling. The autocorrelation function of the pump wave is plotted in Fig. 5(b), grey solid line, and highlights a typical contrast of 1:2 with a coherence time of 25 ps [START_REF] Hammani | Optical roguewave fluctuations in fiber Raman amplifiers[END_REF], [START_REF] Vanholsbeeck | The role of pump incoherence in continuous-wvae supercontinuum generation[END_REF], with a shape typical of the Gaussian distribution (circles) assumed for our numerical simulations [START_REF] Sauter | Incoherent modulation instability in instantaneous nonlinear Kerr media[END_REF].

The polarized signal is launched into a commercially available highly nonlinear fiber (HNLF) from ofs with parameters At the output of the optical fiber, a second WDM coupler enables us to select the amplified signal and remove the residual pump. Previous experiments reported in [START_REF] Hammani | Optical roguewave fluctuations in fiber Raman amplifiers[END_REF] have demonstrated that the extreme statistics generated by this system is in qualitative agreement with numerical predictions resulting from the model described in Section II. In the experimental section of this article, we focus our attention more specifically on the spectral selection process that can be performed by spectral filtering. In the case of the continuous seed, we have used a fiber Bragg grating having a spectral FWHM of 9 GHz. In the case of the pulsed signal, we have inserted a wavelength demultiplexer with eight output channels having each a spectral FWHM of 100 GHz and spaced by 200 GHz. At the output of the system, the signal is finally analyzed by means of a photodiode.

B. Experimental Selection of the Extreme Events

Experimental results obtained in the case of a continuous seed with an initial power of 0.5 mW are plotted in Fig. 6(a). As the position of the central frequency of the fiber Bragg grating is fixed, the filter-signal frequency detuning is obtained by simply adjusting the wavelength of our initial CW signal. It is readily apparent from subplots a1 to a3, that higher the signalfilter detuning is, lower the number of observed spikes is. As expected, for the largest detuning, only the most intense spikes are conserved.

We have also carried out some similar experiments for the 22-MHz picosecond pulsed seed. Initial pulses have a FWHM of 2.5 ps for an average power of 16 dBm (1 pJ energy per pulse). Results are recorded by means of a photodiode and an oscilloscope having a 1-GHz electrical bandwidth so that the experimental observed spikes are mainly correlated to the pulse energy rather than peak-power. Nevertheless, recent studies have shown that statistics of peak-power or energy exhibit similar behavior [START_REF] Lafargue | Direct detection of optical rogue wave energy statistics in supercontinuum generation[END_REF].

If the pulse train is filtered at its corresponding central frequency, we can retrieve after amplification and filtering a pulse train at the initial repetition rate, Fig. 6(b1). However, a high amplitude jitter is clearly visible. Now, if we analyze the output signal at another port of the demultiplexer, corresponding to a higher frequency offset (Figs. b2 andb3), we can observe a dramatic drop in the number of resulting output pulses. The output signal does not present any periodicity, so we have therefore generated a pulse train having a stochastic pulse separation (with a time-spacing corresponding to a multiple of the initial pulse train period). We note that compared to the method developed in [START_REF] Pitois | Asymptotic properties of incoherent waves propagating in an all-optical regenerators line[END_REF] and [START_REF] Pitois | Generation of localized pulses from incoherent wave in optical fiber lines made of concatened Mamyshev regenerators[END_REF], which was also based on the properties of sliced broadened spectra, our resulting pulse train presents here noticeable intensity fluctuations.

Finally, we have experimentally measured the number of output pulses as a function of the initial offset (Fig. 6(c)). In good agreement with results presented in Fig. 6(b), for low filter-signal frequency detuning 200 GHz , the number of detected pulses corresponds to the initial number of pulses. For higher detunings, we have recorded an exponential drop of the number of intensity spikes after spectral filtering. This result is fully consistent with our numerical study developed in Section IV. We can qualitatively see that it is possible to isolate and detect by this technique a pulse having a very low probability of occurrence (around 1 over 1000).

VI. CONCLUSION

In this work, we have proposed a simple model that has enabled us to isolate and characterize the nonlinear dynamics of the temporal and spectral evolution originating from the rare events with a non-Gaussian probability distribution. Based on the evolution of a Gaussian pulse having a temporal width corresponding to the typical coherence time scale of the incoherent wave, it becomes possible to easily understand the physical process stimulating the rogue events. Depending on the nature and power of the initial seed signal (depending if the initial pulse temporal width is below or above the coherence time), there will be a predominating role of the cross or self phase modulations respectively.

Even for a gain as low as 3 dB, resulting fluctuations can be significant, which requires to take into account this effect for the practical design of amplifiers based on quasi-instantaneous gain: large amplitude fluctuations of the partially incoherent pump can therefore lead to large signal distortions and errors under certain conditions. In this context, we believe that our characterization and interpretation of the noise properties in the picosecond temporal domain could be useful to explore further aspects of extreme value fluctuations occurring in optical fiber propagation. Our numerical analysis has been confirmed by experimental results Our conclusions could also complement the well-known RIN measurements carried out in the electrical spectral domain to characterize amplifier noise properties [START_REF] Headley | Raman Amplification in Fiber Optical Communications[END_REF], [START_REF] Seve | Modulational instability and critical regime in a highly birefringent fiber[END_REF], [START_REF] Mermelstein | RIN transfer analysis in pump depletion regime for Raman fibre amplifiers[END_REF], [START_REF] Fludger | Pump to signal RIN transfer in Raman fiber amplifiers[END_REF]- [START_REF] Keita | Relative intensity noise transfer of large-bandwidth pump lasers in Raman fiber amplifiers[END_REF]. Given the close links with the experimental techniques reported here and current approaches to optical regeneration, our results may also impact on the design and implementation of future-generation transmission networks.

Fig. 1 .

 1 Fig. 1. (a) Temporal intensity profiles of the initial pump (a1) and continuous signal (a2). The signal after amplification is plotted on a semilogarithmic scale (a3). (b) Intensity evolution of the gain (defined as the ratio of the output peak power of the signal and the initial average signal power) obtained from our numerical simulation (black dotted-line) and predicted from the formula exp (g L ) (dashed-line) (c) Ouput signal spectrum for various pump powers (same convention as Figs. a). (d) Transfer function describing the output signal peak power for various pump powers and various frequency offset filterings.

Fig. 2 .

 2 Fig. 2. (a) Initial pump intensity profile (a1) and probability of the peak powers (black squares) normalized to the average power of the pump (b1) compared with the amplified signal properties (a2 and b2). Distribution obtained with numerical simulations is compared with the distribution obtained from the initial power pump distribution and the gain derived from part 3B (grey circles). Statistical distributions plotted on a log-log scale are compared with a linear fits (grey dotted lines) (c) Output spectrum of the amplified signal (solid line) compared with the initial pump spectrum (grey dotted line) (d) Evolution of the temporal intensity profile of the signal after filtering by an offset OBPF for various offset values .

Fig. 3 .

 3 Fig. 3. (a) Output peak power of the amplified pulse for various initial pump peak powers and various initial delays. (b) Temporal intensity profiles of the signal (black) and the pump (grey). Output profiles (solid lines) are compared with initial profiles (dotted lines). Results obtained for the optimum initial temporal delay and a pump peak power of 2.5 W. (c) Evolution of the gain versus pump peak power (gain defined as the ratio between the final and initial pulse peak power) for the optimal initial temporal delay. (d) Evolution of the output spectral intensity profile of the pump for various pump powers (results at the optimum initial temporal delay). (e) Transfer function describing the output signal peak power for various pump powers and various values of frequency offset .

Fig. 4 .

 4 Fig. 4. (a) Statistical distribution of the output peak-power probability (black squares) (35 equidistant bins have been used). The tail of the distribution is compared to a linear function (on a log-log scale). Distribution obtained after spectral filtering at =0GHz is plotted with grey diamonds (b) Time-Frequency view of an output pulse sequence of 50 pulses (T is the period of the mode locked train.) (c) Proportion of output pulses (defined as the ratio between the number of pulses detected after spectral filtering and the initial number of pulses) according to the spectral offset . Results for > 0:4 THz are compared to a linear curve (using a semilog scale).

Fig. 5 .

 5 Fig. 5. (a) Experimental setup. (b) Experimental autocorrelation function of the pump wave (grey solid line) compared with the autocorrelation obtained based on the assumption of Gaussian fluctuations (circles) (3).

Fig. 6 .

 6 Fig. 6. (a) Experimental temporal results obtained for a initial continuous wave for different filter-signal spectral detunings: offset of 0 GHz, 100 GHz and 200 GHz, subplots a1, a2 and a3, respectively. (b) Experimental temporal trace (temporal scale is normalized by the repetition rate) of the output amplified 22-MHz pulsed train obtained for various filter-signal frequency detunings: 0 GHz, 600 GHz and 1 THz, subplots b1, b2 and b3, respectively (c) Number of detected output pulses as a function of the spectral detuning imposed by the wavelength demultiplexer. Results are compared with a linear decreasing function (using a semilog scale).

ACKNOWLEDGMENT

The authors would like to thank A. Picozzi and S. Pitois for illuminating discussions.


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Ryonosuke Matsumoto

Ultrasound homogenises suspensions of hydrophobic particles

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Introduction

Ultrasound baths are commonly used for cleaning metal objects. 1 But they have also been proposed as convenient replacement of acoustic shakers for bulk mixing. 2 These latter hand-held devices mix small quantities whilst requiring the ultrasonic tip to be dipped in the liquid to be mixed, which may be undesirable. 3 Hydrophobic particles inherently resist being suspended. Hydrophobic particles might be regarded as tiny solid particles surrounded by a thin gaseous shell. 4 It has been hypothesised that hydrophobic particles act as cavitation nuclei. 4 This cavitation behaviour would explain the translation speeds observed when hydrophobic polystyrene microspheres were driven through a liquid medium by means of ultrasound. 5 These translation speeds corresponded to those observed with gas microbubbles of similar sizes. 5 If hydrophobic particles do have a thin gaseous layer surrounding the solid cores, a sound field of sufficient pressure amplitude might force the gas layer to form and inertial cavity and subsequently fragment during the collapse phase. 6 In this study, we investigated whether hydrophobic particles can be forced to suspend by using ultrasound.

Materials and Methods

The first material studied was TIMCAL SUPER C65 Carbon Black (EQ-Lib-SuperC65) conductive additive (MTI Corportation, Richmond, CA, USA), hereafter referred to as C65. This material has shown to generate harmonic response to a low-amplitude, i.e., non-destructive, ultrasound field. [START_REF] Postema | Proc. IEEE AFRICON[END_REF] The second material studied was hydrophobically modified Zano 10 Plus zinc oxide (Umicore, Brussel, Belgium), hereafter referred to as ZnO. This material is the core component inside acoustically active antibubbles. [START_REF] Postema | [END_REF] For each material, samples of 1 mg were deposited into a FALCON ® 15 mL High-Clarity Polypropylene Conical Tube (Corning Science México S.A. de C.V., Reynosa, Tamaulipas, Mexico), after which 5 mL of 049-16787 Distilled Water (FUJIFILM Wako Pure Chemical Corporation, Chuo-Ku, Osaka, Japan) was added.

Each tube was individually held by hand for 1 minute in a 2510J-MT BRANSONIC ® ULTRASONIC CLEANER (BRANSON ULTRASONICS CORPORATION, Danbury, CT, USA) filled with degassed water. The ultrasonic cleaner operated at a transmitting frequency of 45 kHz.

Following the ultrasonic treatment, for each material, 200 μL was pipetted into the observation chamber of a high-speed observation system. 9 The observation chamber was placed under an IX70 microscope (Olympus Corporation, Shinjuku-ku, Tokyo, Japan) with a LUMPlan FI/IR 40× (N.A. 0.8) objective lens. Attached to the microscope was an HPV-X2 high-speed camera (Shimadzu, Nakagyo-ku, Kyoto, Japan), operating at 10 million frames per second. 10 During camera recording, the materials were subjected to ultrasound pulses, each consisting of 3 cycles with a centre transmitting frequency of 1 MHz and a peak-negative pressure of 200 kPa, from a laboratory-assembled single-element transducer. 9,10 The signal fed into the transducer was generated by an AFG320 arbitrary function generator (Sony-Tektronix, Shinagawa-ku, Tokyo, Japan) and amplified by a UOD-WB-1000 wide-band power amplifier (TOKIN Corporation, Shiroishi, Miyagi, Japan).

Results and Discussion

Photographs of a test tube containing C65 before and after sonication in the ultrasonic cleaner are shown in Fig. 1. The carbon black has been mixed optically homogeneously in the water. † Correspondence to: Michiel.Postema@wits.ac.za Photographs of a test tube containing zinc oxide before and after sonication in the ultrasonic cleaner are shown in Fig. 2. The white ZnO has been mixed optically homogeneously in the water. Fig. 3 shows three frames of a representative example from 56 high-speed video recordings of C65 and ZnO, each consisting of 256 frames. The frames shows a hydrophobic C65 particle before, during, and after 1-MHz sonication. During sonication, an inertial cavity can be clearly appreciated. After sonication, the cavity is seen to be detached and located to the upper right of the deformed or fragmented particle. In later frames (not shown), the cavity has dissolved, leaving the deformed or fragmented C65 particle. During subsequent ultrasound pulses, the C65 particle remains unaffected (not shown).

In general for all experiments, during the first pulse, the hydrophobic particles of both materials were observed to grow into inertial cavities, forcing the gas layer surrounding the particle to be released and dissolved. After the first pulse, no further cavitation activity was observed. This indicates that sonication can remove the thin gas layer surrounding a hydrophobic particle.

Conclusions

Hydrophobic particles of the materials C65 and ZnO can be forced to be suspended in water using ultrasound. The high-speed observations confirm that hydrophobic particles can act as cavitation nuclei. The lack of cavitation after the first pulse indicates that the gas layer surrounding the hydrophobic particle dissolves after inertial cavitation.

Fig. 1

 1 Fig. 1 C65 before (left) and after (right) 1-minute sonication in the ultrasonic cleaner.

Fig. 3

 3 Fig. 3 C65 acting as a cavitation nucleus, before (top), during (middle), and after (bottom) sonication. Each frame width corresponds to 145 μm. Time stamps are shown in the lower right corner of each frame.

Fig. 2

 2 Fig. 2 ZnO before (left) and after (right) 1-minute sonication in the ultrasonic cleaner.


Chao Sun
email: chao.sun@dalembert.upmc.fr

Katarzyna Świrk

Dominik Wierzbicki

Monika Motak

Teresa Grzybek

Patrick Da Costa
email: patrick.da_costa@sorbonne-universite.fr

On the effect of yttrium promotion on Ni-layered double hydroxides-derived catalysts for hydrogenation of CO 2 to methane

Keywords: CO 2 methanation, hydrotalcite, mixed oxides, yttrium, nickel catalyst

Ni-containing mixed oxides derived from layered double hydroxides with various amounts of yttrium were synthesized by a co-precipitation method at constant pH and then obtained by thermal decomposition. The characterization techniques of XRD, elemental analysis, low-temperature N 2 sorption, H 2 -TPR, CO 2 -TPD, TGA and TPO were used on the studied catalysts. The catalytic activity of the catalysts was evaluated in the CO 2 methanation reaction performed at atmospheric pressure. The obtained results confirmed the formation of nano-sized mixed oxides after the thermal decomposition of hydrotalcites. The introduction of yttrium to Ni/Mg/Al layered double hydroxides led to a stronger interaction between nickel species and the matrix support and decreased nickel particle size as compared to the yttrium-free catalyst.

The modification with Y (0.4 and 2 wt.%) had a positive effect on the catalytic performance in the moderate temperature region (250-300 °C), with CO 2 conversion increasing from 16 % for MO-0Y to 81% and 40% for MO-0.4Y and MO-2.0Y at 250 °C, respectively. The improved activity may be correlated with the increase of percentage of medium-strength basic sites, the stronger metal-support interaction, as well as decreased crystallite size of metallic nickel. High selectivity towards methane of 99% formation at 250 °C was registered for all the catalysts.

Introduction

The reduction of CO 2 emissions has gained legislative importance as it is considered one of the major drivers of climate change [START_REF] Aresta | Catalysis for the valorization of exhaust carbon: From CO2 to chemicals, materials, and fuels. technological use of CO 2[END_REF]. The reduction of carbon dioxide emissions is becoming attractive because of the cost of carbon feedstock [START_REF] Wang | Methanation of carbon dioxide: An overview[END_REF].

CO 2 hydrogenation into methane over transition metal-based catalysts using renewable hydrogen from water electrolysis as an example has a huge potential to reduce the emissions and, at the same time, to store the excess renewable energy to equalize the demand and capacity in a power to gas process [START_REF] Guilera | Metal-oxide promoted Ni/Al 2 O 3 as CO 2 methanation micro-size catalysts[END_REF][START_REF] Götz | Renewable Power-to-Gas: A technological and economic review[END_REF][START_REF] Zaǧli | Carbon dioxide adsorption and methanation on Ruthenium[END_REF]. Due to the lack of costly infrastructure for the distribution and storage of hydrogen, CO 2 hydrogenation seems to be a promising alternative approach [START_REF] Li | Metal-oxide interaction enhanced CO 2 activation in methanation over ceria supported nickel nanocrystallites[END_REF][START_REF] Aziz | CO 2 methanation over heterogeneous catalysts: Recent progress and future prospects[END_REF]. Additionally, methane can be easily liquefied and stored in the existing infrastructure [START_REF] Aziz | CO 2 methanation over heterogeneous catalysts: Recent progress and future prospects[END_REF]. Out of all proposed CO 2 hydrogenation reactions, e.g., methanol synthesis, higher hydrocarbons or methanation, the most developed one methanation (CO 2 + 4H 2 = CH 4 + 2H 2 O), with a few plants already operational in European Union [START_REF] Zhang | Visible-to-ultraviolet Upconvertion: Energy transfer, material matrix, and synthesis strategies[END_REF][START_REF] Zhen | Enhancing activity for carbon dioxide methanation by encapsulating (1 1 1) facet Ni particle in metal-organic frameworks at low temperature[END_REF].

The most widely studied catalysts for Sabatier's reaction in literatures are those based on group 8, 9, 10 metals-Fe, Ru, Rh, Co, Ni, or Pt [START_REF] Guilera | Metal-oxide promoted Ni/Al 2 O 3 as CO 2 methanation micro-size catalysts[END_REF][START_REF] Li | Metal-oxide interaction enhanced CO 2 activation in methanation over ceria supported nickel nanocrystallites[END_REF][START_REF] Panagiotopoulou | Selective methanation of CO over supported noble metal catalysts: Effects of the nature of the metallic phase on catalytic performance[END_REF][START_REF] Yaccato | Competitive CO and CO 2 methanation over supported noble metal catalysts in high throughput scanning mass spectrometer[END_REF][START_REF] Frontera | Supported Catalysts for CO 2 Methanation: A Review[END_REF][START_REF] Kruatim | Improvement of cobalt dispersion on Co/SBA-15 and Co/SBA-16 catalysts by ultrasound and vacuum treatments during Post-impregnation step[END_REF][START_REF] Czuma | Ni/zeolite X derived from fly ash as catalysts for CO 2 methanation[END_REF][START_REF] Tada | Promotion of CO 2 methanation activity and CH 4 selectivity at low temperatures over Ru/CeO 2 /Al 2 O 3 catalysts[END_REF][START_REF] Liu | Cobalt doped Ni based ordered mesoporous catalysts for CO 2 methanation with enhanced catalytic performance[END_REF][START_REF] Liang | Methanation of CO 2 over Ni /Al 2 O 3 modified with alkaline earth metals : Impacts of oxygen vacancies on catalytic activity[END_REF][START_REF] Fatah | CO 2 Methanation over Mesoporous Silica Based Catalyst : A Comprehensive Study[END_REF][START_REF] Beuls | Methanation of CO2 : Further insight into the mechanism over Rh /γ-Al 2 O 3 catalyst[END_REF][START_REF] Shin | Cobalt Catalysts Decorated with Platinum Atoms Supported on Barium Zirconate Provide Enhanced Activity and Selectivity for CO 2 Methanation[END_REF][START_REF] Beaumont | Combining in situ NEXAFS spectroscopy and CO 2 methanation kinetics to study Pt and Co nanoparticle catalysts reveals key insights into the role of platinum in promoted cobalt catalysis[END_REF][START_REF] Panagiotopoulou | Hydrogenation of CO 2 over supported noble metal catalysts[END_REF]. However, the most active and selective catalysts towards methane were found to be those based on Rh, Ru and Ni [START_REF] Li | Metal-oxide interaction enhanced CO 2 activation in methanation over ceria supported nickel nanocrystallites[END_REF][START_REF] Zhen | Enhancing activity for carbon dioxide methanation by encapsulating (1 1 1) facet Ni particle in metal-organic frameworks at low temperature[END_REF][START_REF] Panagiotopoulou | Selective methanation of CO over supported noble metal catalysts: Effects of the nature of the metallic phase on catalytic performance[END_REF][START_REF] Beuls | Methanation of CO2 : Further insight into the mechanism over Rh /γ-Al 2 O 3 catalyst[END_REF][START_REF] Panagiotopoulou | Hydrogenation of CO 2 over supported noble metal catalysts[END_REF][START_REF] Iglesias | Zr promotion effect in CO 2 methanation over ceria supported nickel catalysts[END_REF][START_REF] Vrijburg | Ni-Mn catalysts on silica-modified alumina for CO 2 methanation[END_REF]. Nickel-based catalysts have the advantage over noble metal-based catalysts because of their low cost, high availability and accessibility [START_REF] Aziz | CO 2 methanation over heterogeneous catalysts: Recent progress and future prospects[END_REF][START_REF] Yatagai | Mechanochemical CO 2 methanation over LaNi-based alloys[END_REF][START_REF] Everett | The role of oxygen vacancies in the CO 2 methanation employing Ni/ZrO 2 doped with Ca[END_REF][START_REF] Zhang | Mesostructured cellular foam silica supported bimetallic LaNi 1-x Co x O 3 catalyst for CO 2 methanation[END_REF][START_REF] Liang | Methanation of CO 2 over alumina supported nickel or cobalt catalysts: Effects of the coordination between metal and support on formation of the reaction intermediates[END_REF].

Layered double hydroxides (LDH) or hydrotalcite (HT) are materials with di-and tri-valent cations incorporated into the brucite-like layers. The layers of hydrotalcites are positively charged, and anions present in the interlayer spaces are compensating the charge. It was reported in the literature that there is a wide range of cations that maybe incorporated into the hydrotalcites structure, e.g., Li + , Ti 4+ , Sn 4+ or Zr 4+ [START_REF] Cavani | Hydrotalcite-type anionic clays: Preparation, properties and applications[END_REF].

Calcination of such materials leads to the formation of mixed nano-oxides with periclase-like structure, which show very interesting features [START_REF] Aziz | CO 2 methanation over heterogeneous catalysts: Recent progress and future prospects[END_REF][START_REF] Liu | Alkaline-assisted Ni nanocatalysts with largely enhanced low-temperature activity toward CO 2 methanation[END_REF][START_REF] Dębek | Promotion effect of zirconia on Mg(Ni,Al)O mixed oxides derived from hydrotalcites in CO 2 methane reforming[END_REF][START_REF] Dębek | Influence of Ce/Zr molar ratio on catalytic performance of hydrotalcite-derived catalysts at low temperature CO 2 methane reforming[END_REF][START_REF] Liu | La-promoted Ni-hydrotalcite-derived catalysts for dry reforming of methane at low temperatures[END_REF][START_REF] Dębek | Ni-containing Ce-promoted hydrotalcite derived materials as catalysts for methane reforming with carbon dioxide at low temperature -On the effect of basicity[END_REF]. Redox or acid-base properties of such materials may be tailored to some extent by controlling hydrotalcite composition, as shown e.g. in NH 3 -SCR [START_REF] Wierzbicki | Copper, cobalt and manganese: Modified hydrotalcite materials as catalysts for the selective catalytic reduction of NO with ammonia. the influence of manganese concentration[END_REF][START_REF] Chmielarz | Catalytic activity of Co-Mg-Al, Cu-Mg-Al and Cu-Co-Mg-Al mixed oxides derived from hydrotalcites in SCR of NO with ammonia[END_REF][START_REF] Carja | Mesoporous mixed oxides derived from pillared oxovanadates layered double hydroxides as new catalysts for the selective catalytic reduction of NO by NH 3[END_REF][START_REF] Wu | Enhancing DeNOx performance of CoMnAl mixed metal oxides in low-temperature NH 3 -SCR by optimizing layered double hydroxides (LDHs) precursor template[END_REF][START_REF] Quoc | Temporary overvoltages in the Vietnam 500 kV transmission line[END_REF] or DRM [START_REF] Chai | Free-Standing NiO-MgO-Al 2 O 3 Nanosheets Derived from Layered Double Hydroxides Grown onto FeCrAl-Fiber as Structured Catalysts for Dry Reforming of Methane[END_REF][START_REF] Zhang | Ni-Co catalyst derived from layered double hydroxides for dry reforming of methane[END_REF][START_REF] Tsyganok | Dry reforming of methane over catalysts derived from nickel-containing Mg-Al layered double hydroxides[END_REF][START_REF] Dębek | Ni-containing Ce-promoted hydrotalcite derived materials as catalysts for methane reforming with carbon dioxide at low temperature -On the effect of basicity[END_REF][START_REF] Świrk | Yttrium promoted Ni-based double-layered hydroxides for dry methane reforming[END_REF][START_REF] Świrk | Dry reforming of methane over Zr-and Y-modified Ni/Mg/Al double-layered hydroxides[END_REF] reactions. Another advantage of double layered hydroxides is that the incorporated cations are usually homogenously distributed due to their random arrangement in the brucite-like layers. Moreover, such materials exhibit basic properties, which are of great interest when used as catalysts for the reaction of CO 2 methanation [START_REF] Wierzbicki | Copper, cobalt and manganese: Modified hydrotalcite materials as catalysts for the selective catalytic reduction of NO with ammonia. the influence of manganese concentration[END_REF][START_REF] Świrk | Yttrium promoted Ni-based double-layered hydroxides for dry methane reforming[END_REF][START_REF] Wierzbicki | The influence of lanthanum incorporation method on the performance of nickel-containing hydrotalcite-derived catalysts in CO 2 methanation reaction[END_REF][START_REF] Świrk | Effect of low loading of yttrium on Ni-based layered double hydroxides in CO 2 reforming of CH 4[END_REF][START_REF] Wierzbicki | Examination of the influence of La promotion on Ni state in hydrotalcite-derived catalysts under CO 2 methanation reaction conditions: Operando X-ray absorption and emission spectroscopy investigation[END_REF][START_REF] Wierzbicki | The influence of nickel content on the performance of hydrotalcite-derived catalysts in CO 2 methanation reaction[END_REF][START_REF] Wierzbicki | Novel Ni-La-hydrotalcite derived catalysts for CO 2 methanation[END_REF][START_REF] Wierzbicki | Ni-Fe layered double hydroxide derived catalysts for non-plasma and DBD plasma-assisted CO 2 methanation[END_REF].

Several aspects were already investigated in case of hydrotalcite-derived catalysts for CO 2 methanation reaction such as (i) the effect of nickel content, (ii) the particle size of nickel crystallites, (iii) the reducibility of nickel species, (iv) the number and distribution of basic sites, and (v) the promotion with other metals such as La, Fe, etc.

or the new preparation method [START_REF] Wierzbicki | The influence of lanthanum incorporation method on the performance of nickel-containing hydrotalcite-derived catalysts in CO 2 methanation reaction[END_REF][START_REF] Wierzbicki | The influence of nickel content on the performance of hydrotalcite-derived catalysts in CO 2 methanation reaction[END_REF][START_REF] Zhang | Impacts of nickel loading on properties, catalytic behaviors of Ni/γ-Al 2 O 3 catalysts and the reaction intermediates formed in methanation of CO2[END_REF][START_REF] Zhou | High temperature methanation over Ni catalysts supported on high surface area ZnxMg 1-x Al 2 O 4 : Influence on Zn loading[END_REF][START_REF] Wierzbicki | Examination of the influence of La promotion on Ni state in hydrotalcite-derived catalysts under CO 2 methanation reaction conditions: Operando X-ray absorption and emission spectroscopy investigation[END_REF][START_REF] Wang | Application of Ni-Al-hydrotalcite-derived catalyst modified with Fe or Mg in CO 2 methanation[END_REF][START_REF] Fan | Improved activity of Ni/MgAl 2 O 4 for CO2 methanation by the plasma decomposition[END_REF].

Fan et al. [START_REF] Fan | Improved activity of Ni/MgAl 2 O 4 for CO 2 methanation by the plasma decomposition[END_REF] studied Ni impregnated MgAl 2 O 4 derived from hydrotalcite followed by calcination at 500 °C or treated by DBD plasma in order to decompose Ni precursor. The plasma treatment resulted in higher nickel dispersion of 7.1% for plasma decomposition method prepared sample, compared to 6.0% for the traditionally calcined material. The authors claimed that smaller metallic nickel particles resulted in enhanced activity in the reaction of CO 2 methanation. Wang et al. [START_REF] Wang | Application of Ni-Al-hydrotalcite-derived catalyst modified with Fe or Mg in CO 2 methanation[END_REF] studied Ni/Al HTs promoted with 0.05 and 0.25% molar ratio of Fe and found that the introduction of Fe effectively enhanced the H 2 adsorption capacity. Ni/Mg/Al hydrotalcites promoted with a wide range of Fe content (1.2-18 wt.% of Fe) were examined by Mebrahtu et al. [START_REF] Mebrahtu | Hydrotalcite based Ni-Fe/(Mg,Al)O x catalysts for CO 2 methanation-tailoring Fe content for improved CO dissociation, basicity, and particle size[END_REF]. It was found that the activity in CO 2 methanation was effectively increased in the low temperature region when low amounts of iron were introduced. In our previous reports, we investigated the influence of Ni loading and the effect of La introduction on the catalytic activity of LDHs catalysts in CO 2 methanation [START_REF] Wierzbicki | The influence of lanthanum incorporation method on the performance of nickel-containing hydrotalcite-derived catalysts in CO 2 methanation reaction[END_REF][START_REF] Wierzbicki | The influence of nickel content on the performance of hydrotalcite-derived catalysts in CO 2 methanation reaction[END_REF][START_REF] Wierzbicki | Novel Ni-La-hydrotalcite derived catalysts for CO 2 methanation[END_REF]. The incorporation of higher amounts of nickel, as well as introduction of lanthanum, significantly enhanced the activity in CO 2 methanation reaction. This could be correlated with the increased number of medium-strength basic sites, which in case of La-promoted catalysts was strongly dependent on the method of promoter introduction [START_REF] Wierzbicki | The influence of nickel content on the performance of hydrotalcite-derived catalysts in CO 2 methanation reaction[END_REF][59] [START_REF] Pan | Insight into the reaction route of CO 2 methanation: Promotion effect of medium basic sites[END_REF]. According to the study of Pan et al. [START_REF] Pan | Insight into the reaction route of CO 2 methanation: Promotion effect of medium basic sites[END_REF] CO 2 adsorbed on Ni/Ce 0.5 Zr 0.5 O 2 may undergo hydrogenation easier than on Ni/Al 2 O 3 because of the higher content of medium basic sites.

Yttrium had been reported in the literature as a promising dopant in methane dry reforming reaction (CO 2 + CH 4 = 2H 2 + 2CO) [START_REF] Świrk | Yttrium promoted Ni-based double-layered hydroxides for dry methane reforming[END_REF][START_REF] Świrk | Effect of low loading of yttrium on Ni-based layered double hydroxides in CO 2 reforming of CH 4[END_REF][START_REF] Ferna´ndez | New Hydrotalcite-like Compounds Containing Yttrium[END_REF][START_REF] Liu | Nickel Supported Modified Ceria Zirconia Lanthanum/ Praseodymium/Yttrium Oxides Catalysts for Syngas Production through Dry Methane Reforming[END_REF][START_REF] Świrk | Syngas production from dry methane reforming over yttrium-promoted nickel-KIT-6 catalysts[END_REF][START_REF] Świrk | Ce-and Y-Modified Double-Layered Hydroxides as Catalysts for Dry Reforming of Methane: On the Effect of Yttrium Promotion[END_REF][START_REF] Świrk | Dry reforming of methane over Zr-and Y-modified Ni/Mg/Al double-layered hydroxides[END_REF][START_REF] Li | Y 2 O 3 -promoted NiO/SBA-15 catalysts highly active for CO2/CH4 reforming[END_REF]. The increased activity of the Ni-containing hyrotalcites was attributed to the enhanced dispersion of the active phase in comparison with the un-promoted materials [START_REF] Świrk | Yttrium promoted Ni-based double-layered hydroxides for dry methane reforming[END_REF][START_REF] Świrk | Effect of low loading of yttrium on Ni-based layered double hydroxides in CO 2 reforming of CH 4[END_REF][START_REF] Świrk | Ce-and Y-Modified Double-Layered Hydroxides as Catalysts for Dry Reforming of Methane: On the Effect of Yttrium Promotion[END_REF]. The stability of the Zr-containing catalysts in DRM reaction was also enhanced by the introduction of Y, which was assigned to the formation of a solid-solution ZrO 2 -Y 2 O 3 , leading to the increased reducibility of bulk NiO [START_REF] Świrk | Dry reforming of methane over Zr-and Y-modified Ni/Mg/Al double-layered hydroxides[END_REF]. Moreover, Bellido et al. [START_REF] Bellido | Effect of the Y 2 O 3 -ZrO 2 support composition on nickel catalyst evaluated in dry reforming of methane[END_REF] reported that ceria doped with yttrium showed enhanced oxygen mobility and oxygen vacancies.

For CO 2 methanation, Muroyama et al. [START_REF] Muroyama | Carbon dioxide methanation over Ni catalysts supported on various metal oxides[END_REF] To the best of our knowledge, there are no literature reports regarding yttrium promoted Ni-containing hydrotalcite-derived catalysts for CO 2 hydrogenation to methane. Our study was focused on the determination of the influence of Y introduction to Ni-containing layered double hydroxides on the catalytic performance in CO 2 methanation. The catalysts were synthesized using the co-precipitation method at a constant pH and with a fixed molar ratio of M II+ /M III+ =3.0. The assumed loading of yttrium introduced into hydrotalcite was 0.4, 2.0 and 4.0 wt.%. To correlate the changes in activity with the Physico-chemical properties, the studied materials were characterized using various techniques such as X-ray diffraction (XRD), low-temperature N 2 sorption, X-ray fluorescence (XRF), temperature-programmed reduction in H 2 (H 2 -TPR), temperature-programmed desorption of CO 2 (CO 2 -TPD), thermogravimetric analysis (TGA) and temperature-programmed oxidation (TPO).

Experimental

Catalysts preparation

The co-precipitation method with sodium carbonate was carried out for catalyst preparation. An aqueous solution of following nitrates was used: Ni, Y, Al, and Mg, and added dropwise into Na 2 CO 3 solution. NaOH (2 M) was also dripped into the mixture to adjust pH to 10±0.2. The ratio of M 2+ /M 3+ was assumed as 3. The assumed loading of yttrium was 0.4 wt.%, 2.0 wt.% or 4.0 wt.%. After co-precipitation, the slurry was left to react at 65 ºC for 24 h. Then, this mixture was filtered under vacuum and washed with distilled water. After filtration, the obtained cake was dried at 80 °C overnight and calcined in static air at 550 °C for 5 h with a ramp of 5 °C/min. The samples were designated as MO-0Y, MO-0.4Y, MO-2.0Y, and MO-4.0Y.

Catalysts characterization

Elemental composition, structural parameters, and textural properties

X-Ray Fluorescence (XRF) using a Rigaku Supermini200 analyzer to evaluate the elemental analysis of the studied catalysts. The experiment was performed under vacuum at 36.5 ºC in the presence of P-10 gas (a mixture of 10% CH 4 /Ar, flow 24.7 mL/min). A pulse height analyzer was used to calibrate the proportional counter (PC) detector. The calcined sample was homogeneously mixed with boric acid and pelletized under 10 bar. So prepared pellet was then covered by polypropylene film (6 μm) and put into a sample holder for the analysis.

The structural properties of the reduced and spent catalysts were studied by X-ray diffraction (XRD). XRD patterns were collected on a PANalytical-Empyrean diffractometer, equipped with a copper-based anode (Cu-Kα, λ = 0.154059 nm). The instrument settings were 40 mA and 45 kV. For the evaluation of Ni 0 (metallic nickel) particle size, the Scherrer equation was used.

Low-temperature N 2 adsorption-desorption method was conducted in a TriStar II 3020 (Micromeritics) apparatus for the study of the textural properties of the catalysts.

Before the measurement, 100 mg of the sample was degassed at 110 ºC for 3 h. Then the measurement was carried out at liquid nitrogen temperature (-196 ºC). The specific surface area of the sample was calculated by the Brunauer-Emmett-Teller (BET) method, and the mesopore volume and average pore diameter by the Barrett-Joyner-Halenda (BJH) desorption method.

Temperature programmed reduction in H 2

The reducibility of the hydrotalcite-derived mixed-oxide was measured by temperature-programmed reduction of H 2 (H 2 -TPR) method, using a BELCAT-M apparatus (BEL Japan Inc.) equipped with a thermal conductivity detector (TCD). 60 mg of sample was previously degassed in a flow of helium (99.999% He, 50 mL/min) at 100 ºC for 2 h to eliminate impurities, then the sample was reduced from 100 ºC to 900 ºC with the temperature ramp of 10 ºC/min in a 5%H 2 /Ar gas mixture (50 mL/min).

Temperature programmed desorption of CO 2

The number and distribution of basic sites were determined by temperature-programmed desorption of CO 2 , measured in the same equipment as H 2 -TPR. After the TPR experiment, the sample was cooled down to 80 ºC for the TPD test. The sample was pretreated using a flow of pure helium (50 mL/min) at 80 ºC for 2 h, and then CO 2 was adsorbed from 10% CO 2 /He mixture (50 mL/min) for 1 h. Then, the catalyst was cleaned by pure helium for 15 min to desorb weakly physically adsorbed CO 2 . Afterward, the catalyst was heated from 80 ºC to 800 ºC in He (50 mL/min) with a heating rate of 10 ºC/min. The obtained profiles were deconvoluted and integrated as presented elsewhere [START_REF] Zhang | Visible-to-ultraviolet Upconvertion: Energy transfer, material matrix, and synthesis strategies[END_REF][START_REF] Zhen | Enhancing activity for carbon dioxide methanation by encapsulating (1 1 1) facet Ni particle in metal-organic frameworks at low temperature[END_REF].

Thermogravimetric analyses (TGA)

Thermogravimetric analysis was performed on the spent catalysts by the Q5000 IR apparatus. Around 25 mg of material was heated starting from room temperature to 750 °C (heating rate of 10 °C/min). The measurements were performed in synthetic air. The amount of H 2 O and adsorbed CO 2 were estimated by the mass loss registered in the TGA plots.

Temperature-programmed oxidation (TPO)

The TPO analyses were carried out on the spent catalysts by Quadstar Mass equipped with a Pfeiffer Vacuum. Around 30 mg of a sample was heated from ambient temperature to 800 °C with a heating rate of 5 °C/min. The measurements were performed in 5%O 2 /Ar gas of 200 ml/min (Volumetric percentage). During the mass spectroscopy analysis, the following desorbed species were recorded; m/z: 44 (CO 2 ) and 18 (H 2 O). The CO 2 signal in the graph was enlarged 10 times for the analysis.

Catalytic performance tests

The catalytic tests of CO 2 methanation were performed in a fixed-bed flow reactor (inner diameter: 8 mm) under atmospheric pressure. The temperature in the catalytic bed was monitored using a K-type thermocouple, which was placed close to the catalyst bed. Before the tests, the calcined materials were reduced in situ from room temperature to 900 °C with a heating rate of 5°C/min under reduction gas (5%H 2 /Ar: 100 ml/min) and kept 1 h at 900 °C. The reduction temperature was 900 °C because the nickel species could be reduced thoroughly at 900 °C according to the TPR result, which was also used in other literature [START_REF] Wierzbicki | The influence of nickel content on the performance of hydrotalcite-derived catalysts in CO 2 methanation reaction[END_REF]. After the reduction, the reactor was cooled down to 200°C and the reaction mixture was introduced with a molar ratio of Ar/H 2 /CO 2 =25/60/15 and the GHSV of 12,000 h -1 . The methanation tests were performed in the temperature range from 200 to 400 °C with a temperature step of 50 °C, which are appropriate conditions for Ni-containing mixed oxides, as reported in many literatures [START_REF] Wierzbicki | The influence of nickel content on the performance of hydrotalcite-derived catalysts in CO 2 methanation reaction[END_REF][START_REF] Wierzbicki | The influence of lanthanum incorporation method on the performance of nickel-containing hydrotalcite-derived catalysts in CO 2 methanation reaction[END_REF]. At each plateau of temperature, the catalyst was kept for 30 min, corresponding to a steady-state measurement. The flow rates of inlet and outlet were measured by flowmeter at each temperature when the reaction was stable. And the measured flow rates and the compositions obtained from GC were used to calculate the CO 2 conversion (X CO2 ) and CH 4 selectivity (S CH4 ). In which Q is the flow rate ("in" for inlet, "out" for outlet). 1).

Results and discussion

For the MO-4.0Y, some deposition of Yttrium on the external surface may be assumed.

Moreover, the distance between the brucite-like layers (c´=c/3) is in the range of [START_REF] Kovanda | Crystallization of synthetic hydrotalcite under hydrothermal conditions[END_REF][START_REF] Kloprogge | Thermogravimetric analysis-mass spectrometry (TGA-MS) of hydrotalcites containing CO 3 2-, NO 3 -, Cl -, SO 4 2or ClO[END_REF][START_REF] Cavani | Hydrotalcite-type anionic clays: Preparation, properties and applications[END_REF]. The structural parameters revealed that the yttrium loading up to 2.0 wt.% could result in the introduction of this metal into the periclase-like structure. However, the higher content of the yttrium led to the increase of the interlayer space, which was possibly linked with the deposition of the metal on the surface of the layers. This agrees with the textural properties, as the specific surface area of MO-4.0Y significantly decreased compared with that of MO-2.0Y due to their partial blockage.

The elemental composition of nano-mixed oxides obtained by calcination acquired from the XRF method is presented in Table 1. All samples revealed nickel content between 16 and 20 wt.%, whereas the content of yttrium was either the same (MO-0.4Y) or close to the nominal amount (MO-2.0Y and MO-4.0Y). According to Li et al. [START_REF] Li | Y 2 O 3 -promoted NiO/SBA-15 catalysts highly active for CO2/CH4 reforming[END_REF], Ni 2+ can be substituted by Y 3+ , similarly as observed in our study (Table 1). The calculated M 2+ /M 3+ atomic ratios were fairly close to those assumed during the materials synthesis, indicating that the composition of LDHs may be easily controlled as reported before [START_REF] Dębek | Low temperature dry methane reforming over Ce, Zr and CeZr promoted Ni-Mg-Al hydrotalcite-derived catalysts[END_REF]. The textural parameters obtained from the N 2 sorption isotherms for the calcined materials are listed in Table 1. All values agree with those previously reported in the literature [START_REF] Wierzbicki | Copper, cobalt and manganese: Modified hydrotalcite materials as catalysts for the selective catalytic reduction of NO with ammonia. the influence of manganese concentration[END_REF][START_REF] Świrk | Yttrium promoted Ni-based double-layered hydroxides for dry methane reforming[END_REF][START_REF] Świrk | Dry reforming of methane over Zr-and Y-modified Ni/Mg/Al double-layered hydroxides[END_REF][START_REF] Świrk | Effect of low loading of yttrium on Ni-based layered double hydroxides in CO 2 reforming of CH 4[END_REF][START_REF] Wierzbicki | The influence of nickel content on the performance of hydrotalcite-derived catalysts in CO 2 methanation reaction[END_REF][START_REF] Wierzbicki | Novel Ni-La-hydrotalcite derived catalysts for CO 2 methanation[END_REF][START_REF] Wierzbicki | Examination of the influence of La promotion on Ni state in hydrotalcite-derived catalysts under CO 2 methanation reaction conditions: Operando X-ray absorption and emission spectroscopy investigation[END_REF][START_REF] Wierzbicki | The influence of lanthanum incorporation method on the performance of nickel-containing hydrotalcite-derived catalysts in CO 2 methanation reaction[END_REF][START_REF] Świrk | Ce-and Y-Modified Double-Layered Hydroxides as Catalysts for Dry Reforming of Methane: On the Effect of Yttrium Promotion[END_REF][START_REF] Cavani | Hydrotalcite-type anionic clays: Preparation, properties and applications[END_REF]. The obtained specific surface areas ranged between 120 and 192 m 2 .g -1 and the highest area was found for the MO-2.0Y catalyst.

There are no significant difference regarding to BET surface area and pore volume of Ni-containing double-layered hydroxides-derived catalyst when the loading of yttrium is low (≤0.4%) compared with Y-free sample, only the average pore size decreases as the increase of yttrium at low loading of yttrium [START_REF] Świrk | Yttrium promoted Ni-based double-layered hydroxides for dry methane reforming[END_REF][START_REF] Świrk | Effect of low loading of yttrium on Ni-based layered double hydroxides in CO 2 reforming of CH 4[END_REF]. As described in the section before, the structural parameters showed that the yttrium loading up to 2.0 wt.% could result in the introduction of this metal into the periclase-like structure. However, the higher content of the yttrium increased the interlayer space, which was possibly linked with the deposition of the metal on the outer surface of the layers. This agrees with the textural properties, as the specific surface area of MO-4.0 Y significantly decreased due to their partial blockage. The volume of mesopores did not change significantly after yttrium promotion. However, pore diameters diminished for MO-0.4Y and MO-2.0Y catalysts, as compared to the non-promoted material, pointing to the formation of a higher number of smaller pores when yttrium was introduced into the brucite-like layers. Fig. 1 shows XRD diffractograms of the reduced catalysts, in which metallic nickel phase (ICOD 01-087-0712) is evidenced by the presence of reflections at 2θ ca.

44.5, 53 and 76.5°, corresponding to crystal planes of (111), ( 200) and (220), respectively. Moreover, reflections arising from the periclase-like structure at 2θ ca.

36.7, 43 and 62.5° are observed, which corresponds to mixed oxides obtained after thermal treatment of double-layered hydroxides [START_REF] Świrk | Yttrium promoted Ni-based double-layered hydroxides for dry methane reforming[END_REF][START_REF] Świrk | Dry reforming of methane over Zr-and Y-modified Ni/Mg/Al double-layered hydroxides[END_REF][START_REF] Świrk | Effect of low loading of yttrium on Ni-based layered double hydroxides in CO 2 reforming of CH 4[END_REF]. Fig. 2 shows the H 2 -TPR of calcined mixed oxides (MO). As demonstrated in other reports, yttrium cannot be reduced under the conditions used in the measurements [START_REF] Li | Y 2 O 3 -promoted NiO/SBA-15 catalysts highly active for CO2/CH4 reforming[END_REF][START_REF] Bellido | Effect of the Y 2 O 3 -ZrO 2 support composition on nickel catalyst evaluated in dry reforming of methane[END_REF]. The reduction profile of MO-0Y has two main reduction bands that centered at 366 °C and 829 °C, which corresponds respectively to the reduction of nickel oxides weakly bonded with the double layered hydroxides and nickel species that are incorporated into the structure of hydroxides [START_REF] Dębek | Promotion effect of zirconia on Mg(Ni,Al)O mixed oxides derived from hydrotalcites in CO 2 methane reforming[END_REF][START_REF] Świrk | Yttrium promoted Ni-based double-layered hydroxides for dry methane reforming[END_REF][START_REF] Świrk | Syngas production from dry methane reforming over yttrium-promoted nickel-KIT-6 catalysts[END_REF][START_REF] Li | Y 2 O 3 -promoted NiO/SBA-15 catalysts highly active for CO2/CH4 reforming[END_REF][START_REF] Bellido | Effect of the Y 2 O 3 -ZrO 2 support composition on nickel catalyst evaluated in dry reforming of methane[END_REF][START_REF] Sánchez | Hydrogen production from glycerol on Ni/Al 2 O 3 catalyst[END_REF]. The high-temperature peak shifts towards higher temperatures for all Y-promoted catalysts (Table 3, 858-866 °C), which indicates stronger interaction between nickel oxide species and the support matrix in comparison with Y-free sample [START_REF] Świrk | Yttrium promoted Ni-based double-layered hydroxides for dry methane reforming[END_REF]. For 2.0 and 4.0 wt.% of Y, the shift of latter peak was less pronounced, as shown in Table 3, indicating less strong metal-support interaction. This might be due to the segregation of yttrium or lattice substitution of nickel species by yttrium [START_REF] Li | Y 2 O 3 -promoted NiO/SBA-15 catalysts highly active for CO2/CH4 reforming[END_REF]. The reduction peaks at temperatures lower than 600 °C presented low intensity for Y-modified samples in comparison to the unpromoted catalyst (MO-0Y), which means that the loading of Y results in a decreased reducibility. This phenomenon was already observed in hydrotalcite derived mixed oxides catalysts modified by Y and Zr in CO 2 dry reforming reaction, in which the adding of Y and Zr resulted in a decrease of the reducibility of nickel [START_REF] Dębek | Promotion effect of zirconia on Mg(Ni,Al)O mixed oxides derived from hydrotalcites in CO 2 methane reforming[END_REF][START_REF] Świrk | Yttrium promoted Ni-based double-layered hydroxides for dry methane reforming[END_REF]. As calculated in [START_REF] Liu | La-promoted Ni-hydrotalcite-derived catalysts for dry reforming of methane at low temperatures[END_REF][START_REF] Dębek | Ni-containing Ce-promoted hydrotalcite derived materials as catalysts for methane reforming with carbon dioxide at low temperature -On the effect of basicity[END_REF][START_REF] Świrk | Yttrium promoted Ni-based double-layered hydroxides for dry methane reforming[END_REF][START_REF] Wierzbicki | Examination of the influence of La promotion on Ni state in hydrotalcite-derived catalysts under CO 2 methanation reaction conditions: Operando X-ray absorption and emission spectroscopy investigation[END_REF]. Similar peaks were found for yttrium-promoted mixed oxides materials, with the maximum temperature of CO 2 desorption peak shifted towards lower temperature with the increasing yttrium content compared to the MO-0Y sample, indicating that the loading of Y changed the number and distribution of the basic sites. This phenomenon was also observed in other literature [START_REF] Świrk | Yttrium promoted Ni-based double-layered hydroxides for dry methane reforming[END_REF]. As calculated in Table 4, the amount of different type of basic sites for the Y-modified samples increased with the increase of yttrium loading (from 0.4 to 4.0 wt%) and the total number of basic sites also increased with the increased Y content, with MO-4.0Y having the highest number of each type of basic sites as well as the total basic sites. Compared to the basicity of MO-0Y sample, the materials with 0.4 wt.% and 2.0 wt.% of Y showed lower content of total basic sites and individual type of basic sites (weak, medium or strong). But compared to that of the MO-0Y, the percentage share of weak or intermediate basic sites for MO-0.4Y and MO-2.0Y was higher, with lower content of the share of strong basic sites, meaning that the doping of yttrium significantly changed the distribution of basic sites on Y-modified samples.

In conclude, the introduction of Y with low content (0.4 wt.% and 2.0 wt.%) results in the increase of share of medium basic sites as the expense of strong type. The highest share of medium-strength basic sites was found on the MO-0.4Y sample. The thick continuous line shown in Fig. 4 represents the thermodynamic equilibrium calculated for the conditions used in this work [START_REF] Liu | La-promoted Ni-hydrotalcite-derived catalysts for dry reforming of methane at low temperatures[END_REF][START_REF] Wierzbicki | Examination of the influence of La promotion on Ni state in hydrotalcite-derived catalysts under CO 2 methanation reaction conditions: Operando X-ray absorption and emission spectroscopy investigation[END_REF]. According to thermodynamics, CO 2 methanation is favored at low temperatures and it decreases with the increasing temperature due to the co-existence of parallel reactions, such as reverse water-gas shift (RWGS) or reforming [START_REF] Liu | La-promoted Ni-hydrotalcite-derived catalysts for dry reforming of methane at low temperatures[END_REF][START_REF] Wang | Effect of precipitants on Ni-CeO 2 catalysts prepared by a co-precipitation method for the reverse water-gas shift reaction[END_REF]. The latter results in undesired side products, among them carbon monoxide [START_REF] Wierzbicki | The influence of lanthanum incorporation method on the performance of nickel-containing hydrotalcite-derived catalysts in CO 2 methanation reaction[END_REF]. All mixed oxides were catalytically active in CO 2 methanation. The obtained conversions at 250 °C were much lower than the thermodynamic limitations, except for the MO-0.4Y catalyst. Depending on the Y-loading a change in the catalytic performance of the catalysts was observed.

Nevertheless, the increase of the catalytic conversion was not directly correlated to the increase of yttrium loading. For both series of results registered at 250 °C and 300 °C, the sequence for the CO 2 conversion was: MO-0.4Y > MO-2.0Y > MO-0Y > MO-4.0Y. CO 2 conversion increased at 250 °C from 16% for MO-0Y to 40% and 81%

for MO-2.0Y and MO-0.4Y, respectively, and at 300°C, from 71% for MO-0Y to 80% and 88% for MO-2.0Y and MO-0.4Y, respectively. At both temperatures, 250 °C and 300 °C, the selectivity towards methane was higher than 98.5%, with very low differences between the Y-promoted catalysts (Fig. 5). However, in the tested The enhancement of the activity of Y-promoted catalysts except MO-4.0Y can be partially explained by the smaller Ni 0 crystallite size in comparison to the non-promoted sample, which is also found for La-promoted Ni-containing hydrotalcite-derived mixed oxides in CO 2 methanation [START_REF] Wierzbicki | The influence of lanthanum incorporation method on the performance of nickel-containing hydrotalcite-derived catalysts in CO 2 methanation reaction[END_REF].

Simultaneously, the MO-0.4Y catalyst showed the highest percentage share of intermediate-strength basic sites. Pan et al. [START_REF] Wang | CO 2 methanation on Ni/Ce 0.5 Zr 0.5 O 2 catalysts for the production of synthetic natural gas[END_REF] claimed that Lewis acid-base sites are involved in the CO 2 methanation mechanism and the CO 2 adsorbed on strong basic sites did not participate in the reaction and the medium-strength basic sites played an important role in the reaction. In the current study, a linear correlation between CO 2 conversion and percentage share of medium-strength basic sites can be drawn at 250 °C and 300 °C (Fig. 6). It shows that the CO 2 conversion increase as the increase of the percentage share of medium-strength basic sites. The medium-strength basic sites play a significant role in the methanation process.

Wierzbicki et al. [START_REF] Wierzbicki | The influence of nickel content on the performance of hydrotalcite-derived catalysts in CO 2 methanation reaction[END_REF][START_REF] Wierzbicki | The influence of lanthanum incorporation method on the performance of nickel-containing hydrotalcite-derived catalysts in CO 2 methanation reaction[END_REF] found that there was a good linear correlation between the number of medium-strength basic sites and the CO 2 conversion on the unpromoted and La-promoted LDHs catalysts. This work confirms that the percentage of medium-strength basic sites have a considerable influence in the case of carbon dioxide methanation on Ni-containing Y-modified mixed oxides catalysts.

Besides, the TPR results show that MO-0.4Y has the highest intensity of metal-support interaction compared to that of other samples [START_REF] Kumar | Tuning the metal-support interaction of methane tri-reforming catalysts for industrial flue gas utilization[END_REF]. In conclude, the decreased nickel particle size, increased share of medium-strength basic sites and stronger metal-support interactions found for MO-0.4Y catalyst greatly contributed to the enhanced catalytic activity in CO 2 methanation.

Characterization of the spent catalysts

XRD patterns of the spent samples

Ni 0 crystallite sizes calculated for the spent catalysts are reported in Table 2. A decrease of the crystallite size was found for the spent catalysts compared to that of the reduced samples, in agreement with Świrk et al. [START_REF] Świrk | Yttrium promoted Ni-based double-layered hydroxides for dry methane reforming[END_REF] and Dębek et al. [START_REF] Dębek | Promotion effect of zirconia on Mg(Ni,Al)O mixed oxides derived from hydrotalcites in CO 2 methane reforming[END_REF] on similar materials for other CO 2 reactions. This can be explained by the loss of crystallinity of the Ni phase due to its possible re-dispersion of nickel particles. The decreased crystallite size of Ni 0 species also indicates that no sintering happened during reaction. After the methanation tests, no reflections corresponding to graphitic carbon (at 2θ=27˚) were observed in the diffractograms of the spent catalysts (Fig. 7). Thus, extensive coking with graphite formation may be excluded. This is in agreement with the studies of other authors e.g. Wierzbicki et al. [START_REF] Wierzbicki | The influence of nickel content on the performance of hydrotalcite-derived catalysts in CO 2 methanation reaction[END_REF], who confirmed the absence of carbon deposition on Ni/Al LDHs-like catalysts for CO 2 methanation. Thermogravimetric analyses were carried out for the spent catalysts in order to verify if other non-crystalline carbon species may have been formed (Fig. 8). From Fig. 8, two mass loss regions can be observed for all tested MO samples, corresponding respectively to the removal of physically adsorbed water (<250°C) and a higher temperature region (>400°C) corresponding to oxidation of metallic nickel to nickel oxide and the removal of residues. From TGA, one can conclude that no significant amount of carbonaceous species was present on the surface of the spent catalysts. To confirm this, temperature-programmed oxidation tests were performed from RT to 650 °C on MO-0Y (Fig. 9a) and MO-0.4Y catalysts (Fig. 9b). From Fig. 9a andb, one can observe that CO 2 formation corresponding to the decomposition of carbonaceous species (250-500°C) is very low, confirming insignificant amounts of the formed carbonaceous species during the CO 2 methanation reaction on the Y promoted catalysts. Thus, the main byproduct in the reaction is CO.

Conclusions

Yttrium-promoted Ni/Mg/Al hydrotalcite-derived catalysts were synthesized using the co-precipitation method at constant pH. Then, the catalysts were characterized by low-temperature N 2 sorption, X-ray diffraction, elemental analysis, and temperature-programmed reduction/desorption (H 2 -TPR and CO 2 -TPD), and tested as catalysts in CO 2 methanation at GHSV =12000 h -1 using a mixture of CO 2 /H 2 /Ar =15/60/25.

The addition of Y affected the CO 2 adsorption capacity of the materials by changing the distribution of the basic sites, especially those of medium-strength. As proven by H 2 -TPR, the yttrium promotion influenced the nickel/support interaction.

After the introduction of yttrium, a shift of reduction peak towards higher temperatures was observed, which was attributed to the segregation of Y on the support. The Y addition affected strongly the catalytic activity in CO 2 methanation, increasing the CO 2 conversion at 250 °C from 16% for MO-0Y to 40 and 81% for MO-2.0Y and MO-0.4Y, respectively. This could be explained by both increased distribution of medium-strength basic sites and significantly smaller metallic nickel particle size of Y-promoted catalysts. Additionally, the metallic nickel crystallite size decreased after the reaction, which points to the reorganization of Ni at the surface of the support, which could contribute to the increase of the catalytic activity in the moderate temperature region. The selectivity towards methane formation was found around 98 to 99% at 250°C. It is worth noting that the only products of the reaction registered were H 2 O, CH 4 and CO. The XRD, TGA, and TPO analyses confirmed only traces of carbon in the spent catalysts.

  reported that Y 2 O 3 impregnated with Ni revealed very high activity in the low-temperature region in CO 2 methanation when compared to Ni supported on Al 2 O 3 , ZrO 2 and CeO 2 catalysts. It was attributed to the promoted decomposition of formate species formed during the reaction over Ni/Y 2 O 3 catalysts.

  CO 2 conversion (X CO2 ) and CH 4 selectivity (S CH4 ) are defined as:Conversion of CO 2 = X CO2 (%)

  from d-spacing of (110) plane; a = 2d 110 b) calculated from appropriate d-spacings of (003), (006) and (009) planes; c = d 003 + 2d 006 + 3d 009 c) specific surface areas calculated from the BET equation d) mesopore volumes obtained from the BJH desorption calculation method e) pore size distribution derived from the BJH desorption calculation method

Fig. 1 .

 1 Fig. 1. XRD profiles for reduced nano-mixed oxides modified with different yttrium loadings

Fig. 3 .

 3 Fig. 3. CO 2 -TPD profiles for mixed oxides catalysts

Fig. 4 Fig. 4 .

 44 Fig.4presents the CO 2 conversion and Fig.5presents the methane selectivity

Fig. 5 .

 5 Fig. 5. CH 4 selectivity of the studied mixed oxides catalysts (MO-0Y, MO-0.4Y, MO-2.0Y,

Fig. 6 .

 6 Fig. 6. CO 2 conversion at 250 °C and 300 °C versus percentage share of medium basic sites of tested catalysts, the black points represent CO 2 conversion at 250 °C and the red points represent CO 2 conversion at 300 °C

Fig. 7 .

 7 Fig. 7. XRD diffractograms of spent Y modified mixed oxides (0.4, 2.0, or 4.0 wt.%) as compared to the unpromoted catalyst (MO-0Y).

Fig. 8 .

 8 Fig. 8. TGA plots of the studied catalysts (MO-Y0, MO-Y0.4, MO-Y2.0, MO-Y4.0) tested in the methanation process.

Fig. 9 .

 9 Fig. 9. Temperature-Programmed Oxidation results followed by mass spectroscopy (H 2 O m/z=18 and CO 2 m/z=44x10) on catalysts; a) unpromoted MO catalysts, b) MO-0.4Y.

3.1. Characterization of the catalysts before methanation 3.1.1. Structural parameters, elemental composition, and textural properties of nano-mixed oxides derived from hydrotalcite Structural

  García et al.[START_REF] García-García | Chromium and yttrium-doped magnesium aluminum oxides prepared from layered double hydroxides[END_REF], yttrium can be incorporated into layers of double-layered hydroxides, though its ionic radius is somewhat larger than that of Al and Mg (Mg 3+ =0.86 Å,

	Al 3+ =0.675 Å, Y 3+ =1.04 Å) [44,70]. The obtained parameter c (d 003 + 2d 006 + 3d 009 ),
	which refers to the triple thickness between brucite layers in hydrotalcite structure,
	decreased for low Y (under 2 wt.%) modified samples in comparison to the
	non-modified material, except for MO-4.0Y, which increased to 23.51 Å (Table
	were obtained by the equations of a=2d (110) and c=d (003) +2d (006) +3d (009) . The
	crystallographic parameter a (2d 110 ) is associated with the average cation-cation

parameters calculated from the XRD diffractograms acquired for as-synthesized materials are reported in Table

1

. The structural parameters a and c distance in the hydroxide layers

[START_REF] Liu | La-promoted Ni-hydrotalcite-derived catalysts for dry reforming of methane at low temperatures[END_REF]

. The parameter a is stable for all materials (3.06 Å), indicating the lack of possible distortions of the lattice. As stated by García-

Table 1

 1 Structural parameters (XRD), elemental composition (XRF) and textural properties (BET analysis) of yttrium modified nano-mixed oxides derived from hydrotalcite. Additionally, the nominal values are reported in brackets.

	Catalyst	Structural	Elemental composition of the calcined	Textural properties of the
		parameters		materials		calcined materials
		a [Å] a)	c [Å] b)	Ni [wt.%] Y [wt.%]	M 2+ /M 3+ [-]	[m S BET /g] 2	[cm V 3 /g] p	[nm] d p	e)
							c)	d)
	MO-0Y	3.06	23.45	20	-	3.6 (3.0)	120	0.6	19
	MO-0.4Y	3.06	23.38	21	0.4 (0.4)	3.5 (3.0)	120	0.5	15
	MO-2.0Y	3.06	23.42	18	1.8 (2.0)	3.4 (3.0)	192	0.6	14
	MO-4.0Y	3.06	23.51

Table 2

 2

reports the size of Ni 0 crystallites, calculated from the 2θ diffraction peak at ca. 52° (corresponding to (200) crystal plane of Ni 0 ) using the Scherrer equation. The yttrium promotion resulted in a decrease of nickel crystallites size from ca. 13.7 nm for the parent MO to ca. 9.2 nm for MO-0.4Y. The values obtained for MO-2.0Y and MO-4.0Y catalysts were close to the one registered for the unpromoted catalyst, i.e. 12.5 and 12.3 nm, respectively.

Table 2

 2 Ni 0 crystallite size for the reduced and spent materials calculated from XRD

	Catalyst	Ni 0 crystallite size
		Reduced samples [nm] a)	Spent samples [nm] a)
	MO-0Y	13.7	9.3
	MO-0.4Y	9.2	7.9
	MO-2.0Y	12.5	7.6
	MO-4.0Y	12.3	7.5
	a) Calculated from the Scherrer equation at 2θ =52°

Table 3

 3

, the highest H 2 consumption (1.67 mmol) was obtained for the Y-free mixed-oxide sample. After the introduction of yttrium, the H 2 consumptions (1.15-1.38 mmol) of yttrium-promoted mixed oxides decreased in contrast to the yttrium-free sample, demonstrating decreased reducibility of NiO for yttrium-promoted mixed oxides.

Table 3

 3 H 2 consumption according to H 2 -TPR analyses

	Catalyst	Temperature (°C)	H 2 consumption (mmolH 2 /g)
		<600	>600	<600	>600	Total
	MO-0Y	386	829	0.37	1.30	1.67
	MO-0.4Y	320	866	0.07	1.09	1.16
	MO-2.0Y	327	858	0.11	1.27	1.38
	MO-4.0Y	444	858	0.05	1.10	1.15

. Basicity of the catalysts derived from CO 2 -TPD Fig. 3 shows

  the CO 2 -TPD profiles of the reduced MO catalysts. Three types of

	CO 2 desorption peaks could be observed with a maximum temperature of 138, 203
	and 364 °C for MO-0Y sample, which refers to weak, medium (intermediate) and
	strong basic sites, respectively

Table 4

 4 Basicity of the studied catalysts, calculated from TPD-CO 2 for the reduced materials.

	Catalyst		Basic sites [μmol/g]		Basic sites distribution [%]
		Weak	Medium	Strong	Total basicity	Weak	Medium Strong
	MO-0Y	16.4	43.9	46.3	106.6	15.4	41.2	43.4
	MO-0.4Y	9.4	33.7	14.6	57.7	16.2	58.5	25.3
	MO-2.0Y	11.6	35.2	26.4	73.2	15.8	48.1	36.1
	MO-4.0Y	41.4	91.5	91.2	224.1	18.5	40.8	40.7
	3.2

. Catalytic performance tests for CO 2 methanation

Acknowledgments

Chao Sun would like to express his gratitude for the financial support of CSC (China Scholarship Council) for his Ph.D. research in Sorbonne Université. Katarzyna Świrk would like to acknowledge Prof. Magnus Rønning for the possibility to carry out the elemental analysis and low-temperature N 2 sorption at NTNU in Trondheim. Prof. Konrad Świerczek and Anna Olszewska are gratefully acknowledged for thermogravimetric analysis performed at AGH in Cracow.