Christian P Endres

Marie-Aline Martin-Drumel

Oliver Zingsheim

Luis Bonah

Olivier Pirali

Tianwei Zhang

Álvaro Sánchez-Monge

Thomas Möller

Nadine Wehres

Peter Schilke

Michael C Mccarthy

Stephan Schlemmer

Paola Caselli

Sven Thorwirth

SOLEIL and ALMA views on prototypical organic nitriles: C 2 H 5 CN

Keywords: Ethyl cyanide, Propionitrile, Synchrotron, Far-IR rotation-vibration, ALMA observations, G327.3-0.6

) cm -1 states, to be determined. The analysis not only confirms the applicability of the ASAP in the treatment of (dense) highresolution infrared spectra but also reveals some of its limitations. Complementary to the infrared study, the pure rotational spectrum of C 2 H 5 CN was also studied in selected frequency ranges from 75 to 255 GHz.

New observations of a prototypical high-mass star-forming region, G327.3-0.6, performed with the Atacama Large Millimeter Array show that vibrational satellites of C 2 H 5 CN can be very intense, of order several tens of Kelvin in units of brightness temperature.

Introduction

Ethyl cyanide (propionitrile, C 2 H 5 CN) was first detected in space in 1977 by Johnson et al. [START_REF] Johnson | Detection of interstel-lar ethyl cyanide[END_REF] towards star-forming regions associated with the Orion nebula (Orion-KL) and the Galactic center (Sgr B2). Since these early days of radio astronomy, ethyl cyanide has been found in many astronomical sources and has turned into a useful diagnostic of regions of high-and of low-mass star formation [START_REF] Cazaux | The Hot Core around the Low-Mass Protostar IRAS 16293-2422: Scoundrels Rule![END_REF]. In selected sources, the molecule is so abundant, that not only the parent isotopic species 12 CH 3 12 CH 2 12 C 14 N but also singly substituted 13 C species [START_REF] Demyk | Isotopic ethyl cyanide 13 CH 3 CH 2 CN[END_REF][START_REF] Müller | Rotational spectroscopy of isotopic vinyl cyanide, H 2 C=H-C≡N, in the laboratory and in space[END_REF], 15 N species [START_REF] Margulès | Rotational spectrum of deuterated and 15 N ethyl cyanides: CH 3 CHDCN and CH 2 DCH 2 CN and of CH 3 CH 2 C 15 N[END_REF], doubly substituted 13 C species [START_REF] Margulès | Spectroscopic study and astronomical detection of doubly 13 C-substituted ethyl cyanide[END_REF], and possibly also deuterated species [START_REF] Belloche | Exploring molecular complexity with ALMA (EMoCA): Deuterated complex organic molecules in Sagittarius B2(N2)[END_REF] were observed. As ethyl cyanide possesses several energetically low-lying vibrational modes, it has not only been detected in the ground vibrational but also in vibrationally excited states by radio astronomical means [START_REF] Gibb | Chemistry of the Organic-Rich Hot Core G327.3-0.6[END_REF][START_REF] Mehringer | Detection of Vibrationally Excited Ethyl Cyanide in the Interstellar Medium[END_REF][START_REF] Daly | Laboratory Characterization and Astrophysical Detection of Vibrationally Excited States of Ethyl Cyanide[END_REF], more precisely, vi-brational satellites from the CCN in-plane bending mode ν 13 and the methyl torsional mode ν 21 (both of which are located around 210 cm -1 ) as well as the CCN out-of-plane bending mode ν 20 (373 cm -1 ) and the CCC bending mode ν 12 (534 cm -1 ) were assigned.

As a prototypical simple organic nitrile, and also to support astronomical observations, ethyl cyanide has been studied quite extensively in the laboratory probing its pure rotational spectrum up to frequencies as high as 1.6 THz in the ground vibrational state [Refs. 11-13, and references therein]. Micro-, millimeter-and submillimeter-wave techniques have also been applied to the study of vibrational satellites [see Refs. 9, 10, 14, 15, and references therein] and even to multiple substituted isotopic species [Ref. [START_REF] Pienkina | The millimeter and submillimeter rotational spectrum of triple 13 C-substituted ethyl cyanide[END_REF], and references therein]. However, up to now no sufficiently comprehensive and concise picture of the millimeter-/submillimeter wave vibrational satellite pattern has emerged from lab-oratory studies to satisfy the needs from the astronomical community, particularly in view of the capabilities of the most powerful astronomical facilities such as the Atacama Large Millimeter Array, ALMA. Further scarcity is encountered when considering the status of infrared studies. While the infrared spectrum of ethyl cyanide (and selected isotopic species) has been studied at low spectral resolution in the gas phase and in inert gas matrices [e.g., Refs. 17 -21], to some surprise, no highresolution infrared measurements of any vibration mode have been reported so far.

In the present investigation, the first high resolution rotation-vibration spectra of ethyl cyanide have now been collected from 80 to 650 cm -1 at the SOLEIL synchrotron facility by means of high resolution Fourier-transform infrared (IR) spectroscopy. The spectral analysis of the four lowest fundamental vibrational bands was performed using the Automated Spectral Assignment Procedure (ASAP) shown previously on several occasions to offer a fast and convenient way towards spectroscopic analysis of high-resolution infrared data [START_REF] Martin-Drumel | The SOLEIL view on sulfur rich oxides: The S 2 O bending mode at 380 cm -1 and its analysis using an Automated Spectral Assignment Procedure (ASAP)[END_REF][START_REF] Thorwirth | An ASAP treatment of vibrationally excited S 2 O: The ν 3 mode and the ν 3 + ν 2 -ν 2 hot band[END_REF][START_REF] Martin-Drumel | Synchrotron-Based High Resolution Far-Infrared Spectroscopy of trans-Butadiene[END_REF]. Subsequently, to further complement the infrared study, the pure rotational spectrum was re-investigated in the frequency regions from 75 to 119.6 GHz and from 160 to 254.95 GHz using submillimeter-wave spectrometers from the Cologne institute.

Based on new predictions of the pure rotational vibrational satellite spectrum obtained from the new best-fit parameters sets, a number of very strong emission lines from vibrationally excited C 2 H 5 CN were assigned in the spectrum of a prototypical high-mass star-forming region, G327.3-0.6, obtained with the ALMA.

Experiment

Ro-vibrational measurements

Synchrotron-based far-infrared spectra of propionitrile were recorded in the 80-650 cm -1 range on the AILES beamline of the SOLEIL synchrotron facility [START_REF] Brubach | Performance of the AILES THz-Infrared beamline at SOLEIL for High resolution spectroscopy[END_REF]. The Bruker IFS125 Fourier-transform interferometer of the beamline was configured with a 6 µm Mylar beamsplitter, an iris aperture of 1.5 mm, and set for its ultimate resolution, i.e., 0.001 cm -1 . Vapor pressure of the ethyl cyanide sample was introduced into a White-type, multireflection cell aligned for about 150 m absorption path length [START_REF] Pirali | Rotationally resolved infrared spectroscopy of adamantane[END_REF][START_REF] Pirali | The far infrared spectrum of naphthalene characterized by high resolution synchrotron FTIR spectroscopy and anharmonic DFT calculations[END_REF]. A liquid-helium cooled Si bolometer was used for detection. Two spectra of ethyl cyanide (99 % purity; Aldrich), with sample pressures of 26 and 500 µbar and resulting from the co-addition of 240 and 130 interferograms, were recorded to maximise the signal-to-noise ratio of the ν 13 /ν 21 and ν 20 /ν 12 bands, respectively. Residual water lines, present in the spectra, have been used for calibration purposes; their frequencies were taken from Refs [START_REF] Horneman | Transferring calibration from CO2 laser lines to far infrared water lines with the aid of the ν 2 band of OCS and the ν 2 , ν 1 -ν 2 , and ν 1 +ν 2 bands of 13 CS2: Molecular constants of 13 CS2[END_REF][START_REF] Matsushima | Frequency measurement of pure rotational transitions of H2O from 0.5 to 5 THz[END_REF][START_REF] Matsushima | Frequency measurement of pure rotational transitions in the v 2 = 1 state of H2O[END_REF]. The resulting spectra are presented in Fig. 1.

A successful ASAP treatment via cross correlation plots requires that the parts of the spectrum where spectral features are absent-below the noise level or below the confusion limit-exhibit signal intensities close to zero. To do so, the experimental spectra are usually plotted in absorbance. In the present case, in order to fulfill this requirement, it was necessary to further process each of our absorption spectra. Indeed, as can been seen in Fig. 1, the bands are not fully resolved which results in an apparent continuum underlying each band, because of both the large line density and the inherent FT interferometer-limited instrumental resolution. To ensure an optimum ASAP treatment, an artificial background (corresponding to the absorption continuum mentioned above) has been removed from the plots (see Figs. 2, 3, and4). This background has been derived by taking the smallest value of the signal intensity in the vicinity (± 0.006 cm -1 ) of each frequency point. This signal processing improves the suppression of spectral features associated with other transitions present in one of the other portions of the spectrum involved in the multiplication.

Pure rotational measurements

The measurements in the millimeter-wavelength region were conducted in Cologne in the 75-120 GHz and 160-255 GHz regions using two similar experimental setups described in greater detail in Refs. [START_REF] Martin-Drumel | Millimeter-and submillimeter-wave spectroscopy of disulfur dioxide, OSSO[END_REF][START_REF] Ordu | Laboratory rotational spectroscopy of isotopic acetone, CH3 13 C(O)CH3 and 13 CH3C(O)CH3, and astronomical search in Sagittarius B2(N2)[END_REF]. In both cases, the spectrometer follows a relatively simple format: a frequency source generates the millimeter-waves (radiofrequency synthesizer followed by frequency multiplier chains and horn antenna) which probe the chemical composition of the absorption cells and are further detected using Schottky-diode detectors. While the two aforementioned frequency regions could have been measured using one or the other spectrometer, the present choice was guided by the sake of simplicity, as each instrument was for the sake of clarity using HITRAN linelists [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF]. The main motion associated with each vibration of the molecule is indicated by blue arrows. already set for operating in one of each spectral range. The lower frequency range was measured using an absorption cell in single-pass mode with a total absorption path length of 14 m while the upper frequency one was investigated using a double-pass setup, adding up to a total absorption path length of 10 m. Because of the 2f modulation scheme, the resulting line shapes are close to a second derivative of a Gaussian function. Typical integration times were of 50 ms per frequency step. The step size was varied between 20 and 75 kHz, depending on the frequency ranges. All measurements were conducted at room temperature and ethyl cyanide (99 % purity; Aldrich) pressures of about 10 µbar. The spectra recorded in the upper frequency band is displayed in Fig. 5.

Theoretical Background

Ethyl cyanide is a prolate, asymmetric top molecule with one plane of symmetry defined by the heavy atom backbone (C s ). Due to its strong permanent dipole moment (of projections µ a = 3.816 D, µ b = 1.235 D along the molecular-fixed principal axes [START_REF] Kraśnicki | Electric dipole moments of acrylonitrile and of propionitrile measured in supersonic expansion[END_REF]) the pure rotational spectrum shows strong a-and b-type transitions. Because of the internal rotation of the CH 3 -group relative to the rest of the C s frame, the symmetry is given by the molecular symmetry group G 6 and each rotational level is split into A and E symmetric substates. However, the barrier to torsion is quite high (V 3 = 1075 cm -1 [START_REF] Demaison | Torsional barrier and equilibrium structure of ethyl cyanide[END_REF]) thus the classification in terms of C s symmetry of the rigid rotor limit remains useful. The A/E splitting in the vibrational ground state is barely resolved in Doppler limited measurements while doublets spaced by several MHz are typically observed for transitions within the first excited torsional state.

The vibrational spectrum of ethyl cyanide has been described in some more details in Wurrey et al. [START_REF] Wurrey | Vibrational spectra and normal coordinate analysis of ethyl cyanides[END_REF]. Briefly, the 21 fundamental vibrational modes, all of which are IR active, distribute as 13a + 8a in which the a and a vibrations correspond to in-plane and out-of-plane deformations with respect to the plane of symmetry, respectively. Consequently, the a vibrations show hybrid a/btype spectra whereas the a ones show c-type spectra. Four fundamental bands lie in the far-IR domain (see Fig. 6): the CCN in-plane bending mode ν 13 around 206.9 cm -1 [START_REF] Cerceau | Infrared-Spectra of Gaseous Mononitriles -Application to the Atmosphere of Titan[END_REF], the torsional mode ν 21 at 210.7 cm -1 (estimated from combination bands) [START_REF] Heise | The Vibrational-Spectra of Some Isotopic-Species of Propionitrile[END_REF], the CCN out-of-plane bending mode ν 20 around 373 cm -1 [START_REF] Heise | The Vibrational-Spectra of Some Isotopic-Species of Propionitrile[END_REF], and the CCC deformation mode ν 12 around 534.4 cm -1 [START_REF] Heise | The Vibrational-Spectra of Some Isotopic-Species of Propionitrile[END_REF]. Numerous and partially strong interactions are observed between these low-energy vibrational states [START_REF] Daly | Laboratory Characterization and Astrophysical Detection of Vibrationally Excited States of Ethyl Cyanide[END_REF][START_REF] Brauer | Analysis of the Lowest In-Plane Bend and First Excited Torsional State of CH 3 CH 2 CN[END_REF].

A number of effective Hamiltonians have been derived and applied to address rotation-torsionvibration problems. Among others, Pickett [START_REF] Pickett | Theoretical studies of internal rotation for an asymmetric top[END_REF] proposed an effective Hamiltonian that allows to account for the strong interactions between an inplane bending and a torsional mode, that is particularly applicable if the torsional barrier is high. This Hamiltonian has also been applied and described in a previous analysis of the pure rotational spectrum of ethyl cyanide carried out by Mehringer et al. [START_REF] Mehringer | Detection of Vibrationally Excited Ethyl Cyanide in the Interstellar Medium[END_REF].

The general form of the rotation-vibration Hamiltonian [START_REF] Pickett | Theoretical studies of internal rotation for an asymmetric top[END_REF] can be transformed into the commonly used Watson Hamiltonian if the vibrational state is isolated, which is basically the case for the states involved in the CCC deformation and the out-ofplane bending, v 12 = 1 and v 20 = 1, respectively. Here, it is used in the S-reduction. A rotation of the axis system in the ab-plane can be achieved via offdiagonal D ab (P a P b -P b P a ) terms that connect matrix elements of the same vibrational state; a proper choice of the D ab parameter (see Tab. 2) can be useful to decrease the vibrational angular momentum. It has also been shown that the axis system can be rotated, such that the rotation-torsion Hamiltonian takes the form of a Mathieu equation and its Eigenvalues and Eigenvectors can be expressed as Fourier series related to an expansion in free rotor basis functions (shown also by Groner [START_REF] Groner | Large-amplitude motion tunneling parameters in effective rotational Hamiltonians from rotationinternal rotation theory[END_REF]). In this approach, the rotational parameters are basically multiplied by terms of sine-(S), cosine-(C), or both series, dependent on the symmetry of the operator:

C q = cos π 3 q(2σ -(K + K )ρ) (1)
S q = sin π 3 q(2σ -(K + K )ρ) (2)
The internal rotation parameter ρ is the ratio of the inverse mass of inertia of the internal rotor F to the inverse mass of the molecular frame, whereas σ = 0, 1, 2 can be related to the torsional substate (0 =A; 1, 2 =E). q is the ordinal number of the Fourier term and K is the projection of the rotational angular momentum. Thus, the torsional motion is described by additional Fourier constants, tunneling parameters, that have to be included in the set of parameters and that are adjusted in the fit. The series converges rapidly in the high barrier case and usually only very few Fourier constants are necessary. It is important to note that the Fourier constants are rather phenomenological and it is not straightforward to extract quantitative information about the torsional potential. In addition, interactions between different vibrational levels are described by the common off-diagonal matrix elements, such as the Coriolis terms of a and b symmetry applied within this work, that connect here levels between in-plane bend and torsion. In the context of this work, tunneling parameters were included for the excited states v 13 = 1 and v 21 = 1. The excited torsional state v 21 = 1 shows a larger torsional splitting, because its rotational levels are energetically closer to the barrier than those of the other three states. This is also reflected in the size of the tunneling parameters obtained from the combined fit (see Tab. 4), which is discussed in Sec. 4.7.

Analysis

The Automated Spectral Line Assignment Procedure, ASAP

The ASAP software, which was used to assign the spectral features in the ro-vibration spectra, has been described in details in Ref. [START_REF] Martin-Drumel | The SOLEIL view on sulfur rich oxides: The S 2 O bending mode at 380 cm -1 and its analysis using an Automated Spectral Assignment Procedure (ASAP)[END_REF]. Here, we report a brief introduction to the software in its current version, which includes several upgrades compared to the previously reported one. The applicability of ASAP requires that the rotational energy levels within one vibrational state, which is called reference state in the following and which is usually the vibrational ground state, are accurately known from a previous analysis. Furthermore, transition frequencies for the rotational-vibrational transitions of interest have to be calculated based on this analysis. The approach is closely related to the idea of closed loops of three transitions (Ritz combination principle). Here, rovibrational transitions that connect different rotational levels of the reference state to one common rotational level of another vibrational state, the target state, are selected. As these calculated transition frequencies obey exactly the Ritz combination principle, all rovibrational transitions will show the same δν = νobs -νcalc difference between observed and calculated values, because only the energy of the common target state is uncertain whereas the uncertainty of each reference state energies is assumed to be negligible.

Shifting the frequency origin of the experimental spectrum (ν) by subtracting the predicted frequency νt calc of any arbitrarily selected transition t moves its peak position from νt obs to the difference frequency δν t . Thus, transitions are shifted in these scaled spectra Ŝt (ν) = S(ν + δν t ) to the same position if they share a common target state. This position is potentially easy to determine by looking at cross correlation plots. These are obtained by multiplying the intensities of all spectra Ŝt associated with transitions that share a common target state (similarly to the "stacking" procedure, where intensities are summed up). Typically, only one single well-discernible feature (cross-correlation peak) appears in each cross correlation plot as long as the spectral density is relatively low and the spectral features are not too weak. This is nicely seen in the cross correlation plots for S 2 O [see Figs. 5 and 6 in Ref. 22]. The offset frequency δν is then determined from the peak position. The experimental state energy and the frequency can then be derived as the sum of the calculated state energy / frequency and this offset. Line intensities can vary by orders of magnitude along the transitions. Therefore, weighting the spectral intensities S(ν -νcalc ) has been introduced in the present version of the ASAP software in order to increase the contrast in the cross correlation plots. This is realized by replacing the observed signal in the evaluation by the power of the observed signal with the logarithmic value of the calculated intensity as argument:

S ccp (ν) = t S t (ν + νt calc ) (log I t calc -log I min calc ) (3)
where S ccp is the intensity on the cross-correlation plot and I min is the lowest intensity in the set of associated transitions. log I t calc and log I min calc are direct outputs of the spcat software, which is part of H. Pickett's calpgm suite [START_REF] Pickett | Submillimeter, millimeter, and microwave spectral line catalog[END_REF], which was used in the analysis.

Re-fit of the literature data

In the first step of spectroscopic analysis, the fit of the ground vibrational state of propionitrile as presented in the Cologne Database for Molecular Spectroscopy, CDMS [START_REF] Müller | The Cologne Database for Molecular Spectroscopy[END_REF][START_REF] Endres | The Cologne Database for Molecular Spectroscopy, CDMS, in the Virtual Atomic and Molecular Data Centre, VAMDC[END_REF], has been reproduced with calpgm. This fit is based on experimental data from Refs. [START_REF] Johnson | Detection of interstel-lar ethyl cyanide[END_REF][START_REF] Pearson | The submillimeter-wave spectrum of propionitrile (C2H5CN)[END_REF][START_REF] Brauer | New Ground-State Measurements of Ethyl Cyanide[END_REF][START_REF] Mäder | Microwave Spectrum of Ethyl Cyanide; r 0 -Structure, Nitrogen Quadrupole Coupling Constants and Rotation-Torsion-Vibration Interaction[END_REF][START_REF] Burie | Microwave spectrum of propionitrile: Determination of the quartic and sextic centrifugal distortion constants[END_REF][START_REF] Boucher | Determination of a High Potential Barrier Hindering Internal Rotation from the Analysis of the Ground State Spectrum: The Case of Ethyl Cyanide[END_REF][START_REF] Fukuyama | The Microwave Spectrum of Propionitrile (C2H5CN) in the Frequency Range from 8 to 200 GHz[END_REF]. These data include transitions for the A species covering quantum numbers up to J = 130 and K a = 36. Frequencies with experimental uncertainties larger than 50 kHz and 100 kHz below and above 500 GHz, respectively, have not been included in the fit (following the CDMS dataset). The data allowed to constrain the energies of the rotational states in the ground vibrational state within this range of quantum numbers accurately enough to apply ASAP. For these states, the energy uncertainty is more than one order of magnitude smaller than the linewidth observed in the IR spectra. The same applies for the torsional splitting, which is small in the ground vibrational state and has only been observed in few transitions. In particular, it is also much smaller than the IR linewidth. Therefore, it has been neglected in the fit and thus also in the calculation of the ground state energy levels. Transition frequencies for A and E states have been averaged.

CCN deformation ν 12 & CCN out-of-plane

bend ν 20 Cross correlation plots for both ν 12 and ν 20 fundamental bands have been calculated using the 500 µbar experimental spectrum and were based on accurate rotational constants derived from the refit of the literature values for the A symmetry species. Previously published data involving these states [10-12, 45, 46] cover transitions up to J = 71, K a = 25 for v 20 and J = 71, K a = 17 for v 12 . Thus, the predicted transition frequencies were already quite accurate and mainly the band center remained to be determined, although interactions as well as the torsional splitting have been neglected. In addition, both bands are intense and well separated (Figs. 1,2,3). Only weaker hot bands or combination bands complicate the spectrum in these spectral ranges. Therefore, it was straightforward to localize one peak in each cross correlation plot that is associated with its target state; basically, all peaks appeared within a narrow frequency region (Fig. 7). The offset δν for each target state, and thus the associated experimental state energies and frequencies, have then been determined for a number of target states, starting with low K a quantum numbers. In an iterative manner, state energies were assigned and included in the fit in order to improve the predicted frequencies used in the assignment until target states up to K a = 25, J = 80 and K a = 18, J = 80 for ν 20 and ν 12 , respectively, were reached. One avoided crossing has been found in ν 12 at K a = 13 and J ≈ 49.

CCN in-plane bend ν 13 & Torsion ν 21

The energetically lowest fundamental modes ν 21 and ν 13 are only separated by a few cm -1 . Thus, they appear in the same spectral region and are overlapped significantly (Fig. 1). Strong interactions between these states have been reported previously [START_REF] Mehringer | Detection of Vibrationally Excited Ethyl Cyanide in the Interstellar Medium[END_REF][START_REF] Fukuyama | Analysis of Rotational Transitions in Excited Vibrational States of Propionitrile (C 2 H 5 CN)[END_REF][START_REF] Brauer | Analysis of the Lowest In-Plane Bend and First Excited Torsional State of CH 3 CH 2 CN[END_REF]. Effectively, treating the vibrational states separately becomes impractical and as a result the notation v 13 + v 21 = 1 may be used, which accounts for one quantum of excitation in either v 13 or v 21 . The spectral features turned out to be much stronger than those seen for the two other modes, ν 20 and ν 12 , which required to record this spectral range separately and at lower pressure. First, predictions were prepared only for A symmetry species of the ν 13 mode. The initial fit included frequencies obtained by Fukuyama et al. [START_REF] Fukuyama | Analysis of Rotational Transitions in Excited Vibrational States of Propionitrile (C 2 H 5 CN)[END_REF]. Interactions as well as the torsional splittings were neglected. Although a larger number of peaks (false positives) were present in the cross correlation plots of ν 13 compared to the previous ones, series of cross correlation peaks (true positives) could be determined and allowed to deter-mine already a large number of state energies that could be included in the fit. In a following step, transitions from Fukuyama et al. [START_REF] Fukuyama | Analysis of Rotational Transitions in Excited Vibrational States of Propionitrile (C 2 H 5 CN)[END_REF] for v 21 = 1 were included in the analysis. They constrained not only rotational constants for v 21 = 1, but provided also some information on the interaction and the energy difference between both vibrational states.

Step by step, more and more ν 13 state energies were assigned. In the subsequent analysis of ν 21 , the previous determination of first interaction terms, and thereby improved accuracy of predicted frequencies and band center of ν 21 , was crucial to identify and assign series of cross correlation peaks. As ν 21 transitions are weaker than those from the other band, the cross correlation plots for ν 21 show many more peaks (false positives) caused by strong transitions in this spectral region that are not well enough suppressed by the multiplication process (Fig. 7). Nevertheless, the assignment of ν 21 state energies was possible, because the cross correlation peaks (true positives) could be localized within a narrow spectral window of only a few tenths of a wavenumber. Again, higher J, K a levels were assigned and stepwise refined the predictions. In general, assignments for ν 21 are less secure compared to those for the other bands, because the identification of cross correlation peaks is ambiguous in a number of cases. This can also be seen in the cross correlation plots (Fig. 7) for the series of target states with K a = 10, K c = J -K a .

Wavenumber accuracy of the ro-vibrational lines

Energy levels obtained via ASAP have been used to calculate frequencies for pure rotational transitions within vibrationally excited states that either were previously reported [START_REF] Daly | Laboratory Characterization and Astrophysical Detection of Vibrationally Excited States of Ethyl Cyanide[END_REF][START_REF] Fukuyama | Analysis of Rotational Transitions in Excited Vibrational States of Propionitrile (C 2 H 5 CN)[END_REF] or observed within this work. By comparison with accurate values observed with millimeter-wave techniques, the accuracy of state energies derived from IR spectra using ASAP was estimated. Fig. 8 shows the probability density of frequency differences calculated for each vibrational state. Standard deviations between σ = 4.4 MHz (∼ 0.00015 cm -1 ) and σ = 11.9 MHz (∼ 0.0004 cm -1 ) were determined from the data assuming a normal distribution. By taking the largest value and weighting it with a √ 0.5 factor, because the energy differences are calculated from two experimental values, the accuracy of ASAP-derived state energies should at least be better than 0.0003 cm -1 . Also, it is worth noting that the mean frequency difference is below 500 kHz (∼ 0.00002 cm -1 ) in all cases. The smaller standard deviation obtained for ν 13 results from a larger number of observed transitions that contribute to each individual cross correlation plot and thus cause a narrowing of the cross correlation peak. This can also be seen in the cross correlation plots of ν 13 shown in Fig. 7. Overall, the comparison confirms that the frequency accuracy in the IR data is better than the assigned uncertainty of 0.0005 cm -1 . Nevertheless, a slightly higher uncertainty is assigned, because uncertainties of the vibrational ground state energies are not taken into account in this comparison.

4.6. Pure rotational spectra within v 13 + v 21 = 1

A substantial number of pure rotational transitions within the excited states v 13 + v 21 = 1 have been assigned in the millimeter-wave spectra recorded in Cologne (see Fig. 5), although a comprehensive analysis of the rotational spectrum is beyond the scope of this paper. Here, the main goal was to evaluate if predictions derived from the IR study help to facilitate substantially the assignments and could already support astronomical line identifications. It turned out that line positions were generally well predicted and transitions involving K a quantum numbers above 10 could easily be assigned. Nevertheless, the torsional splitting, observed not only for transitions in v 21 = 1, but also for many in v 13 = 1, had to be taken into account. Thus, torsional parameters had to be included in the fit, whose values were constrained by frequencies reported for the E-symmetry species by Fukuyama et al. [START_REF] Fukuyama | Analysis of Rotational Transitions in Excited Vibrational States of Propionitrile (C 2 H 5 CN)[END_REF]. In the following, transitions were assigned in the millimeter-wave spectrum in the usual stepwise manner, starting from low to high J and K a quantum numbers.

Combined effective fit

In total, 13473 energy offsets and additional 1292 distinct pure rotational transition frequencies were determined and assigned to 86063 and 1813 transitions, respectively. Energy levels up to K a = 25 and J = 90 were accessed. A summary of the experimental dataset is given Tab. 1. Line accuracies of 0.0005 cm -1 were assigned to state energies and IR transitions while for the pure rotational transitions they were individually estimated with regard of the fit of the line profiles and take typical values of 50 kHz for isolated lines and 100 kHz for blended ones. Previously reported lines were treated with their reported uncertainty. 331 of these frequencies (v 12 = 1 and v 20 = 1) were not included, because assigned and calculated position deviated by more than four times their uncertainty, most likely, caused by perturbations with higher energy levels (see Fig. 6). State energies rather than transition wavenumbers were included in the experimental dataset derived via ASAP (as discussed in Ref. [START_REF] Martin-Drumel | The SOLEIL view on sulfur rich oxides: The S 2 O bending mode at 380 cm -1 and its analysis using an Automated Spectral Assignment Procedure (ASAP)[END_REF]). The state energies are coded in spfit as transitions from the lowest level in the vibrational ground state (J Ka,Kc = 0 0,0 , v = 0) to the corresponding target state.

At first, parameters of an asymmetric rotor Hamiltonian in Watson's S reduction were used to reproduce frequencies of previously published rotational transitions and the newly assigned rovibrational transitions for the A symmetry species. Be-sides the state energy, only the parameters that led to an improvement of the fit were released. Otherwise their value was fixed to the corresponding value obtained for the vibrational ground state. Coriolis coupling terms with a-and b-symmetry were included to describe the strong interactions that are observed between the torsion and the inplane-bending vibrational state. The importance of individual coupling terms has been judged based on the achieved improvement of the fit. This led to an extensive set of parameters. A qualitative and more detailed analysis of the single interaction terms is beyond the scope of this work and will be carried out later in combination with a comprehensive study of the pure rotational spectra. The far better accuracy achieved at millimeter-wavelengths will provide superior constraints to these parameters.

In a second step, transitions within the E symmetric substates of the torsion and the in-plane bend were also taken into account. In this phenomenological approach (see section 3), the description of the internal rotation is achieved by expanding the energy and the rotational terms of each vibrational state into Fourier series. Here, only the internal rotation parameter ρ and the first cosine term for the energy with its coefficient 1 , and for the rotational operators P 2 , P 2 z , P 2 + -P 2 -with their coefficients T 001 1 , T 010 1 , and T 100 1 , were included for the torsionally excited states. The observed splitting of transitions within the in-plane bend was already reasonably described by the strong mixing of levels with torsional states. Nevertheless, adding 1 also for the in-plane bend, improved the fit noticeably.

Details about the coding of these parameters in spfit are given by Drouin [START_REF] Drouin | Practical uses of SPFIT[END_REF]. The splitting that was observed by Fukuyama et al. [START_REF] Fukuyama | Analysis of Rotational Transitions in Excited Vibrational States of Propionitrile (C 2 H 5 CN)[END_REF] for some btype transitions of the out-of-plane bending vibrational state v 20 = 1 has been neglected and only frequencies reported for the A symmetry species have been included in the fit. spfit does not allow to determine the internal rotation parameter ρ in the fit. Thus, its initial value was calculated using the structural information reported by Heise et al. [START_REF] Heise | Rotation-Torsion-Vibration Interaction in the Rotational Spectra of Isotopic Species of Ethyl Cyanide[END_REF] and moments of inertia derived from the rotational constants. Later on, ρ was manually adjusted to better reproduce the observed transition frequencies. Changing the value of ρ in steps of 0.001 within a range of about ±0.01 has only little impact on the final rms value and only values beyond this range considerably worsen the fit.

Tabs. 2, 4, 3 and 5 show the final set of parameters that were obtained from the combined fit. A common problem in the spectral analysis of molecules with internal rotation is the state labeling by asymmetric top quantum numbers, because it depends on the diagonalization and energy ordering. Thus, the assigned asymmetric top quanta might change for a small subset of states during the fitting process, in particular if the asymmetric splitting is of the same magnitude as the torsional splitting. Therefore, all lines that deviate by more than 20σ, i.e. 145 out of 13618 state energies, were rejected from the fit. Also, 14 pure rotational transitions are not reproduced within this limit and are rejected from the fit. ν 12 transitions that involve K a = 13 states were not included. These levels are probably perturbed by one of the nearby vibrational states ν 20 + ν 13 or ν 20 + ν 21 . The final fit reproduces the experimental dataset with almost experimental uncertainty with unitless, weighted standard deviation of 1.46. The standard deviation is considerably different between IR and microwave data sets, because deficiencies of the model are more significant for the microwave data with its much higher absolute accuracy. The standard deviation for each individual dataset is included in Tab. 1.

Transition frequencies and intensities have been calculated with spcat based on the current analysis and used to simulate all four fundamental bands (Figs. 2,3,4) and the rotational spectrum at millimeter-wavelength (Fig. 5). The very good agreement between simulation and experiment shows the quality of the predictions and validates also the overall correctness of assignments done with ASAP. Partition functions have been calculated based on the summation of energies. All states investigated in this work (v = 0, v 12 = 1, v 13 = 1, v 20 = 1, v 21 = 1) and energy levels up to J = 150 and K a = 70 have been taken into account. A listing of the experimental dataset and partition functions will be given in the supplementary material in electronic form. Predictions will also be provided via CDMS.

Astronomical observation of vibrational satellites

Ethyl cyanide has been detected in several astronomical sources in the last years [see e.g., [START_REF] Belloche | Increased complexity in interstellar chemistry: detection and chemical modeling of ethyl formate and n-propyl cyanide in Sagittarius B2(N)[END_REF][START_REF] Belloche | Complex organic molecules in the interstellar medium: IRAM 30 m line survey of Sagittarius B2(N) and (M)[END_REF], and it is expected to be abundant in star-forming regions where newly-born stars heat up their surroundings and release large amounts of complex or-ganic species from grain surfaces into the gas phase. Once in the gas phase, these species are detectable with telescope facilities operating in the millimeter and sub-millimeter regimes such as the Atacama Large Millimeter/submillimeter Array [ALMA; 51].

We have studied the high-mass star-forming complex G327.3-0.6 (hereafter G327) with ALMA during its Cycle 4 (project code 2016.1.00168.S). G327, with a luminosity of ∼ 2 × 10 5 L and at a distance of 3.3 kpc [START_REF] Urquhart | The Red MSX Source survey: distribution and properties of a sample of massive young stars[END_REF], is best known as one of the brightest and chemically richest hot molecular cores in our vicinity [see e.g., [START_REF] Schilke | Submillimeter spectroscopy of southern hot cores: NGC 6334(I) and G327.3-0.6[END_REF][START_REF] Wyrowski | Revealing the environs of the remarkable southern hot core G327.3-0.6[END_REF][START_REF] Bisschop | Dimethyl ether in its ground state, v = 0, and lowest two torsionally excited states, v 11 = 1 and v 15 = 1, in the high-mass star-forming region G327.3-0.6[END_REF]. Our ALMA observations have imaged the region where the hot molecular core G327 is located at an angular resolution of 1. 4 (corresponding to ≈ 4500 au) and in different frequency ranges across the ALMA band 6 (211-275 GHz). In Fig. 9 (see black line), we present a spectrum extracted towards G327 in three frequency ranges.

The spectrum towards G327 is rich in many spectral line features. We have modeled it using the software XCLASS [eXtended CASA Line Analysis Software Suite; 56], which makes use of the Cologne Database for Molecular Spectroscopy [CDMS; [START_REF] Müller | The Cologne Database for Molecular Spectroscopy[END_REF][START_REF] Müller | The Cologne Database for Molecular Spectroscopy, CDMS: a useful tool for astronomers and spectroscopists[END_REF] and Jet Propulsion Laboratory [JPL; 58] catalogs, via the Virtual Atomic and Molecular Data Centre [VAMDC; 41]. In the synthetic spectrum (see inverted grey line in Fig. 9), we have considered more than 23 different molecular species (excluding isotopologues and excited states; Zhang et al., in prep). A number of bright and isolated spectral lines remained unidentified in the synthetic spectrum (e.g., at frequencies 216.05, 216.55, 217.95 GHz). Most of these unidentified features are now assigned to vibrationally excited C 2 H 5 CN (v 13 + v 21 = 1) transitions measured in this work (cf. blue line in Fig. 9). We derive a C 2 H 5 CN column density of 9.5 × 10 17 cm -2 with a temperature of 250 K. This column density and temperature are comparable to the values derived for other commonly-studied species such as CH 3 OH (1.8×10 19 cm -2 , 260 K) CH 3 OCHO (3.4× 10 18 cm -2 , 270 K), CH 3 COCH 3 (1.1 × 10 18 cm -2 , 170 K), HC 3 N (5.0 × 10 17 cm -2 , 235 K), HNCO (3.9 × 10 17 cm -2 , 290 K). Comparison between C 2 H 5 CN ground and vibrationally-excited states can be used to obtain information on the temperature and density structure of G327 (Zhang et al., in prep.). Furthermore, given the bright detections of the v 13 + v 21 = 1 transitions, we expect other vibrationally excited states (e.g., v 13 + v 21 = 2) to be equally bright. Further laboratory measurements involving these excited states will be key to better characterize and understand the structure of astronomical sources such as star-forming regions.

Conclusions and prospects

The high resolution infrared spectrum of ethyl cyanide, C 2 H 5 CN, a prototypical saturated organic nitrile abundantly found in the interstellar medium, has been studied for the first time. The four lowest fundamental vibrational modes of ethyl cyanide have been measured on the AILES beamline of the SOLEIL synchrotron facility, and analyzed allowing the derivation of highly accurate vibrational state energies. The Automated Spectral Assignment Procedure, ASAP, has been improved and demonstrated once more to be a very useful analysis tool greatly simplifying the line assignment even of rather dense rotational-vibrational spectra.

Some limitations of ASAP became evident in the analysis of the fundamental torsional band ν 21 , where the identification of cross correlation peaks was hampered by severe spectral congestion. Nevertheless, this band along with the close-by lying and strongly interacting CCN-bending mode ν 13 could finally be disentangled. Based on the available molecular parameters for the ν 20 and ν 12 states from previous millimeter-/submillimeterwave studies, the ASAP treatment of the corresponding vibrational fundamentals was accomplished in a rather straightforward fashion. Subsequent pure rotational measurements within the ground state and the four lowest vibrationally excited states have supported further refinement of the spectroscopic constants.

Although an even more comprehensive and detailed analysis of the milli-meter-and submillimeter wave spectra within these excited states is still highly desirable, the current quality of predicted rest frequencies has already proven very reliable for the interpretation of astronomical spectra. The ALMA spectrum recorded towards the high-mass star-forming region G327.3-0.6, demonstrates the very favorable agreement between the predicted frequencies and the astronomical observations. The very strong spectral features related to transitions within excited vibrational states also shows their importance for the interpretation of astronomical spectra. Given the intensity of the vibrational satellites observed towards G327.3-0.6 it seems likely that vibrational satellites from energetically higher lying vibrational states might also be detected once their laboratory millimeter-/submillimeter-wave spectra are known to sufficient accuracy. Besides satellites from the ν 20 and ν 12 states also studied here, future investigations of overtones and combination modes of ν 13 and ν 21 seem indicated, as seem studies of the combination modes of ν 13 and ν 21 with either ν 20 and ν 12 . Close inspection of the vibrational fundamentals observed here already reveal some weak signatures that may hint towards the presence of hot bands, however, no attempt has been made here towards their analysis. Also, spectroscopic studies of vibrational modes above 600 cm -1 followed by spectroscopic analysis using ASAP should be feasible.

In the future, comprehensive infrared laboratory studies of vibrational bands of complex organic species followed by sophisticated spectroscopic analyses with the help of ASAP turns into a very promising avenue towards understanding their vibrational satellite pure rotational spectra. This strategy should be applicable to many astronomical species known to contribute substantially to the rich emission features observed towards line-rich astronomical sources.

After completion of the present manuscript, right before submission, we learned about a manuscript by Zbigniew Kisiel and collaborators just accepted to the Journal of Molecular Spectroscopy [START_REF] Kisiel | Propionitrile in the two lowest excited vibrational states in the laboratory and on Titan[END_REF]. In their study, the authors investigated the pure rotational spectrum of ethyl cyanide in the v 13 + v 21 = 1 states employing millimeter wave measurements and present a new global fit. Since the models used in their and in our study are not strictly identical, quantitative agreement cannot be expected. However, qualitatively, the two parameters sets seem in reasonable accord. For example, the energy difference between ν 21 and ν 13 derived in their millimeter wave study is 6.2070246(14) cm -1 compared to a value of 6.207002(25) cm -1 derived here from the vibrational band centers of the A states. Also, the leading Coriolis type interaction parameters G a and G b compare well and agree to within some 4% (G a ) and 18% (G b ). Future predictions should benefit from one unified model comprising both new datasets.

Figure 9: Spectra towards the high-mass star-forming region G327.3-0.6, with the intensity in brightness temperature unit (T B ). ALMA observational data in black. Synthetic spectrum including all identified molecular species (see Sect. 5) in grey, and with the intensity multiplied by a factor -1. The contribution from C 2 H 5 CN v = 0 and C 2 H 5 CN v 13 + v 21 = 1 transitions are highlighted in orange and blue, respectively. been supported via Collaborative Research Centre 956, sub-projects B3 and A6, funded by the Deutsche Forschungsgemeinschaft (DFG; project ID 184018867) and DFG SCHL 341/15-1 ("Cologne Center for Terahertz Spectroscopy"). The work in Cambridge is supported from NASA grant 80NSSC18K0396. We thank Holger S. P. Müller for helpful discussions. Note. ρ was manually adjusted. See text for details. The mkj values in the Fourier series coefficients T mkj q determine the corresponding rotational operator P 2j P 2k z (P 2 + -P 2 -) m that is expanded and q determines the order of the Fourier series.

Figure 1 :

 1 Figure1: Overview of the far-IR spectra, presented in transmittance, recorded in this work with a pressure of 500 (in dark red) and 26 (in black) µbar. Strong lines of water and its isotopologues have been removed for the sake of clarity using HITRAN linelists[START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF]. The main motion associated with each vibration of the molecule is indicated by blue arrows.

Figure 2 :

 2 Figure 2: Experimental (post-processed, 500 µbar) and calculated (final set of parameters, this work) spectrum of the fundamental ν 20 mode. Maroon vertical lines indicate the spectral range enlarged in the lower panels of the figure. The simulation is obtained by convolution of the predicted transitions (SPCAT) with a FWHM=0.0015 cm -1 Gaussian profile.

Figure 3 :

 3 Figure 3: Experimental (post-processed, 500 µbar) and calculated spectrum (final set of parameters, this work) of the fundamental ν 12 mode. Maroon vertical lines indicate the spectral range enlarged in the lower panels of the figure. The simulation is obtained by convolution of the predicted transitions (SPCAT) with a FWHM=0.0015 cm -1 Gaussian profile.

Figure 4 :

 4 Figure 4: Experimental (post-processed, 26 µbar) and calculated (final set of parameters, this work) spectrum of the fundamentals ν 21 and ν 13 . Maroon vertical lines indicate the spectral range enlarged in the lower panels of the figure. The simulation is obtained by convolution of the predicted transitions (SPCAT) with a FWHM=9 • 10 -4 cm -1 Gaussian profile. Narrow gaps in the experimental spectrum are due to removal of strong water lines. 6

Figure 5 :

 5 Figure 5: Experimental and calculated spectrum of pure rotational transitions in the ground vibrational state (blue) and v 12 = 1 (green), v 20 (red), and v 13 = 1 and v 21 = 1 (yellow, same plot) excited states. The combined simulation of all vibrational states is shown in grey. The simulation is obtained by convolution of the predicted transitions (SPCAT) with the second derivative of Gaussian profile.

Figure 6 :

 6 Figure 6: Location and symmetry of the four lowest vibrational states of ethyl cyanide along with nearby combination and overtone states. All states are labelled according to the (v 12 , v 13 , v 20 , v 21 ) formalism where the number of quanta of excitation in each state is reported.

Figure 7 :

 7 Figure 7: Cross correlation plots for K a = 10, K c = J -K a for the fundamental modes ν 13 , ν 21 , ν 12 , and ν 20 . Intensities are normalized with respect to the strongest peak in the displayed spectral range. A larger number of transitions included in the cross correlation plots leads to a narrowing of peaks, which can be seen clearly in the plots for ν 13 .

Figure 8 :

 8 Figure 8: Probability density of frequency differences for pure rotational transitions determined between observed frequencies of C 2 H 5 CN (Refs. [10, 15] and this work) and calculated ones derived from the state energies derived using ASAP. The different plots show values for each of the vibrational states studied in this work. Only A symmetry states are taken into account.

  ab 11.20[START_REF] Pienkina | The millimeter and submillimeter rotational spectrum of triple 13 C-substituted ethyl cyanide[END_REF] Note. Units are MHz. Standard errors are given in parenthesis. Parameters of the ground state are applied to all excited states and difference values are fitted for the individual excited states. Here, the ground state values and the difference values are summed up to facilitate readability. Thus, parameters among states and their uncertainty are exactly the same if no difference parameter was included. a Simultaneous fit to the rotation and rotation-vibration data of the v = 0, v 13 = 1, v 21 = 1, v 12 = 1, and v 20 = 1 states.

Table 1 :

 1 Summary of the individual datasets that were included in the fit.

	State	max. J max. K a max. Energy # Levels	σ
	v 12 = 1	90	18	1731 cm -1	2141	0.96
	v 20 = 1	90	25	1537 cm -1	2277	0.88
	v 13 = 1, A	80	25	1617 cm -1	2887	1.12
	v 21 = 1, A	66	23	1092 cm -1	2012	0.96
	Transitions	max. J max. K a	max. Freq.	# Trans.	σ
	Ground State	130	36	1160 GHz	5259	1.03
	v 12 = 1	71	17	605 GHz	1578	2.76
	v 20 = 1	71	25	605 GHz	1338	1.69
	v 13 = 1	43	15	255 GHz	1244	2.92
	v 21 = 1	42	17	254 GHz	1068	2.86

Table 2 :

 2 Molecular parameters of CH 3 CH 2 CN derived from the combined fit a .

	Parameter	v = 0	v 12 = 1	v 20 = 1	v 13 = 1	v 21 = 1
	A		27 663.681 22(79)	28 082.0334(51)	27 445.3437(37)	27 809.08(87)	27 643.22(87)
	B		4714.187 49(11)	4707.357 69(22)	4715.646 15(25)	4728.844(10)	4712.789(11)
	C		4235.084 92(10)	4228.628 90(21)	4240.783 39(23)	4240.6283(11)	4233.1663(11)
	D J	×10 3	3.007 878(47)	2.980 446(80)	3.015 183(85)	3.036 48(19)	2.958 27(33)
	D JK	×10 3	-47.266 51(63)	-48.4881(23)	-46.5426(23)	-45.609(15)	-47.172(15)
	D K	×10 3	547.7867(57)	602.58(12)	510.003(33)	531.03(14)	567.16(16)
	d 1	×10 3	-0.685 828(10)	-0.681 012(14)	-0.683 429(15)	-0.709 74(10)	-0.663 26(12)
	d 2	×10 3	-0.032 791 7(35)	-0.034 197 6(88)	-0.028 829 0(89)	-0.039 280(40)	-0.028 411(34)
	H J	×10 6	0.009 326 7(85)	0.009 235(11)	0.009 228(12)	0.009 326 7(85)	0.008 836(66)
	H JK	×10 6	-0.119 08(21)	-0.109 30(33)	-0.113 72(42)	-0.119 08(21)	-0.119 08(21)
	H KJ	×10 6	-1.5876(13)	-2.5255(84)	-1.4433(51)	1.675(43)	-4.548(41)
	H K	×10 6	31.373(23)	33.42(40)	25.685(60)	5.82(38)	55.22(37)
	h 1	×10 9	3.8835(20)	3.8835(20)	3.8835(20)	3.8835(20)	3.8835(20)
	h 2	×10 9	0.519 67(78)	0.519 67(78)	0.519 67(78)	0.519 67(78)	0.519 67(78)
	h 3	×10 9	0.063 32(39)	0.063 32(39)	0.063 32(39)	0.063 32(39)	0.063 32(39)
	L J	×10 12	-0.039 48(64)	-0.039 48(64)	-0.039 48(64)	-0.039 48(64)	-0.039 48(64)
	L JJK	×10 12	0.556(28)	0.556(28)	0.556(28)	0.556(28)	0.556(28)
	L JK	×10 12	-5.74(24)	-5.74(24)	-5.74(24)	-5.74(24)	-5.74(24)
	L KKJ	×10 12	85.42(98)	85.42(98)	85.42(98)	85.42(98)	85.42(98)
	L K	×10 9	-2.195(39)	-2.195(39)	-2.195(39)	-2.195(39)	-2.195(39)
	l 1	×10 15	-19.10(11)	-19.10(11)	-19.10(11)	-19.10(11)	-19.10(11)
	l 2	×10 15	-4.708(50)	-4.708(50)	-4.708(50)	-4.708(50)	-4.708(50)
	l 3	×10 15	-1.213(29)	-1.213(29)	-1.213(29)	-1.213(29)	-1.213(29)
	l 4	×10 15	-0.153(12)	-0.153(12)	-0.153(12)	-0.153(12)	-0.153(12)
	P J	×10 18	0.106(17)	0.106(17)	0.106(17)	0.106(17)	0.106(17)
	P JJK	×10 15	-0.0060(13)	-0.0060(13)	-0.0060(13)	-0.0060(13)	-0.0060(13)
	P JK	×10 15	0.121(12)	0.121(12)	0.121(12)	0.121(12)	0.121(12)
	P KJ	×10 15	-2.04(14)	-2.04(14)	-2.04(14)	-2.04(14)	-2.04(14)
	P KKJ	×10 15
	P K	×10 12	0.165(23)	0.165(23)	0.165(23)	0.165(23)	0.165(23)
	D

Table 3 :

 3 State energies for the A symmetry species derived from the combined fit.

	State	Symmetry	Energy [cm -1 ]
	v = 0	a	0.0 a
	v 12 = 1	a	532.699 617(16)
	v 20 = 1	a	372.635 293(15)
	v 13 = 1	a	205.934 099(8)
	v 21 = 1	a	212.141 101(8)

a Fixed.

Table 4 :

 4 Tunneling Parameters for v 21 = 1 and v 13 = 1 obtained from the combined fit.

	Parameter	spfit notation	v 21 = 1	v 13 = 1
	ρ		9100vv	0.134
	1	[MHz]	10000000vv	37.163(45)	-3.528(35)
	T 001 1 T 010 1 T 100 1	[MHz] [MHz] [MHz]	10000001vv 10000010vv 10000400vv	0.0489(19) -0.016 870(68) -0.009 499(25)

Table 5 :

 5 Interaction parameters for v 21 = 1 and v 13 = 1 obtained from the combined fit.Note. Units are MHz. {, } is the anticommutator. v1, v2 are labels for the vibrational states v 13 and v 21 used in spfit. See par-file for details.

	Parameter Operator		spfit notation	Value
	G a	Ĵa							2000v1v2	20 122.6(40)
	G a,J	{ Ĵ2 , Ĵa }			2001v1v2	0.015 90(26)
	G a,K	{ Ĵz	2	, Ĵa }		2010v1v2	-1.5197(31)
	F bc	{ Ĵb , Ĵc }			2100v1v2	-0.001 371(21)
	G 2a	{ Ĵa , ( Ĵb	2	-Ĵc	2	)}	2200v1v2	-0.075 55(82)
	G b	Ĵb							4000v1v2	1014.94(91)
	G b,K	{ Ĵz	2	, Ĵb }			4010v1v2	-1.804(12)
	F ca	{ Ĵc , Ĵa }			4100v1v2	-0.045 76(21)
	G 2b	{ Ĵb , ( Ĵc	2	-Ĵa	2	)}	4200v1v2	-0.010 710(67)

Acknowledgement

We acknowledge the SOLEIL facility for provision of synchrotron radiation under the proposals 20170138 & 20190316.

This work has

Appendix: Supplementary data Supplementary data associated with this article (parameter and fit files) are available on ScienceDirect (www.sciencedirect.com).


domain: chim sde chim.mate

text:
Taher Selmi
email: taher-selmi@hotmail.com

Mongi Seffen

Alain Celzard

Vanessa Fierro

Effect of the adsorption pH and temperature on the parameters of the Brouers-Sotolongo models

Keywords: Adsorption, activated carbon, dyes, fractal kinetics, Brouers-Gaspard isotherm, heterogeneous surface

The goal of the present paper was to elucidate ifand howthe parameters of the Brouers-Sotolongo fractal BSf (n,α) kinetic model (α and τ C ) on the one hand, and of the generalised Brouers-Sotolongo GBS isotherm model (a and b) on the other hand, are correlated with adsorption pH and temperature. For that purpose, adsorption of aqueous solutions of two common dyes, methylene blue (MB) and methyl orange (MO) was carried out on four activated carbons (ACs) at three temperatures (25, 35 and 50°C) and three pH (2.5, 5 and 8). Adsorption kinetics and isotherms were measured, and the corresponding curves were best fitted with specific forms of the aforementioned models, and corresponding to equations known as BSf (1,α) kinetic and Brouers-Gaspard isotherm models. Correlations between all models parameters and adsorption conditions were found, bringing some information about the adsorbate-adsorbent interaction.

Introduction

Adsorption is a complex process that can combine interactions of different physical and/or chemical natures between the adsorbate (solute) and the active sites of the adsorbent, including electrostatic forces and Van der Waals interactions, ligand exchange, hydrogen bounding, or hydrophobic interactions (Volesky 2007). In order to understand the adsorption phenomena, several kinetic and isotherm models have been applied. Concerning kinetics, the most well-known models are intraparticle diffusion (Weber and Morris 1963), pseudo-first order [START_REF] Lagergren | Zur Theorie der Sogenannten Adsorption Gelöster Stoffe[END_REF], pseudo-second-order [START_REF] Ho | Pseudo-second order model for sorption processes[END_REF] and Elovich (Wu et al. 2009) models. As for adsorption, Freundlich [START_REF] Freundlich | Over the adsorption in solution[END_REF], Langmuir [START_REF] Langmuir | The adsorption of gases on plane surfaces of glass, mica, and platinum[END_REF], Sips [START_REF] Sips | The Structure of a Catalyst Surface[END_REF] and Temkin (Temkin 1941) isotherm expressions are among the most frequently used.

However, these conventional models are based on unrealistic assumptions, such as monolayer or multilayer adsorption, one single molecule per active site, no interaction between adsorbed molecules, etc., and sometimes they give little information on the adsorbate-adsorbent system. Experimental studies by [START_REF] Klymko | Heterogeneous exciton kinetics: triplet naphthalene homofusion in an isotopic mixed crystal The[END_REF][START_REF] Kopelman | Rate processes on fractals: Theory, simulations, and experiments[END_REF]) on the kinetic reaction of excitons in molecular macroclusters (inside crystalline isotopic alloy) prepared in fractal form have shown that the rate constant depends on time, which is not expressed in classical models.

For this reason, Kopelman (Kopelman 1988) and Meilanov et al. [START_REF] Meilanov | Fractal nature of sorption kinetics[END_REF] expressed the need of developing new kinetic and isotherm models taking into accounts the fractal porosity and the heterogeneity of adsorbate-adsorbent systems. This new approach was developed by Brouers andcollaborators. In 2006, Brouers and[START_REF] Brouers | Generalized fractal kinetics in complex systems (application to biophysics and biotechnology)[END_REF][START_REF] Brouers | Generalized fractal kinetics in complex systems (application to biophysics and biotechnology)[END_REF] developed a new kinetic fractal model called BSf (n,α) based on Hill [START_REF] Jones | The additive damage model: A mathematical model for cellular responses to drug combinations[END_REF], Weibull (Tonkin et al. 2014) and Tsallis (Sotolongo-Grau. O et al. 2010;Sotolongo-Grau. O et al. 2013) kinetic formulae, and taking into account the systems fractality by using the probability function and the notion of fractional derivative (Pereira 2010). BSf (n,α) encompasses several other models, depending on the values of the parameters n and α. This new fractal kinetic model was applied to pharmacokinetics (Pereira 2010), water treatment [START_REF] Hamissa | Kinetic Modeling Study on Methylene Blue Sorption onto Agave americana fibers: Fractal Kinetics and Regeneration[END_REF], and is presently more and more employed [START_REF] Brouers | Kinetic modeling of antibiotic adsorption onto different nanomaterials using the Brouers-Sotolongo fractal equation[END_REF][START_REF] Gaspard | Parameters from a new kinetic equation to evaluate activated carbons efficiency for water treatment[END_REF][START_REF] Sandro | Adsorption studies of methylene blue and phenol onto vetiver roots activated carbon prepared by chemical activation[END_REF]Selmi et al. 2018c).

In terms of adsorption at equilibrium, Brouers et al. [START_REF] Brouers | Microporous and heterogeneous surface adsorption isotherms arising from Levy distributions[END_REF] Brouers extended the empirical model of Langmuir to simple Brouers-Sotolongo (BS) isotherm and generalised the BS model by replacing the exponent in the Weibull function by a deformed exponential used in the formalism of non extensive thermodynamics [START_REF] Robledo | q-deformed statistical-mechanical property in the dynamics of trajectories en route to the Feigenbaum attractor[END_REF]Tsallis 2009). The GBS isotherm also encompasses several other models, depending on the value of its parameters c and a, and has become increasingly employed in several domains such as medical application using bacteriophages for the optimised capture of bacteria [START_REF] Naidoo | Surface-immobilization of chromatographically purified bacteriophages for the optimized capture of bacteria[END_REF], water treatment, and adsorption in general [START_REF] Brouers | On the optimal use of isotherm models for the characterization of biosorption of lead onto algae[END_REF][START_REF] Ncibi | Modelling single compound adsorption onto porous and non-porous sorbents using a deformed Weibull exponential isotherm[END_REF][START_REF] Ncibi | Optimized removal of antibiotic drugs from aqueous solutions usingsingle, double and multi-walled carbon nanotubes[END_REF].

Applying the BSf and GBS models presents many advantages compared to traditional ones as they give valuable information on the adsorbent surface and on the adsorbate/adsorbent interface. The main issue is that there is little information on the parameters of BSf and GBS models. In a previous manuscript (Selmi et al. 2018c), these parameters were determined and their relationships with the physicochemical characteristics of four ACs: F200, F300, Acticarbone® and Cecalite® were clarified. The objective of the present study was to elucidate whether there is a correlation between the aforementioned parameters and pH and temperature when studying the adsorption of two dyes: methylene blue (MB) and methyl orange (MO) onto the same ACs.

Experimental

Materials

Four activated carbons (ACs) were used: Filtrasorb 200 (F200) and Filtrasorb 300 (F300) from Calgon Cooperation, and Acticarbone® and Cecalite® from CECA. Complete details about those materials ACs can be found elsewhere (Selmi et al. 2018c), whereas their main relevant physicochemical characteristics, i.e., those having an effect on adsorption, are reported in Table 1. MB and MO dyes were provided by Sigma-Aldrich (purity > 85%). The AC suspensions in dye solutions were stirred magnetically and, after a given time, a sample of 4 mL was withdrawn and the residual dye concentration was determined with a UV-Vis spectrophotometer (Perkin-Elmer Lambda 35) at a wavelength of 663 nm for MB, and 464 nm for MO. Once the absorbance was measured, the liquid sample was put back into the flask in order to maintain a constant liquid volume. The amount of adsorbed dye at equilibrium, q e (mg/g), was calculated by: Equation 1where C 0 and C e (mg/L) are the initial and equilibrium dye concentrations, respectively, V (L)

is the volume of solution, and m (g) is the mass of AC.

Dyes adsorption thermodynamics parameters such as standard entropy ∆S°, enthalpy ∆H°, and free energy ∆G° were calculated from adsorption data at three temperatures: 25, 35 and 50°C, using a thermostatic bath regulated at ± 1°C and following the method reported in detail elsewhere [START_REF] Enaime | Preparation and characterization of activated carbons from olive wastes by physical and chemical activation: Application to Indigo carmine adsorption[END_REF]).

Brouers-Sotolongo kinetic (BSf) and adsorption equilibrium (GBS) models

The Brouers-Sotolongo fractal kinetic (BSf) model takes into account the adsorption process complexity (Brouers 2014a) and reads:

Equation 2

where α is the fractal time exponent, which is a measure of the average energy and width of the adsorption energy distribution; it decreases when the average energy and the width of the energy distribution increase. n is a (possibly fractional, i.e., non-integer) reaction order, and q n,α (t) and q e are the adsorbed amounts at any time t and at saturation, respectively. τ C is the characteristic time of the complex kinetics, and corresponds to the necessary time to reach equilibrium so that the BSf model can predict the equilibrium time. In relation to the parameters n, α and τ C , a time of half-reaction τ 1/2 can be determined to predict the time necessary to sorb half of the amount at equilibrium; more details are given elsewhere (Selmi et al. 2018c). Several other models can be recovered from the expression of BSf, depending on the values of n and α, as shown in Table 2. More details can be found elsewhere (Brouers 2014a). The GBS isotherm model takes into account the physical and chemical heterogeneity of the adsorbent and of the adsorbate/adsorbent system [START_REF] Brouers | On the optimal use of isotherm models for the characterization of biosorption of lead onto algae[END_REF]. It reads: Equation 7Depending on the parameters a and c, several other models can be derived from the GBS equation, as shown in Table 3; more details can be found elsewhere (Brouers 2014b). [START_REF] Langmuir | The adsorption of gases on plane surfaces of glass, mica, and platinum[END_REF])

C e << b Freundlich
Eq. 12 [START_REF] Freundlich | Over the adsorption in solution[END_REF] The experimental data were non-linearly fitted by using the Levenberg-Marquardt iteration algorithm supplied with OriginPro® 2016 Software.

Results and discussion

Effect of initial dye concentration on adsorption kinetics

Figure 1 shows the effect of the initial concentration of MB (Fig. 1(a)) and of MO (Fig.

1(b)) on the time required for reaching the equilibrium, which increased with the initial dye concentration. As can be seen, adsorption occurred in two stages: (i) the initial adsorption stage was fast, probably due to the high number of sites available for sorption; (ii) the second phase was slower due to the fact that the number of easily accessible sites decreased and the adsorbate needed longer times to reach the last remaining adsorption sites [START_REF] Kesraoui | Biosorption of alpacide blue from aqueous solution by lignocellulosic biomass: Luffa cylindrica fibers[END_REF]. As an example, the necessary time to reach the equilibrium on F300 was 50 min and 25 min when using C 0 =5 mg/L of MB and MO, respectively. The equilibrium time was multiplied by a factor 4 when increasing the initial dye concentration up to 80 mg/L, suggesting that adsorption was controlled by intraparticle and boundary layer diffusion [START_REF] Enaime | Preparation and characterization of activated carbons from olive wastes by physical and chemical activation: Application to Indigo carmine adsorption[END_REF]. Similar results were found with the other 3 ACs (see Figures SI 1 to SI 3 of the Supplementary Information).

Effect of initial pH and temperature on adsorption

Figure 2 and Table SI 1 shows the effect of pH and temperature on MB and MO adsorption capacities of the four ACs when the initial dye concentration C 0 was fixed to 10 mg/L. These effects were investigated at pH 2.5, 5 and 8 at each temperature of 25, 35 and 50°C. MB adsorption at equilibrium onto F300 increased slightly from 3.18 to 3.39 mg/g when the pH increased from 2.5 to 8 at 25°C, indicating that MB was favourably adsorbed at basic pH. On the contrary, MO adsorption at equilibrium onto F300 decreased slightly from 3.15 to 3.00 mg/g when the pH increased from 2.5 to 8 at 25°C indicating that MO was favourably adsorbed at acidic pH. This fact is in agreement with the pH PZC of F300 (8.03), suggesting that the adsorbent surface was approximately neutral at pH 8 and positively charged at pH 2.5, i.e., was attracting anions. MB is a cationic dye, and hence it is positively charged in solution and thus more adsorbed at basic pH when the surface of the carbon is not charged, than at acidic pH when the surface of the carbon is positively charged. The opposite was observed for MO, which is an anionic dye.

Therefore, the study of the effect of temperature on adsorption onto was made by fixing the pH to 8 for MB and to 2.5 for MO. The amounts of MB and MO adsorbed onto F300 increased with temperature from 25 to 50°C from 3.39 to 3.84 mg/g for MB, and from 3.15 to 3.51 mg/g for MO (Table SI 1). The corresponding data will be examined in terms of thermodynamic parameters in the next section.

Figure 2 shows the MB and MO equilibrium adsorption capacities of the four ACs as a function of temperature and pH. All adsorbents had pH PZC between 7.20 and 8.03, therefore they essentially had the same behaviour, i.e., MB adsorption was more favourable at pH 8, when the surface of the AC was nearly neutral, than at pH 2.5, when it was positively charged and thus led to higher electrostatic repulsion. On the contrary, MO adsorption was more favourable at pH 2.5 when surface of AC was positively charged and thus led to higher electrostatic attraction since MO is an anionic dye. Dissociation and electrostatic repulsion are also largely influenced by temperature [START_REF] Ncibi | Optimized removal of antibiotic drugs from aqueous solutions usingsingle, double and multi-walled carbon nanotubes[END_REF], and the same general trend was observed for the four ACs. Adsorption increased with temperature in the range 35 to 50°C. MO, both at C 0 =10 mg/L. Figure 4 shows the variations of standard adsorption enthalpy ∆H° and of standard adsorption entropy ∆S° with pH for MB and MO adsorption onto the four ACs; the corresponding numerical results are given in Table SI 2 of the Supplementary Information.

Thermodynamic analysis

∆H° was always positive: it decreased when the pH was increased for the adsorption of MB, but increased with pH for the adsorption of MO onto all ACs (Figure 4 and Table SI 2 of the Supplementary Information).

∆S° was always positive and showed the same behaviour as ∆H° with pH (Figure 4 and

Kinetic data analysis

Herein, based on our former work (Selmi et al. 2018c), the reaction order n =1 was used for the BSf kinetics model because of the excellent fits it let for all ACs. The Weibull equation (n = 1 and α ≠ 1) was indeed the most relevant one for fitting the kinetic data, and this was in agreement also with previous studies on Indigo Carmine adsorption onto F200 [START_REF] Kesraoui | Influence of alternating current on the adsorption of indigo carmine[END_REF]. Figure 5 Previous studies [START_REF] Brouers | Kinetic modeling of antibiotic adsorption onto different nanomaterials using the Brouers-Sotolongo fractal equation[END_REF][START_REF] Hamissa | Kinetic Modeling Study on Methylene Blue Sorption onto Agave americana fibers: Fractal Kinetics and Regeneration[END_REF]Selmi et al. 2018b;Selmi et al. 2018c) showed that the interactions between adsorbate/adsorbent were fractal when α, sometimes referred to as the global fractal time, was lower than 1.  represents the memory effect produced in systems where the reaction at any time, t, depends on the history of the process. α arises from the energetic and geometric heterogeneity of the adsorbent (Ben [START_REF] Hamissa | Kinetic Modeling Study on Methylene Blue Sorption onto Agave americana fibers: Fractal Kinetics and Regeneration[END_REF]. Figure 6(b) and Table SI 3 of the Supplementary Information show that the adsorption of MB onto F300 is slightly fractal (α MB between 0.80 and 1.12) and the adsorption of MO onto F300 is clearly fractal (α MO between 0.67 and 1.13). On the one hand, α MB increased from 0.92 to 1.07 when the pH was increased from 2.5 to 8 at 25°C, indicating that raising the pH diminished the fractal nature of the phenomena. On the other hand, α MO decreased from 1.13 to 0.92 when increasing the pH from 2.5 to 8 at 25°C, indicating that, instead, raising the pH promoted fractal adsorption of MO onto F300. In fact, fractal phenomena became stronger when increasing the pH at temperatures above 35°C for both MB and MO adsorption. The same results were found when studying MB adsorption onto F200

and Acticarbone®, and MO adsorption onto Acticarbone® and onto Cecalite® (see Figure SI Since the increase of pH had a positive effect on the adsorption of MB and a negative effect on the adsorption of MO, the characteristic time decreased with pH for MB adsorption (e.g. from 16.69 to 12.14 min at 25°C for MB adsorption onto F300), and increased with pH for MO adsorption (e.g. from 16.78 to 20.16 min at 25°C for MO adsorption onto F300). The same behaviour was clearly apparent for the adsorption of MB and MO onto all other ACs (see Figure 6, and Figure SI 5 and Tables SI 3 to SI 6 of the Supplementary Information).

On the other hand, the temperature had a positive effect on both MB and MO adsorption, the increase of temperature increasing the initial rate of dye adsorption. Consequently, the characteristic time decreased with temperature. This behaviour is clearly apparent for the adsorption of MB and MO onto all ACs in Figure 6, Figure SI 5, and Tables SI 3 to SI 6 of the Supplementary Information. At favourable pH (8 for MB and 2.5 for MO), the characteristic time for the adsorption onto F300 of MB, τ cMB , and of MO, τ cMO , decreased when increasing the temperature, from 12.14 to 6.23 min and from 16.78 to 8.25 min, respectively (see Table SI 3 of the Supplementary Information). These results agree with previous studies (Ben [START_REF] Hamissa | Kinetic Modeling Study on Methylene Blue Sorption onto Agave americana fibers: Fractal Kinetics and Regeneration[END_REF][START_REF] Kesraoui | Influence of alternating current on the adsorption of indigo carmine[END_REF]Selmi et al. 2018b).

Increasing pH and temperature at the same time produced a decrease of the fractality degree α and the adsorption became faster, reducing in turn the characteristic time, τ C .)

Adsorption isotherm fitting

The GBS isotherm was used by fixing the heterogeneity degree, c, equal to 0.5, based on a previous study (Selmi et al. 2018c). And indeed, excellent fits were obtained with c = 0.5, hence the Brouers-Gaspard (BG) equation (a ≠ 1 and c = 0.5) was the most relevant one for fitting the isotherm adsorption data of MB and MO onto ACs. A stochastic analysis of physicochemical reactions in complex systems (Stanislavsky and Weron 2013) showed that the exponent c is related to the cluster or aggregation organization of the system. Figure 7 shows that the experimental isotherms of MB and MO adsorbed onto F300 were very well with pH (from 0.48 to 0.93 at 25°C) and temperature (from 0.93 to 2.15 at pH 8), see Table SI 7, for MB adsorption onto F300. On the other hand, a decreased when increasing the pH from 2.5 to 8 (from 1.06 to 0.98 at 25°C) for MO adsorption onto F300, and increased with temperature from 25 to 50°C (from 1.06 to 1.26 at pH 2.5) due to the unfavourable effect of pH and favourable effect of temperature (Table SI 7). The same behaviours were clearly observed for the adsorption of MB and MO onto the 3 other ACs (Tables SI 8 to SI 10).

BG sorption model assumes that adsorption takes place on a heterogeneous surface with a distribution of sorption energies representative of different active sites which are progressively occupied. a represents a degree of the fractal nature of a heterogeneous system (Brouers 2014a;[START_REF] Brouers | On the optimal use of isotherm models for the characterization of biosorption of lead onto algae[END_REF][START_REF] Brouers | Dubinin isotherms versus the Brouers-Sotolongo family isotherms: A case study[END_REF]. When a > 1, fast initial sorption kinetics occurs, and there is probably more than one molecule sorbed by active site; when a < 1, slow initial sorption kinetics is observed. Brouers et al. [START_REF] Brouers | Microporous and heterogeneous surface adsorption isotherms arising from Levy distributions[END_REF] showed that the exponent a is proportional to kT/E s , where k, T and E s are Boltzmann constant, absolute temperature and sorption energy distribution, respectively. For a typical E s , 1/α measures the energy distribution width, and therefore the energy heterogeneity of the surface.

The parameter b was also correlated with pH and temperature. At 25°C, the values of b related to MB and MO adsorption onto F300 decreased from 3.49 to 2.37 mg/L and increased from 2.49 to 8.74 mg/L, respectively, when increasing the pH from 2.5 to 8. At favourable pH (8 for MB and 2.5 for MO), the b parameter of MB and MO adsorption onto F300 decreased from 2.37 to 0.20 mg/L and from 2.49 to 0.79 mg/L, respectively, when increasing the temperature from 25 to 50°C. Similar results were clearly observed for the adsorption of MB and MO onto the other three ACs (see again Tables SI 8 to SI 10 of the Supplementary Information). The increase of temperature speeds up the adsorption, so that the isotherm reaches quickly at saturation and thereafter the equilibrium concentration decreases. b is thus related to equilibrium concentration, in agreement with previous results (Selmi et al. 2018c).

Conclusion

In this work, the adsorption of two different dyes in aqueous solution, methylene blue (MB) and methyl orange (MO), was investigated as a function of pH and temperature on four different activated carbons. The thermodynamics studies revealed that the adsorption process is spontaneous and endothermic. Both the nonlinear Brouers-Sotolongo fractal, BSf (n,α), kinetic model and the generalised Brouers-Sotolongo, GBS, isotherm model were found to fit very adequately the corresponding experimental results.

The experimental kinetic data were best described by the BSf (1,α) model involving the adsorption of MB and MO on a fractal surface of AC. The parameter α, named global fractal time index, can be correlated with both pH and temperature, indicating its effects on the surface fractality and leading to the conclusion that its value comes from the assumed fractal diffusion and sorption kinetics. This is due to the energetic and geometric heterogeneity of the surface of adsorbent. The characteristic time τ C necessary to reach the equilibrium could also be correlated with both pH and temperature: the favourable effect of pH and temperature decreased τ C .

As for the data at equilibrium, the isotherms were best described by the Brouers-Gaspard (BG) model, which involves the adsorption of MB and MO onto a heterogeneous AC surface.

The exponent a, which measures the energy heterogeneity of the surface, was found to be proportional to the adsorption energy distribution. The favourable effect of both pH and temperature decreased the constant b of the model, which was found to be related to equilibrium concentration.

Figure caption

  developed a new stochastic model called general Brouers-Sotolongo (GBS) isotherm, which is based on an empirical isotherm using Burr distribution (I.W Burr 1942; Mohan D. Pant and Headrick 2013), Weibull distribution (Tonkin et al. 2014), and a cumulative probability distribution.

Figure 1 :

 1 Figure 1: Effect of contact time and initial concentration on: (a) MB at pH 8; and (b) MO at pH 2.5 onto F300 at 25°C (lines are just guides for the eye).

Figure 2 :

 2 Figure 2: Effect of pH and temperature on the adsorbed amount onto ACs of: (a) MB; and (b)

Figure 3

 3 Figure3shows the variation of standard free energy ∆G° with pH and temperature for MB

Figure 3 :

 3 Figure 3: Effect of pH and temperature on the free energy of adsorption ∆G° onto the four ACs of: (a) MB; and (b) MO, both at C 0 =10 mg/L.

Figure 4 :

 4 Figure 4: Effect of pH on: (a and b) standard adsorption enthalpy ∆H°; and (c and d) on standard adsorption entropy ∆S° for: (a and c) MB; and (b and) MO onto the four ACs.

  shows the experimental kinetic data of MB and MO adsorption onto F300, and the corresponding non-linear fits using the BSf (1,α) model (i.e., n was fixed to 1). The BSf (1,α) model fitted very well the experimental data and equally good results were obtained for the other three ACs, as shown in Figure SI 4 of the Supplementary Information.

Figure 5 :

 5 Figure 5: BSf (1,α) kinetics model applied to the adsorption of: (a,b) MB; and (c,d) MO onto F300 for different pH and temperatures, using an initial dye concentration C 0 =10 mg/L.

Figure 6

 6 Figure6shows the effect of pH and temperature on the BSf (1,α) constants τ C and α for the

5

  Figure SI 5 andTable SI 6 of the Supplementary Information.

Figure 6 :

 6 Figure 6: Variation with pH and temperature of BSf (1,α) parameters: (a) τ C ; and (b) α, for the

  fitted with BG equation. Equally good results were obtained for the other three ACs, and the corresponding results are given in Figure SI 6 of the Supplementary Information.

Figure 7 :

 7 Figure 7: Fits of the BG isotherm to the adsorption data onto F300 of: (a and b) MB; and (c and d) MO, for different temperatures and pH.

Figure 8

 8 Figure8shows the effect of pH and temperature on the BG parameters a and b for the

Figure 8 :

 8 Figure 8: Variation with pH and temperature of BG parameters, a and b, determined by adsorption of: (a and c) MB; (b and d) MO, onto F200, F300, Acticarbone® and Cecalite®.

Figure 1 :

 1 Figure 1: Effect of contact time and initial concentration on: (a) MB at pH 8; and (b) MO at

Figure 2 :

 2 Figure 2: Effect of pH and temperature on the adsorbed amount onto F300 of: (a) MB; and (b)

Figure 3 :

 3 Figure 3: Effect of pH and temperature on the free energy of adsorption ∆G° onto the four

Figure 4 :

 4 Figure 4: Effect of pH on: (a and b) standard adsorption enthalpy ∆H°; and (c and d) on

Figure 5 :

 5 Figure 5: BSf (1,α) kinetics model applied to the adsorption of: (a,b) MB; and (c,d) MO onto

Figure 6 :

 6 Figure 6: Variation with pH and temperature of BSf (1,α) parameters: (a) τ C ; and (b) α, for the

Figure 7 :

 7 Figure 7: Fits of the BG isotherm to the adsorption data onto F300 of: (a and b) MB; and (c

Figure 8 :

 8 Figure 8: Variation with pH and temperature of BG parameters, a and b, determined by

Table 1 :

 1 Characteristics of the four ACs used herein(Selmi et al. 2018c): surface area (S BET ), total pore volume measured by nitrogen adsorption at -196°C (V tot ), total amount of surface functional groups, and pH at the point of zero charge (pH PZC ).

	Activated carbon	F200	F300	Acticarbone®	Cecalite®
	S BET (m 2 /g)	795	884	1014	582
	V tot (cm 3 /g)	0.39	0.43	0.56	0.24
	Total amount of surface functional groups (mmol/g)	1.145	0.605	1.150	0.787
	pH PZC	7.20	8.03	7.36	7.75
	2.2 Adsorption studies
	MB and MO adsorption kinetics and equilibrium isotherms were performed in batch
	experiments as follows: 0.3 g of AC adsorbent, used in granular form with a grain size not
	exceeding 1 mm, were added to 100 mL of MB or MO solution with the desired dye

Table 2 :

 2 Kinetic models derived from the BSf kinetic model

	n	α	Model	Expression	Eq. number	Reference
	1	1	pseudo-first order (PFO)		Eq. 3	(Lagergren 1898)
	2	1	pseudo-second order (PSO)		Eq. 4	(Ho and McKay 1999)
	1	--	Weibull		Eq. 5	(Brouers 2014a)
	2	--	Hill		Eq. 6	(Brouers 2014a)

Table 3 :

 3 Adsorption isotherms models derived from the GBS isotherm.

	c	a	Model	Equation form	Eq. number	Reference
	0	--	BS		Eq. 8	(Brouers 2014b)
	0.5 --	BG		Eq. 9	(Brouers and Al-Musawi 2015)
	1	--	HS		Eq. 10	(Sips 1948)
	1	1	Langmuir		Eq. 11

Table SI 2

 SI of the Supplementary Information). The positive values of ∆S° suggest an increased randomness at the AC/solution interface during the sorption process. Similar results were found by other investigators working on dye adsorption onto various adsorbents

[START_REF] Bouhamed | Multi-component adsorption of copper, nickel and zinc from aqueous solutions onto activated carbon prepared from date stones[END_REF][START_REF] Enaime | Preparation and characterization of activated carbons from olive wastes by physical and chemical activation: Application to Indigo carmine adsorption[END_REF][START_REF] Kesraoui | Influence of alternating current on the adsorption of indigo carmine[END_REF] Selmi et al. 2018a

).

Acknowledgements

The authors gratefully acknowledges the financial support from the EU-METALIC: Erasmus Mundus project and the Tunisian Ministry of Higher Education and Scientific Research.

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