# How Adsorption Affects the Gas-Ice Partitioning of Organics Erupted from Enceladus

Alexis Bouquet, Christopher R. Glein, J. Hunter Waite

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Alexis Bouquet, Christopher R. Glein, J. Hunter Waite. How Adsorption Affects the Gas-Ice Partitioning of Organics Erupted from Enceladus. The Astrophysical Journal, 2019, 873, 10.3847/1538-4357/ab0100. insu-03666764

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# How Adsorption Affects the Gas-Ice Partitioning of Organics Erupted from Enceladus

Alexis Bouquet¹,² ID, Christopher R. Glein¹ ID, and J. Hunter Waite, Jr.¹,³ ID

¹Space Science and Engineering Division, Southwest Research Institute, 6220 Culebra Road, San Antonio, TX, 78238, USA; alexis.bouquet@lam.fr

²Aix Marseille Université, CNRS, CNES, LAM, Marseille, France

³Department of Physics and Astronomy, University of Texas at San Antonio, San Antonio, TX, USA

Received 2018 September 14; revised 2018 November 27; accepted 2019 January 9; published 2019 February 28

## Abstract

We study the effect of adsorption of volatile organic compounds (VOCs) in Enceladus' geysers, both onto the ice grains ejected in the plumes, and onto the ice walls of the cracks connecting Enceladus' internal ocean to its surface. We use a model of adsorption/desorption based on the Polanyi-Wiegner equation and experimental values of binding energies (energy of desorption $E_{des}$) of the adsorbed compounds to water ice. We find that under conditions expected at Enceladus, the process of adsorption tends to ensure that the VOCs with the highest binding energy are over-represented on the ice surface, even if their abundance is comparatively lower than those of other compounds. We find that VOCs with $E_{des} \le 0.5$ eV are insignificantly affected by adsorption while compounds with $E_{des} \ge 0.7$ eV are readily retained on the surface and compete to occupy most of the adsorption sites. We also deduce that ice grains falling back onto the surface are likely to retain most of the molecules adsorbed on their surface. The implication is that remote observation or sampling of the ice in the cracks or of the surface around it would show a mixture of VOCs that would not be representative of the gas phase of the plumes, with the high $E_{des}$ VOCs dominating the adsorbed phase.

**Key words:** astrobiology – planets and satellites: individual (Enceladus) – planets and satellites: oceans

## 1. Introduction

The geysers found by Cassini erupting from Enceladus' South Polar Terrain (Porco et al. 2006) offer a unique opportunity to gain insights on the state of the internal liquid water ocean. The plumes formed by these geysers include a gas phase and ice grains that have been studied in situ, respectively, with the Cassini Ion and Neutral Mass Spectrometer INMS (Waite et al. 2004, 2006, 2009, 2017) and the Cosmic Dust Analyzer CDA (Srama et al. 2004; Spahn et al. 2006; Postberg et al. 2008, 2009; Kempf et al. 2010; Postberg et al. 2011, 2018), and remotely with the UltraViolet Imaging Spectrograph UVIS (Esposito et al. 2004; Hansen et al. 2006, 2008, 2011), establishing the presence of a variety of organic compounds. Observations by UVIS and the Visible and Infrared Mapping Spectrometer (Brown et al. 2004) have probed the surface composition of Enceladus (Brown et al. 2006; Hodyss et al. 2009; Hendrix et al. 2010), which is partly related to fallback from the plumes. Determining the abundance of organics at Enceladus is an important step toward understanding its ocean's chemistry and possible habitability, as well as developing future missions to search for biosignatures.

However, the plume gas has ample opportunity to interact with cold ice between the (liquid) water table and the surface. This interaction would involve both the ice walls of the cracks and the ice grains that are erupted. The adsorption of organics onto ice is a phenomenon that is known to have important implications for trace organics in the Earth's atmosphere, which has motivated a number of experimental studies (Sokolov & Abbatt 2002; Abbatt 2003; Collignon & Picaud 2004; Jedlovszky et al. 2006, 2008). The adsorption of organics at Enceladus could have repercussions for our understanding of remote observations of its surface as well as the analysis of ice grains. These compounds could adsorb onto the walls and the grains falling back onto the surface or feeding the E ring, affecting remote observations or potential sampling of the surface.

In this study, we model the adsorption/desorption of volatile organic compounds (VOCs) to ice grains and ice walls at Enceladus, using experimental data available thanks to studies of adsorption in the context of the Earth's atmosphere. In Section 2 we explain the model of adsorption/desorption that we used, and how we applied it to the conditions at Enceladus: in the cracks and on the grains ejected from the vents. In Section 3 we present the results and their variations with the parameters of the study. Section 4 discusses the factors susceptible to affect our results, and the implication for future observations. Section 5 is dedicated to the conclusion and the main takeaways of our study.

## 2. Models

### 2.1. Vent Conditions

We are interested primarily in the adsorption behavior of organic compounds that may be present in the gas phase in Enceladus' plumes. Heavier compounds will most likely be present only inside ice grains (Postberg et al. 2018) and are not the subject of our study. Studies of the adsorption of VOCs onto ice have been performed to investigate the behavior of trace organics present in Earth's atmosphere and their possible scavenging by ice grains. To discuss the relevance of these studies' conclusions for our work, it is first necessary to identify the conditions we wish to model.

The first parameter of importance is the temperature of both the gas phase and the ice surface in contact with it. The exact temperature of Enceladus' vents is still an open question, since vent size is below the resolution of IR observations, and these observations constrain the heat flux rather than the surface temperature (Spencer et al. 2006; Howett et al. 2011; Goguen et al. 2013). Modeling studies of the vents (Ingersoll & Pankine 2010; Yeoh 2015; Nakajima & Ingersoll 2016) indicate temperatures up to 236 K in the last meters below the surface. We adopt the temperature profile number 13 from
<table><caption>**Table 1**
Organic Compounds Considered in the Present Study and Their Desorption Energies, Whether They Have Been Detected by *Cassini* INMS (Limit between High and Moderate Ambiguity at 100 ppm) and Estimates of Their Residence Time on Ice at 230 K as per Equation (5)</caption><thead><tr><th>Compound</th><th>Formula</th><th><i>E</i><sub>des</sub> (eV)</th><th>Reference</th><th>Detected by INMS?<br>(Magee & Waite 2017)<br>(Ambiguity)</th><th><i>τ</i><sub>res</sub> (s)</th></tr></thead><tbody><tr><td>Acetic Acid</td><td>CH<sub>3</sub>COOH</td><td>0.76 ± 0.12</td><td>Sokolov & Abbatt (2002)</td><td>Yes (High)</td><td>16</td></tr><tr><td>Acetylene</td><td>C<sub>2</sub>H<sub>2</sub></td><td>0.16</td><td>Devlin & Buch (1995)</td><td>Yes (Moderate)</td><td>≤ms</td></tr><tr><td>Benzene</td><td>C<sub>6</sub>H<sub>6</sub></td><td>0.42 ± 0.013</td><td>Hoff et al. (1995)</td><td>No</td><td>≤ms</td></tr><tr><td>Butanol</td><td>C<sub>4</sub>H<sub>10</sub>O</td><td>0.7 ± 0.04</td><td>Sokolov & Abbatt (2002)</td><td>Yes (High)</td><td>1</td></tr><tr><td>Ethanol</td><td>C<sub>2</sub>H<sub>5</sub>OH</td><td>0.6 ± 0.017</td><td>Sokolov & Abbatt (2002)</td><td>Yes (High)</td><td>10<sup>-2</sup></td></tr><tr><td>Ethylene</td><td>C<sub>2</sub>H<sub>4</sub></td><td>0.16</td><td>Silva & Devlin (1994)</td><td>Yes (Moderate)</td><td>≤ms</td></tr><tr><td>Formaldehyde</td><td>H<sub>2</sub>CO</td><td>0.27 ± 0.02</td><td>Collignon & Picaud (2004)</td><td>Yes (Moderate)</td><td>≤ms</td></tr><tr><td>Formic Acid</td><td>HCOOH</td><td>0.64/0.8</td><td>Jedlovszky et al. (2008)</td><td>No</td><td>10<sup>-2</sup></td></tr><tr><td>Hexanal</td><td>C<sub>6</sub>H<sub>12</sub>O</td><td>0.67 ± 0.06</td><td>Sokolov & Abbatt (2002)</td><td>No (Out of mass range)</td><td>10<sup>-1</sup></td></tr><tr><td>Methanol</td><td>CH<sub>3</sub>OH</td><td>0.52 ± 0.06</td><td>Collignon & Picaud (2004)</td><td>Yes (High)</td><td>10<sup>-4</sup></td></tr><tr><td>Pentanol</td><td>C<sub>5</sub>H<sub>12</sub>O</td><td>0.74 ± 0.07</td><td>Sokolov & Abbatt (2002)</td><td>No</td><td>6</td></tr><tr><td>Propanol</td><td>C<sub>3</sub>H<sub>8</sub>O</td><td>0.71</td><td>Donaldson & Anderson (1999)</td><td>Yes (High)</td><td>1</td></tr></tbody></table>

**Note.** The two different values for formic acid are for interaction with ice only (low value) and interaction with both ice and neighboring formic acid adsorbed molecules at high coverage (high value).

Nakajima & Ingersoll (2016), which produced a mass flow rate at the surface of 239 kg s⁻¹ with a 0.1 solid mass fraction. These values are consistent with the estimates derived from UVIS observations (Hansen et al. 2011) for vapor production rate, and with the solid mass production rate featured in Southworth et al. (2018) that we use in our calculations in Section 2.5.

Another critical parameter is the water vapor pressure in the cracks. Since measurements of the plumes' composition give compound abundance relative to water (Waite et al. 2009, 2017), the pressure of water vapor is tied to the partial pressure of other compounds. The partial pressure of a compound is a determining factor in how much can be adsorbed onto a surface in contact with the gas (Limousin et al. 2007, and references therein). Sublimation/freezing equilibrium between the ice walls and the gas phase is fast, and therefore the gas phase should be close to the saturation vapor pressure (SVP) of water ice at the walls' temperature Ingersoll & Pankine (2010). The water vapor pressure can therefore be calculated as:

$$e(T) = A e^{-\frac{B}{T}}, \qquad (1)$$

where *e*(*T*) is the SVP, *A* and *B* are constants (*A* = 3.63 10¹² Pa and *B* = 6147 K) obtained by fitting the vapor pressure of ice at relevant temperatures from 213 to 273 K; the difference between fitted curve and data is less than 3% (Ingersoll & Pankine 2010; Lide et al. 2012). As an example, this calculation yields a pressure of 17 Pa at a temperature of 236 K.

The bulk mixture of VOCs relative to water can be assumed to be similar in the upper sections of the vents and in the plumes. As such, inputs of VOC abundance in our model (which focuses on the upper section of the vents) should be chosen to be consistent with *Cassini-INMS* measurements of these compounds, when available. Major compounds other than water (CO₂, CH₄, H₂, and NH₃) are present in the plumes with abundances from 0.3% to 1.4%. VOCs are detected with “High” or “Moderate” ambiguity; the crossover between these two categories is at 100 ppm (≈0.01%) (see Table 1 as well as Magee & Waite 2017). This value is our default abundance for all VOCs considered here, except when testing the effect of coexisting compounds with different abundances.

## 2.2. Adsorption/Desorption Behavior

This section first provides a general description of the adsorption behavior of VOCs, based on the available literature, then explains the modeling choices of this study.

VOC interaction with water ice has been found to be consistent with physisorption, reversible on the timescale of the experiments, and the uptake of VOCs on the surface can be described by a Langmuir isotherm (see Jedlovszky et al. 2006 and references therein: Dominé & Rey-Hanot 2002; Hudson et al. 2002; Sokolov & Abbatt 2002; Winkler et al. 2002; Bartels-Rausch et al. 2004; Picaud et al. 2005). Experimental evidence for *n*-alcohols indicates that they have the same saturation coverage, consistent with these compounds binding to the surface through their hydroxyl group (Sokolov & Abbatt 2002), a behavior clearly exhibited by methanol in Grand Canonical Monte Carlo simulations (Jedlovszky et al. 2008). However, the same study of methanol shows a significant effect of lateral interactions between adsorbed molecules at high coverage.

The Langmuir isotherm model describes the adsorbed quantity *Q* by (Limousin et al. 2007 and references therein):

$$Q = Q_{\max} \frac{LC}{1 + LC}, \qquad (2)$$

where *L* is a coefficient representing the affinity of the compound for the surface and *C* the concentration of the compound in the gas phase. In the case of competitive adsorption between *q* compounds, the adsorbed quantity of compound *i* is given by:

$$Q_i = Q_{\max,i} \frac{L_i C_i}{1 + \sum_{j=1}^{q} L_j C_j}. \qquad (3)$$

There are two important points to emphasize about the Langmuir model for the purpose of our study. First, as indicated by the term *isotherm*, the coefficient *L*<sub>*j*</sub> is valid for one given temperature, which is an issue for exploring the range of possible temperatures in Enceladus' vents. Second, it describes an equilibrium, which is probably appropriate in the case of the ice walls of the vents, but not necessarily for ice grains that can be exposed to very different conditions over a
short timescale, the most obvious example being the transition from the vents to the surface environment.

For our study we turn to a model based on the Polanyi-Wiegner desorption rate equation:

$$ \frac{d\theta}{dt}_{\text{desorb}} = -\nu_0 \theta^n \exp\left(-\frac{E_{\text{des}}}{RT}\right), \quad (4) $$

where $\theta$ is the coverage of the surface (molecules per unit area), $\nu_0$ is a prefactor ($s^{-1}$), $n$ is the desorption order, $E_{des}$ is the desorption energy of the compound, $R$ is the gas constant, and $T$ is the surface temperature (K). This equation assumes that desorption is the only process affecting $\theta$. A value of $n = 1$ (first order adsorption) neglects the possible interactions between adsorbed molecules. The prefactor $\nu_0$ is not explicitly tied to a physical constant and can be determined empirically or calculated through statistical rate theory of desorption (Elliott & Ward 1997). Experimental results on amorphous ice indicate a value of the order of $10^{15} \text{ s}^{-1}$ (Smith et al. 2015), similar for different molecules including some noble gases and light alkanes. We elect to use this value as the nominal in our study. $E_{des}$ is an experimental parameter, determined by fitting Equation (4) to measurements during temperature programmed desorption experiments. The $E_{des}$ values used in our study are presented in Table 1.

From Equation (4) we can define a time constant $\tau_{res}$, or residence time, that gives an average amount of time an adsorbed molecule would spend on the surface before desorbing:

$$ \tau_{res} = \left( \nu_0 \exp\left(-\frac{E_{des}}{RT}\right) \right)^{-1}. \quad (5) $$

This value can be used for comparison of the potential of different compounds to occupy the surface, and to put in perspective the time evolution of the adsorbed mixture with the timescale of grain ejection.

Equation (4) represents the desorption of molecules present on the surface; to account for adsorption we use a simple probabilistic approach:

$$ \frac{d\theta}{dt}_{\text{adsorb}} = \left(1 - \frac{\theta}{\theta_{\text{max}}}\right) s_0 J(T) P. \quad (6) $$

where $\theta_{max}$ is the saturation coverage (molecules per unit of surface, experimental value), $s_0$ is the sticking coefficient (probability that a molecule is going to stick to the surface when colliding), $P$ is the partial pressure of the compound in gas phase, and $J(T)$ is:

$$ J(T) = \frac{c(T)}{4k_B T}, \quad (7) $$

where $c$ is the thermal speed of the compound, $k_B$ is the Boltzmann constant, and $J(T)P$ is therefore a collision rate (collisions per unit of surface area per unit of time). We discuss the values and impact of $\theta_{max}$ and $s_0$ in Section 2.6. For $c_i(T)$ we use the mean magnitude of the velocity of molecules:

$$ c_i(T) = \sqrt{\frac{8\pi k_B T}{m}}, \quad (8) $$

where $m$ is the mass of the molecule of interest.

<figure><img src="image_3.png" /><figcaption>Figure 1. Variables of the flow model. The population density adsorbed on the grains is $n_G$ (molecules per m$^3$ of gas + grains mixture), while the density present in the gas phase is $n_V$ (molecules m$^{-3}$). The gas phase moves upward along the z axis at $v_v$ while the grains move at $v_G$.</figcaption></figure>

In the case of ice exposed to a multicomponent gas mixture, our model of adsorption/desorption therefore expresses the evolution of $\theta_i$, coverage of the ice surface by compound $i$, as:

$$ \frac{d\theta_i}{dt} = \left(1 - \frac{\theta}{\theta_{\text{max}}}\right) s_i J_i(T) P_i - \nu_0 \theta_i^n \exp\left(-\frac{E_{\text{des},i}}{RT}\right). \quad (9) $$

Note that $\theta$ and $\theta_{max}$ represent the current and maximum coverage by the mixture of compounds and not only by compound $i$.

## 2.3. Grain-gas Exchange Model in the Cracks

The coverage of the cracks' ice walls can be described by considering that $\frac{d\theta_i}{dt} = 0$ for all compounds in Equation (9), representing equilibrium between the gas phase and the ice phase. Ice grains, however, may not be exactly at this equilibrium due to their transient exposure to the cracks' conditions. The adsorbed mixture at a grain's surface is influenced by its adsorption history as it encountered a changing temperature when traveling upward. To represent this, we apply Equation (9) from Section 2.2 along successive sections of a crack (Figure 1).

Assuming the walls have reached equilibrium with the gas phase, exchanges occur only between the phase adsorbed on the grains (density $n_G$) and the gas phase (density $n_V$). Due to the difference in flow velocity between grain and gas, the evolution of $n_G$ and $n_V$ along the vertical direction (axis $z$) follows:

$$ \frac{v_G}{v_V} \frac{dn_G}{dz} = - \frac{dn_V}{dz}, \quad (10) $$

where $v_V$ is the flow velocity of the vapor, and $v_G$ is the grains' velocity. If we assume $v_V \gg v_G$, we can consider the gas composition does not change from the point of view of the grains when modeling the variation of $n_S$ during a short time interval through Equation (9).
The profile of temperature, vapor pressure, and density is obtained from a published profile that results from solving the equations of fluid dynamics and thermal exchange between solid and gas phases (Nakajima & Ingersoll 2016). We use the profile that was the most successful in reproducing the observed vapor to solid ratio at the exit of the vents. We consider a slower grain phase (Schmidt et al. 2008) with a default of $\frac{\nu_g}{\nu_v} = 0.1$. The model includes the option to set the ratio. Collisions between grains and walls are assumed to be frequent enough for the grains to stay at the temperature of the walls. Once the grains are out of the cracks, their temperature evolves as dictated by radiative cooling, as discussed in the next section.

## 2.4. Grain Cooling Model out of the Cracks

We now want to determine the amount of adsorbate that can stay on the surface of an ice grain ejected from Enceladus' vents. We do so by combining desorption as per Equation (4) and a simple radiative cooling model with the grain temperature decreasing as a function of radiative cooling following the Stefan-Boltzmann law:

$$ \delta E_g = -4\pi r_g^2 \sigma T^4 dt, \quad (11) $$

where $\delta E_g$ is the amount of thermal energy lost from a spherical grain over time interval $dt$, $r_g$ is the radius of the grain, $T$ is its temperature, and $\sigma$ is the Stefan-Boltzmann constant ($5.67 \times 10^{-8} \text{ W m}^{-2} \text{ K}^{-4}$). The temperature is assumed to be homogeneous inside the grain: the loss of $\delta E_g$ causes a decrease $\Delta T$ in temperature of the grain according to:

$$ \Delta T = \frac{\delta E_g}{C_p \frac{4}{3} \pi r_g^3 \rho_{\text{ice}}}, \quad (12) $$

where $\rho_{\text{ice}}$ is the density of ice ($940 \text{ kg m}^{-3}$) and $C_p$ is the specific heat of ice, which we represent as a linear function of $T$ based on the results of Giauque & Stout (1936). This linear approximation breaks down at lower $T$ (below 120 K), but once a grain reaches this temperature, further desorption is negligible, and a precise representation of the rate of cooling is not needed.

It is also possible that due to the transition of the gas to supersonic regime at the vents' exit (Yeoh 2015; Nakajima & Ingersoll 2016), the grains could be exposed to a still dense but much colder gas. This would accelerate their cooling and help keep the adsorbate on their surface. We represent an end-member of this situation by assuming a surrounding 50 K gas with a density of $10^{21} \text{ m}^{-3}$ (Yeoh 2015). This gas is composed of water molecules that collide with the grains at a rate given by:

$$ \nu_g = \frac{4}{3} n_{\text{gas}} r_g^2 c_{\text{vapor}}, \quad (13) $$

where $\nu_g$ is the collision frequency on one grain, $n_{\text{gas}}$ is the density of water vapor, and $c_{\text{vapor}}$ is the thermal velocity of water vapor as per Equation (8). This expression is derived from Schunk & Nagy (2009), Equation (4.156), accounting for the negligible radius and mass of water molecules compared with those of the grains.

Each collision is assumed to transfer enough heat from the grain to the water molecule to bring up the latter's thermal

velocity to a value consistent with the grain's current temperature.

Solar heating is included in our model but we found its influence to be negligible on desorption. For the compounds we consider, most of the desorption occurs at a relatively high temperature, at which the solar energy input is small compared to the radiative loss (50 times for a grain at 230 K, even considering an albedo of zero). The calculated energy flux from Saturn (81 K blackbody emission) is smaller by almost two orders of magnitude, thus we do not take it into account.

## 2.5. Quantification of Adsorbed Organics brought to the Surface by Snowfall

Many grains, especially among the biggest, fall back onto Enceladus' surface, possibly carrying with them organics adsorbed on their surface. If abundant enough, these organics could then be observable by remote means.

To quantify this amount of organics, we elaborate on the model of Southworth et al. (2018). For an arbitrary quantity (fraction of the saturation surface density) of a compound with a given $E_{\text{des}}$ present on the grain's surface, we calculate the remaining quantity after cooling as a function of grain size as per the model described in Section 2.4. We then use the results from Southworth et al. (2018) that describe the deposition rate on the surface as a function of grain radius to calculate and map the deposition rate for this organic compound. By assuming a lifetime of the compound at the surface (before it is broken down by radiation), it is possible to determine a predicted surface abundance of this compound. The results of Southworth et al. (2018) include grains down to a size of $0.6 \ \mu\text{m}$. While smaller grains are able to better retain VOCs, they also tend to have higher velocity and therefore escape Enceladus' gravity instead of falling back onto the surface (therefore bringing their VOC adsorbate into the E ring where they could possibly be observed). The results from Southworth et al. (2018) are a function of the assumption on the grain sources, including 98 jets identified by Porco et al. (2014) or a curtain jet emission as per Spitale et al. (2015). We include these two cases when mapping the deposition of VOCs.

## 2.6. List of Compounds and Constants

The list of VOCs we include in our study is dictated by the following considerations:

1. compounds that are in the mass range of INMS and that have been detected (even with high ambiguity) at slower flybys should be favored.

2. The model can only include compounds for which an experimental value of desorption energy ($E_{\text{des}}$) is available. Desorption rate depends exponentially on $E_{\text{des}}$, which makes it a critical parameter in the end result of adsorption processes.

Our list of compounds is presented in Table 1, along with their values of $E_{\text{des}}$ and an estimate of their residence time on ice at 230 K. The comparison of residence times shows that acetylene, ethylene, formaldehyde, and benzene are not prone to stick to the ice surface. Oxygenated compounds other than formaldehyde, on the other hand, show much longer residence time. Presumably, an alcohol group plays a major role in binding a VOC to an adsorption site (e.g., Jedlovszky et al. 2006). Another finding is that the experimental uncertainties on
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Evolution of coverage ($\theta/\theta_{max}$) of the ice walls at 236 K, in contact with water vapor accompanied by 100 ppm of each compound in Table 1. The sticking coefficient $s_0$ is assumed to be 0.1 for all compounds.</figcaption></figure>

$E_{des}$ translate into a large variation in $\tau_{res}$. For example, for acetic acid, with $E_{des}$ between 0.64 and 0.88 eV, $\tau_{res}$ can go from 0.04 s to almost 100 hr. For this reason, most of the results in Section 3 are given as a function of $E_{des}$, and specific compounds are used for illustrative purposes.

The sticking coefficient $s_i$ is poorly constrained, but theoretical considerations indicate it should stay within an order of magnitude of 1 (Clement et al. 1996). We generally assume it to be 0.1 for all the VOCs, but study its effects in Section 3. The order of magnitude of $s_i$ affects the timescale of changes in the adsorption, and different values between compounds change their relative abundance on the surface in equilibrium; however, unless assuming differences of several orders of magnitude in $s_i$, $E_{des}$ is the most influential factor on the equilibrium state of the surface.

The saturation coverage $\theta_{max}$ has been experimentally determined for a variety of compounds, in experiments that put ice surfaces in contact with a gas phase containing only one compound to be studied (generally in addition to a carrier gas and to water vapor in equilibrium with the ice surface). We are interested in a value applicable to a mixture of VOCs competing for adsorption sites, a result that would require a specific experiment. However, we can note that experiments on VOCs yield very similar $\theta_{max}$ values, of the order of $3 \times 10^{14}$ molecules cm$^{-2}$ (Hudson et al. 2002; Sokolov & Abbatt 2002). We elect to use this value for $\theta_{max}$.

# 3. Results

## 3.1. Ice Walls

We first investigate the evolution of wall coverage. We consider the upper section of the vents (which is the most relevant to future observations or even sampling) at 236 K (Nakajima & Ingersoll 2016). Figure 2 displays the evolution of coverage with time, when starting from a surface of pure ice at 236 K exposed to water vapor with VOCs from Table 1 present at a 0.01% abundance. We see that saturation coverage is reached on a timescale of a few seconds, consistent with the experiments of Sokolov & Abbatt (2002) with 1-butanol. This gives us some confidence in the order of magnitude of the

sticking coefficient we have adopted. We note, however, that when assuming a sticking coefficient closer to unity (calculation run at $s_i = 0.9$, not displayed), equilibrium is reached in a few tenths of seconds.

Figure 3 shows the state of a 236 K ice wall after equilibrium with four different gas mixtures: one including the VOCs of Table 1, and three charts including compounds identical in their properties except for $E_{des}$, $s_i$, and mixing ratio. As expected from the exponential dependence in Equation (4), $E_{des}$ impacts greatly which compound is most likely to be present on the surface. Due to the competitive nature of adsorption, the compound with the higher $E_{des}$ is likely to be over-represented on the surface, as illustrated by the dominance of acetic acid. Pentanol is only a distant second even though its desorption energy differs only by 0.02 eV from acetic acid's, which is well within the experimental uncertainties for both values. By contrast, the effect of $s_i$ and of abundance in the gas phase are found to be linear, as expected from considering a steady state in Equation (9). Therefore, remote observations or sampling of the upper section of the vents should show an excess of the higher $E_{des}$ VOCs compared with their abundance in the gas phase. This excess is a function of a compound's relative abundance and of the competition with other high $E_{des}$ compounds. Small variations in $E_{des}$ can induce major changes in the representation of a compound compared with others. In the particular case of acetic acid versus pentanol, parameters for the Langmuir isotherm derived by Sokolov & Abbatt (2002) point to pentanol being the dominant compound. The large experimental uncertainty of acetic acid's $E_{des}$ allows for it to be lower than pentanol's, which in our model would translate into the same result of pentanol dominating the surface.

## 3.2. Ice Grains within the Cracks

The adsorbed population on ice grains reaching the top of the cracks is expected to be similar to the one on the walls, with the possibility of differences caused by the history of the grains: progressive cooling as they go up the cracks and only brief exposure to the cold gas near the exit make the timescale of adsorption a potentially impactful factor. However, as Figure 4 illustrates, there should not be any significant difference. The ice grains approaching the exit of the vents would be covered by the same mixture as the ice walls.

Grains are exposed to the cold gas for a duration dependent on their velocity. This duration affects the adsorbed population depending on the kinetics of adsorption; i.e., the sticking coefficient $s_i$ may affect the result. As discussed earlier $s_i$ would be expected to be close to unity but lower values seem to yield results more consistent with experimental evidence. We investigate the effect of this uncertainty by running calculations for a fast flow ($v_V = 0.9$ cS) and fast grains ($v_G = 0.9$ vV), with $s_i = 0.1$ and $s_i = 0.9$. We find that a lower $s_i$ for all compounds reduces the proportion of high $E_{des}$ compounds on the surface, but this effect is small compared to other factors such as uncertainties on $E_{des}$. Acetic acid, the dominant compound, goes from 63.5% of the adsorbed phase for the $s_i = 0.9$ case to 59.8% for the $s_i = 0.1$ case.

## 3.3. Ice Grains Out of the Cracks

We model the desorption of VOCs from grains at the exit of the crack. We consider a mixture of VOCs with a range of $E_{des}$ from 0.4 to 0.8 eV. We first consider a case with a 1 µm radius
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Composition of the mixture adsorbed on the walls in the upper section of the vents (236 K). Top left: VOC mixture made of 0.01% of each compound in Table 1. Top right: VOC mixture made of 0.01% of compounds of identical properties, with different $E_{des}$ going from 0.4 to 0.8 eV. Bottom left: VOC mixture made of 0.01% of compounds of identical properties, with different $s_i$ going from 0.1 to 1. Bottom right: VOC mixture made of compounds of identical properties, with different abundances going from 0.01% to 1%.</figcaption></figure>

grain (on the lower side of the size range considered by Southworth et al. 2018), initially at 236 K, with and without cooling by a surrounding 50 K gas. The results are shown in Figure 5. We have adapted the range of $E_{des}$ displayed to the case treated. In both cases a threshold in $E_{des}$ is apparent, under which a compound is not retained on the surface. The presence of a surrounding cool gas lowers this threshold by 0.04 eV. Another aspect worth noting is that the highest $E_{des}$ compounds are fully retained. Compounds with $E_{des} \ge 0.7$ eV are retained in their initial quantity. We then run the same calculation for different grain sizes (0.1 and 10 µm) and initial temperatures (230 and 220 K) to quantify the effects of these parameters. The results are presented in Figures 6 and 7. Due to the slower cooling of bigger grains, there is almost a 0.1 eV shift in the

threshold of retention between 0.1 and 10 µm grains. This would affect the retention of compounds in the 0.5–0.6 eV $E_{des}$ range (near the threshold for retention). Bigger grains are more likely to fall back onto Enceladus’ surface, so this effect has implications for observations of organics on the surface compared with analysis of grains in Enceladus’ vicinity or in the E ring. The effect of a 30 K shift amounts to a 0.07 eV shift to the threshold for retention, on par with the experimental uncertainties on $E_{des}$ for compounds like pentanol or methanol.

### 3.4. Ice Grains Falling Back onto Enceladus’ Surface

By comparing results from Sections 3.2 and 3.3, we can see that the threshold in $E_{des}$ for a compound to be present on a
Grain fraction coverage

<figure><img src="image_6.png" /><figcaption>**Figure 4.** Composition of the mixture adsorbed on the ice grains in the upper section of the vents at 236 K (left) vs. composition of the bulk VOC mixture (right). Compounds present on the right chart but absent from the left chart have a low enough *E*<sub>des</sub> to not be appreciably adsorbed.</figcaption></figure>

Gas mixture composition

<figure><img src="image_7.png" /></figure>

Without surrounding vapor

<figure><img src="image_8.png" /><figcaption>**Figure 5.** Mixture still adsorbed after cooling on 1 µm radius grains starting at 236 K in an environment without VOCs, as a function of *E*<sub>des</sub> (in eV), for a case without (left) and with (right) surrounding 50 K water vapor.</figcaption></figure>

With surrounding vapor

<figure><img src="image_9.png" /></figure>

grain when it is about to exit the cracks is higher than the threshold required to keep the compound on the grain throughout the cooling process (0.7 eV and 0.6 eV, respectively). In other words, if a compound would be lost due to the cooling process, it is likely that it was not present on the grains in the first place. Considering this, the abundance of VOCs falling back with the grains onto Enceladus' surface depends only on the deposition rates and the quantity of VOCs present on the grains at the vents (a fraction of the saturation coverage).

We show in Figure 8 the map of abundance of a VOC with an *E*<sub>des</sub> of 0.7 eV (comparable to acetic acid, pentanol, or propanol). This VOC is assumed to be initially present at saturation coverage on the grains, and to have a 39 day average lifetime on the surface, corresponding to the 27 day half-life calculated by Hodyss et al. (2009) for methanol. The result is shown both for multiple jets and a curtain source. We see that the maximum abundance, of the order of one millimole m<sup>-2</sup>, is limited to the immediate surroundings of the sources.
<figure><img src="image_10.png" /><figcaption>**Figure 6.** Mixture still adsorbed after cooling on grains starting at 236 K in an environment without VOCs, as a function of *E*<sub>des</sub> (in eV) and with surrounding vapor, for ice grains with a radius of 0.1 µm grain (left) and 10 µm(right). The difference in color scheme is due to the necessity to use different energy scales.</figcaption></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /><figcaption>**Figure 7.** Mixture still adsorbed after cooling on 1 µm radius grains as a function of *E*<sub>des</sub> (in eV) and with surrounding water vapor, for an initial *T* of 230 K (left) and 200 K (right).</figcaption></figure>

<figure><img src="image_13.png" /></figure>

The tentative detection of methanol on Enceladus' surface (Hodyss et al. 2009) raises the question of whether ice grains could contribute to its presence. It is apparent in our nominal case that methanol is not supposed to be present on grains in the vents (Figure 4). Grains would only keep methanol on the ice surface if we assume cooling of grains by a surrounding cold gas, and that methanol's *E*<sub>des</sub> is on the upper end of the range suggested by experiments (i.e., 0.58 eV). It is possible for

grains in the vents to retain methanol on their surface if we assume both methanol's abundance and sticking coefficient to be one order of magnitude higher than for competing compounds. Methanol then represents 1.5% of the adsorbed content (Figure 9). Still assuming the highest *E*<sub>des</sub> of 0.58 eV, we then map the expected abundance after methanol-bearing grains cool down and fall back down onto Enceladus' surface. We present the results in Figure 10. We see that even in this
<figure><img src="image_14.png" /><figcaption>**Figure 8.** Abundance on the surface of a compound with a $E_{des}$ of 0.7 eV, assuming a 39 day lifetime, and initial presence at saturation coverage on the grains, coming from a jet source (left; Porco et al. 2014) and a curtain source (right; Spitale et al. 2015). Enceladus surface background picture: JPL PIA18435.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>**Figure 9.** Composition of the mixture adsorbed on the ice grains in the final section of the vents at 236 K, assuming for methanol: $E_{des} = 0.58$ eV, $s_i$ and abundance 10 times higher than for other VOCs.</figcaption></figure>

favorable scenario, the maximum abundance of methanol is considerably lower (4 orders of magnitude) than for high $E_{des}$ compounds such as acetic acid (the portion it occupies in Figure 9 suggests that the results of Figure 8 are practically unchanged as far as acetic acid is concerned). Whether this abundance is enough to explain the remote detection (Hodyss et al. 2009) remains to be determined. If we assume there is no higher $E_{des}$ competitor to methanol present in the plumes, a higher abundance, more comparable to values displayed in Figure 8, would be possible. Without this assumption, the

process of grain deposition is unlikely to directly contribute to the surface abundance of methanol; but it might be bringing other, higher $E_{des}$ VOCs that can then be broken down through photolysis and/or radiolysis and form methanol.

## 4. Discussion

**Over-representation of sticky compounds on the walls and grains:** The most straightforward takeaway of our calculations is the predominance of VOCs with the highest $E_{des}$ both on the walls of the vents and on the surface of ice grains. As illustrated by Figure 10, even ascribing higher $s_i$ and abundance to lower $E_{des}$ compounds does not cancel this effect. Changes in the profile temperature of the vents (calculations not shown) do not affect this result either. Compounds with a high enough $E_{des}$ to dominate in the vents are fully retained on the surface of most ice grains as they escape. Compounds with $E_{des} \le 0.5$ eV are not retained on the surface of grains in the range of conditions we have tested; therefore, they stay properly proportioned in gas phase according to their vapor pressure above the water table.

**Implications for individual compounds:** Translating this result into a conclusion about individual compounds is more delicate for two reasons. First, the experimental uncertainties on $E_{des}$ have a significant impact on the fate of a compound. This is illustrated by the case of acetic acid, which features the highest $E_{des}$ but also the largest uncertainty. The lower end of the $E_{des}$ range would make it comparable to the lowest estimate for formic acid, therefore making pentanol and propanol more likely to dominate the adsorbate mixture. Second, the competitive nature of adsorption means that the presence of a VOC on the surface does not only depend on its $E_{des}$ being high enough, but also on whether other compounds with comparable or higher $E_{des}$ are present in the gas phase. This is compounded by the absence of constraints on $s_i$, although $E_{des}$ is the most important factor; experimental studies to better constrain $E_{des}$
<figure><img src="image_16.png" /><figcaption>**Figure 10.** Abundance on the surface of methanol, assuming a 39 day lifetime, initial abundance on the grains at 1.5% of saturation coverage (as in Figure 9), coming from a jet source (left; Porco et al. 2014) and a curtain source (right; Spitale et al. 2015). Enceladus surface background picture: JPL PIA18435.</figcaption></figure>

would in all likelihood better help in narrowing down our conclusions than studies of $s_i$.

**Possibility of burying VOC molecules in the walls:** The most abundant compound in the gas phase both in the vents and the plumes is water vapor. As this vapor rises through the vents, it meets colder ice walls and equilibrates with them at the SVP of water at this temperature. This has the effect that condensation is expected to happen on the upper (colder) sections of the cracks (Ingersoll & Pankine 2010; Nakajima & Ingersoll 2016), with the possible effect of building up enough ice to close the vents. This raises the scenario of organics adsorbed on the ice surface being trapped in the ice. The possible effect would be to keep the amount of organics on the surface below saturation coverage (making remote detection less likely) and to keep the surface out of equilibrium with the gas, effectively depleting these compounds in the gas phase. The rate of condensation calculated by Nakajima & Ingersoll (2016) translates into the formation of a water monolayer in 10 ms, which is up to three orders of magnitude shorter than the residence time $\tau_{res}$ of the highest $E_{des}$ compounds. However, we hereafter review experimental evidence that indicates the above scenario may not be occurring. The work by Sokolov & Abbatt (2002), in conditions similar to the vents, including the presence of water vapor near the SVP, shows an adsorption that is “reversible on the timescale of the experiments.” They observed that when the ice is no longer exposed to the VOC, said VOC desorbs in amounts corresponding to what was adsorbed during the experiment. Experiments of water uptake on alcohol-covered ice show that methanol (Thomson et al. 2013) has no noticeable effect on the uptake, while butanol (Kong et al. 2014) only reduces the uptake by 20%. Most water molecules briefly adsorb onto the surface before crossing the alcohol layer and bond to the water ice. The VOCs considered in this study are unlikely to behave differently, therefore, allowing for an equilibrium both between the ice walls and the water vapor, and between the VOCs in gas phase and those adsorbed at the

surface. The VOC mixture in the gas phase would therefore not be altered by adsorption once the walls have reached their equilibrium composition.

**Ice grains in the E ring:** A consequence of our model would be that the ice grains originating from the vents and feeding the E ring would be likely to have a mixture of VOCs on their surface. These VOCs might then contribute to measurements in the E ring by CDA or INMS. To our knowledge no analysis of the signal caused by E ring grains in INMS has been performed. The CDA data features three types of grains: type 1 grains are almost entirely water ice and display no significant organic signal, type 2 grains have some organic content, while type 3 grains are predominantly water ice and salts (Postberg et al. 2008, 2009, 2011, 2018). The current understanding of the formation of type 2 grains is that they originate either in release of refractory organics by bubble bursting, or adsorption of VOC onto icy grains. The first subcategory carries a heavy refractory content generating a large amount of High Mass Organic Cations (HMOC) in the CDA signal (Postberg et al. 2018). In these HMOC type 2 grains we would expect the internal organic content to dwarf any peak created by VOCs adsorbed on their surface. A 1 µm grain with a surface saturated in VOCs would carry $3.7 \times 10^7$ VOCs molecules, while a type 2 HMOC-carrying grain of this size with a 1% (by number) internal organic content would carry $1.3 \times 10^9$ heavier organic molecules. We then consider the second, more numerous subcategory, VOC-carrying type 2 grains. We find that a pure water ice grain population between 0.1 µm and 1 µm, assuming a grain size distribution in $r^{-3}$ (consistent with Southworth et al. 2018) and a surface saturated in VOCs ($3 \times 10^{14}$ molecules cm$^{-2}$, see Section 2.6), would show a ratio VOC/water of 0.2% by number, which generally agrees with the VOC-carrying type 2 population detected by CDA. Smaller grains would feature a higher VOC/water ratio but their origin and therefore size distribution may be different: Southworth et al. (2018) speculates that nano grains may originate in the
supersonic part of the flow near the surface. In that case these
grains may not have enough time to accumulate large quantities
of VOCs on their surface and this may be the origin of the type
1 population.

The organic content (or lack thereof) of type 3 grains has not
been compared to type 1 and 2, but since they originate from
the ocean (Postberg et al. 2009, 2011) and went through the
cracks, they are susceptible to accumulate high E<sub>des</sub> VOCs on
their surface; some organic compound features do appear in
their spectra (supplemental material of Postberg et al. 2011).
Due to their generally larger size (≥0.6 µm, Postberg et al.
2011), type 3 grains would display a generally low adsorbed
VOC population (we calculate a number VOC/water ratio of
0.03%). Additionally, salts may suppress ionization of organics
in CDA, making VOC detection more difficult in type 3 grains
(F. Postberg & N. Khawaja 2019, private communication).

Finally, the amount of adsorbed VOCs detected on the E ring
grains would depend on the loss processes. At a temperature of
80 K (comparable to Enceladus' surface) spontaneous deso-
rption is negligible for VOCs, so the main loss processes would
be radiolysis and photolysis. The lifetime of 0.1 µm grains or
bigger in the E ring is counted in years (Juhász et al. 2007), a
long timescale when compared to, e.g., methanol's lifetime on
Enceladus' surface (Section 2.5, Hodyss et al. 2009). This
implies most grains in the E ring would have had their adsorbed
VOCs sputtered away and/or converted into radiolytic and
photolytic products.

**5. Conclusion**

We have modeled the effects of the adsorption of VOCs onto
ice at Enceladus, on the crack’s walls, on ice grains in the
cracks, and on ice grains outside of the cracks. Our general
conclusion is that in conditions relevant to Enceladus,
adsorption will segregate strongly between compounds as a
function of their E<sub>des</sub>. Compounds with E<sub>des</sub> ≥ 0.7 eV
dominate the ice surface, and compounds with E<sub>des</sub> ≤ 0.5 eV
are negligibly present on it. Compounds of intermediate E<sub>des</sub>
may be present on the surface only as competition with high
E<sub>des</sub> compounds allows. Our results indicate E<sub>des</sub> values to be
the most important factor in the composition of the adsorbed
phase. This is a critical piece of information for the
interpretation of future measurements: the preponderance of a
compound on the ice surface does not represent its abundance
in gas phase. This is relevant to remote observations, analysis
of small ice grains (that do not carry an internal organic
content), collecting and concentrating grains emitted from the
plume, or sampling of ice in the vents.

The other implication is that as ice grains fall back on the
surface, they bring with them small amounts of these adsorbed
compounds that can then participate in photochemistry and/or
radiation chemistry on the surface. Understanding the flux of
VOCs reaching the surface is critical to interpreting observa-
tions that may result from this chemistry.

Uncertainties in E<sub>des</sub> make it difficult to conclude the
individual fate of given compounds, and additional exper-
imental data are desirable for some compounds (see the
Appendix for a discussion on the possibility to infer E<sub>des</sub> from
existing data). However, our results already indicate that
oxygen-bearing VOCs are much more likely to be retained on
ice, and among compounds possibly detected by Cassini
INMS, propanol, butanol, and acetic acid are likely to be over-
represented on the ice surface relative to their gas phase

abundance, leading to increased participation in Enceladus'
surface chemistry.

The conclusions of our work are likely to be relevant to
Europa, where plumes have tentatively been identified (Roth
et al. 2014; Sparks et al. 2016; Jia et al. 2018). Europa’s
stronger gravity could increase the fraction of grains that fall
back onto the surface unless their ejection velocity is faster than
at Enceladus. An influx of a given set of VOCs onto Europa’s
surface, concentrated around the plume emission regions,
would be one additional factor to take into account to
understand Europa’s rich surface chemistry (e.g., Carlson
et al. 1999a, 1999b; Brown & Hand 2013).

Plots drawn with Matplotlib (Hunter 2007). A.B. acknowl-
edges support by CNES. This work is supported by the *Cassini*
Project through JPL subcontract 1405853. Thanks are due to
Miki Nakajima and Ben Southworth for sharing and explaining
their respective model results. Thanks are also due to Nozair
Khawaja and Frank Postberg for their explanations about the
CDA data set and findings.

**Appendix**

Estimating Desorption Energies without Experiments?

Since experimental data for desorption energy are not
available for many compounds, we try to link it to another
physical quantity that, where available, could be used as a
predictor for E<sub>des</sub>.

Adsorption of a gas onto an ice surface is similar to the process
of dissolving a gas in water (hydration) since it rests on the
creation of intermolecular forces between the compound and
water molecules. They differ in that adsorption can be achieved
through linking only a part of the compound to the ice surface,
such as the C-O bond of an oxygen-bearing organic forming a
hydrogen bond with OH (Gao & Leung 2005), rather than having
it surrounded by water molecules. However, the interaction of
this C-O bond with water would be, in the hydration process,
responsible for a large part of the variation in enthalpy. We use
standard values of enthalpy of hydration from the ORCHYD
(ORganic Compounds HYDration) database (Plyasunova et al.
2004) and compare them to desorption energies where available.
In the case of formic and acetic acid, the enthalpy of hydration is
obtained by subtracting the enthalpy of formation of the gas from
the enthalpy of formation of the aqueous compound (values from
Wagman et al. 1982).

We find that the available values exhibit a linear correlation
following ΔH<sup>0</sup><sub>hyd</sub> = -87.229 E<sub>des</sub>, with an R<sup>2</sup> of 0.934 (see
Figure 11). This is obtained with simple and oxygen-bearing
compounds, aromatic or aliphatic, but formic and acetic acid
are not included. These two last compounds do not seem to
follow the correlation, which may indicate a specificity in the
interaction of carboxyl groups with the ice surface. It should be
noted that the highest E<sub>des</sub> value for formic acid accounts for
interaction between adsorbed molecules on the surface
(Jedlovszky et al. 2008). We can only speculate as to whether
such an increase in E<sub>des</sub> due to these interactions is specific to
carboxylic acids.

This graph includes methyl formate (C<sub>2</sub>H<sub>4</sub>O<sub>2</sub>), which is an
isomer of acetic acid and shows much lower E<sub>des</sub> and ΔH<sup>0</sup><sub>hyd</sub>
while falling close to the correlation. This could be due to the
lower polarity of methyl formate and the absence of an OH group
and its hydrogen bond forming capability. Outside the case of
acetic and formic acid, the most discrepant case is formaldehyde,
<figure><img src="image_17.png" /><figcaption>**Figure 11.** Desorption energies vs. hydration enthalpy. The green line is the best linear fit ($\Delta H_{\text{hyd}}^{0} = -87.229 E_{\text{des}}$) that goes through (0, 0) not including acetic acid nor formic acid.</figcaption></figure>

at a predicted $E_{\text{des}}$ of 0.38 eV versus an experimental value of 0.27 ± 0.02 eV, a difference on par with the largest experimental uncertainty in our list of compounds (acetic acid). This difference could be due to formaldehyde forming methylene glycol in solution, increasing the amount of hydrogen bonding. Experimental data are needed to include amino acids, which would be of great astrobiological interest in the context of Enceladus and Europa. Standard hydration enthalpy for glycine is calculated to be –124 kJ/mole (Wagman et al. 1982 and NIST database citing Ngauv et al. 1977), and its adsorption energy on ice at 0.81 eV/molecule (Escamilla-Roa & Moreno 2013); this would place glycine well out of the correlation, but the value of adsorption energy has been obtained for a thin film of amorphous ice on top of forsterite. The film is thin enough to allow for interaction with the forsterite, possibly increasing the adsorption energy. More laboratory/simulation data are required for organic compounds featuring nitrogen atoms or carboxyl groups to understand if this promising correlation can be used predictively.

## ORCID iDs

Alexis Bouquet https://orcid.org/0000-0001-8262-9678

Christopher R. Glein https://orcid.org/0000-0002-2161-4672

J. Hunter Waite, Jr. https://orcid.org/0000-0002-1978-1025

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