Mid-infrared Imaging spectroscopic measurements of C2H4 frost simulating the outer solar system environments

In the dense and cold atmosphere of Titan, the presence of C 2 H 4 haze has been con�rmed by the observations of satellite explorers. In the present study, an original cryogenic experimental equipment was developed to simulate the low-temperature solid formation of C 2 H 4 in combination with in-situ infrared spectroscopic measurements to understand the spectral band properties of C 2 H 4 condensation in the haze component of Titan. As a result, out-of-plane bending vibration ν 7 of solid-phase C 2 H 4 located at λ ~ 10.5 µm was successfully detected with high sensitivity, and two-dimensional spectrographs of C 2 H 4 at low temperatures were obtained. The obtained spectra of C 2 H 4 can be �tted to the double Lorentzian function with various heights, central wavelengths, and full widths at half maximum of the two-component Lorentzian functions. They were classi�ed into three types whose spectral shapes are similar to the amorphous, metastable crystal, and crystalline forms obtained by the previous laboratory experiment.


Introduction
The atmosphere of Saturn's largest moon Titan is a dense layer of gases with ~ 1.5 atm at the surface, which is the thickest among all natural satellites.Titan's lower atmosphere is primarily composed of nitrogen (94.2%) and the simplest hydrocarbon, methane (5.65%).Since the temperature of the atmosphere is as low as ~ 90 K (Mitri et al., 2007), Titan's atmosphere supports opaque haze layers blocking most visible light from the Sun.The rst observation of Titan's atmosphere was conducted by the Voyager I spacecraft (Smith et al., 1982).Titan's atmosphere has a complex system of atmospheric variability, especially the asymmetric north-south haze is intensively investigated (Lorenz et al., 1999).
Further information about the composition and character of Titan's atmosphere is summarized in Hörst (2017).
According to the phase diagram of ethylene calculated by Fray & Schmitt (2009) using thermodynamic equations in their study of sublimation and condensation of ice in planetary systems, it can be seen that ethylene is solid at the temperature and atmospheric pressure conditions of Titan.Roe et al. (2004) reported the spatially resolved chemical abundance of hydrocarbon in Titan's atmosphere observed by the W.M. Keck I 10-meter telescope.They showed the seasonal change and signi cant accumulation of ethylene (C 2 H 4 ) gas in the south polar stratosphere.Recently, the content of C 2 H 4 was found to be 3.91 ppm in Titan's atmosphere located at 1050 km from the surface, by using Cassini's mass spectrometer (Magee et al., 2009).In other celestial bodies, C 2 H 4 was detected during the New Horizon yby at Pluto (Gladstone et al., 2016).Haze particles dominated by C 2 hydrocarbon C 2 H 2 , C 2 H 4, and C 2 H 6 settle out on Pluto's surface (Grundy et al., 2018).C 2 H 4 was also detected in the interstellar environment of CRL 618 (Cernicharo et al., 2001).There is a feasibility study that aims for future spacecraft missions such as Europa Clipper to detect the hydrocarbon in the Jupiter system (Teolis et al., 2017).
To understand the process of morphological changes in solid C 2 H 4 , Jacox (1962) rst observed the laboratory infrared vibration absorption spectra of solid-phase C 2 H 4 in low temperatures.They found signi cant differences in the position, splitting, and linewidth of the absorption peaks at 4 K and 53 K.
Rytter & Gruen (1979) conducted the matrix isolation experiments and interpreted the data in terms of a monomer, dimer, aggregate, and crystal scheme.They pointed out that Crystalline belongs to the orthorhombic crystal system.Its factor group is bipyramidal (D 2h ), its space group is Pnnm ( ) and pnn ( ) in Primitive.Nes & Vos (1979)  Spectra in the previous experiments were obtained averaged over an aperture range of a few mm or more, and it was not possible to determine whether the spectra varied by location on the deposited plate surface.In this study, we measured the spatially resolved spectra of solid C 2 H 4 in sub-millimeter for the rst time and discovered the ununiformed spectral shape.

Experimental Procedures
An original cryogenic optical equipment was developed for conducting laboratory simulation of lowtemperature C 2 H 4 solid formation with in-situ infrared spectroscopic measurement, as shown in Fig. 1.
The vacuum chamber was fabricated by using a 5-axis simultaneous machining center at the Nagoya University Instrument Development Center.The liquid N 2 cooling dewar bottle is mounted on the upper part and directly connected to the oxygen-free high-conductivity copper (OFHC) sample holder with a center hole of ~ 3 mm in diameter.The sample holder adopted with the cold head was cooled to ~ 90 K.A ZnSe crystal plate 1 mm thick is attached to the OFHC sample holder for the infrared transmissive substrate.The stabilized silicon nitride globar lamp unit (SLS303, Thorlabs Co.) was used for the high emittance light source in the wavelength range 0.55 < λ < 15 µm.
As shown in Fig. 2, we constructed the near-equivalent optical system between the sample plate and detector by employing appropriate two ZnSe lens windows and optimized the distance from the chamber to the spectrometer.Transmittance spectral measurements were conducted by employing the imaging Fourier transform mid-infrared spectrometer (2D FT-IR, nisin-kikai NK-0812-TD-NU).The operation principle of 2D FT-IR with a common-optical path wavefront splitting type phase shift interferometry enables the easy acquisition of the infrared spectral images instantaneously by adopting the focal plane array detector (Inoue et al., 2006).The interference-pattern visibility is optimized by a suitable design of the multi-slit array, which is based on the theories of Fraunhofer diffraction and convolution imaging (Qi et al., 2015).The input light is collimated and incident as a parallel beam to the Fourier transform plane and then re ected at a certain installation angle of the movable and xed mirrors to the focal plane array detector through the objective lens.The detector mounted in the imaging spectrometer is the bolometer camera (Boson, FLIR Co.) operating in the ambient temperature condition, in which the pixel number is 640 x 512 with the unit pixel size of 12 µm.The wavelength range guaranteed by the manufacturer is 8 µm < λ < 12 µm.We con rmed that spectra below 7.0 µm are obtainable, even with the deteriorated signalto-noise ratio (S/N).The wavelength resolution of 2D FT-IR is ~ 70.7 nm, which corresponds to 7 cm − 1 at 10 µm.The 800 frames IR image data set in the time domain are obtained subsequently during the linear motion of the phase shifter and then are Fourier-transformed to acquire the frequency domain data by applying Fast Fourier Transform (FFT) method for each pixel data to obtain a 2-dimensional spectral image.
Table 1 summarizes the conditions of measurement.For the production of low-temperature solid C 2 H 4 before the spectroscopic measurement, the vacuum chamber was initially pumped out to reach ~10 -3 Pa by using the turbo-molecular pump (TSU-261, Pfeiffer Co.).After closing the gate valve, the liquid N 2 coolant was poured into the Dewar bottle.Approximately 10 minutes after lling the coolant, the ZnSe substrate temperature was lowered to ~83 K.After the cooling, the pure C 2 H 4 gas sample enclosed in the spray-can (GL science Co., 99.9 % purity) was introduced onto the cold ZnSe substrate.After con rming the adsorption of C 2 H 4 introduced, the two-dimensional absorption spectra of C 2 H 4 in the out-of-plane bending mode ν 7 vibrational band at about 10 μm were obtained at 0, 10, 26, and 35 min.We developed the data analysis program to convert raw interferogram data obtained by the 2D FT-IR to a 3D spectral data cube as shown in Fig. 3 and Fig. 4. It is also possible to execute spectral analysis such as binning, baseline correction, creating a spectral map and tting.The interferogram of each pixel was shifted so that the maximum value is at the center of the array, which is called a center-burst correction.

Then, interferogram f(n) is multiplied by Hamming window function w(n)
where N is number of pictures.The number of elements increased from N = 800 to N' = 4096 by zerolling.Finally, the interferogram is converted into the array y(k) by Fast Fourier Transform (FFT).
The absolute value of the array y(k) is the relative intensity spectrum.Wavelength calibration was done in this experiment to determine the install angle of the movable and xed mirrors φ y by using the technique of view angle correction, which is shown in Qi (2020).The phase difference L of the light received by the pixel at the center position of the detector can be represented as where M is the moving distance of the mirror.When calculating the phase difference for any given pixel except for the center position of the detector, it is necessary to calculate the view angle of the light incident on the phase shifter.In case the pixel at the center of the detector is taken as the origin, x and y components at any pixel (a, b) can be represented as where n x , and n y are pixel numbers on x and y coordinates, respectively.At the origin of the pixel, n x = 320 and n y = 256.s pix is the pixel size of the detector of 12 µm.View angle on x and y coordinates can be represented as where f = 25 mm is focal distance of the imaging lens.The phase difference after view angle correction L' can be represented as For wavelength calibration, light from the same source was transmitted in a narrow bandpass lter (BPF) Spectrogon NB-9585-135, and a blank spectrum was measured by 2D FT-IR.The known transmittance data of this BPF is plotted as blue dots in the upper left panel of Fig. 5.When the installation angle wasφ y = 44.874º± 0.016º, the relative intensity spectrum at the center pixel (n x , n y ) = (300, 256) shown as the red solid line could be best tted to the BPF transmittance data.The right panel of Fig. 5 shows the spectrum map with 7×7 bins of the light passing through BPF in the case ofφ y = 44.874º.The spectrum of one bin is averaged in the range of 35×35 pixels.In bins where the signals were detected, the peaks of the spectrum are in the range of 9590-9620 nm.The difference between the peaks is smaller than the wavelength resolution of 2D FT-IR.Therefore, the wavelength calibration is thought to be adequate.
Relative intensities at 0.01 µm intervals in the 7-14 µm range are calculated by linear interpolation based on the wavelength array determined by view angle correction.The absorbance spectrum at each pixel can be represented as Z ref and Z sam are the relative intensity data cubes of reference and sample.The baseline undulation needs to be corrected because the in uence of absorption of natural leaks of atmospheric gas such as H 2 O and CO 2 cannot be ignored.As shown in Fig. 4(e), linear interpolations with zero-order (linear), rstorder and second-order polynomials were performed using the spectrum in the range of 7.0-9.8and 11.8-14.0µm.The absorbance of the rst-order baseline was larger than that of the linear baseline.It shows the absorbance may be underestimated if the linear baseline is used.In this study, the original spectra were differenced at the second-order baseline.Finally, we detected three C 2 H 4 absorption bands of the bending vibration mode as shown in Z ref (n x ,n y ,z) Z sam (n x ,n y ,z) *1 The data with baseline correction at the center of the aperture was measured 26 minutes after the rst gas input.

Results
Spectral maps of the ν 7 band in 11 x 11 bins are illustrated in Fig. 6, in which the 3 mmφ aperture in the sample holder is shown in the black solid circle of top spectral images.The spectrum for each bin is the average of the data in the range of 30×30 pixels, corresponding to ~ 400×400 µm on the detector.The untrustworthy spectra of gray bins in the maps are removed since they seem to be outside the edges of the aperture, and therefore almost no light is transmitted.Spectral maps of ν 10 and ν 12 bands are also shown in Fig. 7.
Initially, a single spectral line at 10.6 µm of ν 7 band was identi ed in all spectral bins without bottom edges of the aperture when the C 2 H 4 partial pressure was ~ 700 Pa.After 10 min from the rst gas input, the spectral shape at any bin did not change and the peak absorbance slightly decreased.The uniformity of the spectra indicates that the IR absorption was mainly caused by gaseous C 2 H 4 .At the same time, the absorptions of ν 10 and ν 12 bands were not detected.After 25 min, when the C 2 H 4 partial pressure was ~ 1000 Pa, the spectral shapes of ν 10 and ν 12 bands are single peaks regardless of the place.On the other hand, the spectral map of the ν 7 band showed a signi cant change in spectral shape with two absorption peaks except for the top and bottom edges of the aperture.The ununiformed spectra suggest that the condensation of the C 2 H 4 frost started at this time.One possible speculation for the reason for different spectral shapes between the ν 7 band and ν 10 and ν 12 bands is that out-of-plane bending is greatly affected when C 2 H 4 aggregates and π-π stacking occurs.After 35 min, the spectral absorbance gradually increased, suggesting the growth of the frost.Hereafter we call the initial data "before condensation" and the data after 25 min from the rst gas input "after condensation".
To understand the detailed properties of the spectral shapes, the spectra before condensation were tted to the single Gaussian function f(x) shown in Fig. 8.
where x represnts the wavelength of the data point, and tting prameters a, and µ represents the peak height and peak wavelength, respectively.The full width at half maximum (FWHM) is .The error of each parameter is equal to the square root of the diagonal component of the variance-covariance matrix.The area lled between x-axis and a single Gaussian function is de ned as .Error propagation was considered to estimate the error of area.The correlation between a and σ was not taken into account.The left side of Fig. 9 show contour maps of peak height, peak wavelength, FWHM, and area of the tting function.The maps of these errors on the right side of Fig. 9 show tting accuracy is high except for the left top and bottom edge of the aperture such as the non-detection part of (i 1 , j 4 ), (i 7 , j 11 ), and (i 8 , j 11 ).The position of the maximum area is (i 5 , j 6 ), which is thought to be the center where the gas is blown directly.Because both peak height and FWHM are roughly correlated with the area of the Gaussian function, spectral shapes are almost the same regardless of the place of frost on the plate.
The map of spectra after condensation with tting is shown in Fig. 10.Because most of the spectral shapes are double peaks, tting to a single Gaussian function is not suitable.Using the double Gaussian function, the accuracy of tting to the spectrum after condensation is low, especially at the wavelength of the steep gradients around the peaks.Then, we tted the spectrum to the double Lorentzian function g(x).
g 1 (x) and g 2 (x) are blue and red-shifted components, respectively.x is the wavelength of the data point, σ 1 , σ 2 are the half of FWHM, and µ 1 , µ 2 are wavelength at the peak position (µ 1 < µ 2 ).Peak heights can be represented as where a 1 , a 2 are the tting parameters (a 1 > 0, a 2 > 0).In the top of Fig. 9, the spectral peaks are negative in the non-detection part of (i 1 , j 4 ), (i 4 , j 1 ), and (i 7 , j 11 ).The coe cient of determination of a t is less than R 2 = 0.9 in the regions of (i 2 , j 3 ) and (i 8 , j 11 ).In the rest of the regions, the coe cient is greater than R = 0.9, which shows the tting accuracy is su cient.According to the maps of tting parameters in Fig. 10, the distance between the peaks is large on the left side, and it is small on the right side.The large difference in FWHM of the blue-shifted component does not appear.However, that of the red-shifted component is large on the top side compared to the other place.It is the factor that the spectral shapes on the top side are single peaks with gentle slopes in the long wavelength direction (e.g., (i 4 ,j 2 )) or double peaks with different peak heights (e.g., (i 3 ,j 4 )).On the other hand, the spectral shape on the middle and bottom sides are double peaks with symmetry height.The single peak structure appears in the bottom edge of the aperture such as (i 3 ,j 10 ).
The frost thickness of C 2 H 4 can be estimated by Beer-Lambert law, which is that the absorbance peak is equal to the multiplication of the absorption coe cient and light path.Hudson et al. (2014) calculated the absorption coe cients of the ν 12 band to be 13,180 and 13,620 cm − 1 under the phase of Metastable.
In the top and middle regions of the map, peak absorbances of most spectra are around 1. If their data is used, the estimated frost thickness is ~ 0.7 µm in these regions.Focusing on the distribution of the tting parameters shown in Fig. 11, we classi ed the spectral map in the top panel by using a histogram in the top panel of Fig. 12 as follows: 1.In case either peak absorbance or is below 0.1, the double gaussian tting to the spectrum is failed (the background of the map is lled in gray).If it is over 0.1, we consider the absorption of solid C 2 H 4 is detected with su cient S/N. 2. In case the FWHM of the red-shifted component σ 2 is over 390, the spectrum is categorized as "type 1" (white) If conditions 1 and 2 do not satisfy, 3.In case the distance between the peaks µ 2 -µ 1 is over 335, the spectrum is categorized as "type 2" (green).It includes the estimated center position where the gas is blown directly (see Results).
Except for (i 1 , j 7 ) and (i 5 , j 11 ), three regions of white, blue, and green colors are separated.The spectra of type 1, type 2, and type 3 are distributed in the top, middle left, and the other side in the spectral map of Fig. 10, respectively.In Fig. 13, we plotted the representative spectrum at points (i 4 , j 2 ) of type 1, at (i 5 , j 5 ) of type 2, and (i 9 , j 7 ) of type 3 in this study.The spectra in Hudson et al. (2005) are also superimposed.It is noted that the wavenumber resolution of their study is 1 cm − 1 , which is 7 times better than this study.It can be seen from the diagram that the line shapes of the spectra of type 1, type 2, and type 3 are roughly similar to Hudson's spectra under the phase of Amorphous, Metastable, and Crystalline, respectively.Both Metastable and Crystalline appear to have double peaks and valleys between them.In Crystalline, the distance between the peaks is smaller and the depth of the valley becomes shallower rather than in Amorphous.
It is clear that the distance between peaks 1 and 2 in this study is greater than that in Hudson's results, and there is some variation in the shape of the peaks for Amorphous.In Hudson's study, the out-of-plane bending vibration ν 7 of C 2 H 4 at wavelengths of 10 < λ < 11 µm has only a single peak at about 10.53 µm in the case of amorphous ice.In the state of Metastable ice, the peak becomes double at the wavelength of 10.52 µm and 10.63 µm, respectively.The difference between the peaks is 0.11 µm.When it becomes crystalline ice, the distance between the two peaks becomes smaller, causing the shape of the double peak to change.The peaks change at 10.54 µm and 10.60 µm, respectively, with a difference of 0.06 µm.In contrast, in this study, a single peak of the spectrum at point (i 4 , j 2 ) of type 1 appears at the wavelength of 10.40 µm.The difference in absorption peaks at (i 5 , j 5 ) of type 2 and (i 9 , j 7 ) of type 3 are 0.39 µm and 0.3 µm, respectively.The spectrum with a peak difference under 0.14 µm is not found.The discrepancy in the peak separations between Hudson et al. (2014) and the present study may result from the difference in deposition temperature and subsequent annealing.The possible reason for an inconsistent distance between the bimodal peaks is a gap at the temperature level.In Hudson's experiments, Crystalline was The ν 7 vibration spectrum of the solid C 2 H 4 measured in this study can be described by the classical mechanical spring model.In the Lorentz oscillator model, electrons are bound to the atomic nucleus analogously to springs of different strengths.In spectroscopy, the Lorentz model describes the shape of a spectral line that is broadened by resonance or other mechanisms.The electrical dipoles here are springbound positive and negative charges and are regarded as harmonic oscillators whose vibration resistance is proportional to the speed of movement.In real molecules, the mass of the nucleus is much greater than that of the electron, so an approximation can be made by considering the electron only as changing its position due to uctuations in the electric eld. the complex dielectric function is are short wavelength and long wavelength in nity of ε r , q is effective electric charge, m is effective mass, γ is dumping factor, ω, and ω 0 are the angular frequency and natural angular frequency, respectively.The real component ε 1 of ε r is known as the resonant component and the imaginary component ε 2 corresponding to the decay of the electric eld is known as the absorption component.
Only the absorption component of the electric eld can be measured in this study.This equation can be approximated in terms of wavenumber Finally, the damping factors in Fig. 14 are derived by the tting of the double Lorentzian tting to the spectral data with the horizontal axis converted to wavenumber.In this experiment, the averaged factors of blue-and red-shifted components where the tting is succussed are estimated to be 3.7×10 12 , and 4.6×10 12 sec, respectively.They are larger than the coe cients derived by the double Lorentz tting of Hudson's spectra, which are estimated to be 3.1×10 12 and 1.5×10 12 sec under the phase of Metastable and to be 2.2×10 12

Supplementary Files
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Discussion 1 .
Comparison to other experimental results

Figures Figure 1
Figures

Figure 2 Top
Figure 2

Figure 3 Flow
Figure 3

Figure 13 Representative
Figure 13

Figure 14 Distribution
Figure 14 determined the Single-Crystal structure of C 2 H 4 at 85 K by X-ray diffraction method.They suggested that there are two non-equivalent C 2 H 4 molecules in the unit lattice.Molecules on the sides of the cube are oriented in the same direction, only the molecular in the center is not parallel to the other molecules.Later,Hudson etal.(2014) measured the bending vibration ν 7 , ν 10, and ν 12 of solid C 2 H 4 .They found the various vibration spectra attributable to the solid forms of stable crystalline, metastable, and amorphous.Although the exact structure of Metastable is not yet known, its spatial structure may be similar to that of Crystalline.Molpeceres et al. (2017) also measured the physical and spectroscopic properties of ices of mixed C 2 H 4 and CH 4 , which possibly simulated Pluto's surface.

Table 1
Summary of the experimental properties.
obtained by slow deposition of and cooling the C 2 H 4 solid from 60 K to 20 K; Metastable was obtained by rapid deposition at 20 K; Amorphous is obtained by heating the C 2 H 4 solid from 12 K to 20 K. On the other hand, the temperature for the experiments in this study was constant at around 83 K.It suggests that C 2 H 4 solid has a different crystal structure in 20 K and 83 K environments.2.Classical oscillator model of C 2 H 4 Hudson et al. ( 2014) the phase of Crystalline, respectively.Further simulation study will be needed to verify that the C 2 H 4 solid has a different crystal structure and dumping timescale of oscillation in 20 K and 83 K environments.SummaryIn this study, the authors used a self-developed cryogenic infrared optical device for performing laboratory simulations of the formation and in-situ infrared spectroscopic measurements of lowtemperature C 2 H 4 solids.In this experiment, 2-dimensional IR spectra of the out-of-plane bending vibration ν 7 and in-plane bending vibration ν 10 and ν 12 bands of C 2 H 4 solid were obtained by measurement at a low temperature of ~ 80 K. Then Double Lorentzian function was used to perform a least-squares t to the obtained C 2 H 4 IR spectrogram, and the tted image was obtained.The spectra of the single peak in the edge region, the double-peaked region with deeper troughs, and the double-peaked region with shallower troughs.Their spectral shapes are similar to those ofHudson et al. ( 2014)under the phase of amorphous, metastable, and crystalline, respectively.However, the distance between the peaks observed in this study is much larger than the previous study possibly because of the difference in the sample plate temperature.