domain: sdu chim phys.astr phys

text:
T Cours

D Cordier

B Seignovert

L Maltagliati

L Biennier

The 3.4 µm absorption of the Titan's stratosphere: contribution of ethane, propane, butane and complex hydrogenated organics

Keywords: planets and satellites, individual, Titan -planets and satellites, general -solar system, general 2

The complex organic chemistry harbored by the atmosphere of Titan has been investigated in depth by Cassini observations. Among them, a series of solar occultations performed by the VIMS instrument throughout the 13 years of Cassini revealed a strong absorption centered at ∼ 3.4 µm. Several molecules present in Titan's atmosphere create spectral features in that wavelength region, but their individual contributions are difficult to disentangle.

In this work, we quantify the contribution of the various molecular species to the 3.4 µm band using a radiative transfer model. Ethane and propane are a significant component of the band but they are not enough to fit the shape perfectly, then we need something else. Polycyclic Aromatic Hydrocarbons (PAHs) and more complex polyaromatic hydrocarbons like Hydrogenated

Introduction

Titan is an extraordinary object among the planets and satellites of the solar system. Its thick atmosphere, mainly composed of nitrogen and methane, harbors a complex photochemistry producing organic compounds that participate to the formation of haze which produces its typical orange/brown color. Due to its unique and exotic properties, Titan's atmosphere remains a very active field of research in investigating the possible origin and main properties [START_REF] Johnson | Evolution of an early Titan atmosphere[END_REF][START_REF] Charnay | Titan's past and future: 3D modeling of a pure nitrogen atmosphere and geological implications[END_REF][START_REF] Newman | Simulating Titan's methane cycle with the TitanWRF General Circulation Model[END_REF]. Its composition can be modeled by complex chemical network [START_REF] Krasnopolsky | Chemical composition of Titan's atmosphere and ionosphere: Observations and the photochemical model[END_REF][START_REF] Lavvas | N 2 state population in Titan's atmosphere[END_REF], but also by laboratory experiments [START_REF] Bourgalais | Elusive anion growth in Titan's atmosphere: Low temperature kinetics of the C 3 N -+ HC 3 N reaction[END_REF][START_REF] Romanzin | An experimental study of the reactivity of CNand C 3 Nanions with cyanoacetylene (HC 3 N)[END_REF] to match the observations made by Cassini's instruments (Vinatier et al., 2015;[START_REF] Coustenis | Titan's temporal evolution in stratospheric trace gases near the poles[END_REF][START_REF] Bellucci | Titan solar occultation observed by Cassini/VIMS: Gas absorption and constraints on aerosol composition[END_REF]. In [START_REF] Bellucci | Titan solar occultation observed by Cassini/VIMS: Gas absorption and constraints on aerosol composition[END_REF], the authors raised an issue about the CH 4 3.3 µm band.

In 2006, during Cassini's 10 th flyby of Titan (T10), [START_REF] Bellucci | Titan solar occultation observed by Cassini/VIMS: Gas absorption and constraints on aerosol composition[END_REF] observed features in CH 4 3.3 µm band with the Visible and Infrared Mapping Spectrometer (VIMS). VIMS is an imaging spectrometer onboard the Cassini spacecraft. This instrument is composed of a visible channel (0.3 -1.05 µm) and a infrared channel (0.89 -5.1 µm). The FWHM of the 256 infrared spectral pixels are in the range 13 -20 nm. VIMS can be used in different observation modes corresponding to nadir, limb and occultation geometry.

Our study use the latter mode. More details can be found in [START_REF] Maltagliati | Titan's atmosphere as observed by Cassini/VIMS solar occultations: CH 4 , CO and evidence for C 2 H 6 absorption[END_REF]. [START_REF] Bellucci | Titan solar occultation observed by Cassini/VIMS: Gas absorption and constraints on aerosol composition[END_REF] tentatively attributed the observed features in CH 4 3.3 µm band to solid state organic compounds, similar to those observed in the InterStellar Medium (ISM) [START_REF] Sandford | The interstellar C-H stretching band near 3.4 microns -Constraints on the composition of organic material in the diffuse interstellar medium[END_REF]Pendleton 3 J o u r n a l P r e -p r o o f Journal Pre-proof [START_REF] Pendleton | The Organic Refractory Material in the Diffuse Interstellar Medium: Mid-Infrared Spectroscopic Constraints[END_REF]. However, this interpretation was far to be firm and [START_REF] Bellucci | Titan solar occultation observed by Cassini/VIMS: Gas absorption and constraints on aerosol composition[END_REF] concluded that precise comparison of their data with laboratory spectrum needed in future work.

Interestingly, a similar feature had been observed by VIMS during a stellar occultations in Saturn's atmosphere [START_REF] Nicholson | Probing Saturn's Atmosphere with Procyon[END_REF][START_REF] Kim | The three-micron spectral feature of the Saturnian haze: Implications for the haze composition and formation process[END_REF].

Continued by [START_REF] Kim | The three-micron spectral feature of the Saturnian haze: Implications for the haze composition and formation process[END_REF], these analysis shown that the optical-depth spectra exhibit a broad peak at 3.36-3.41 µm for the observations obtained at 12 pressure levels between 0.0150 and 0.0018 mbar in the Saturnian atmosphere. [START_REF] Kim | The three-micron spectral feature of the Saturnian haze: Implications for the haze composition and formation process[END_REF], in particular, attributed these 3.4 µm spectral features to the aliphatic C-H stretching bands of solid-state hydrocarbons, such as C 5 H 12 , C 6 H 12 , C 6 H 14 and C 7 H 14 . [START_REF] Kim | Retrieval and tentative indentification of the 3 µm spectral feature in Titan's haze[END_REF] reached a similar conclusion for Titan in analyzing the occultation T10. However, the formation of such organic microcrystals in the atmosphere of Titan is questionable due to thermodynamic arguments (see Sec. 2).

More recently, [START_REF] Maltagliati | Titan's atmosphere as observed by Cassini/VIMS solar occultations: CH 4 , CO and evidence for C 2 H 6 absorption[END_REF] analyzed an extended set of four VIMS solar occultations, performed between January 2006 and September 2011. In Fig. 1, we reporte an example of transmission data derived from [START_REF] Maltagliati | Titan's atmosphere as observed by Cassini/VIMS solar occultations: CH 4 , CO and evidence for C 2 H 6 absorption[END_REF]. Spectra have been normalized by a 3 th order polynomial and data have been interpolated at the altitude of 145 km to allow easy comparisons. This value offers a good compromise: at lower altitudes, the stronger absorptions damp spectral features and at higher altitudes, the absorptions are weak and the spectra are more noisy due to a weaker signal. Deviations between the four curves ploted in Fig. 1 give an idea of transmittance uncertainties, and spatial or temporal variations in Titan's atmosphere.

4

J o u r n a l P r e -p r o o f Journal Pre-proof Table 1: Triple points coordinates for the sample of hydrocarbon species considered by [START_REF] Kim | Retrieval and tentative indentification of the 3 µm spectral feature in Titan's haze[END_REF]. The temperatures have all been taken in the NIST database † , for CH 3 CN, C 5 H 12 and C 6 H 12 . The pressures are not available in this database, we then estimated their values by using their Antoine's equation at the triple point temperature.

Species

Chemical In their line-by-line radiative transfer model, [START_REF] Maltagliati | Titan's atmosphere as observed by Cassini/VIMS solar occultations: CH 4 , CO and evidence for C 2 H 6 absorption[END_REF] took into account the absorption caused by 9 molecules : CH 4 , CH 3 D, CO, In this work, we specifically focus our efforts on the highest absorption spectral range, i.e. between 3.3 and 3.5 µm. In Sec. 2 we examine, in the light of an advanced thermodynamic model, the possibility of the existence of hydrocarbon ices in the stratosphere of Titan, as proposed by [START_REF] Kim | Retrieval and tentative indentification of the 3 µm spectral feature in Titan's haze[END_REF]. In Sec. 3 and 4 we revisit the absorption of gases in the 3.4 µm spectral region while in Sec. 5 we discuss the possible presence of PAHs or more complex polyaromatic hydrocarbons like Hydrogenated Amorphous Carbons (HACs). In Sec. 6, we further discuss these issues and present our conclusions.

CO 2 , C 2 H 2 , C 2 H 4 , C 2 H 6 ,

Solid-Vapor equilibria in Titan's stratosphere

An explanation for the nature of Titan's 3.4 µm absorption was put forward by [START_REF] Kim | Retrieval and tentative indentification of the 3 µm spectral feature in Titan's haze[END_REF] who could reproduce the VIMS solar occultations by using hydrocarbon ices like C 2 H 6 , CH 4 , CH 3 CN, C 5 H 12 and C 6 H 12 ices. However, the real existence of such ices in the stratosphere of Titan needs to be discussed. Indeed, as mentioned by [START_REF] Kim | Retrieval and tentative indentification of the 3 µm spectral feature in Titan's haze[END_REF], above 130 km (the lowest altitude explored by these authors) the temperature remains in 160 -190 K interval while the pressure decreases below 5 × 10 -3 bar. A look at Table 1, in which we have gathered the triple points coordinates of involved species, shows that at least C 2 H 6 , CH 4 and C 5 H 12 should not be in solid form at these relatively high temperatures. In order to investigate more provided by HASI instruments, between the altitudes 127 km and 800 km in the atmosphere of Titan [START_REF] Fulchignoni | In situ measurements of the physical characteristics of Titan's environment[END_REF]. Panel (c) represents the molar fraction of ethane as computed by Lavvas et al. (2008a,b). In panel (d) the thermodynamic quantities ∆ 1 and ∆ 2 (defined in the text by Eq. (1) and Eq. ( 2)) for ethane. We recall that ∆ 1 and ∆ 2

∆ 2 ∆ 1 (1) ∆ 1 (10 3 ) (a) (b) (c) (d)
correspond respectively to the chemical potential, of a given species, in the gas phase and in the solid phase, the coexistence of both is reached when ∆ 1 = ∆ 2 (see Eq. ( 3)). ∆ 1 (1) corresponds to the abundances found by Lavvas et al.'s while ∆ 1 (10 3 ) has been obtained by multiplying the mole fraction x C2H6 by 10 3 .

deeply the existence of these ices, we introduce two quantities, the first is:

95 ∆ 1,i = ln (Γ vap i y i ) (1)

8

J o u r n a l P r e -p r o o f where y i is the mole fraction of the compound i at equilibrium, in the vapor, and Γ vap i is the activity coefficient of the considered species. The second introduced term is written as :

∆ 2,i = - ∆H i,m RT i,m T i,m T -1 (2)
The thermodynamic equilibrium between the species i in the vapor, and its icy counterpart , is reached when the equation :

∆ 1,i = ∆ 2,i (3)
is satisfied [START_REF] Poling | The Properties of Gases and Liquids[END_REF]. Eq. ( 3) correspond to a thermodynamic equilibrium between the considered organic ice i and the vapor -Eq. ( 3)

is an equality of chemical potential. The activity coefficient Γ vap i is given by the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT).

Originally proposed by [START_REF] Gross | Perturbed-Chain SAFT: An Equation of State Based on a Perturbation Theory for Chain Molecules[END_REF], PC-SAFT is now widely employed in the chemical engineering community, due to its very good performances. This theory has been successfully employed in several recent studies of Titan to model liquid-vapor and solid-liquid equilibria [START_REF] Tan | Titan's atmosphere and surface liquid: New calculation using Statistical Associating Fluid Theory[END_REF][START_REF] Luspay-Kuti | Experimental Constraints on the Composition and Dynamics of Titan's Polar Lakes[END_REF][START_REF] Tan | Titans liquids: Exotic behavior and its implications on global fluid circulation[END_REF]Cordier et al., 2016;Cordier, 2016).

In Eq. (1) the activity coefficient Γ vap i quantifies the degree of ideality of the considered gas mixture. When Γ vap i ∼ 1 the system has an ideal behavior, i.e. all the molecules of the same species and those of different species interact with the same intensity. In our context, for all the molecules listed in Table 1, we found the Γ vap i 's very close to unity, whatever the altitude. This indicates an ideal behavior of the gases, which is not a surprise at densities provided by HASI measurements [START_REF] Fulchignoni | In situ measurements of the physical characteristics of Titan's environment[END_REF]. Practically, this means that Eq. ( 3) can be satisfied only if ∆ 2,i is negative,

9

J o u r n a l P r e -p r o o f meaning that the molar fraction y i has to be smaller than unity. In the case of ethane, ∆ 2,i remains slightly larger than zero (see Fig. [START_REF] Bézard | Detection of acetonitrile on Titan[END_REF], between roughly 10 -9 and 10 -7 in molar fraction, while Lavvas et al. (2008a,b) computed values around 10 -8 . Our calculations show that even in the most favorable case (i.e. when the abundances of CH 3 CN is taken equal to 10 -7 ) the term ∆ 1,i is more than ten orders of magnitude smaller than the typical value of ∆ 2,i in stratospheric conditions. As a consequence, we conclude that the compounds proposed by [START_REF] Kim | Retrieval and tentative indentification of the 3 µm spectral feature in Titan's haze[END_REF] cannot exhibit solid-vapor equilibria in the stratosphere of Titan. The only possibility remaining is the presence of these icy hydrocarbon aerosols in a non-equilibrium state, but such a situation seems unlikely.

Radiative transfer modeling of the 3.4 µm absorption

In order to simulate the properties of the flux of photons that emerges from the Titan's atmosphere during a solar occultation, we have built a simple radiative transfer model. On one hand, the structure of the atmosphere is represented by a set of concentric spherical shells; on the other hand, the solar radiations are assumed to follow a straight optical path througth the atmosphere. The refraction is neglected in our entire approach, this approx-10 J o u r n a l P r e -p r o o f imation is relevant due to the low density probed in these explored regions.

For a given altitude z, the transmittance T (λ, z) of the atmosphere at the wavelength λ is estimated using

T (λ, z) = exp(- i,j,k N j x i,j σ i,k l j ) (4)
where the indexes i, j and k denote respectively the chemical species, the atmospheric layers and the spectral lines. The cross-sections are σ i,k , N j represents the total number of molecules (per units of volume) in layer j, while x i,j is the molar fraction of species i in the same layer. Finally l j stands for the distance travelled by photons in the layer j (see Fig. 3). Doing several tests on the number of layers, we found N layers = 70 to be a sufficient total number of shells, linearly distributed between the ground and a maximum altitude of 700 km. The pressure and temperature profiles come from HASI measurements [START_REF] Fulchignoni | In situ measurements of the physical characteristics of Titan's environment[END_REF]. The cross-section σ i,k

(in cm 2 /molecule) are written as

σ i,k (ν) = I i,k (ν i,k ) f (ν -νi,k ) (5)
where f is a Voigt profile, ν and νi,k are respectively the wavenumber (in cm -1 ) and the spectral line k wavenumber of the chemical species i, I i,k are the intensities (in cm/molecule) of the spectral line k of the chemical species i. In the cases where high resolution spectral data are available, the crosssection σ i,k are computed using k-correlated coefficient method [START_REF] Arking | The Influence of the line Shape and Band Structure on Temperature in Planetary Science[END_REF][START_REF] Chou | Computation of Infrared Cooling Rates in the Water Vapor Bands[END_REF][START_REF] Fu | On the Correlated k-Distribution Method for Radiative Transfert in Nonhomogeneous Atmospheres[END_REF] coefficient method is not necessary to compute cross-section and therefore a Gauss profile has been proved to be sufficient.

Our initial composition is based on the one published by [START_REF] Maltagliati | Titan's atmosphere as observed by Cassini/VIMS solar occultations: CH 4 , CO and evidence for C 2 H 6 absorption[END_REF] and include the following molecules : CH Egress (T10E), T53 Egress (T53E), T78 Egress (T78E) and T78 Ingress (T78I) acquired during three flybys, T10, T53 and T78 respectively. For each occultation, the altitude ranges between ∼ 50 km and ∼ 690 km. We provide, in supplementary material, four cube's name lists used in our analysis, one name list by occultation. The name lists are in Excel cvs format and can be downloaded from the pds-rings site 4 . For all these occultations, the retrieved transmittance curves, at a given altitude, are extremely similar (see for instance Fig. 11 of [START_REF] Maltagliati | Titan's atmosphere as observed by Cassini/VIMS solar occultations: CH 4 , CO and evidence for C 2 H 6 absorption[END_REF]. In order to facilitate comparison between our theoretical output, and observational determinations, we have chosen the Ingress occultation T78 (T78I) as a typical case. We also selected the altitude of 145 km because it offers a good compromise between A first model-observation comparison can be seen in Fig. 4, the disagreement is clear, particularly around 3.4 µm our domain of interest. This nicely confirms the findings by [START_REF] Maltagliati | Titan's atmosphere as observed by Cassini/VIMS solar occultations: CH 4 , CO and evidence for C 2 H 6 absorption[END_REF].

4 , CH 3 D, CO, C 2 H 2 , C 2 H 4 , C 2 H 6 , H 2 O, C
4. The possible absorption of ethane, propane and butane around 3.4 µm

Ethane

As already mentioned, the C-H stretching bands produce a strong absorption at 3.2-3.5 µm, this is why any compound containing one or several C-H bounds can potentially contribute to the observed 3.4 µm absorption. In this context, ethane, quantitatively the main product of Titan's photochemistry (Lavvas et al., 2008a,b;[START_REF] Krasnopolsky | Chemical composition of Titan's atmosphere and ionosphere: Observations and the photochemical model[END_REF], should be the object of our first intentions. The presence of ethane in the Titan's atmosphere is firmly established by previous observations, e.g. it has been detected by Cassini's instruments: UVIS [START_REF] Koskinen | The mesosphere and lower thermosphere of Titan revealed by Cassini/UVIS stellar occultations[END_REF], INMS [START_REF] Cui | Analysis of Titan's neutral upper atmosphere from Cassini Ion Neutral Mass Spectrometer measurements[END_REF] and CIRS [START_REF] Vinatier | Analysis of Cassini/CIRS limb spectra of Titan acquired during the nominal mission. I. Hydrocarbons, nitriles and CO 2 vertical mixing ratio profiles[END_REF]. Unfortunately, in HITRAN and GEISA databases,

Propane

According to photochemical models (Lavvas et al., 2008a,b;[START_REF] Krasnopolsky | Chemical composition of Titan's atmosphere and ionosphere: Observations and the photochemical model[END_REF], propane should also be produced in Titan's upper-atmosphere. This C 3 hydrocarbon has been detected by several Cassini's instruments: approximately one order of magnitude less abundant than ethane. In fact, due to its larger numbers of C-H, propane is an absorber roughly one order of magnitude more efficient than ethane.

Butane

Butane has not yet been detected, in the atmosphere of Titan. The presence of butane is predicted by photochemical models [START_REF] Krasnopolsky | A photochemical model of Titan's atmosphere and ionosphere[END_REF][START_REF] Krasnopolsky | The photochemical model of Titan's atmosphere and ionosphere: A version without hydrodynamic escape[END_REF][START_REF] Krasnopolsky | Chemical composition of Titan's atmosphere and ionosphere: Observations and the photochemical model[END_REF]

Conclusion about ethane, propane, butane and others linear hydrocarbon

We have summarized our simulations results in Fig. 7, clearly the addition of propane to our set of considered gaseous species reduced the disagreement between theoretical output and solar occultation data. However, the situation is far from satisfactory, and there is room for other efficient absorbers around 3.4 microns. It is likely that other larger linear hydrocarbons are present in the atmosphere, but they are not yet retrievable from the occultation data. Moreover, their molar fractions could be very small in comparaison with the molar fraction of butane. Thus, no additional linear hydrocarbon larger than butane was considered in our model.

The absorption due to Polycyclic Aromatic Hydrocarbons and

Hydrogenated Amorphous Carbons

As mentioned in the introduction, PAHs or more complex polyaromatic hydrocarbons like HACs [START_REF] Dartois | Diffuse interstellar medium organic polymers[END_REF][START_REF] Dartois | Ultraviolet photoproduction of ISM dust. Laboratory characterisation and astrophysical relevance[END_REF][START_REF] Dartois | IRAS 08572+ 3915: constraining the aromatic versus aliphatic content of interstellar HACs[END_REF], considered as organic compounds in solid state, are detected in the ISM [START_REF] Sandford | The interstellar C-H stretching band near 3.4 microns -Constraints on the composition of organic material in the diffuse interstellar medium[END_REF][START_REF] Pendleton | The Organic Refractory Material in the Diffuse Interstellar Medium: Mid-Infrared Spectroscopic Constraints[END_REF]. For instance in [START_REF] Dartois | Diffuse interstellar medium organic polymers[END_REF] the features observed in the ISM spectra fitted very well with those observed in spectra of HACs produced in laboratory [START_REF] Dartois | Diffuse interstellar medium organic polymers[END_REF][START_REF] Dartois | Ultraviolet photoproduction of ISM dust. Laboratory characterisation and astrophysical relevance[END_REF]. Furthermore, PAHs are detected on the Iapetus' and Phoebe's surface [START_REF] Cruikshank | Hydrocarbons on Saturn's satellites Iapetus and Phoebe[END_REF], in micro-meteorites in Antarctic (Becker et al., 1997) and in the meteorite Allende [START_REF] Becker | Fullerenes, fulleranes and PAHs in the Allende meteorite[END_REF]. Observations of comets reveal the presence of PAHs (Li, 2009) and in addition they were considered in Titan's upper atmosphere to explain an unidentified emission at 3.3 µm [START_REF] Dinelli | An unidentified emission in Titan's upper atmosphere[END_REF][START_REF] López-Puertas | Large Abundances of Polycyclic Aromatic Hydrocarbons in Titan's Upper Atmosphere[END_REF]. According to [START_REF] Bellucci | Titan solar occultation observed by Cassini/VIMS: Gas absorption and constraints on aerosol composition[END_REF] for Titan's atmosphere and [START_REF] Dartois | Diffuse interstellar medium organic polymers[END_REF][START_REF] Dartois | Ultraviolet photoproduction of ISM dust. Laboratory characterisation and astrophysical relevance[END_REF][START_REF] Dartois | IRAS 08572+ 3915: constraining the aromatic versus aliphatic content of interstellar HACs[END_REF]; [START_REF] Sandford | The interstellar C-H stretching band near 3.4 microns -Constraints on the composition of organic material in the diffuse interstellar medium[END_REF]; [START_REF] Pendleton | The Organic Refractory Material in the Diffuse Interstellar Medium: Mid-Infrared Spectroscopic Constraints[END_REF] for the ISM, the features observed between 3.38 µm and 3.48 µm are due to the symmetric and asymmetric stretching of the C-H bond in -CH 2 and -CH 3 groups of the aliphatic chains.

Likewise the features around 3.3 µm are signatures of stretching of aromatic C-H bond [START_REF] Bellucci | Titan solar occultation observed by Cassini/VIMS: Gas absorption and constraints on aerosol composition[END_REF][START_REF] Dartois | Diffuse interstellar medium organic polymers[END_REF][START_REF] Dartois | Ultraviolet photoproduction of ISM dust. Laboratory characterisation and astrophysical relevance[END_REF][START_REF] Dartois | IRAS 08572+ 3915: constraining the aromatic versus aliphatic content of interstellar HACs[END_REF]. These latter signatures emphasize the presence of aromatic compounds like PAHs and the signatures at 3.38 µm and 3.48 µm together with the signatures of aromatic C-H stretching show the presence of complex particles containing aromatic cycles and aliphatic chains as it would expect in HACs. In [START_REF] Dartois | Ultraviolet photoproduction of ISM dust. Laboratory characterisation and astrophysical relevance[END_REF], possible structures of HACs compatible with the ISM spectra were simulated with a neuronal network simulation: The resulting structure shows aromatic cycles and aliphatic chains as expected.

Thus, to clarify the observed transmission in the 3.3 -3.5 µm spectral region we considered PAHs and HACs compounds in our model.

21

J o u r n a l P r e -p r o o f

Polycyclic Aromatic Hydrocarbons

The information on PAHs's transition intensities come from the NASA Ames PAHs IR Spectroscopic Database 8 . In our calculations the line widths were fixed to a reasonable value of 30 cm -1 . This value is approximatively comparable to the different values used for HACs [START_REF] Dartois | IRAS 08572+ 3915: constraining the aromatic versus aliphatic content of interstellar HACs[END_REF]. we introduce a correction factor α i,k for the intensities I i,k , with the same meaning for index i and k than the index in Eq. ( 4), to account for two sources of uncertainty : (1) the temperature dependence of the intensities I i,k , (2) the uncertainties on the I i,k 's themselves. Indeed, the spectral data provided by the Ames Database are valid for a temperature of 296 K while the actual temperature in Titan's stratosphere is substantially lower (see for instance Fig. 2a). In the spectral window of interest (i.e. 2700 cm -1 -3570 cm -1 ), for the 716 species reported in the Ames database, we counted a total of 11, 307 calculated spectral lines against only 127 coming from an experimental determination. Even if some overlaps are present, we see that the majority of available spectral data are calculated theoretically. This rises the question of the degree of confidence that can be placed in these computed data. In this context, we have searched for theoretical and experimental spectral lines that coincide in terms of wavelength, adopting a given tolerance, respectively: 1 cm -1 , 2 cm -1 and 3 cm -1 . This way, we identified 52 lines that correspond to both theoretical and laboratory determinations with a tolerance of 1 cm -1 , 108 when is increased to 2 cm -1 and 144 when the tolerance is increased to 3 cm -1 . Consequently, we formed the log ratio I th /I exp for each identified tend to be underestimated, compared to their experimental counterparts, by a factor up to two orders of magnitude. Then, these results motivated our introduction of a factor α i,k that represents the uncertainties that affect the spectral lines intensities available in the Ames database. In this manner, the intensity I i,k in Eq. ( 5) is replaced by the product α i,k I i,k . Finally, if we combine Eq. ( 4) with Eq. ( 5), the product β i,j,k = x i,j α i,k , with the same meaning for index j than the index in Eq. ( 4), appears in the expression of the transmission. In first approach, we considered that the correction factors α i,k are independent of the spectral lines. Therefore, β i,j,k = x i,j α i,k becomes β i,j = x i,j α i . We took 118 neutral and charged PAHs in the Ames database. We have chosen PAHs with less than 100 carbon atoms, free of Fe, Mg, Si (not relevant for Titan's atmosphere) and for which the intensities are significant in the 3.3 -3.5 µm band.

Hydrogenated Amorphous Carbons

The HACs (sometimes noted a-C:H or a-C:H:N if the HACs contain nitrogen), are considered as smallest haze particle and precursor of more complex Journal Pre-proof spectrum parameters given in Table 1 of [START_REF] Dartois | IRAS 08572+ 3915: constraining the aromatic versus aliphatic content of interstellar HACs[END_REF]. We do not consider HACs with nitrogen (a-C:H:N) because the vibrational modes containing N are not present in 3.3 -3.5 µm band [START_REF] Dartois | Ultraviolet photoproduction of ISM dust. Laboratory characterisation and astrophysical relevance[END_REF]. As

with PAHs, we also introduce a correction factor α i,k on the intensities I i,k , with the same meaning for index i and k than the index in Eq. ( 4), taking into account for an uncertainty source: the temperature dependence of the intensities I i,k . Indeed, the intensities coming from the study of IRAS 08572+3915 spectrum the temperature must be different than that in Titan's stratosphere. In [START_REF] Dartois | IRAS 08572+ 3915: constraining the aromatic versus aliphatic content of interstellar HACs[END_REF] no distinction was made between the different HACs but just between the vibration modes. Consequently, in our model for HACs we omit index i. Thus, our correction factor α i,k becomes α k and the intensities are I k . In first approach, as with PAHs, the correction factors α k are independent of the spectral lines. Consequently, we define a product β j = x j α.

Results

For PAHs, x i,j is the molar fraction of PAHs number i with respect to the C 6 H 6 abundance profile in layer j. As a first approximation, the vertical profile of this molar fraction of PAHs number i vs the C 6 H 6 (used as proxy)

abundance and the vertical profile of the molar fraction of HACs were kept constant. Thus for PAHs and HACs respectively, β i,j = x i,j α i turns into with the Titan's 3.4 µm band spectra. But these differences could be due to a lower amount of nitrogen compounds in Saturn's atmosphere [START_REF] Bellucci | Titan solar occultation observed by Cassini/VIMS: Gas absorption and constraints on aerosol composition[END_REF]. Thus, the PAHs and HACs in Titan's atmosphere could be slightly different from those in Saturn's atmosphere.

β i = x i α i
Our study of 3.4 µm band observed by solar occultation at 145 km of altitude suggests the presence of aromatic molecules like PAHs and more complex like HACs at low altitudes. Some insights can be gained by examining the results from laboratory experiments. [START_REF] Dartois | Diffuse interstellar medium organic polymers[END_REF][START_REF] Dartois | Ultraviolet photoproduction of ISM dust. Laboratory characterisation and astrophysical relevance[END_REF] synthesized HACs (called a-C:H in these references) by ultraviolet photolysis of methane [START_REF] Dartois | Diffuse interstellar medium organic polymers[END_REF] and other hydrocarbons and nitrogen compounds to form a-C:H:N compounds [START_REF] Dartois | Ultraviolet photoproduction of ISM dust. Laboratory characterisation and astrophysical relevance[END_REF] by UV radiation with wavelengths shorter than 120 nm in the EUV domain. Then, they made spectral Infra-Red (IR) analysis of the residues. The aim of these previous studies was to explain the spectral features observed in the ISM. Due to the presence of methane, others hydrocarbons and nitrogen compounds as well as the ultraviolet radiation in EUV domain going down to 600 km (Yoon et al., 2014), the same HACs production process as in the ISM could occur in the Titan's upper atmosphere. But this explanation is not completely satisfactory, mainly because we should find absorptions in the wavelength range 3.38 µm-3.48 µm in high altitude occultation spectra which is not the case [START_REF] Courtin | Three-micron extinction of the Titan haze in the 250-700 km altitude range: Possible evidence of a particleaging process[END_REF]. In this latter reference, the authors do not observe strong features (in extinction) in this wavelength range above 500 km but rather below 480 km (Courtin et al., 2015, Fig. 2). The authors computed the ratio extinction coefficient at 3.33 µm / extinction coefficient at 3.38 µm, the wavelength at 3.33 µm being characteristic of aromatic C-H stretching and the wavelength at 3.38 µm characteristic of aliphatic C-H stretching. Thus, this ratio is function of the ratio between the aromatic and aliphatic components in the haze particles.

This ratio is about 3 at 700 km and decreases to about 0.5 below 300 km.

Then the conclusion of [START_REF] Courtin | Three-micron extinction of the Titan haze in the 250-700 km altitude range: Possible evidence of a particleaging process[END_REF] is a growth of molecules from PAHs to more complex organics by particle-aging and coating process when the altitude decreases. So, even if the explanation in [START_REF] Dartois | Diffuse interstellar medium organic polymers[END_REF][START_REF] Dartois | Ultraviolet photoproduction of ISM dust. Laboratory characterisation and astrophysical relevance[END_REF] about the HACs production in the ISM is not completely relevant for Titan's upper atmosphere, it is possible to have HACs at low altitude, by particle-aging and coating process. This process was also studied in laboratory [START_REF] Carrasco | The evolution of Titan's high-altitude aerosols under ultraviolet irradiation[END_REF] Other studies were conducted [START_REF] Gudipati | Photochemical activity of Titans low-altitude condensed haze[END_REF]Yoon et al., 2014).

In

Conclusion

To conclude, the present study was to explain the strong absorption around 3.4 µm observed in the occultation spectra by VIMS at low altitudes typically lower than 450 km. We opted for the altitude 145 km which offers a good compromise : at lower altitudes, the stronger absorptions damp spectral features and at higher altitudes, the absorptions are too weak to be extracted from the signal. As a first step in our radiative transfer modeling, we have altitudes. This result is also consistent with several laboratory studies showing a complexification of hydrogenated molecules from small hydrocarbons to more complex by UV irradiations (Yoon et al., 2014;[START_REF] Couturier-Tamburelli | Simulation of Titan's atmospheric photochemistry. Formation of non-volatile residue from polar nitrile ices[END_REF], 2018;[START_REF] Carrasco | The evolution of Titan's high-altitude aerosols under ultraviolet irradiation[END_REF].

JFigure 1 :

 1 Figure 1: Transmittance curves derived from solar occultations T10E, T53E, T78E and T78I studied by Maltagliati et al. (2015). Altitude interpolations, at 145 km, have been performed to allow easy comparisons. Boxes delineate domains where data are significantly noisy.

Figure 2 :

 2 Figure 2: Panels (a) and (b) stand respectively for the temperature and pressure profiles,

  2.d), then, in the conditions of pressure and temperature in the Titan's stratosphere, according to the present model, C 2 H 6 can never form solid particles. For the other species, even if ∆ 2,i < 0, the measured or estimated values of their mole fractions are order of magnitude too small for Eq. (3) to be satisfied. For instance, concerning CH 3 CN,[START_REF] Lara | Vertical distribution of Titan's atmospheric neutral constituents[END_REF] (see their Fig. 10 p. 279) reported abundances, derived from ground-based millimeter-wave observations

  Figure3: A schematic representation of our "onion-skin" radiative tranfer model, used in this paper and suitable for the analysis of Titan's solar occultations data published by[START_REF] Maltagliati | Titan's atmosphere as observed by Cassini/VIMS solar occultations: CH 4 , CO and evidence for C 2 H 6 absorption[END_REF]. In the text, the term altitude refers to the parameter called "z" in this figure. After tests with different numbers of layers, a total number N layers = 70 of atmospheric layers was found sufficient to describe the atmosphere. Layers have been linearly distributed between the ground and 700 km.

  6 H 6 and HCN. In this entire paper, we adopt this list of species as our First Guess composition (hereafter FG composition), the influence of other compounds will be made by comparing what it is obtained using this FG composition. Nitrogen is voluntarily omitted since it is extremely poor absorbant in the domain of interest. Moreover, the collision-induced effects are negligible within the band 3.3 -3.5 µm. The CH 4 , C 2 H 2 , C 2 H 4 , C 2 H 6 , C 6 H 6 and HCN vertical mixing ratio profiles come from photochemical models developed by[START_REF] Krasnopolsky | Chemical composition of Titan's atmosphere and ionosphere: Observations and the photochemical model[END_REF]. The abundance of deuterated 12 J o u r n a l P r e -p r o o f Journal Pre-proof methane (CH 3 D) with respect to the methane has been kept constant with a CH 3 D/CH 4 ratio of about 5.3 × 10 -4[START_REF] Bézard | Detection of 13 CH 3 D on Titan[END_REF]. Concerning water, we performed tests including molar fractions corresponding to the highest value given by[START_REF] Coustenis | Evidence for water vapor in Titan's atmosphere from ISO/SWS data[END_REF]. Finally, the abundance of CO has been taken from[START_REF] Flasar | Titan's Atmospheric Temperatures, Winds, and Composition[END_REF].

Figure 4 :

 4 Figure 4: Comparison between observed transmittance (dashed line) acquired during occultation T78I at the altitude of 145 km (Maltagliati et al., 2015), and the computed transmittance due to our FG composition: with only CH 4 , CH 3 D, CO, C 2 H 2 , C 2 H 4 , C 2 H 6 , H 2 O, C 6 H 6 and HCN. For C 2 H 6 , only spectral lines provided by HITRAN have been taken into account.

3

  http://theorets.tsu.ru 4 https://pds-rings.seti.org/cassini/vims/ 14 J o u r n a l P r e -p r o o f Journal Pre-proof high altitudes data for which the transmittance curves are pretty flat, and low altitudes measurements presenting a global strong absorption that masks or damps spectral features.

  ethane spectral lines in the band of interest are pretty scarce. Surprisingly, the absorption spectrum of the C-H stretching region of ethane, measured by Pine & Lafferty (1982) (hereafter PL82) at T= 119 K, is not available in these compilations. Then, we included the ∼ 3000 lines provided by PL82 data in our model; 1614 entries specify wavenumbers, intensities and the lower state energies whereas for 1426 other entries the lower state energy is 15 J o u r n a l P r e -p r o o f Journal Pre-proof not available. Thus, in the latter case, we have neglected the temperature corrections of the intensities. The contribution to the absorption around 3.4 µm, of ethane alone, is plotted in Fig. 5(a). Unfortunately, Pine & Lafferty (1982) did not include ethane PQ-branches which should have a non-negligible contribution in the domaine of interest. To tackle the issue, we used an empirical pseudo-line list based on the crosssection measurements developed by Harrison et al. (2010) (hereafter H10 dataset) and freely available on the web 5 . Compared to the absorption obtained with PL82 spectral lines, the effect of ethane is significantly enhanced by the use of this more comprehensive list (Fig. 5.b). If both, the PL82 and H10 spectral data, are simultaneously included in our model (Fig. 5.c),the actual effect of PL82 is not noticeable. Finally, if we merge PL82 and H10 spectral lines sets, with those employed for our FG composition model, the disagreement with Cassini/VIMS observations is considerably reduced(Fig. 5.d). This clearly demonstrates the prominent role of ethane, as an absorber, at wavelengths around 3.4 µm. Nonetheless, the simulated transmittance remains significantly above the observed one. This fact suggests the presence of other absorbers, possibility which we discuss further in next paragraphs.

5Figure 5 :

 5 Figure 5: Comparison between simulated transmittances and VIMS for the T78I occultation data (Maltagliati et al., 2015). Observational data are in dashed line, the altitude is 145 km. This figure shows the transmittance of C 2 H 6 using: (a) only Pine & Lafferty (1982) spectral lines (red), (b) only pseudo-lines lists based on the cross-section measurements (Harrison et al., 2010) (red), (c) the combination of PL82 and H10 spectral data (red), (d) the combination of our FG composition model with PL82 and H10 (blue), the absorption computed with our FG composition is also plotted for comparison (green solid line).

  17

Figure 6 :JFigure 7 :

 67 Figure 6: Occultation T78I at 145 km (observed transmittance in dash line) : (a) Absorption due to propane alone, (b) computed absorption using our FG composition complemented by propane (ethane is not taken into account).

8

  http://www.astrochem.org/pahdb/ 22 J o u r n a l P r e -p r o o f Journal Pre-proof couple of lines, with I th the theoretical intensity and I exp the corresponding laboratory measurement. The histograms of log ratio I th /I exp values is plotted in Fig. 8. This figure shows clearly that the theoretical intensities

  haze particle (called tholins)[START_REF] Lavvas | Surface chemistry and particle shape: Processes for the evolution of aerosol in Titan's atmosphere[END_REF]) (and p. 304 of Müller- Wodarg et al. (2014)). In[START_REF] Dartois | Diffuse interstellar medium organic polymers[END_REF][START_REF] Dartois | Ultraviolet photoproduction of ISM dust. Laboratory characterisation and astrophysical relevance[END_REF][START_REF] Dartois | IRAS 08572+ 3915: constraining the aromatic versus aliphatic content of interstellar HACs[END_REF] no identified structure was given but just different vibration modes together with their vibrational frequencies or wavelengths. Analyzing the spectrum of the galaxy named IRAS 08572+3915, Dartois et al. (2007) fitted the intensities, wavelengths and widths of the lines for these vibration modes. Then, we use 23 J o u r n a l P r e -p r o o f

Figure 8 :Figure 9 :

 89 Fig.9shows that the combination of all gases, plus the 118 PAHs and HACs allow a satisfactory modelization of the observed transmittance at 145 km.

  by ultraviolet irradiation of analogs of Titan's thermosphere aerosols (and Couturier-Tamburelli et al. (2018)). Carrasco et al. (2018) analyzed the absorption peaks of residues and their time evolution. They found shifts and modifications of vibrational signatures reflecting aerosols transformation during the irradiation. The observed spectra after 24 h of irradiation appear to tend toward Titan's spectra observed in VIMS spectra at altitude 200 km. The conclusion of Carrasco et al. (2018) is that a particle aging process by ultraviolet irradiation occurs in Titan's atmosphere 28 J o u r n a l P r e -p r o o f from aerosol embryos in thermosphere to more complex haze particles in low altitudes according the following process : (1) aerosol embryos generation, (2) sedimentation and (3) chemical evolution by UV irradiation.

  photolysis in the lower atmosphere. Then this photolysis would lead to the production of PAHs and more complex particles. In the same way, Gudipati et al. (2013); Couturier-Tamburelli et al. (2014) proceeded to photochemical experiments with C 4 N 2 ice and photons in FUV domain, reproducing the environment of Titan's lower atmosphere and highlighting the fact that at low altitudes (below 200 km) the UV flux at 350 nm is comparable to the upper radiation field at shorter wavelengths. Their conclusion is that photoabsorption by haze particles in this FUV domain would trigger a rich solid-state chemistry at low altitudes. In a similar way photolysis of HC 5 N led to residues containing aromatic signatures around 3.3 µm and C-H stretching around 3.4 µm (Couturier-Tamburelli et al., 2015). The authors concluded that this photolysis drives the formation of more and more complex polymers which are precursors of haze particles. These results about the PAHs and HACs production at low altitudes are in agreement with our spectral analysis of the 3.4 µm band for the occultation at 145 km of altitude. Finally, NASA has recently announced the selection of the Dragonfly

  included 9 molecules following[START_REF] Maltagliati | Titan's atmosphere as observed by Cassini/VIMS solar occultations: CH 4 , CO and evidence for C 2 H 6 absorption[END_REF] : CH 4 , CH 3 D, CO, C 2 H 2 , C 2 H 4 , C 2 H 6 , H 2 O, C 6 H 6 and HCN. This composition leads to a poor reproduction of the observed transmittance curve. The disagreement was reduced by including C 2 H 6 spectroscopic data as the data coming from[START_REF] Pine | Torsional Splittings and Assignments of the Doppler-Limited Spectrum of Ethane in the C-H Stretching Region[END_REF] or the more exhaustive data, but empirical pseudo-line, coming fromHarrison et al. (2010). This way, the agreement has been improved, but the simulated transmittance remained above the observed one. The inclusion of propane improved the result but there was still a lack of efficient absorbers around 3.4 µm. Knowing that spectral signatures around 3.4 µm are present in the ISM and identified as PAHs or HACs, we have considered these complex hydrocarbon compounds in our model as possible absorbers in the Titan's atmosphere at about 145 km of altitude. The fit of abundance of PAHs and HACs, taking into account some uncertainty by means of a 30 J o u r n a l P r e -p r o o f Journal Pre-proof correction factor, allowed a rather satisfactory modelization of the observed transmittance at 145 km of altitude. Thus, the model suggests the presence of complex hydrocarbon compounds and precursors of haze particles at low

  . The quantity of butane should be lower than what it is measured

	and GEISA databases, we used cross-sections provided by the NIST 7 . Ac-
	and computed for propane. Available models indicate a butane mixing ratio about four order of magnitude smaller than what Krasnopolsky (2014) ob-cording to this approach and taking vertical profile provided by Krasnopolsky (2014), we have checked that butane has no detectable influence on the 3.4 J o u r n a l P r e -p r o o f µm atmospheric transmittance.
	tained for propane. Since no data concerning butane were found in HITRAN
	19

http://webbook.nist.gov 20 J o u r n a l P r e -p r o o f

Acknowledgement

We thank Laurence Regalia, Bruno Bézard, Walter Lafferty and Jean Vander Auvera for scientific discussion. We are grateful to Christiaan Boersma for his kind technical help in using the NASA Ames PAH database. Finally, we warmly thank Vladimir Krasnopolsky for providing us with vertical profiles of organics.

40

J o u r n a l P r e -p r o o f


Sébastien Lalanne
email: sebastien.lalanne@chu-rennes.fr

Caroline Jézéquel

Camille Tron

Marie-Clémence Verdier

Marion Mercerolle

Charlotte Pronier

Dominique Guyader

Florian Lemaitre

TDM-guided Crushed Sofosbuvir-velpatasvir Treatment: A case study

Keywords: Sofosbuvir, velpatasvir, crushing, pharmacokinetics, exposure

Herein, the authors report the case of a patient diagnosed with hepatitis C virus who was treated with sofosbuvir-velpatasvir (400/100 mg). As the patient was unable to swallow whole tablets, therapeutic drug monitoring was performed to evaluate the effect of crushing sofosbuvir-velpatasvir tablets on drug absorption and global exposure.

CLINICIAN

The patient was a 70-year-old woman with a history of rectal cancer in 2009 and a right oropharyngectomy owing to carcinoma in 2016. She had been a heavy smoker with excessive alcohol intake for several years. A CT-scan performed in February 2019 as part of the oropharyngeal carcinoma follow-up revealed 2 liver tumors (20 mm each) in the right lobe of the liver. Liver enzymes were moderately increased: aspartate aminotransferase (AST) = 87 IU/L (N < 31); alanine aminotransferase (ALT) = 67 IU/L (N < 34); γ-glutamyltransferase (GGT) = 152 IU/L (N < 38). Albumin (42 g/L), total bilirubin (6 µmol/L), and prothrombin index were normal. Alpha-fetoprotein was dramatically increased up to 14,207 g/L (N < 10), and the biopsy of the tumor and non-tumorous liver confirmed the diagnosis of bifocal hepatocellular carcinoma (HCC) developed on a non-cirrhotic METAVIR F3 fibrotic liver. [1] Hepatitis B and human immunodeficiency virus serology were negative. Hepatitis C virus (HCV) serology was positive, and active replication was confirmed by HCV RNA detection with a high viral load of 6.8 log IU/mL and genotype 1b virus infection. She underwent satisfactory surgical resection of the HCC tumors in May 2019.

A C C E P T E D

The multidisciplinary team evaluating the HCV cases in the institution proposed a treatment with a direct-acting antiviral (DAA) agent comprising glecaprevir and pibrentasvir (Maviret, AbbVie) [2] for 8 weeks. This combination was selected for its high efficacy and short treatment duration. However, owing to previous oropharyngectomy, the patient was not able to swallow tablets.

TDM CONSULTANT

Glecaprevir-pibrentasvir is a fixed-dose combination tablet indicated in the treatment of HCV with a pangenotypic activity at the dosage of 300/120 mg per day (3 tablets of 100/40 mg simultaneously). The drug is a combination of a NS5A (a protein responsible for regulation of the viral replicative complex and involved in assembly and release of viral particles) inhibitor (pibrentasvir) and a NS3/4A protease inhibitor (glecaprevir), which, as clearly stated in the summary of product characteristics (SmPC), should be taken with food and should not be chewed or crushed. The drug is formulated as a bilayer tablet; therefore, crushing can lead to unintended variations in bioavailability with a decrease in area under the curve (AUC) of 27-61% for glecaprevir and an increase in AUC of 21-83% for pibrentasvir compared to the exposure from whole tablets.[2,3] No other formulation such as an oral solution or dispersible tablet is available; therefore, the drug cannot be given to the patient. However, no clear recommendation is available for sofosbuvir-velpatasvir (Epclusa), an RNA-dependent RNA polymerase NS5B and NS5A inhibitor with pangenotypic anti-HCV activity. Indeed, SmPC does not recommend crushing these tablets because of their bitter taste, but there is a lack of information about the effect of crushing on sofosbuvir-velpatasvir pharmacokinetics. Velpatasvir is also highly sensitive to the acidic stomach environment, as underlined by the decrease in drug exposure ranging from 26% to 60% when given with

A C C E P T E D

omeprazole,[4-6] and influenced by food with an increase in AUC of 20% to 30% with a high and moderate fat meal, respectively. [START_REF]Epclusa® Summary of product characteristics[END_REF] Moreover, taking the drug with an acidic beverage may enhance velpatasvir absorption. [5] We then suggested administering crushed sofosbuvirvelpatasvir with an acidic beverage during a meal and conducting therapeutic drug monitoring (TDM) of sofosbuvir and velpatasvir by monitoring peak on the first day and global exposure of the drugs by measuring steady-state trough plasma drug concentrations (C ss ).

CLINICIAN

Sofosbuvir-velpatasvir treatment for 12 weeks was approved by the multidisciplinary team, according to French and European guidelines for the management of patients with acute and chronic HCV infections. [START_REF] Liver | EASL recommendations on treatment of hepatitis C 2018[END_REF][START_REF]Association française pour l'étude du foie (AFEF). Recommendations on treatment of hepatitis C[END_REF] In addition, TDM was planned to assess the absorption of the drugs. Blood samples were collected on the first day of treatment before DAA administration (trough concentration (C min ) and 2 (C2), 3 (C3), and 4 (C4) hours after the first DAA administration. Additional trough blood samples measured at steady-state (Css) were collected 1 week and 10 weeks after commencement of treatment.

TDM CONSULTANT

Sofosbuvir and velpatasvir peak (C max ) and Css are well documented, with sofosbuvir having a C max of 511 ± 174 ng/mL [START_REF]Sovaldi® Summary of product characteristics[END_REF] and a rapid elimination (half-life elimination: 30 min), leading to a trough concentration generally below the limit of quantification of the analytical method, and velpatasvir having C max and Css of 575 ± 213 and 42 ± 28 ng/mL respectively. [START_REF]Epclusa® Summary of product characteristics[END_REF][START_REF] Mogalian | Preclinical pharmacokinetics and first-inhuman pharmacokinetics, safety, and tolerability of velpatasvir, a pangenotypic hepatitis C virus NS5A inhibitor, in healthy subjects[END_REF] Therefore, these parameters could be easily compared to the value measured in the patient. Drug levels were determined using a liquid chromatography-tandem

A C C E P T E D

mass spectrometry method validated according to the European Medicines Agency guidelines. [START_REF]Guideline on bioanalytical method validation[END_REF] C min , C2, C3, and C4 for sofosbuvir were <20, 1,544, 1,497, and 642 ng/mL, respectively, while for velpatasvir, these were <20, 285, 966, and 1,244 ng/mL, respectively. C ss at day 7 and week 10 were <20 ng/mL for sofosbuvir and 116 and 107 ng/mL for velpatasvir.

The time to reach maximal concentration (t max ) was 1 and 3 h for sofosbuvir and velpatasvir respectively. [START_REF]Epclusa® Summary of product characteristics[END_REF][START_REF] Mogalian | Preclinical pharmacokinetics and first-inhuman pharmacokinetics, safety, and tolerability of velpatasvir, a pangenotypic hepatitis C virus NS5A inhibitor, in healthy subjects[END_REF][START_REF] Brieva | Pharmacokinetic drug evaluation of velpatasvir plus sofosbuvir for the treatment of hepatitis C virus infection[END_REF] The results of sofosbuvir and velpatasvir TDM were consistent with an increase in the absorption of both drugs in this patient after crushing the tablet. Sofosbuvir is rapidly metabolized, and its C ss values were consistent with its pharmacokinetic parameters. [START_REF] German | Clinical pharmacokinetics and pharmacodynamics of ledipasvir/sofosbuvir, a fixed-dose combination tablet for the treatment of hepatitis C[END_REF] More importantly, velpatasvir C ss values were in favor of a correct exposure to the drug (C ss range 14-70 ng/mL; mean reported concentration ± standard deviation). [START_REF] Mogalian | Preclinical pharmacokinetics and first-inhuman pharmacokinetics, safety, and tolerability of velpatasvir, a pangenotypic hepatitis C virus NS5A inhibitor, in healthy subjects[END_REF]

CLINICIAN

The drugs seemed to be very well resorbed. When compared with usual C max , their concentrations were in favor of an increase in sofosbuvir and velpatasvir absorption when crushed. Velpatasvir C ss measurements appeared to be related to a high drug exposure without any accumulation of the compound as confirmed by the very similar C ss reported at week 1 and week 10. After completion of sofosbuvir-velpatasvir combination treatment, the patient reported no treatment-related adverse events. Liver parameters improved: AST, 13 IU/L; ALT, 30 IU/L; GGT, 20 IU/L; total bilirubin, 6 µmol/L; and albumin, 47 g/L. HCV viral load decreased rapidly, became undetectable after 4 weeks of treatment, and remained undetectable after 12 weeks of treatment.

A C C E P T E D TDM CONSULTANT

In conclusion, this report describes the first case of a successful HCV treatment in a treatment-naïve patient by using crushed sofosbuvir-velpatasvir tablets. TDM showed that, when taken with food and an acidic beverage, the absorption of both drugs increased. As velpatasvir is a low solubility drug, particularly in gastric pH above 4.5, crushing the tablet may enhance the drug solubility. TDM of velpatasvir trough C ss also allowed the verification of treatment exposure during the treatment period, thereby ensuring its efficacy.

Reference List

[1] Bedossa P, Poynard T. An algorithm for the grading of activity in chronic hepatitis C.

The METAVIR Cooperative Study Group. Hepatology 1996;24:289-293.

[2] European Medicines Agency. Maviret®Summary of product characteristics, https://www.ema.europa.eu/en/documents/product-information/maviret-epar-product-information_en.pdf (accessed August 8, 2019).

[3] Oberoi RK, Zhao W, Sidhu DS, et al. A phase 1 study to evaluate the effect of crushing, cutting into half, or grinding of glecaprevir/pibrentasvir tablets on exposures in healthy subjects. J Pharm Sci. 2018;107:1724-1730.

[ 4 ]

 4 Mogalian E, McNally J, Shen G, et al. Drug-drug interaction profile of sofosbuvir/velpatasvir fixed-dose combination. J Hepatol. 2016;64:S613-S614. [5] van Seyen M, Colbers A, Abbink EJ, et al. Concomitant intake of Coca-Cola® to manage the drug-drug interaction between velpatasvir and omeprazole studied in


D Tournier

Ph Godignon

J Montserrat

D Planson

J P Chante

F Sarrus

Simulation study of a novel current limiting device : a vertical a-SiC JFET -Controlled Current Limiter

Keywords: Current limiter, JFET, serial protection device, high voltage

. Although Current Regulative Diode components exist [2, 3], the voltage and current capabilities (VBR=100 V, Imax=10 mA), do not allow to use them in power systems. A comparison of a silicon Current Regulative Diode (CRD) and an equivalent SiC one demonstrates the thermal and electrical limitations of silicon. This paper deals with a novel bi-directional current limiter structure based on a vertical a-SiC VJFET, with both buried gate and source. This device was designed for short circuit protections. Simulations were performed with ISE-TCAD [4] to evaluate static and transient electrical characteristics of the VJFET, according to several specifications : voltage capability, current rating, time during which the device can sustain a short circuit. Simulations allow geometrical design and doping profile estimation as well as the technological process to realize such a component. Both 6H and 4H-SiC Controlled Current Limiter (CCL) have been realized. Electrical characterizations of fabricated devices underline the limiting effect and the command ability.

INTRODUCTION

Silicon carbide, thru its electrical properties allows to foresee the realization of new power components with higher capabilities than silicon. Its band-gap energy (Eg=3eV@300K) and its high critical electric field (Ec = 2×10 6 V/cm) allow to make components such as diode with reverse voltage capability up to 6,2 kV [START_REF] Sugawara | 6.2 kV 4H-SiC PiN Diode with low forward voltage drop[END_REF]. Moreover its thermal conductivity ( l = 4,9 W×cm -1 ×K -1 ) allows components to work with high current density and under high temperature. Most of silicon components have been realized in SiC and show good electrical and thermal characteristics like Schottky diode [START_REF]Cree research 99[END_REF], MOSFET [START_REF] Schröner | Rugged Power MOSFET in 6H-SiC with blocking capability up to 1800V[END_REF], MESFET… As in steady state, the voltage drop across the component must be as low as possible, in the active state, (limiting phase), a current limiter must sustain a high current, under high voltage bias. The resulting high power density must not cause the failure of the component. Silicon carbide authorize to work at high temperature and high voltage and is a good candidate for the design of a new current limiter for high voltage and high current.

CURRENT LIMITATION : COMPARISON OF Si AND 6H-SiC CRD as DEVICES

Current Regulative Diode : Structure Description.

(CRD) [START_REF]Current limiter circuit[END_REF] are currently used to limit current in low power applications. The current limitation is based on field effect. A cross section of the simulated device is presented in Fig. 1 . When applying a positive voltage on the cathode, the extension of space charge in the preformed channel region (6) will cause the current saturation.

CRD : Simulations and Comparison Between Si / SiC.

Simulation comparison of Si and 6H-SiC CRD like components were performed with ISE-tcad software to estimate the potentiality of this kind of device to realize a high voltage and high current CCL. The figure 2 shows the electrical characteristics comparison of the simulated silicon device and the equivalent silicon carbide one.

Conclusion :

Considering the self heating of the CRD silicon device, thermal limitation induces low voltage capabilities. For the same specific resistance, limitations appear : the avalanche breakdown voltage (VBR = 120 V), and thermal limitation of silicon (T = 480 °K). For the SiC device, good electrical characteristics could be envisaged (with high breakdown voltage value) but require difficult technology steps such as the realization of a deep p-well difficult with SiC technology. For those reasons, vertical unipolar SiC structure were investigated in order to design a component with a low specific resistance, high voltage breakdown (>1kV) and high current capability.

3. a-SiC VJFET Controlled Current Limiter.

1 Structure description.

Several current limiters have been recently presented, based on vertical MOSFET structure [START_REF] Schröner | Rugged Power MOSFET in 6H-SiC with blocking capability up to 1800V[END_REF]. The novelty of this device consists in the design of the gate, which is formed by a buried layer. The figure 3 shows the cross section of the a-SiC VJFET. This device presents a channel divided in two parts : a vertical one and a surface one. When the drain voltage rises, the current saturates at a voltage corresponding to the pinch off of the vertical and horizontal channels. In saturation mode, the device presents an important on resistance (RON), resulting from the serial resistance of both parts of the channel and the drift resistance of the epitaxial layer. In saturation mode, as the voltage VDS rises, the extension of the space charge in the epitaxial layer leads to a modification of the vertical

2 a-SiC VJFET : Simulations

For the simulation of the upper structure, different models are used, such as the carrier mobility and ionization coefficient models. Most of parameters were given by Ruff [START_REF] Ruff | SiC devices : Physics and Numerical Simulation[END_REF]. The P buried layers are designed in such a way that the component presents a normally on electrical behavior. Main parameters to be adjusted are presented in figure 4. Doping concentration of the epitaxial layer, were first adjusted to sustain required voltage. Then channel parameters have been investigated as presented on figure 5. Other parameters such as passivation layer effect have been investigated (fixed charge effect on the channel). The simulated specific resistance Rd in the linear mode is in the range of 150 mW×cm² @ Vf = 3V. The optimal solution for a current limiter is to find a trade off between Rd, Vbr, Vsat, Isat. The novel gate structure allows to control the current in the VJFET. When a negative bias is applied between gate and source, the PN junction formed by the Pwell and the epitaxial layer is reverse biased. Simulation results give : at a bias voltage of VDS = 40 V, a current density of 50 A/cm², a bias voltage of VGS = -42 V allows to stop the current.

Device fabrication and characterization

P wells are assumed to be realized by high energy ion implantation (2 MeV). The width of the vertical channel is determined by the implantation mask and the lateral dispersion of the implanted impurities. The implantation doses and energies are adjusted with Monte Carlo simulations [START_REF] Morvan | modélisation de l'implantation ionique dans a-SiC et application à la conception de composant de puissance[END_REF] in order to define a surface channel of an average depth of 0.5µm. Source and gate contacts are assumed to be realized by RIE etching, stopped into P buried layers. The epitaxial layer is determined to sustain a VBR reverse voltage of 1750V. The figure 7 presents the measured electrical characteristics for an unidirectional and a bidirectional device. Unidirectional measurements were done with 0,5s pulse (f = 2Hz), with drain bias up to 400 V. The specific resistance is in the range of 176 mW×cm² up to 237 mW×cm² for matrix structures. Figure 7 highlights the power sustaining ability up to 400V.The power density dissipated in the limiting state can reach a value of 160 kW/cm². Limiting capabilities have also been measured for a bi-directional device. This one exhibits a specific resistance of 700 mW×cm² and a limitation current up to ± 400V (with no gate bias applied).

Conclusion :

This work has demonstrated the feasibility of a current limiter which could be used for serial protection in industrial applications. The design of the limiter was made using the ISE software with respect to the technological limitations. The first demonstrator measurements exhibit optimistic results, although few adaptations are necessary to reach the foreseen characteristics. Bi-directional components were measured by associating two devices head to tail. This device could be used in application such as current limitation in case of a short circuit of an electrical system. It could permit an elevation of the current ratings of classical mechanical switch with the serial addition of this device.

Fig. 1

 1 Fig. 1 Cross section of a silicon CRD.

Fig 2 .

 2 Fig 2. CRD simulated characteristics.

Fig. 5 -

 5 Fig.5-a Epitaxial layer investigation Fig.5-b Surface channel adjustment. Fig. 5 Electrical simulated characteristics

Fig. 4 .

 4 Fig. 4. VJFET parameters to be optimized.

Fig. 6

 6 Fig.6 view of fabricated device and test structures.

Fig. 7 .

 7 Fig.7. Electrical measured characteristics.Conclusion :This work has demonstrated the feasibility of a current limiter which could be used for serial protection in industrial applications. The design of the limiter was made using the ISE software with respect to the technological limitations. The first demonstrator measurements exhibit optimistic results, although few adaptations are necessary to reach the foreseen characteristics. Bi-directional components were measured by associating two devices head to tail. This device could be used in application such as current limitation in case of a short circuit of an electrical system. It could permit an elevation of the current ratings of classical mechanical switch with the serial addition of this device.Acknowledgment.We would like to thank Ferraz-Shawmut Company for their financial support of this work and the European Community for the Access to Research Infrastructure action of the improving Human Potential Program. The realization of this device has been achieved at the CNM (Barcelona). References:[START_REF]Current limiter circuit[END_REF] "Current limiter circuit ", Patent n°W09727657 du 30/07/97, Siemens.[2] Szé, "Physics of semiconductors", p351-353, 2 nd Edition Wiley.[3] Semitec CRD corp. Distributor.[4] ISE Software Manual.[5] Y.Sugawara, "6.2 kV 4H-SiC PiN Diode with low forward voltage drop". ICSCRM99.[6] E.O. Johnson, "Physical limitations on frequency and power parameters of transistors", RCA Rev. 1965[7] M. Shur, on line : "http://www.virginia.edu"[START_REF]Cree research 99[END_REF] Cree research 99 best results on line :"http://www.cree.com" [9] Schröner, "Rugged Power MOSFET in 6H-SiC with blocking capability up to 1800V", ICSCRM99.[10] E Morvan, PhD thesis, "modélisation de l'implantation ionique dans a-SiC et application à la conception de composant de puissance". Dec 1999. Insa-Lyon.[11] M. Ruff, "SiC devices : Physics and Numerical Simulation", IEEE Trans. Electron Devices ED-41 n°6 June 1994.

Acknowledgment.

We would like to thank Ferraz-Shawmut Company for their financial support of this work and the European Community for the Access to Research Infrastructure action of the improving Human Potential Program. The realization of this device has been achieved at the CNM (Barcelona).