A Cross-laboratory Comparison Study of Titan Haze Analogs: Surface Energy

In this study, we characterized seven tholin samples produced by three laboratories with different experimental setups and conditions: the PAC chamber at UNI, the PHAZER chamber at JHU, and the COSmIC chamber at ARC (Figure 1). Doing comparative studies of samples produced in different experimental facilities is not trivial, as each facility will have their own characteristics and many experimental parameters can be different from one setup to the other. A systematic analysis allowing the investigation of the effects of a limited number of experimental parameters takes time and becomes more and more difficult when increasing the number of facilities to be compared. In the study presented here, we considered laboratory setups that use two different types of energy sources to simulate Titan's atmospheric chemistry: cold plasma discharges and UV/deuterium lamps. The UV lamps simulate the solar UV irradiation above 115 nm, and the cold plasma discharges simulate energetic particle bombardment from Saturn's magnetosphere. These processes are the two main drivers of chemistry in Titan's atmosphere. By doing a comparative study of tholin samples produced in these three laboratories, we can compare tholins produced from plasma chemistry in two different setups (JHU/PHAZER and ARC/COSmIC) and tholins produced from UV chemistry in two different setups (JHU/PHAZER and UNI/PAC) as detailed below.

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To investigate the effect of the energy source on the surface properties of tholins produced in different experimental setups, four tholin samples (two from UV chemistry and two from plasma chemistry) were produced from the same N₂/CH₄ (95/5) gas mixture in the three laboratories. Because the JHU/PHAZER setup allows the use of both energy sources to produce tholins, we could also investigate the effect of the energy source on the surface properties of two tholin samples produced within a specific experimental setup. Similarly, the COSmIC setup was also used to produce three additional tholin samples using different gas mixtures, in order to investigate the effects of initial gas mixtures on the surface properties of tholin samples produced with the same laboratory setup. Details on the seven tholin samples characterized in this study are provided in Table 1. From now on, the samples will be referred to by the sample names listed in this table. The study presented here is one of only a few studies that have compared tholins from different laboratories, and we are planning to conduct more experiments with these laboratories to examine the effect of gas mixtures and other parameters in depth. The encouraging results presented here will hopefully lead to more comparative studies involving more experimental setups in the future.

2.1.1. Photochemical Aerosol Chamber (PAC) at UNI

2.1.2. Planetary HAZE Research Chamber (PHAZER) at JHU

2.1.3. Cosmic Simulation Chamber (COSmIC)

Prior to shipping, the UNI samples were collected and sealed with parafilm in a sample container in a dry N₂, oxygen-free glove box and then stored in a 4°C refrigerator; the JHU samples were collected and stored in a dry N₂, oxygen-free glove box (<0.1 ppm H₂O, <0.1 ppm O₂); and the ARC samples were collected in ambient air and then stored in a dark, continuously dry-air purged container with desiccant. All samples were sealed in small containers for transportation. After receiving the tholin samples, they were immediately unsealed and transferred to a vacuum desiccator that is continuously pumped down through a vacuum line. During this transfer, the samples were briefly exposed to air. However, because all seven tholin samples were stored in the vacuum desiccator for an extended period of time (days to weeks), it is considered that any water adsorbed on the surface would be desorbed from the surface prior to the contact angle measurements, as Chatain (2020) demonstrated that water desorbs from tholin surface under vacuum in around 30 minutes. By having the samples in a continuous vacuum prior to measurement, we are not only minimizing the air exposure and removing adsorbed water on the samples but also reducing the differences between the surface properties due to their different collection and storage methods prior to shipping.

The first step in the contact angle measurement protocol was to place the vacuum desiccator inside a glove box (relative humidity RH < 1%) purged with 99.999% high-purity dry nitrogen. This allowed the samples to be extracted in a nitrogen atmosphere in order to avoid water adsorption, contamination, and surface aging in ambient air. All the contact angle measurements conducted on the samples were then performed inside the glove box. We first measured the surface roughness of the tholin samples with a Mitutoyo surface roughness tester to examine the smoothness of the tholin samples. We used a stylus with a small measuring force of 0.75 mN to prevent it from scratching the surface. All tholin samples and substrates were measured to be relatively smooth with rms roughness between 12 and 15 nm, measured with a cutoff length of 0.08 mm and a sample length of 0.4 mm.

The contact angles were then measured through the sessile drop method using two different test liquids: HPLC-grade water (Fisher Chemical^TM) and diiodomethane (>99%; ACROS Organics^TM). The surface tensions of the two test liquids and their partitioning components are summarized in Table 2. The surface energy calculations are highly sensitive to the choice of the two test liquids, and the combination of a polar liquid and a nonpolar liquid typically returns more reliable results (Shimizu & Demarquette 2000). In particular, the water/diiodomethane pair tends to return the most accurate values, as they have, respectively, the largest polar and nonpolar components in all the test liquids that are commonly used (Hejda 2010; Yu et al. 2020a).

Table 2. Surface Tensions and Surface Tension Components (in mN m⁻¹) of the Two Test Liquids Used in This Study at 20°C

Liquid	CAS Number		Total Surface Tension		Surface Tension Components
			${\gamma }_{{lv}}^{\mathrm{tot}}$		${\gamma }_{{lv}}^{d}$	${\gamma }_{{lv}}^{p}$
Water	7732-18-5		72.8		21.8	51.0
Diiodomethane	75-11-6		50.8		50.8	0

Note. Where ${\gamma }_{{lv}}^{\mathrm{tot}}$ Is the Total Surface Tension of the Test Liquid and ${\gamma }_{{lv}}^{d}$ and ${\gamma }_{{lv}}^{p}$ Are, Respectively, the Dispersive and Polar Components of the Surface Tension of the Test Liquids. The surface tension values are from Van Oss (2006).

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Using a microsyringe, two to seven droplets of each test liquid were dispensed onto the tholin samples, forming sessile drops. The number of droplets we dispensed depends on the total available surface area of each sample. To avoid the flattening effect of gravity on the droplets, the volume of each droplet was controlled to be <2 μL (Zhang et al. 2008; Extrand & Moon 2010), forming sessile drops with diameters around 1–3 mm on the samples. The sessile drops were recorded as 30–60 s videos, with a frame rate of 2–20 frames s⁻¹, using the Ossila goniometer software. Note that although each video was recorded for either 30 s or 60 s, the length of video containing contact angle data was typically shorter than the total length of video acquired. This is because the video recording needs to be started before dispensing the liquid droplet, and the operator often needs a few seconds to dispense the liquids from the syringe onto the tholin samples.

The static contact angles were measured by both the Ossila software of the goniometer and the contact angle plug-in of the ImageJ software (Schneider et al. 2012). For the Ossila software, an adjustable box was used to enclose the region of interest. The base of the box was chosen to level the base of the droplet, and an edge detection algorithm was used to find the edge of the droplet inside the box. A polynomial fit was used for contact angles that were above 10° as shown in Figure 2(a), and a circle fit was used for contact angles that were below 10° as shown in Figure 2(b). For the contact angle plug-in of the ImageJ software, the baseline was defined via the selection of the left and right triphase points. The placement of three or more extra points along the droplet profile completed the definition of the droplet edge. The software fitted the profile to both a circle and an ellipse. Examples of the ImageJ fitting technique can be found in Figure 3 of Yu et al. (2020a).

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We performed a comparison between the Osilla and ImageJ fits and confirmed that they returned similar contact angle values for a given droplet profile. For each tholin sample and for each test liquid, we compared around 10 random frames throughout a video that could be measured by both software packages. A total of about 100 individual frame comparisons were performed, and the differences found between the two software packages were typically less than 5°. Because of this relatively small difference, we use the two packages interchangeably.

The solid surface energies of the tholin samples (γ_sv , in mJ m⁻²) can be obtained using the known surface tensions of the test liquids and the measured contact angles with the test liquids via the Young–Dupré equation (Young 1805; Dupré 1869):

$$\begin{eqnarray}&&{W}_{\mathrm{sl}}^{\mathrm{ad}}={\gamma }_{{lv}}^{\mathrm{tot}}(1+{\rm{\cos }}\theta ),\end{eqnarray} \tag{ 1 }$$

where W^ad _sl is the work of adhesion between the test liquid and the solid or the free energy change to separate the liquid and solid phase per unit area, θ is the measured contact angle formed between the solid and the test liquid, and ${\gamma }_{{lv}}^{\mathrm{tot}}$ is the total surface tension of the test liquid (in mN m⁻¹). The solid surface energy γ_sv is included in the work of adhesion W^ad _sl.

The Young–Dupré equation enables the study of solid surface energy with the measurement of θ using a test liquid of known total surface tension ${\gamma }_{{lv}}^{\mathrm{tot}}$. The surface tension component method (Fowkes 1964) can then be used to link the work of adhesion, W^ad _sl, to the solid surface energy, γ_sv . This theory assumes that the total surface free energy can be partitioned into different individual components representing contributions from different intermolecular forces, so ${W}_{\mathrm{sl}}^{\mathrm{ad}}$ can be expressed in terms of the surface free energy components.

In this study, we used the Owens–Wendt–Rabel–Kaelble (OWRK) method (Owens & Wendt 1969; Kaelble 1970; Rabel 1971) which follows the Young–Dupré theory to describe the relationship between W^ad _sl and ${\gamma }_{{sv}}^{\mathrm{tot}}$. This method, also known as the geometric mean method, assumes that the total surface energy (${\gamma }_{{sv}}^{\mathrm{tot}}$) or total surface tension (${\gamma }_{{lv}}^{\mathrm{tot}}$) can be partitioned into two parts: a dispersive component (γ^d ) and a polar component (γ^p ). Each part reflects independent intermolecular forces, with the dispersive component including the London dispersive forces between nonpolar molecules and the polar component including dipole–dipole and H-bonding interactions. The work of adhesion W^ad _sl can be expressed as the sum of the geometric means of the surface free energy components:

$$\begin{eqnarray}&&{W}_{\mathrm{sl}}^{{ad}}=2(\sqrt{{\gamma }_{{sv}}^{d}{\gamma }_{{lv}}^{d}}+\sqrt{{\gamma }_{{sv}}^{p}{\gamma }_{{lv}}^{p}}),\end{eqnarray} \tag{ 2 }$$

where ${\gamma }_{{sv}}^{d}$ and ${\gamma }_{{sv}}^{p}$ are the dispersive and polar components of the surface energy of the solid, whereas ${\gamma }_{{lv}}^{d}$ and ${\gamma }_{{lv}}^{p}$ are the dispersive and polar components of the surface tension of the liquid.

Combining Equations (1) and (2), we have

$$\begin{eqnarray}&&{\gamma }_{{lv}}^{\mathrm{tot}}(1+{\rm{\cos }}\theta )=2(\sqrt{{\gamma }_{{sv}}^{d}{\gamma }_{{lv}}^{d}}+\sqrt{{\gamma }_{{sv}}^{p}{\gamma }_{{lv}}^{p}}).\end{eqnarray} \tag{ 3 }$$

Due to the partitioning of ${\gamma }_{{sv}}^{\mathrm{tot}}$ into ${\gamma }_{{sv}}^{d}$ and ${\gamma }_{{sv}}^{p}$ in Equation (3), two unknowns are present. Therefore, contact angles measured between two known liquids and the solid are needed to form two sets of Equation (3) in order to solve for the total surface energy of the solid (${\gamma }_{{sv}}^{\mathrm{tot}}$) and its partitioning components (${\gamma }_{{sv}}^{d}$ and ${\gamma }_{{sv}}^{p}$). The analytical solutions of the OWRK method and the 1σ standard deviations for ${\gamma }_{{sv}}^{\mathrm{tot}}$, ${\gamma }_{{sv}}^{d}$, and ${\gamma }_{{sv}}^{p}$, computed through the propagation of uncertainty, can be found in Appendix A.

Figures 3(a) and (b) show one set of measured contact angles formed between each of the seven tholin samples and single droplets of each of the two test liquids, water and diiodomethane, as well as their variation with time. The whole contact angle data set for all droplets can be found in a supplementary data file in a Dryad repository available at 10.7291/D13T16. The contact angles were measured by either the Ossila software or the ImageJ contact angle plug-in as described above. Most contact angles were measured by the Ossila software, however, because the automatic edge detection algorithm is extremely sensitive to the defects of the background enclosed in the area of interest (see Figure 2): if a defect in the background (such as another droplet) is detected, no result is returned. For those cases with defects, the contact angles were instead measured using the ImageJ contact angle plug-in.

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With water as the test liquid, all tholin samples have decreasing contact angles over time, as shown in Figure 3(a). The decrease in contact angles for diiodomethane is more subtle during the ≲60 s video recording period and is only visible when the contact angle variation is recorded over an extended amount of time; an example is shown in Figure 5 in Appendix B. The decay of contact angle with time could be caused by the spreading of the liquid droplet, penetration of the test liquid into pore spaces, dissolution of the solid material into the test liquid, and evaporation of the test liquid to the measuring atmosphere. Wolf & Gambaryan-Roisman (2020) classified the process of contact angle decay into three stages. The spreading kinetics dominates the first stage, which lasts for only tens of milliseconds and is usually hard to be experimentally measured. This stage is dependent on the porosity of the material (Clarke et al. 2002) and independent of the solubility of the material. At the second stage, spreading starts to depend on the solubility of the solid material in the test liquid. This stage typically lasts for a few seconds, and higher solubility would lead to shorter decay timescales. The contact angle decays exponentially in this stage, and higher solubility leads to more rapid decay. The third stage starts after the contact lines are pinned. At the third stage, evaporation dominates the mass loss of the droplet, and the contact angle decays linearly with time until the droplet is completely evaporated.

Our experimental data (as shown in Figure 3) do not have the resolution (0.05–0.5 s per data point) to reflect the first stage of spreading. However, we are able to fit the data with a combination of exponential and linear fits to examine the effect of dissolution and evaporation. Consistent with the theory described by Wolf & Gambaryan-Roisman (2020), we found that dissolution typically occurred in the first few seconds after the sessile drop was placed onto the tholin sample, while evaporation happened later on. Dissolution also led to sharper decreases of contact angles, while the decrease due to evaporation was more gradual. Among all the tholin samples, only three samples are strongly affected by dissolution, the JHU-plasma sample, the ARC-Plasma-N₂-1 sample, and the ARC-Plasma-N₂-2 sample. We are able to fit an exponential decay function to the first few seconds of the data and a linear fit for the remaining data in Figure 3(a) for these three samples. The JHU sample is known to be partially soluble in water (Yu et al. 2020a). The ARC-Plasma-N₂ samples do not have measured solubility, but their contact angle decay data suggest that the ARC tholin samples produced with cold plasma discharge in N₂-based gas mixtures are also soluble in water. Among the three samples that show signs of dissolution with water, the JHU-plasma sample has the fastest dissolution-driven decay (highest slope in the exponential fit) and thus has the highest solubility. For the rest of the tholin samples, a linear fit was sufficient for capturing the contact angle decay data with water (Figure 3(a)). Unlike their N₂-based counterparts, the tholin samples produced in Ar-based mixtures, ARC-Plasma-Ar-1 and ARC-Plasma-Ar-2, had much slower decline rates in their contact angles with water in the first few seconds, indicating that they are much less soluble or even insoluble in water. This insolubility is likely attributed to the polarity of these samples. Water is more likely to dissolve polar materials, such that samples containing nitrogen more readily dissolve in water (see more detailed discussion in the following section). The gas mixtures used to produce the ARC-Plasma-Ar samples only contained nonpolar elements, so it is expected that the resulting solid samples are largely nonpolar as well. Therefore, it is reasonable to conclude that the ARC samples produced in Ar-based gas mixtures are insoluble in water because they are nonpolar. Also, both the JHU-UV and UNI-UV tholin samples, which were produced from the same initial gas mixture as the JHU-Plasma and ARC-Plasma-N₂-1 tholin samples, have little solubility or are insoluble in water. This is likely due to the fact that they were produced using UV lamps as the energy source to induce the chemistry and that UV lamps cannot directly dissociate nitrogen. Indeed, the UV lamps used in the PAC and PHAZER experimental setups emit photons from 115 to 400 nm, while the wavelength required for direct photolysis of nitrogen has to be shorter than 80 nm (Richards et al. 1981). It is therefore expected that less nitrogen is incorporated in these UV-generated tholin samples, resulting in compounds that have minimal solubility in water.

Tholins are typically found to be much less soluble in nonpolar solvents than polar solvents (McKay 1996; Carrasco et al. 2009; Kawai et al. 2013; He & Smith 2014; Moran et al. 2020). As shown in Figure 3(b), clearly none of the samples dissolve in diiodomethane, as there is no sharp decay of contact angles in the first few seconds of the data. We attempted to fit the 60 s contact angle decay data with linear fits but were unable to find good correlations (coefficient of determination R² < 0.6) owing to the scattering of the data. We recorded an extended contact angle decay for the JHU-plasma sample, and we were able to fit the data with a linear fit with a more significant R² = 0.83. The slope of the linear decay for diiodomethane (∼002 s⁻¹) is much smaller than that of water (∼01–05 s⁻¹). This could be due to diiodomethane's higher boiling point (∼180°C) than water (∼100°C) and thus lower vapor pressure at room temperature, so water more readily evaporates in a dry nitrogen environment than diiodomethane, leading to a more drastic contact angle decrease.

To accurately capture the surface properties of the tholin samples, we wanted to record the contact angles shortly after the first stage of spreading and minimize the effects of dissolution and evaporation. For diiodomethane, we averaged the contact angles measured for the full 60 s period (Table 3), as the sessile drop was relatively stable with little change of the contact angles due to evaporation and/or dissolution, as shown in Figure 3(b). For the water droplet measurements, only the contact angle values from the first 5 s after the water droplet was dispensed on the surfaces of tholins were taken into consideration for all samples, to minimize the effect of water evaporation. In the case of the three plasma tholin samples (JHU-Plasma, ARC-Plasma-N₂-1, and ARC-Plasma-N₂-2) that partially dissolve in water, this time was even shorter to reduce the effect of dissolution in water, and only the contact angle values from the first 2.5 s after the dispensary of droplets were taken into account. For each droplet, we averaged the contact angles measured from all selected frames and calculated the 1σ contact angle standard deviation due to frame-to-frame variations. We then averaged the contact angle values for all the droplets to obtain the final contact angle value for each sample with each test liquid and propagate contact angle error using the average and 1σ contact angle standard deviation values of each droplet. The final averaged contact angles and their 1σ standard deviations between each tholin sample and the two test liquids are summarized in Table 3.

Ideally, the contact angle measurement would most accurately probe for the surface property of the tholin samples when they have perfectly smooth surfaces with no voids (i.e., by measuring the "intrinsic" contact angles). The existence of surface roughness and porosity could both lead the measured contact angles (or the "apparent" contact angle) to deviate from the intrinsic contact angles. All seven tholin samples used in this study were measured to be very smooth, with rms roughness of 12–15 nm on a scale of 0.08 mm. Such small surface roughness indicates low porosity (less than a few percent) as well, as these two properties are linearly correlated (Qiu et al. 2015). Previous microscopic images of the JHU-plasma tholin sample used here (Yu et al. 2017) also show that its surface is densely packed with few voids. Given that our contact angle measurements already have standard deviations around ∼5° for each liquid on each sample owing to frame-to-frame variations and variations between droplets at different locations (see Table 3), the effect of the porosity and surface roughness would be minimal compared to the measurement error. Thus, the apparent contact angles measured for the tholin samples here should be close to their intrinsic contact angles, and the subsequent surface energy calculations likely capture the intrinsic surface energy of the tholin samples.

The surface energies of the tholin samples were computed using the OWRK method described in Section 2.4 with the contact angle values from Table 3 and the known surface tensions of the test liquids in Table 2. We also calculated the surface energies of the samples using the Wu method described in Yu et al. (2020a) as a way to validate our results. The Wu method returned slightly higher total surface energy values than the OWRK method, but the deviation in the values obtained by the two methods was only a few mJ m⁻². The total surface energies, ${\gamma }_{{sv}}^{\mathrm{tot}}$, and their partitioning components calculated with the OWRK method are listed in Table 4. The resulting total surface energies, spanning from 47.0 to 73.3 mJ m⁻², are similar to or higher than the high end of surface energies obtained for common polymers made of C, N, and H (20–50 mJ m⁻²; Owens & Wendt 1969; Wu 1971, 1982). Thus, the tholins studied here are stickier than common polymers and other materials that have been used in past studies to simulate Titan sediments (Burr et al. 2015; Méndez Harper et al. 2017). If the surface sediments on Titan resemble the tholins studied here, then they are likely relatively sticky, which would have an impact on their transport on the surface of Titan (Comola et al. 2021).

Table 4. Derived Surface Energies, ${\gamma }_{\mathrm{tot}}^{{sv}}$, and Their Two Partitioning Components, ${\gamma }_{{sv}}^{d}$ and ${\gamma }_{{sv}}^{p}$, with Their Respective 1σ Standard Deviation in mJ m⁻² for all Seven Tholin Samples Studied, as well as the "Average" and "End-member" Surface Energies of Tholins

Sample	OWRK Method
	${\gamma }_{{sv}}^{d}$		${\gamma }_{{sv}}^{p}$		${\gamma }_{\mathrm{tot}}^{{sv}}$
UNI-UV	33.9 ± 2.9		15.8 ± 5.7		49.7 ± 5.8
JHU-UV	31.8 ± 1.8		15.2 ± 2.9		47.0 ± 2.9
JHU-Plasma	37.3 ± 1.5		36.0 ± 1.5		73.3 ± 1.3
ARC-Plasma-N2-1	45.7 ± 2.1		20.1 ± 1.8		65.8 ± 1.9
ARC-Plasma-N2-2	44.4 ± 1.0		9.0 ± 5.1		53.4 ± 5.2
ARC-Plasma-Ar-1	48.3 ± 0.2		0.4 ± 0.2		48.7 ± 0.3
ARC-Plasma-Ar-2	47.5 ± 0.6		1.7 ± 1.0		49.2 ± 1.2
Average surface energy	37.2		21.8		59.0
End-member surface energy—low γsv	31.8		15.2		47.0
End-member surface energy—high γsv	45.7		36.0		81.7

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Out of all the tholin samples, the JHU-Plasma sample has the highest overall surface energy. Even though the two JHU samples (JHU-Plasma and JHU-UV) were produced under very similar experimental conditions (same pressure, temperature, gas mixture) other than their energy sources, the differences in their surface energies are significant. Both the JHU-plasma and JHU-UV samples have a relatively large dispersive component (over 30 mJ m⁻²), but the JHU-plasma sample has a much higher polar component compared to the JHU-UV sample. The smaller polar component of the JHU-UV sample can be attributed to the hydrogen UV lamp's inability to directly dissociate the triple-bonded nitrogen in the gas mixture. Because nitrogen-containing compounds are the main contributors to the polar components of the tholin samples, the lower polar component observed with the JHU-UV sample can therefore be explained by the lack of directly dissociated molecular nitrogen during the JHU-UV sample production with the UV lamp. The nonzero polar component of the JHU-UV sample, however, is consistent with the fact that nitrogen can still be indirectly dissociated through various secondary processes (Hodyss et al. 2011; Trainer et al. 2012; Hörst et al. 2018) and incorporated into the tholin sample.

In a previous study of the same JHU tholin samples by Yu et al. (2020a), closer surface energy values between the JHU-plasma and JHU-UV samples were reported. The values, obtained using the two-liquid method, ranged from 60 to 70 mJ m⁻² for both samples. The surface energy value reported for the JHU-Plasma sample was close to the one obtained in this study. However, the surface energy value reported for the JHU-UV sample in Yu et al. (2020, ${\gamma }_{{sv}}^{\mathrm{tot}}=66.0\pm 4.7\ \mathrm{mJ}\,{{\rm{m}}}^{-2}$, ${\gamma }_{{sv}}^{d}=41.1\pm 0.9\ \mathrm{mJ}\,{{\rm{m}}}^{-2}$, ${\gamma }_{{sv}}^{p}=24.9\pm 4.7\ \mathrm{mJ}\,{{\rm{m}}}^{-2}$) was much higher than the value obtained in this study (${\gamma }_{{sv}}^{\mathrm{tot}}=47.0\pm 2.9\ \mathrm{mJ}\,{{\rm{m}}}^{-2}$, ${\gamma }_{{sv}}^{d}=31.8\pm 1.8\ \mathrm{mJ}\,{{\rm{m}}}^{-2}$, ${\gamma }_{{sv}}^{p}\,=15.2\pm 2.9\ \mathrm{mJ}\,{{\rm{m}}}^{-2}$). The JHU-UV sample used here and the one used in Yu et al. (2020a) are the same batch of samples that have been stored in a dry nitrogen, oxygen-free glove box to prevent sample aging. Thus, the most likely cause of the discrepancy comes from the different measurement environments: ambient air (Yu et al. 2020a) versus dry nitrogen in this study. As discussed in Yu et al. (2020a), the surface properties of the tholin samples could be affected in several different ways when the contact angle measurements were performed in ambient air: (1) the tholin samples could be chemically altered upon exposure to oxygen and water, (2) water moisture from the atmosphere may adsorb on the surfaces and steer the surface energy of the samples toward water (72.8 mN m⁻¹), and (3) airborne organic contaminants like hydrocarbons/oils could also adsorb on the surfaces and steer the surface energy of the samples toward hydrocarbons/oils (∼20 mN m⁻¹). For the JHU-UV sample, the water adsorption seems to be more significant than hydrocarbon adsorption in Yu et al. (2020a), since the JHU-UV sample has lower surface energies measured here in an inert environment compared to ambient air. It is reasonable to expect the difference between the measurements in ambient air versus dry nitrogen to be smaller for the JHU-plasma sample than the JHU-UV sample, because the JHU-plasma sample (in dry nitrogen) has a surface energy (∼70 mJ m⁻²) that is closer to water (72.8 mN m⁻¹) than the JHU-UV sample (∼50 mJ m⁻²), so the adsorbed water likely has less effect on the JHU-plasma sample. Thus, the discrepancy between this study and Yu et al. (2020a) demonstrates the need to perform the contact angle measurements in inert atmospheres to accurately capture the surface properties of tholin samples to avoid adsorption and contamination from ambient air.

If we now compare the UNI-UV and JHU-UV samples, which were made with two completely different experimental setups under different pressure and temperature experimental conditions but similar energy sources and the same gas mixture, we can see that they have similar overall surface energies and surface energy partitioning patterns. This resemblance between the two samples could be attributed to the common experimental parameters used during their production: the energy source, a UV lamp, and the initial gas mixture, N₂:CH₄ (95:5). The UV lamps used for the production of the UNI-UV and JHU-UV samples emit photons at similar wavelength ranges (115–400 nm), which means that neither emits the range of photons that directly dissociates nitrogen in the gas mixture, as discussed above. The amount of polar molecules formed during the production of both these samples was therefore lower compared to tholins formed with plasma discharges, which can dissociate nitrogen. The similarity of total surface energies of both UV samples is thus likely attributable to the energy source used to produce them.

The ARC samples all have very high dispersive components (> 44 mJ m⁻²) that are higher than the JHU and UNI samples. The surface energies of the ARC samples made with different gas mixtures differ mainly in their polar components. The ARC-Plasma-N₂-1 sample, made with the same gas mixture as the UNI and JHU samples, has a surface energy polar component that is higher than that of the two UV samples but lower than that of the JHU-Plasma sample. For both the ARC-Plasma-N₂-1 and JHU-Plasma samples, the use of a plasma discharge as the energy source allowed for the dissociation of molecular nitrogen during production of tholins. A possible explanation for the higher polar component of the JHU-Plasma sample's surface energy compared to that of the ARC-Plasma-N₂-1 sample is the exposure time of the gas mixture to the energy source: ∼3.5 μs for the ARC-Plasma-N₂-1 sample versus 3 minutes for the JHU-Plasma sample, i.e., ∼50,000 times shorter for the ARC sample. Note that the ARC samples are also collected and stored differently compared to the JHU-plasma sample (see Section 2.2), which could cause different degrees of sample degradation. Some of the differences in collection and storage could be reduced by the prolonged storage of samples under a continuous vacuum prior to measurements, such as water and hydrocarbon adsorption. However, chemical alteration in air is irreversible and could also contribute to the differences between the ARC and JHU samples. On the other hand, the higher polar component of the surface energy observed for the plasma-generated ARC-Plasma-N₂-1 tholin sample compared to the UV-generated PAC and JHU tholin samples is in agreement with our previous assessment that direct dissociation of nitrogen must play an important role in forming molecules with high-polarity indices in tholins. Given that the two UV samples (JHU-UV and UNI-UV) have similar surface energy values and partitioning values and both the plasma samples (JHU-Plasma and ARC-Plasma-N₂-1) have higher surface energies than the UV samples, it seems like the energy source has the largest impact on the surface energies or the bulk chemical compositions of the tholin samples, which is in agreement with a previous study by Hörst et al. (2018).

A previous mass spectrometry study of the plasma-generated gaseous chemical products formed in COSmIC, where the ARC tholin samples were produced, has shown that mixtures containing heavier precursors, like N₂:CH₄:C₂H₂, produce more complex molecular compounds than simpler gas mixtures like N₂:CH₄ (Sciamma-O'Brien et al. 2014). It is interesting to observe, however, that the surface energies of the tholins formed in N₂:CH₄:C₂H₂ are not necessarily higher than those of tholins formed in simpler N₂-CH₄ gas mixtures. The ARC-Plasma-N₂-1 tholin sample produced without C₂H₂ has a much higher surface energy polar component than the ARC-Plasma-N₂-2 tholin sample produced with C₂H₂ (20 mJ m⁻² vs. 9 mJ m⁻²). This result suggests that the addition of a more complex nonpolar hydrocarbon precursor in the initial gas mixture leads to the formation of a tholin sample that contains more complex nonpolar products in COSmIC. This is consistent with a recent X-ray Absorption Near Edge Structure (XANES) spectroscopy study of COSmIC tholins that allowed the measurement and comparison of the C/N ratios of the tholin samples and demonstrated that COSmIC tholin samples produced in N₂:CH₄ (95:5) had a higher nitrogen content than the ones produced in N₂:CH₄:C₂H₂ (94.5:5:0.5) (1.3 vs. 2.4; Nuevo 2021).

The ARC-Plasma-Ar-1 and ARC-Plasma-Ar-2 samples have very similar total surface energies and surface energy partitioning components, as seen in Figure 4. The polar components of the surface energy for both the ARC-Plasma-Ar-1 and ARC-Plasma-Ar-2 samples are almost 0 mJ m⁻². Because the initial gas mixtures for these two samples contained only nonpolar constituents, these two samples are likely composed of only nonpolar compounds. This result confirms that nitrogen indeed plays a prominent role in the formation of polar compounds for the tholins studied here.

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From the measured surface energies of the different tholin samples, we can extract their commonalities and end-member properties. These can then be used to infer what properties could be expected to be present in Titan's aerosols and to estimate the processes that are likely happening on Titan. This end-member selection method was previously used to determine the range of possible optical properties of tholins to compare DISR and VIMS observations (Bernard et al. 2006). Here we considered only the four tholins produced in the same Titan-representative gas mixture that is commonly used in the literature, N₂:CH₄ (95:5), i.e., UNI-UV, JHU-UV, JHU-Plasma, and ARC-Plasma-N₂-1. These four samples are selected to balance the effect of each apparatus and each energy source, such that two plasma tholin samples and two UV samples from two different laboratories go into the decision of the "average" and the "end-member" properties.

As shown in Figure 4, the four tholin samples produced in N₂:CH₄ (95:5) gas mixtures all have relatively high dispersive components above 30 mJ m⁻². This suggests that a high dispersive component (${\gamma }_{{sv}}^{d}$) may be a common trait among all tholin samples. Thus, the actual Titan haze particles could likely also share this trait and have a high dispersive component (${\gamma }_{{sv}}^{d}$). The differences between the tholin samples are mainly their polar components (${\gamma }_{{sv}}^{p}$), which range from 15 to 36 mJ m⁻². Overall, cold plasma energy sources seem to produce tholin samples with higher polar components than UV energy sources. However, differences in other experimental conditions could also lead to the observed differences in the polar components of the tholin samples.

We have defined an "average" and two "end-member" surface energies, as shown in Table 4. The dispersive and polar components of the average surface energy were obtained by averaging the dispersive and polar components, respectively, of the four Titan tholins produced in N₂:CH₄ (95:5, UNI-UV, JHU-UV, JHU-Plasma, and ARC-Plasma-N₂-1). Note that the average dispersive surface energy component also represents the common trait of all the tholin samples. The surface energy partitioning components of the end-member surface energies correspond to the end-member dispersive and polar components, i.e., the highest and lowest possible values, of the four Titan tholin samples.

If the surface energy of Titan haze particles were known, we could determine two processes happening on Titan: cloud formation through haze−condensate interactions and haze−lake interactions (Yu et al. 2020a). In Section 3.3, we determined the "average" and "end-member" surface energies of the tholin samples studied here. We used these surface energies as inputs in theoretical calculations to estimate a range of cloud formation and haze−lake interaction scenarios on Titan.

In Titan's atmosphere, simple organics such as methane and ethane can condense and form clouds (e.g., Barth 2017; Anderson et al. 2018). Clouds can form through both heterogeneous and homogeneous nucleation with the condensation of the organic species. However, heterogeneous nucleation is typically more favorable, as it usually requires a lower degree of supersaturation (Pruppacher & Klett 1978). Because of the prevalence of haze particles in Titan's atmosphere, they are natural potential CCN for heterogeneous nucleation. Thus, determining haze−condensate interactions on Titan can tell us the cloud-forming efficiency for certain condensates and the likelihood of observing these clouds in Titan's atmosphere.

Using the surface energy of the Titan tholins and the average and end-member surface energies, along with the surface free energies for methane and ethane condensates, the theoretical contact angles with these hydrocarbon condensates can be calculated using the following equation (Yu et al. 2020a):

$$\begin{eqnarray}&&\begin{array}{l}\mathrm{when}\ \sqrt{{\gamma }_{{sv}}^{d}{\gamma }_{{lv}}^{d}}+\sqrt{{\gamma }_{{sv}}^{p}{\gamma }_{{lv}}^{p}}\leqslant {\gamma }_{{lv}}^{\mathrm{tot}},\\ \theta =\arccos (\frac{2(\sqrt{{\gamma }_{{sv}}^{d}{\gamma }_{{lv}}^{d}}+\sqrt{{\gamma }_{{sv}}^{p}{\gamma }_{{lv}}^{p}})}{{\gamma }_{{lv}}^{\mathrm{tot}}}-1),\\ \mathrm{when}\ \sqrt{{\gamma }_{{sv}}^{d}{\gamma }_{{lv}}^{d}}+\sqrt{{\gamma }_{{sv}}^{p}{\gamma }_{{lv}}^{p}}\geqslant {\gamma }_{{lv}}^{\mathrm{tot}},\theta =0,\end{array}\end{eqnarray} \tag{ 4 }$$

where ${\gamma }_{{lv}}^{\mathrm{tot}}$, ${\gamma }_{{lv}}^{d}$, and ${\gamma }_{{lv}}^{p}$ represent, respectively, the total surface free energy and the dispersive and polar components of the surface free energy (surface tension/surface energy) of cloud condensates; and ${\gamma }_{{sv}}^{\mathrm{tot}}$, ${\gamma }_{{sv}}^{d}$, and ${\gamma }_{{sv}}^{p}$ represent, respectively, the total surface energy and the dispersive and polar components of tholins. Since the cloud condensates studied here (methane, ethane) and the lake liquid components (nitrogen, methane, ethane) are all nonpolar in nature, their polar parts of the surface free energy are zero (${\gamma }_{{lv}}^{p}=0$), and their dispersive and total surface free energies are equal to each other (${\gamma }_{{lv}}^{d}={\gamma }_{{lv}}^{\mathrm{tot}}$). Thus, Equation (4) can be simplified as

$$\begin{eqnarray}&&\begin{array}{l}\mathrm{when}\ {\gamma }_{{sv}}^{d}\leqslant {\gamma }_{{lv}}^{d},\theta =\arccos (2\sqrt{\frac{{\gamma }_{{sv}}^{d}}{{\gamma }_{{lv}}^{d}}}-1),\\ \mathrm{when}\ {\gamma }_{{sv}}^{d}\leqslant {\gamma }_{{lv}}^{d},\theta =0.\end{array}\end{eqnarray} \tag{ 5 }$$

Equation (5) has two parts. When ${\gamma }_{{sv}}^{d}\leqslant {\gamma }_{{lv}}^{d}$, the condensate will form a finite contact angle on the surface of the tholin sample. When ${\gamma }_{{sv}}^{d}\geqslant {\gamma }_{{lv}}^{d}$, the first part of Equation (5) does not apply anymore, as once the surface energy of the tholin sample is larger than the condensate, the condensate will completely wet (or spread on) the solid surface (Fox & Zisman 1950, 1952), forming a contact angle θ of zero. Yu et al. (2020a) have also validated the second part of this theory on tholins; by dispensing droplets of n-hexane (${\gamma }_{{lv}}^{d}=18.4$ mN m⁻¹) on the JHU tholin samples (both have higher ${\gamma }_{{sv}}^{d}$), they form contact angles of zero on both samples. Based on Equation (5), the dispersive component of the haze particles solely determines the interaction between the haze and the cloud condensates/lake liquids. Thus, using the "average" surface energy determined in Section 3.3 for the following calculations essentially corresponds to using the commonality in surface energy of the tholin samples studied here, which would likely be representative of the surface energy of Titan's aerosols. On the other hand, the modeling results obtained when considering the end-member surface energies provide the upper and lower limits of a range of scenarios that could happen on Titan.

Considering the surface energy values for the main clouds, methane and ethane from Table 5, and the surface energy values provided in Table 4, we have calculated theoretical contact angles for all four Titan tholin samples produced in N₂:CH₄ (95:5) gas mixtures, as well as the "average" and "end-member" surface energies defined above. The results are shown in Table 6. For the tholin samples, the standard deviations of the calculated contact angles are determined through error propagation using the 1σ standard deviations of the surface energies of the tholin samples in Table 4. When the calculations need to use both parts of Equation (5), we calculate a range of θ values using upper- and lower-limit values of tholins' surface energies (surface energy plus/minus 1σ standard deviation).

Table 5. Surface Tensions of Titan's Lake Liquids (Methane, Ethane, and Nitrogen) in mN m−1, and the Surface Energies of Titan's Methane and Ethane Ice Cloud Condensates, Adopted from Yu et al. (2020a)

Species	Liquid at 94 K				Solid < 90 K
	Total Surface Tension	Surface Tension Components			Total Surface Energy		Surface Energy Components
	${\gamma }_{{lv}}^{\mathrm{tot}}$	${\gamma }_{{lv}}^{d}$	${\gamma }_{{lv}}^{p}$		${\gamma }_{{sv}}^{\mathrm{tot}}$		${\gamma }_{{sv}}^{d}$	${\gamma }_{{sv}}^{p}$
Methane	17.8	17.8	0		23.5		23.5	0
Ethane	31.8	31.8	0		43.4		43.4	0
Nitrogen	5.3	5.3	0		N/A		N/A	N/A

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Calculations with all four Titan tholin samples result in 0° contact angle with liquid methane and methane ice. For liquid ethane the JHU-UV and UNI-UV samples have contact angles ranging from 0° to 20° considering their measurement standard deviations, whereas for ethane ice the contact angles range from 0° to 45°. For the "average" surface energy, a contact angle of 0° is obtained with liquid methane/ethane and methane ice, and a contact angle of 317 is obtained with ethane ice. For the "end-member" surface energy with the highest total surface energy γ_sv , 0° contact angles are obtained with methane and ethane in both liquid and solid phases, while for the "end-member" surface energy with the lowest surface energy γ_sv a 0° contact angle is obtained with liquid methane/ethane and methane ice, but a contact angle of 446 is obtained with ethane ice. For a material to be an ideal CCN for efficient heterogeneous nucleation to form a cloud, the condensate has to have low contact angle with this material. Previous studies have demonstrated that the upper limit of contact angle values for good CCN ranges from 12° to 45° (McDonald 1964; Mahata & Alofs 1975; Yu et al. 2021). Thus, all tholins studied here should be good CCN for methane and ethane clouds. Assuming that the haze particles are similar to the tholins studied here, the haze particles will likely be good CCN for methane and ethane clouds on Titan. There are other species that can condense in Titan's atmosphere, such as HCN, C₆H₆, and HC₃N (Anderson et al. 2018), and the study of additional possible condensates is ongoing.

As the haze particles on Titan grow bigger and fall toward Titan's surface, they may fall on top of the lakes, which are mainly composed of methane, ethane, and nitrogen (e.g., Mastrogiuseppe et al. 2016, 2018; Poggiali et al. 2020). If the haze particles float on top of the lakes, they could potentially dampen the surface waves (Cordier & Carrasco 2019), which may explain the smooth and almost waveless lakes observed by Cassini (Stephan et al. 2010; Barnes et al. 2011; Soderblom et al. 2012; Zebker et al. 2014; Grima et al. 2017). If they sink, they will sediment to the bottom of the lake and become a part of the lake-bed sediment. Based on the work of Cordier & Carrasco (2019), Yu et al. (2020a) determined the flotation criteria for aerosol-sized particles on Titan's lakes: (1) if the aerosol particles are less dense compared to the lake liquids, they will float; (2) if the aerosol particles are denser compared to the lake liquids, they will float if the contact angle formed between the aerosols and the lake liquids is above 0°; (3) otherwise, they will sink into the lakes. So far, among all the tholin samples measured here, only the density of the JHU-Plasma sample has been determined, which is around 1400 kg m⁻³. However, the density of some tholins has been measured to be as low as 500 kg m⁻³ (Hörst & Tolbert 2013). The density of the lake liquids is around 450–700 kg m⁻³ (Cordier & Carrasco 2019). If the haze particles on Titan are on the lower end of the density spectrum, they could float on Titan's lakes based on criterion 1. Here, we assume that the Titan haze particles are on the high-density end of the tholin samples and are denser than the lake liquids, and we use criteria 2 and 3 to determine the floatability of haze particles on Titan's lakes.

Using the derived surface energies of the tholin samples in Table 4 and the surface tension values for each individual lake component in Table 5, the theoretical contact angles formed with the lake liquids and all tholin samples studied here can be calculated using Equation (5). The calculated theoretical contact angles between the lake liquid components and all tholins are shown in Table 6. Among all the measured tholin samples, we find a 0° contact angle between liquid methane/liquid nitrogen and the tholin samples. For liquid ethane, the UV samples could have nonzero contact angles up to 20° when considering the standard deviations of their measured surface energies. Tholins with the "average" and the "end-member" surface energies have zero contact angles with all lake liquid components. Assuming that these tholins are a good representation of the haze particles, the haze particles are likely completely wetted by the lake liquids, unless the lakes are very ethane-rich and the haze particles are similar to the UV samples.

The high dispersive component among all the tholin samples can lead to similar behaviors toward methane/ethane cloud formation and aerosol-lake interactions on Titan. Because both methane and ethane are nonpolar substances, their polar components of surface energies/surface tensions are zero. Thus, when predicting the interactions between these nonpolar substances with tholins through the wetting theory (Equation (5)), the magnitude of the dispersive components of the tholins is the only determining factor. The small contact angles formed between tholins and hydrocarbons can then be attributed to the shared characteristic all tholin samples studied here have: the high dispersive component, ${\gamma }_{{sv}}^{d}$. Our results imply that, on Titan, it is very likely that methane and ethane clouds can nucleate effectively with the actual haze particles as the CCN, and haze particles that fall toward the hydrocarbon lakes would likely sink to the bottom, if they are denser than the lake liquids.