Mélanie Petitjean

György Hantal

Coline Chauvin

Philippe Mirabel

Stéphane Le Calvé
email: slecalve@illite.u-strasbg.fr

Paul N M Hoang

Sylvain Picaud
email: sylvain.picaud@univ-fcomte.fr

Pál Jedlovszky

Adsorption of Benzaldehyde at the Surface of Ice, Studied by Experimental Method and Computer Simulation

Adsorption study of benzaldehyde on ice surfaces is performed by combining experimental and theoretical approaches. The experiments are conducted over the temperature range 233 -253 K using a coated wall flow tube coupled to a mass spectrometric detector. Besides the experimental way, the adsorption isotherm is also determined by performing a set of grand canonical Monte Carlo simulations at 233 K. The experimental and calculated adsorption isotherms show a very good agreement within the corresponding errors. Besides, both experimental and theoretical studies permit us to derive the enthalpy of adsorption of benzaldehyde on ice surfaces Hads, which are in excellent agreement: Hads = -61.4 ± 9.7 kJ/mol (experimental) and Hads = -59.4 kJ/mol (simulation).

The obtained results indicate a much stronger ability of benzaldehyde of being adsorbed at the surface of ice than that of small aliphatic aldehydes, such as formaldehyde or acetaldehyde. At low surface coverages the adsorbed molecules exclusively lie parallel with the ice surface. With increasing surface coverage, however, the increasing competition of the adsorbed molecules for the surface area to be occupied leads to the appearance of two different perpendicular orientations relative to the surface. In the first orientation, the benzaldehyde molecule turns its aldehyde group toward the ice phase, and, similarly to the molecules in the lying orientation, forms a hydrogen bond with a surface water molecule. In the other perpendicular orientation, the aldehyde group turns to the vapor phase, and its O atom interacts with the delocalized  system of the benzene ring of a nearby lying benzaldehyde molecule of the second molecular layer. In accordance with this observed scenario, the saturated adsorption layer, being stable in a roughly 1 kJ/mol broad range of chemical potentials, contains, besides the first molecular layer, also traces of the second molecular layer of adsorbed benzaldehyde.

Introduction

The upper troposphere is characterized by low temperatures ranging from about 188 to 233 K and by the presence of ice (cirrus) as well as mixed ice/water clouds covering a substantial portion (up to 25 %) of the Earth's surface. 1 Ice clouds are formed in the troposphere at altitudes of 4-15 km, where they can reflect the incoming solar radiation and trap the terrestrial infrared radiation. Depending on the dominant effect, this results either in cooling or warming of the underlying layers of air, according to the particle density, their morphology as well as their (surface) chemical composition. The change of their frequency and distribution, therefore, impacts substantially on the regional and global climate.

The interaction between trace gases and mixed or ice clouds can promote heterogeneous chemistry, and therefore initiate the transfer of chemical species from the gas into the condensed phases. Hydrometeors hence appear to offer a favorable environment for fast physical and chemical transformations that can modify both trace gas and aerosol compositions. [START_REF] Seinfeld | Atmospheric Chemistry and Physics[END_REF] Below approximately 230 K, clouds are predominantly composed of ice crystals with number density ranging from 0.001 to 50 cm -3 . 1,[START_REF] Hoyle | [END_REF] The presence of oxygenated Volatile Organic Compounds (VOCs), such as alcohols, aldehydes, ketones and carboxylic acids in the upper troposphere is also well established, [4][5][6][7] and could be explained as a consequence of a rapid convection from the polluted boundary layer. 8 The photolysis of carbonyl compounds, such as aldehydes and ketones is a net source of OH and HO2 radicals, and hence leads to an enhanced abundance of these oxidants as well as of peroxyacetyl nitrate. Enhanced production of main oxidants of the atmosphere can then affect the concentrations of many other trace gases, and is likely to modify the ozone cycling reactions in this region. Many recent experimental and theoretical studies have been focused on the adsorption of oxygenated VOCs (alcohols, acetic acid, acetone, etc.) on pure ice surfaces. [9][10][11][12][13][14][15][16][17][18] The experimental results have highlighted that even if the interaction between the organic compounds and pure ice is strong enough to lead to a monolayer adsorption in laboratory experiments, [10][11][12][13][14]19 the occurrence of cirrus clouds in the upper troposphere region will not affect significantly the gas phase concentrations of oxygenated organic compounds.

Experimental investigations can be well complemented by computer simulations, which provide an atomistic level insight into the three-dimensional structure of the adsorption layer.

On the other hand, results of computer simulation studies can only be verified by comparing them to experimental data. Among the various computer simulation techniques the grand canonical Monte Carlo (GCMC) method 20,[START_REF] Allen | Tildesley Computer Simulation of Liquids[END_REF] is of particular importance in addressing this problem, since in such simulations a real adsorption experiment can be modeled by systematically varying the chemical potential of the VOC and determining its surface concentration as a function of the chemical potential. The GCMC method has successfully been applied to a set of different adsorption processes, such as the adsorption of VOCs on ice, [15][16][17][18] as well as of water at the surface of various carbonaceous materials, [START_REF] Muller | [END_REF][23][24][25][26][27] covalent organic frameworks, 28 silica, 29,30 self-assembled monolayers, 31 and several metal oxides. [32][33][34][35] In spite of the increasing interest of the problem of VOC adsorption at the ice surface due to its great atmospheric relevance, to the best of our knowledge, no study has been focused so far on the adsorption of aromatic oxygenated VOCs on ice surfaces, although the presence of a phenyl group can likely modify the behavior of the adsorbed molecule.

Benzaldehyde represents the dominant species of aromatic carbonyl compounds in the troposphere. [START_REF] Atkinson | Gas-phase tropospheric chemistry of organic compounds[END_REF] In addition, benzaldehyde can be considered as a simple model of aromatic aldehydes. It can be found in fruits, and is used as a soil fumigant and in the manufacturing of deodorants/air fresheners and loose mineral wool fiber. 16 Benzaldehyde is also produced in situ in the atmosphere by oxidation of various VOCs, such as toluene. [START_REF] Atkinson | Gas-phase tropospheric chemistry of organic compounds[END_REF] The goal of the present study is to examine the interaction of benzaldehyde with ice surfaces at temperatures relevant for the upper troposphere. Our approach of investigation combines experiments (adsorption measurement) and theory (computer simulation), as in this way we can get more detailed and relevant information on the system studied than what could be reached either by experiment or theory alone. Surface coverages of benzaldehyde on ice have been experimentally measured for temperatures ranging from 233 K to 253 K. Our experimental data were then compared with those obtained in this work by GCMC simulations performed at 233 K on a model proton-disordered ice surface. To our knowledge, this work is the first to report uptake of benzaldehyde on ice surfaces for temperatures relevant of the mid and upper troposphere. This paper reports also the first joint experimental and theoretical adsorption study of an aromatic species on ice.

Methods

Adsorption Experiments.

The uptake of benzaldehyde on ice surfaces was studied using a vertical coated wall flow tube coupled to a mass spectrometer, already described elsewhere. 10,11,[START_REF] Journet | [END_REF]38 We will therefore provide only a brief summary of its principle operation. The apparatus has a double jacket to allow the system to be operated at low temperature. The cooling fluid was circulated in the inner jacket from a cooler/circulator (Huber, Unistat 385) while vacuum was maintained in the outer jacket for thermal insulation.

The temperature of the flow tube could be cooled down and regulated between 188 and 253 K. The jacketed flow tube was approximately 40 cm in length with an internal diameter of 2.8 cm. The ice surface was prepared by totally wetting, with Milli-Q water (18 M cm), the inner wall of the flow tube that was precooled to 263 K. The viscous aqueous film was then cooled down to 253 K to obtain a solid film that can be retained during the course of the experiments. Finally, the film was cooled directly to the desired temperature over a period of 10-15 min. The thickness of the ice film was estimated between 48 and 60 µm by weighting the resulting liquid water, when the ice film was melted at the end of the experiment.

The helium carrier gas (UHP certified to > 99.9995 % from Messer) was used without further purification. During the experiment, water vapor was added to the main helium flow in order to provide a partial pressure of water, equal to the vapor pressure of water over the ice film and therefore inhibit net evaporation of this film. The resulting humidified helium flow was injected at the upstream end of the flow reactor.

Benzaldehyde ( 98 %) purchased from Acros Organics was further purified before being used by repeated freeze, pump, and thaw cycles. To perform an experiment, benzaldehyde was premixed with helium in a 10 l glass light-tight bulb to form 5.6810 -2 -0.116 % mixtures, at a total pressure of  0.99  10 5 -1.03 10 5 Pa. The mixture containing benzaldehyde was injected into the flow tube reactor via a sliding injector that allows changing the exposed ice surfaces (140 -270 cm 2 ). The injector was jacketed, and a heating tape was wound up in the jacket, to ensure a gentle heating. 11 All the gases flowed into the reactor through Teflon tubing. The gas mixture containing benzaldehyde and water vapor diluted in helium was flowed through the reactor with a linear velocity ranging between 30 and 100 cm/s. Concentrations of benzaldehyde in the gas phase were calculated from their mass flow rates, temperature and pressure in the flow tube. All the flow rates were controlled and measured with calibrated mass flowmeters (Millipore, 2900 series). The pressure that ranged between 250 and 330 Pa was measured with two capacitance manometers (Edwards, 622 Barocel, range 0-13000 Pa, and Keller, PAA-41, range 0-10000 Pa) connected at the top and bottom of the flow tube. Under our experimental conditions, the mixing time mix between benzaldehyde flow and the main He flow was lower than 2 ms, 19 which corresponds to a mixing length smaller than 0.3 cm.

The gas stream coming out of the flow tube was analyzed using a differentially pumped mass quadruple spectrometer Pfeiffer Vacuum QMS. Benzaldehyde was monitored at the main fragment ion CH3CO + peak at m/z = 43 amu using a temporal resolution of 30 ms, an ionization energy of 60 eV and an emission current of 1000 µA.

Computer Simulations.

In modeling the adsorption of benzaldehyde on ice, a series of 29 Monte Carlo simulations has been performed on the grand canonical (,V,T) ensemble at the temperature T = 233 K. The X, Y and Z edges of the basic simulation box have been 100 Å, 35.926 Å, and 38.891 Å long, respectively, X being the axis perpendicular to the ice surface.

Standard periodic boundary conditions have been applied. In modeling the ice phase 18 molecular layers of water, containing 160 molecules each, have been placed in the middle of the basic simulation box in the arrangement corresponding to the geometry of proton-disordered Ih ice. The chemical potential of benzaldehyde  has been systematically varied in the simulations from -70.31 to -60.66 kJ/mol. In this way, the adsorption isotherm has simply been obtained as the average number of the benzaldehyde molecules in the system <N> as a function of their chemical potential. The benzaldehyde chemical potential values corresponding to the different simulations as well as the resulting values of <N> are collected in Table 1.

Water molecules have been described by the rigid five site TIP5P potential, 40 since the melting point of this model is known to be rather close to that of real water. 41 Benzaldehyde has been modeled by the OPLS force field 42 using the charge distribution calculated by Canneaux et al. 43 The interaction energy of two molecules has been calculated as the sum of their site-site Lennard-Jones and charge-charge Coulomb interactions. All interactions have been truncated to zero beyond the molecular centre-centre cut-off distance of 12.5 Å. The total potential energy of the system has been calculated as the sum of the pair interaction energies of all molecule pairs. In the simulations, performed by using the program MMC [START_REF] Mezei | Monte Carlo program for simulation of molecular assemblies[END_REF] particle displacement and benzaldehyde insertion/deletion attempts have been done in alternating order. In a particle displacement step a randomly chosen molecule has been randomly displaced by no more than 0.25 Å and randomly rotated around a randomly chosen space-fixed axis by no more than 15 o . Water and benzaldehyde molecules have been selected for such moves with equal probabilities.

Particle insertion/deletion steps have been done using the cavity biased algorithm of Mezei. [START_REF] Mezei | [END_REF]46 Thus, new molecules have only been tried to be inserted into empty cavities of the minimum radius of 2.9 Å. Suitable cavities have been searched for in the system along a 100  100  100 grid, which has been regenerated after every million Monte Carlo steps. Particle insertion and deletion attempts have been done in alternating order.

The systems have been equilibrated by performing 100 -500 million Monte Carlo steps.

The number of benzaldehyde molecules in the system has then been averaged over 300 -400 million equilibrium configurations. Finally, at selected chemical potential values 2000 sample configurations, separated from each other by 100000 Monte Carlo steps each, have been saved for detailed analyses. In these analyses the two ice surfaces present in the basic box have been treated separately, thus, all the results have been averaged not only over the 2000 sample configurations, but also over these two ice surfaces per system.

Adsorption Isotherm

Experimental Isotherms.

Uptake experiments were performed by first establishing a highly stable flow of benzaldehyde in the injector, this injector being positioned past the end of the ice film. The injector was then moved quickly to an upstream position so that the ice film was exposed to benzaldehyde. The uptake of benzaldehyde on the ice film leads to a drop of signal as shown in Figure 1. After a time-scale ranging from several seconds to a few minutes depending on the concentration of the gas mixture, the ice surface was then saturated, and the MS-signal returned to its initial level. When the injector was pushed back, benzaldehyde desorbed from the ice surface and the signal increased and then again returned to its initial level.

Similar experiments were conducted over the temperature range of 233 -253 K and for gas phase concentrations varying from 1.5610 12 to 1.8710 13 molecules/cm 3 .

Surface Coverage.

The number of benzaldehyde molecules adsorbed on the ice surface Nads was determined from the integrated area of the adsorption peak and the total flow rate in the flow tube. The surface coverage N of benzaldehyde was then calculated from the geometric exposed ice surface area Aice as to N = Nads / Aice. The experiments were performed several times, using newly generated ice surfaces and several gas mixtures in order to ensure the reproducibility of the data.

Surface coverage N versus gas phase concentrations is plotted in Figure 2 for three temperatures, i.e., 233, 243 and 253 K. The relative errors on the gas phase concentrations, which range between 8 and 16 % (horizontal error bars in this figure) have been calculated from the possible uncertainties of the total pressure in each flow. The quoted errors on N (vertical error bars) arise from uncertainties made on the total flow rate, exposed ice area and concentrations in the gas phase. They also include a systematic 2 % error that corresponds to the error on the integrated area of adsorption peaks. These resulting errors on N vary between 15 and 27 %.

Langmuir Fit of the Isotherms and Heat of Adsorption.

Since the main assumptions of the Langmuir theory, namely that (i) adsorption cannot proceed beyond monolayer coverage, and (ii) the adsorption of a new particle occurs independently from the occupancy of other adsorption sites, are certainly valid in the pressure range of our measurements, we used this theory to analyze our experimental data. According to this theory, the number of molecules adsorbed per unit area of ice surface is related to the concentration of benzaldehyde in the gas phase as gas ads

gas ads M ] de benzaldehy )[ ( 1 ] de benzaldehy )[ ( T K T K N N + = =  , ( 1
)
where  is the fractional coverage, NM is the monolayer capacity, the brackets [...]gas stand for the gas phase concentration, and Kads(T) is the temperature dependent adsorption constant that describes partitioning between adsorbed and non-adsorbed molecules.

From a thermodynamic point of view, the equilibrium between the gas phase and the surface can also be expressed by using a dimensionless, temperature dependent partition coefficient, K(T):

) ( exp ] de benzaldehy [ ads gas T K RT G V A N =        =  , ( 2
)
where R is the gas constant, A/V is the area-to-volume ratio of an ideal gas adsorbed at the surface, and Gads is the free energy of adsorption. A/V defines the standard state for the adsorbed phase. In absence of general agreement on the choice of a standard state, the ratio of A/V is conveniently considered equal to ~1.7  10 7 cm -1 , 47,48 which corresponds to the molar area of 3.74  10 7 m 2 /mol. Note that the enthalpy does not depend on the choice of standard states. 49 The advantage of the chosen standard state is its independence of temperature, particle size, and absolute values of both V and A. 50 Gads is related to the enthalpy and entropy of adsorption (Hads and Sads, respectively) via the Gibbs equation:

) ( ln ads ads ads T K RT S T H G - =  -  =  . (3)

At low concentrations Kads(T)

[benzaldehyde]gas << 1, therefore, using eqs. 1 and 2, the relation of K and Kads can be written as follows:

A V T K N T K  =  ) ( ) ( M ads . ( 4
)
In addition, N increases linearly with the concentration of benzaldehyde with a slope of

NMKads(T) or K(T)V/A:

gas gas M ads de] benzaldehy [ ) ( de] benzaldehy [ ) (   =   = A V T K N T K N . ( 5
)
Figure 2 shows linear isotherms on pure ice of N versus [benzaldehyde]gas at 233, 243 and 253 K. The resulting values of both K(T) and Kads  NM are derived from the slope of these plots according to eq. 5 and are reported in Table 2. For each temperature, Gads can be obtained from the value of K according to eq. 3.

The temperature dependence of K(T) between 233 and 253 K can, in principle, be used to determine the adsorption enthalpy Hads of benzaldehyde on pure ice according to eq. 3. The plot of ln K versus 1/T is linear for the temperature range 233 -253 K (see Figure 3). However, the linear fit of ln K versus 1/T leads to large uncertainties since we only have three points to be fitted. Indeed, the adsorption enthalpy value resulted from a linear weighted least-squares fitting of these data is Hads = -46 ± 8 kJ/mol (the quoted error is given at 2 level + 5%). Further, this value of Hads is slightly higher than the enthalpy of condensation of -50.3 kJ/mol, 51 which is thermodynamically not consistent. Therefore, we used a different approach to determine the adsorption enthalpy of benzaldehyde on ice at the temperatures of the measurements. Thus, Sads was fixed according to the Trouton's rule, [START_REF] Atkins | Physical chemistry[END_REF] where Sads  Svap = vap/Tb, Tb being the boiling temperature. According to this last equation, Sads is then -111.3 J/K mol for benzaldehyde.

Substituting the obtained value to eq. 3 Hads can be then calculated. As shown in Table 2, the resulting values for Hads are the following (in units of kJ/mol): -61.4 ± 9.7 (233 K), -61.85 ± 9.9 (243 K), and -62.7 ± 10.0 (253 K), where the quoted errors correspond to 2 levels + 5%.

Comparison with Previous Studies.

Since this study is the first to report adsorption of benzaldehyde on ice surfaces, the comparison is rather limited. Nevertheless, our experimental data can be conveniently compared with those obtained in a previous work for acetaldehyde. 9 As shown in Figure 4, for a given gas phase concentration, the number of benzaldehyde molecules adsorbed on ice is much higher than that obtained for acetaldehyde at 233 K. The same behavior has been observed for the two other studied temperatures, i.e. 243 and 253 K. The ratio between the two slopes is 1.7 at 253 K and reaches up to 12.1 at 233 K.

Isotherm Resulted from Computer Simulations. The calculated adsorption

isotherm is shown in Figure 5 in the <N> vs.  form. As is seen, at low chemical potentials it shows an exponential increase up to the  value of about -62 kJ/mol. The exponential increase of the isotherm indicates that the adsorption of an individual molecule at the ice surface is independent from the presence or absence of other adsorbed benzaldehyde molecules. Then, in the chemical potential range between -62.0 and -61.1 kJ/mol the isotherm exhibits a saturation plateau, where the surface density of the benzaldehyde molecules is about 6.7 mol/m 2 . This plateau corresponds to the presence of a particularly stable adsorption layer. It should be noted that such a saturation plateau was found to be completely missing from the adsorption isotherm of formaldehyde on ice. 16 Properties of this stable layer are analyzed in detail in a following section. Finally, between the  values of -61.1 and -61.05 kJ/mol condensation of benzaldehyde occurs; above this chemical potential the system contains liquid benzaldehyde.

Considering the behavior of the calculated isotherm we have chosen three different chemical potential values at which detailed analysis of the adsorption layer is performed. Thus, system I, corresponding to the chemical potential value of -63.75 kJ/mol is located at the exponentially rising part of the isotherm. At this chemical potential value even the first molecular layer of the adsorbed benzaldehyde molecules is far from being saturated. System II, being at the  value of -62.21 kJ/mol is located close to the saturation plateau, whereas system III is chosen to be at this plateau, at  = -61.44 kJ/mol, where the benzaldehyde molecules form their particularly stable adsorption layer. Instantaneous equilibrium snapshots of systems I-III are shown in Figure 6 as taken out from the simulations.

Comparison of the Experimental and Simulated Isotherms.

The experimental and calculated isotherms can be compared by plotting the surface density of the adsorbed molecules  versus the relative vapor pressure of benzaldehyde prel (i.e., its pressure p normalized by the pressure of its saturated vapor p0). Although the experimental saturated vapor pressure p0 of benzaldehyde at 233 K is not available in the literature, it can be extrapolated from vapor pressure measurements performed at other temperatures using the Antoine equation:

C T B A p + - = 0 ln . ( 6
)
Using the Antoine parameter values [START_REF] Sinnot | Chemical Engineering Design, Coulson and Richardson's Chemical Engineering Series[END_REF] of A = 16.35, B = 3748.62 K, and C = -66.12 K, corresponding to the pressure value in Torr units, the p0 value of 0.295 Pa can be derived at 233 K.

The simulated isotherm can be converted to the  vs. prel form using the relation 32

) exp( ) exp( 0 0   = = p p p rel , (7)
where  = 1/kBT, kB being the Boltzmann constant, and 0 is the chemical potential value corresponding to the point of condensation. From the calculated isotherm the value of 0 has been determined to be -61.075 kJ/mol. The  and prel values corresponding to the different systems simulated are also included in Table 1.

The comparison of the experimental and calculated isotherms obtained at 233 K is presented in Figure 7. As is seen, the two isotherms are in excellent agreement with each other, It should finally be noted that the simulated isotherm, determined in the entire 0  prel  1 pressure range clearly shows a non-Langmuir behavior above the pressure range explored in the experiments. This non-Langmuir behavior, already suggested by the presence of the saturation plateau of the isotherm in the <N> vs  form (see Fig. 5), is in a clear contrast with our previous finding concerning the adsorption of formaldehyde on ice, 16 and it is very probably due to the non-negligible lateral interaction of the adsorbed benzaldehyde molecules at moderate and high surface coverages. As is seen, in system I the obtained profile is unimodal, having its peak at the X value of 33.9 Å, just about 2 Å away from the point where the ice density drops to zero. This close contact with the ice phase suggests that the benzaldehyde molecules in this system are probably lying parallel with the ice surface. However, in system II the density peak of the benzaldehyde molecules is already bimodal. The first maximum of the broad, split peak is close to the position of the peak in system I, whereas the second maximum appears farther away from the ice phase, i.e., at X = 35.1 Å. The fact that the density peak is now split into two separate maxima indicates that the adsorbed molecules are aligned in two different orientations relative to the ice surface.

Characterization of the

Further, the fact that the second maximum is almost 1 Å farther away from the ice phase than the first one suggests that, besides the parallel-like orientation corresponding to the first maximum, the other preferred alignment of the benzaldehyde molecules is probably close to be perpendicular to the surface. This point is investigated in detail in the following sub-section.

Finally, in system III the benzaldehyde density profile exhibits again a unimodal peak, now at X = 35.4 Å, close to the position of the second maximum of the split peak of system II, and only a shoulder is seen around the X value of 34 Å. This main peak is followed by a small second peak around the X value of 37.7 Å. This finding suggests that (i) in system III, i.e., when benzaldehyde forms a particularly stable adsorption layer at the ice surface, the dominant orientation of its molecules is already more or less perpendicular to the surface (in accordance with the simple expectation that the number of adsorbed molecules being in contact with the ice surface can be maximized this way), and (ii) besides the already saturated first molecular layer, traces of a second molecular layer are also present in this stable adsorption layer of the benzaldehyde molecules.

Orientation of the Adsorbed Molecules.

In describing the orientational statistics of rigid molecules relative to an external surface the bivariate joint distribution of two independent orientational variables has to be calculated. [START_REF] Jedlovszky | [END_REF]55 We have shown that the angular polar coordinates  and  of the surface normal vector in a local Cartesian frame fixed to the individual molecules are a sufficient choice of such variables. [START_REF] Jedlovszky | [END_REF]55 However, since the polar angle  is formed by two general spatial vectors, but  is the angle of two vectors restricted to lie in a given plane (i.e., the xy plane of the local frame) by definition, uncorrelated orientation of the molecules with the surface results in a uniform bivariate distribution only if cos and  are chosen to be the independent variables.

In analyzing the orientation of the adsorbed benzaldehyde molecules relative to the ice surface we defined this local Cartesian frame in the following way. The origin of this frame is the O atom, its z axis points along the O=C double bond, axis y also lies in the plane of the molecule in such a way that the y coordinate of the H atom of the CHO group is negative, and axis x is perpendicular to the molecular plane. Finally, we use the convention that the surface normal vector X is directed from the bulk ice phase towards the adsorption layer. It should also be noted that, due to the planar symmetry of the benzaldehyde molecule, this frame is always chosen in such a way that  does not exceed 180 o . The definition of this local Cartesian frame and of the polar angles  and  of the surface normal vector pointing away from the ice phase X in this frame is illustrated in Figure 9.

The P(cos,) orientational maps of the adsorbed benzaldehyde molecules in systems I-III are shown in Figure 10. As is seen, at low surface coverages (i.e., in system I) the P(cos,) With increasing surface coverage also another peak of the P(cos,) map, marked here by , emerges around its cos ~ 0.2,  = 90 o point. Thus, in system II this peak is only seen as a small secondary maximum, but in system III it becomes the dominant feature of the orientational map.

distribution
In this alignment the plane of the benzaldehyde molecule is perpendicular to the ice surface, the C=O double bond declines from the parallel alignment with the surface by about 15 -20 o , the benzene ring points to the vapor, whereas the C-H bond of the aldehyde group rather straight to the ice surface. Finally, in system III, i.e., in the stable adsorption layer of benzaldehyde a third orientation, corresponding to the cos value of -1 is also slightly preferred. In this orientation, denoted by  the benzaldehyde molecule is again perpendicular to the ice surface, but now points by its C=O group straight away from the ice phase. The preferred orientations ,  and  of the adsorbed benzaldehyde molecules are illustrated in Fig. 10.

The preference of the adsorbed molecules for an almost parallel alignment with the surface at low coverages, and the increasing importance of the nearly perpendicular alignments with increasing surface coverage are in accordance with our previous assumptions, made in the density profile analysis. In order to demonstrate the relation between these orientational preferences with the shape of the density peaks in the systems of relatively high surface coverages we have calculated in systems II and III the density profiles of the molecules of different orientations separately. This deconvolution of the density peaks according to the molecular orientations is shown in the insets of Fig. 8. This analysis reveals that the first maximum of the split density peak in system II and the shoulder at the ice phase side of the main peak in system III, similarly to the entire peak in system I, are indeed given by the benzaldehyde molecules of orientation , i.e., the ones that lie almost parallel with the ice surface. Further, the second maximum of the split density peak of system II as well as the main peak of system III are given by the molecules that are perpendicular to the surface. Benzaldehyde molecules of orientation  in system III contribute to the high X side of the main density peak, leading to a broadening of this peak with respect to that in system II farther away from the ice surface.

Finally, it is also seen that the molecules forming traces of the second molecular layer in system III (i.e., the ones contributing to the small second density peak in this system) are again in orientation , lying parallel with the ice surface.

In understanding the origin of these preferences of the adsorbed molecules their possible interactions with the rest of the system at different surface coverages have to be considered.

Thus, in the case of highly unsaturated outmost molecular layers, such as the first molecular layer in system I and the second molecular layer in system III the interaction of the molecules of this layer with the rest of the system can be maximized in their lying orientation , when all of their atoms can get as close to the ice phase or to the inner layer as possible. Further, in this alignment the delocalized  electron system of the benzene ring can interact with the nearby O atoms of high electronegativity (i.e., with the water O atoms at the ice surface in the case of system I, and with the outward oriented O atoms of the benzaldehyde molecules of alignment  in the first molecular layer in the case of system III). Finally, the slight, 5-10 o deviation of the  oriented molecules from the exactly parallel alignment with the surface in system I allows them to form hydrogen bonds with the flatly aligned surface O-H groups 15 of the ice phase, as illustrated in Figure 11a.

Upon saturation of the first molecular layer, however, the increasing amount of the adsorbed benzaldehyde molecules increasingly compete for the area to be occupied at the surface, and this competition gives rise to their preference for the perpendicular orientation.

Among these alignments orientation  is stabilized by a hydrogen bond formed with a surface water molecule (see Fig. In system I the distribution of the ice contribution to the total binding energy P( ice b U ) is unimodal, having its peak at about -64 kJ/mol. The unimodality of this peak is in accordance with our previous finding that here all the adsorbed molecules are aligned in a rather similar way.

The mean value of this distribution turns out to be -59.4 kJ/mol, which agrees roughly with the sum of ice-substrate interaction energies obtained for benzene (-39 kJ/mol, measured at the surface of amorphous solid water at 141 K) 56 and for formaldehyde (-27.3 kJ/mol, obtained from computer simulation at the surface of Ih ice at 200 K) 16 at low surface coverages. Further, this value is in an excellent agreement with the experimental value of the adsorption enthalpy of -61.2 ± 10.2 kJ/mol, obtained at very low surface coverages (i.e., when benzaldehydebenzaldehyde interactions are negligible), as derived from eq. 3.

In system II the P( ice b U ) distribution is bimodal: besides its peak around -58 kJ/mol it also exhibits another, higher peak at about -38 kJ/mol. This bimodal shape of the P( ice b U ) distribution is consistent with the dual orientational preferences of the adsorbed molecules in this system. Clearly, the peak at lower energies is given by the , whilst that at higher energies by the  oriented benzaldehyde molecules (see the upper inset of Fig. 12). Considering the fact that the benzaldehyde molecule can form one hydrogen bond with the surface water molecules in both of these orientations, the roughly 20 kJ/mol difference between the positions of these peaks provides an estimate for the strength of the electron transfer interaction from the aromatic benzene ring toward the highly electronegative water O atom, which occurs only in orientation .

Finally, in system III the P( ice b U ) distribution exhibits only a shoulder at -58 kJ/mol, its main peak appears at about -34 kJ/mol, this peak exhibits another shoulder at its high energy side around -14 kJ/mol, and the distribution has another small peak close to zero. As is expected, the shoulder at low energies are given by the few  oriented molecules, similarly to system II the main peak is again due to the molecules of orientation , the high energy side shoulder of this peak can be attributed to the molecules of orientation , which cannot form hydrogen bond with the ice surface, whereas the peak around zero energies is given by the  oriented molecules of the second molecular layer, already not being in contact with the ice phase (see the lower inset of Fig. 12).

The distribution of the binding energy contribution coming from the other benzaldehyde molecules P( BA b U ) has a peak at zero and another one around -10 kJ/mol in system I. The zero energy peak is clearly coming from the isolated benzaldehyde molecules. The presence of the other, lower energy peak in the system of low surface coverage is somewhat surprising, as it indicates the tendency of the adsorbed benzaldehyde molecules for forming lateral selfaggregates rather than being always isolated from each other. At higher surface coverages, however, the P( BA b U ) distribution becomes unimodal, having its peak around -28 kJ/mol. This energy is given by the - interaction of the neighboring benzene rings and by the dipole-dipole interaction of the neighboring aldehyde groups.

The distribution of the entire Ub binding energy exhibits a single peak around -75 kJ/mol both in system I and system II. The total energy accompanying the adsorption of a benzaldehyde molecule in these systems is rather low, certainly much lower than that of formaldehyde, 16 being comparable with that of substrates forming multiple hydrogen bonds with the ice surface, such as methanol 15 or formic acid. 17 The lack of the possibility of multiple hydrogen bond formation is compensated here by the electron transfer-like interaction between the aromatic benzene ring of the benzaldehyde molecules in orientation  and the surface water O atoms, and by the - interaction of the benzene rings of neighboring benzaldehyde molecules in orientation . Further increase of the surface coverage leads to somewhat weaker average attraction experienced by the individual molecules, as reflected in the fact that the peak of the P(Ub) distribution appears around -50 kJ/mol in system III. This weakening of the average binding energy is, however, overcompensated by the large increase of the number of adsorbed molecules, making the adsorption layer corresponding to the plateau of the adsorption isotherm particularly stable.

Summary and Conclusions

In this paper we presented a combined experimental and computer simulation investigation of the adsorption of benzaldehyde at the surface of ice at temperatures characteristic to the mid and upper troposphere. The power of using such a combined approach is clearly demonstrated. The simulated isotherm agrees almost perfectly with the experimental curve at 233 K. Further, the experimental and simulated values of the heat of adsorption, i.e., -61.4 ± 9.7 kJ/mol (experiment) and -59. It is found that benzaldehyde forms a rather stable saturated adsorption layer at the surface of ice in an about 1 kJ/mol broad range of chemical potentials. This saturated adsorption layer is not monomolecular, but contains several molecules belonging to the second molecular layer, as well. At low surface coverages the adsorbed benzaldehyde molecules lie almost parallel with the ice surface, forming a hydrogen bond with a surface water molecule. This arrangement is further stabilized by the electron transfer interaction of a water O atom of high electronegativity and the delocalized  electron system of the benzene ring. With increasing surface coverages the adsorbed benzaldehyde molecules increasingly compete for the surface area to be occupied, leading to the increasing preference of a nearly perpendicular alignment of the molecules to the surface. In this preferred alignment the aldehyde group is still turned toward the ice phase, and the adsorbed molecule forms a hydrogen bond with the surface waters. Finally, the first molecular layer is saturated by the adsorption of benzaldehyde molecules in a third orientation, i.e., being perpendicular to the ice surface and turning their aldehyde group to the vapor phase. However, simultaneously with the appearance of these latter molecules several adsorbed benzaldehyde molecules appears also in the second molecular layer, lying parallel with the ice surface. These molecules can stabilize each other via the electron transfer interaction between the perpendicular aligned molecules of the first molecular layer and the  electron system of the benzene ring of the nearby lying molecules of the second layer. This interaction leads to the presence of traces of the second molecular layer in the stable saturated adsorption layer of benzaldehyde at the surface of ice.

Finally, this present work permits us to estimate the potential partitioning of benzaldehyde in tropospheric ice clouds. The fraction of benzaldehyde scavenged by ice surfaces contained in a cirrus cloud, fBA,cirrus, can be estimated as follows:

cirrus ads M cirrus ads M solid g solid cirrus BA, D K N 1 D K N [A] [A] [A]   +   = + = f ( 8
)
where Dcirrus is the surface area densities of ice ranging between 110 -4 and 110 -7 cm 2 /cm 3 [57].

Even in the densest ice clouds and in the most favorable case experimentally studied here, i.e.

T = 233 K, only 0.05 % of benzaldehyde could be adsorbed on pure ice surfaces at mid altitudes, which could be considered as negligible. Even if we assume that adsorption on ice surfaces may be more efficient at the lowest temperatures encountered in the upper troposphere, i.e. in the range of 213 -193 K, the atmospheric behavior of benzaldehyde can probably be only described by its gas phase chemistry, including both photolysis and OH reactions. a Determined from the slopes of the plots of N versus benzaldehyde concentration (see eq. 5) b Gads is obtained from eq. 3. Hads is derived from eq. 3, where Sads was set to be -111.3 J/K mol. The three preferred benzaldehyde orientations are also illustrated. X is the surface normal vector pointing away from the ice phase.

Tables

  although the simulation data correspond to slightly lower surface coverage values, the two set of data agrees with each other almost within the error bars. The observed agreement of the simulated and experimental isotherms confirms the validity of the computer model used, and demonstrates the relevance of the detailed analysis of the simulated configurations.

Adsorption Layer 4 . 1 .

 41 Density Profiles. The density profile of the benzaldehyde molecules in systems I-III is shown in Figure 8. In calculating these profiles the position of the benzene ring C atom to which the CHO group is attached has represented the position of the entire benzaldehyde molecule.

  exhibits two sharp peaks at about cos = 0.1 and  = 0 o , and at cos ~ 0.1 and  = 180 o . These peaks correspond to the same preferred alignment, denoted here by , i.e., when the benzaldehyde molecule lies almost parallel with the ice surface, and the C=O bond declines slightly, by about 5 -10 o from the surface plane pointing towards the ice phase with the O atom.

4 . 3 .

 43 11.b). Finally, the preference of the benzaldehyde molecules for orientation  occurs simultaneously with the appearance of the second molecular layer in system III, since  oriented molecules of the first molecular layer can stabilize the  oriented, lying molecules of the second molecular layer through the interaction of the outward oriented O atom of the former, and the lying aromatic benzene ring of the latter molecule (see Fig.11.c). Energetics of the Adsorption. In order to analyze also the energetic background of the adsorption we have calculated the distribution of the Ub binding energy of an adsorbed benzaldehyde molecule (i.e., its interaction energy with the rest of the system) as well as that of its contributions coming from the interaction with the ice phase, ice b U , and with the other adsorbed benzaldehyde molecules, BA b U . The distribution of the Ub binding energy and its contributions ice b U and BA b U are shown in Figure 12 as obtained in systems I-III.

  4 kJ/mol (simulation) also agree with each other very well. The observed good reproduction of the experimental data by the simulation confirms the relevance of the computer model used, and validates the results of the detailed analyses of the simulated configurations.

Figure 1 .

 1 Figure 1. Gas phase concentration of benzaldehyde as a function of time during its adsorption on ice surfaces at 233 K (with [benzaldehyde] gas phase = 5.3  10 12 molecules/cm 3 ).

Figure 2 .

 2 Figure 2. Adsorption isotherms of benzaldehyde on pure ice at 233 K (full circles), 243 K (open circles), and 253 K (full triangles). The solid lines correspond to the linear fits according to eq. 5.

Figure 3 .

 3 Figure 3. Plot of K as a function of 1/T corresponding to benzaldehyde adsorption on pure ice. The adsorption enthalpy is derived from the slope according to eq. 3.

Figure 4 .

 4 Figure 4. Comparison of adsorption isotherms of benzaldehyde (full circles) and acetaldehyde 9 (open circles) on pure ice at 233 K. Plot of the number of molecules adsorbed per surface unit versus the absolute gas phase concentration of aldehyde.

Figure 5 .

 5 Figure 5. Average number of benzaldehyde molecules in the basic simulation box as a function of the benzaldehyde chemical potential. The arrows indicate the three systems considered for detailed analysis.

Figure 6 .

 6 Figure 6. Instantaneous equilibrium snapshot of the benzaldehyde layer adsorbed at the ice surface as taken out from the simulations of system I (top row), system II (middle row) and system III (bottom row). The snapshots are shown both in side view (first column) and in top view (second column).

Figure 7 .

 7 Figure 7. Comparison of the experimental (full circles) and simulated (open circles) adsorption isotherms of benzaldehyde on ice at 233 K. The error bars of the simulated data points are always smaller than the symbols. The inset shows the same comparison in the entire 0  prel  1 pressure range. The arrows indicate the three systems considered for detailed analysis.

Figure 8 .

 8 Figure 8. Number density profile of the adsorbed benzaldehyde molecules in system I (dashdotted line), system II (dashed line) and system III (solid line). The number density profile of the surface waters is also indicated (dotted line). The insets show the contribution of the  (full circles),  (open circles) and  (asterisks) oriented benzaldehyde molecules to the total density profile in systems II (upper inset) and III (lower inset).

Figure 9 .Figure 10 .

 910 Figure 9. Definition of the local Cartesian frame fixed to the individual benzaldehyde molecules, and of the polar angles  and  of the surface normal vector, pointing, by our convention, away from the ice phase, X, in this

Figure 11 .

 11 Figure 11. Illustration of the strong attractive interactions stabilizing the adsorbed benzaldehyde molecules in different orientations. (a) Hydrogen bonding between a surface water and an adsorbed benzaldehyde molecule of orientation . (b) Hydrogen bonding between a surface water and an adsorbed benzaldehyde molecule of orientation . (c) Electron transfer-like interaction between a benzaldehyde molecule of orientation  in the first molecular layer and another benzaldehyde molecule of orientation  in the second molecular layer. X is the surface normal vector pointing away from the ice phase.

Figure 12 .

 12 Figure 12. Distribution of the total binding energy of an adsorbed benzaldehyde molecule (i.e., the energy of its interaction with the rest of the system, bottom panel), and its contributions coming from the interaction with the other adsorbed benzaldehyde molecules (middle panel) and with the ice phase (top panel) in systems I (dash-dotted line), II (dashed line), and III (solid line). The insets show the contribution of the  (full circles),  (open circles) and  (asterisks) oriented benzaldehyde molecules to the ice contribution of the binding energy in systems II (upper inset) and III (lower inset).

Figure 1

 1 Figure 1. Petitjean et al.

Figure 7

 7 Figure 7. Petitjean et al.

Table 1 . Data of the Adsorption Isotherm of Benzaldehyde on Ice, as Obtained from the Simulations

 1

	/kJ mol -1	<N>	/mol m -2	p/p0
		-60.66	280.0
		-61.05	280.0
		-61.10	114.7	6.84	0.988
		-61.15	114.3	6.82	0.963
		-61.24	113.0	6.74	0.916
		-61.34	112.4	6.71	0.872
	-61.44 a	111.7	6.66	0.829
		-61.53	112.4	6.70	0.789
		-61.63	112.9	6.73	0.750
		-61.73	113.7	6.78	0.714
		-61.82	112.1	6.68	0.679
		-61.92	110.1	6.57	0.646
		-62.01	111.2	6.63	0.614
	-62.21 b	59.67	3.56	0.556
		-62.59	45.13	2.69	0.455
		-62.98	32.63	1.95	0.373
		-63.36	29.31	1.75	0.305
	-63.75 c	21.86	1.30	0.250
		-64.14	18.77	1.12	0.204
		-64.52	13.09	0.781	0.167
		-64.91	12.15	0.725	0.137
		-65.29	7.61	0.454	0.112
		-65.68	7.35	0.438	9.19  10 -2
		-66.07	7.47	0.446	7.52  10 -2
		-66.45	5.18	0.309	6.16  10 -2
		-67.42	3.66	0.218	9.19  10 -2
		-68.38	2.66	0.099	3.73  10 -2
		-69.35	1.98	0.118	2.27  10 -2
		-70.31	0.99	0.059	8.33  10 -3
	a system I	b system II c systemIII

Table 2 : Values of NMKads(T), K(T), Gads and Hads for Benzaldehyde Adsorption on Pure Ice at 233, 243 and 253 K. The Quoted Errors Correspond to 2 Level + 5% (See the Text).

 2

	T/K	NM  Kads/cm a	R²	K  10 -7 a	-Gads/kJ mol -1 b	-Hads/kJ mol -1 b
	233	5.26 (±0.52)	0.93	8.94 (±0.88)	35.5 (±2)	61.4 (±9.7)
	243	1.79 (±0.24)	0.88	3.04 (±0.41)	34.8 (±2)	61.8 (±9.9)
	253	0.80 (±0.11)	0.86	1.36 (±0.19)	34.5 (±2)	62.7 (±10.0)

Acknowledgements

. This project is supported by the Hungarian OTKA Foundation under project No. 75328, by the French Ministry of Research through the LEFE/CHAT program, by the region of Alsace and the REseau Alsace de Laboratoires en Ingénierie et Sciences pour l'Environnement (REALISE), by the MTA-CNRS bilateral collaboration program, and by the Hungarian-French Intergovernmental Science and Technology Program (BALATON). P. J. is a Bolyai János fellow of the Hungarian Academy of Sciences, which is gratefully acknowledged.


N Peybernès

S Le Calvé
email: slecalve@illite.u-strasbg.fr

Ph Mirabel

S Picaud

P N M Hoang

Experimental and theoretical adsorption study of ethanol on ice surfaces

Adsorption study of ethanol on ice surfaces were performed by combining experimental and theoretical approaches. The experiments were conducted using a coated wall flow tube coupled to a mass spectrometric detection. The surface coverage increases with decreasing temperature and with increasing ethanol concentrations. The obtained experimental surface coverages were fitted according to the B.E.T. theory in order to determine the enthalpy of adsorption ∆H ads and the monolayer capacity N M : ∆H ads = -57 ± 8 kJ mol -1 , N M = (2.8 ± 0.8)×10 14 molecule cm -2 . The adsorption characteristics of ethanol on a proton disordered Ih(0001) ice surface were also jointly studied by performing classical molecular dynamics simulations. More specifically, the configurations of the molecules in their adsorption sites and the corresponding adsorption energies have been studied as a function of temperature and coverage. In the simulations, the saturation coverage is around N M = 3.2×10 14 molecule cm -2 , and corresponds to an adsorption energy equal to -56.6 kJ mol -1 , in good agreement with the experimental value. The results are discussed and compared with previous determinations for alcohols.

Introduction

Recent measurements in the upper troposphere (UT) have revealed the presence of Partially Oxidised Hydrocarbons (POHs), such as alcohols, and these POHs may play an important role on the ozone cycle in this region. The upper troposphere defines a region of the atmosphere (between 8 and 12 km) characterised by its low temperatures (188 to 228 K) and where cirrus clouds cover a substantial portion (~25 %) of the earth's surface 1,2 . Upper tropospheric air which has been transported from the warm boundary layer, may become highly supersaturated with respect to water or ice resulting in the formation of large number densities of ice particles 3 . At temperatures below 233 K, cirrus clouds are predominantly composed of ice crystals 4 and these crystals can provide surfaces for trace gas interactions, that may promote heterogeneous reactions and therefore a re-partitioning of the different species between the gaseous and the solid phase.

The uptake of atmospheric pollutants on ice surfaces has been extensively studied for more than ten years, given their potential impact on the stratospheric ozone hole. Therefore, attention has mainly focused on halogenated or nitrated species such as HX, HOX, XONO 2 (X = Cl, Br), N 2 O 5 and HNO 3 [5][6][7][8][START_REF] Kroes | Comments At[END_REF] . By contrast, very few articles have been devoted to the characterization of POHs on ice, although their photo-oxidation can provide a substantial source of HO x radicals that are involved in photochemical and chemical cycles leading to ozone loss in the atmosphere. Among these POHs, acetone on ice is certainly the system that has been the most experimentally studied [10][11][12][13][14] and a relatively clear understanding of the acetone behavior on ice has emerged from the convergence of the various experimental data, in fair agreement with theoretical results 15,16 .

In a series of experiments, Sokolov and Abbatt have investigated the adsorption of different alcohols on ice as a function of their size (from ethanol to 1-hexanol) 11 , by using a coated-wall flow tube coupled to a mass spectrometer, between 213 and 245 K. The results

show that the saturated surface coverages are all within ±50 % of 3.0×10 14 molecules cm -2 , and correspond to monolayer-like coverages for alcohols. These results also suggest that the alkyl chains are aligned perpendicular to the surface at monolayer coverage 5,11 . In order to characterize the influence of the organic function (C=O, O-H, C(O)OH, C(O)H) on the interaction between POHs and ice, the adsorption on ice of acetic acid 11 , formaldehyde 12 , methanol 12,13 , acetaldehyde 13 , and 2,3-butanedione 14 has also been experimentally investigated, using a Knudsen cell flow reactor 13 or a coated-wall flow tube 11,12,14 . The corresponding adsorption energies have been measured within the same range, i.e. [-70, -50] kJ mol -1 for all these organic molecules except for formaldehyde, for which no significant adsorption has been evidenced.

From our knowledge, the theoretical studies devoted to the interaction between POHs and ice are very scarce. In a previous paper, we have used molecular dynamic simulations to characterize the adsorption of acetone on an ideal proton-ordered ice surface between 50 and 150 K 15 , and shown that this approach leads to theoretical results that are in good agreement with experimental data [10][11][12][13][14] , as well as with results issued from ab initio calculations at 0 K 16 .

However, the main advantage of molecular dynamics simulations with respect to ab initio calculations is the inclusion of temperature effects, and the possibility of taking into account a large number of molecules in the simulation cell. These two characteristics allow calculations within the same temperature range and the same coverage conditions as in the experiments.

The goal of the present study is to re-examine the interaction of ethanol with ice surfaces, at temperatures relevant for the UT, with an approach that combines experiments and theory.

Surface coverages of ethanol on ice have been experimentally measured in order to determine the values of the monolayer capacities N M and of the corresponding enthalpies of adsorption ∆H ads for temperature ranging from 193 K to 223 K. Our experimental data were then compared with those obtained in this work by Molecular Dynamics (MD) simulations performed in the same temperature range on a model proton-disordered ice surface. Although one previous experimental study has already been devoted to the ethanol/ice system 11 , this paper reports the first joint experimental and theoretical adsorption study of ethanol on ice.

Experimental section

The uptake of ethanol on ice surfaces was studied using a vertical coated wall flow tube (CWFT) coupled to a mass spectrometer, already described elsewhere 14 . We will therefore provide only a brief summary of its principle operation. The apparatus, which is shown in figure 1, has a double jacket to allow the system to be operated at low temperature. The cooling fluid was circulated in the inner jacket from a cooler/circulator (Huber, Unistat 385) while vacuum was maintained in the outer jacket for thermal insulation. The temperature of the flow tube could be cooled down and regulated between 193 and 223 K.

The jacketed flow tube was approximately 40 cm in length with an internal diameter of 2.8 cm. The ice surface was prepared by totally wetting with Milli-Q water (18 MΩ cm) the inner wall of the flow tube that was typically precooled between 258 and 263 K. The water film was then rapidly cooled down to 253 K to form an ice film and then to the desired temperature over a period of 10-30 min. The thickness of ice film was estimated between 30 and 200 µm by weighting the resulting liquid water, when the ice film was melted at the end of the experiment.

The helium carrier gas (UHP certified to > 99.9995 % from Alphagaz) was used without further purification. During the experiment, water vapour was added to the main He flow in order to provide a partial pressure of water, equal to the vapour pressure of water over the ice film and therefore inhibit net evaporation of the ice film. In practice, a small fraction of the helium flow, varying typically between 1 and 5 mL min -1 , was passed through a water bubbler thermostated at about 278 K and was diluted with a main flow of dry helium (100-200 mL min -1 ). The resulting gas mixture was then cooled down to the same temperature as that of the ice film in a glass tube of 20 cm in length (internal diameter 2.8 cm) where the excess of water was trapped. The resulting humidified helium flow was injected at the upstream end of the flow reactor.

Ethanol (≥ 99.8 %) was purchased from Carlo Erba and was further purified before use by repeated freeze, pump, and thaw cycles as well as by fractional distillation. To perform an experiment, ethanol was then premixed with helium in a 10 L glass light-tight bulb to form 1.1×10 -2 -2.4×10 -1 % mixtures, at a total pressure of ≈ 800 -950 Torr. The mixture containing ethanol was injected into the flow tube reactor via a sliding injector (figure 1). This later permits to change the reaction distance which can be varied up to 40 cm in order to change the gas/ice interaction time (0 -700 ms) or the exposed ice film surface (50 -260 cm 2 ). The injector was jacketed and a heating tape was wound up in the jacket, to ensure a gentle heating of the injector 14 .

All the gases flowed into the reactor through Teflon tubing. The gas mixture containing ethanol and water vapour diluted in helium was flowed through the reactor with a linear velocity ranging between 60 and 120 cm s -1 . The concentrations of ethanol in the gas phase were calculated from their mass flow rates, temperature and pressure in the flow tube (CWFT). All the flow rates were controlled and measured with calibrated mass flowmeters (Millipore, 2900 series) and the pressure that ranged between 2.5 and 7.0 Torr, was measured with two capacitance manometers (Edwards, 622 Barocel range 0-100 torr and Keller, PAA-41 range 0-76 torr) connected at the top and bottom of the flow tube. Under our experimental conditions, the mixing time τ mix between ethanol flow and the main He flow was lower than 2 ms 15 which corresponds to a mixing length smaller than 0.3 cm.

The gas stream coming out of the flowtube was analysed using a differentially pumped mass quadruple spectrometer Pfeiffer Vacuum QMS. Ethanol was monitored at the parent ion C 2 H 5 (O + )H peak at m/z = 46 amu, using a temporal resolution of 60 ms, an ionisation energy of 70 eV and an emission current of 1000 µA.

Experimental Results

Our work is the second experimental study of adsorption of ethanol on ice surfaces 11 .

Uptake experiments were performed by first establishing a highly stable flow of ethanol in the injector, this injector being positioned past the end of the ice film. The injector was then moved quickly (at ≈ 45 s, see figure 2) to an upstream position so that the ice film is exposed to ethanol. The uptake of ethanol on the ice film leads to a drop of signal as shown in figure 2.

On a time scale of about 15 s, the surface became saturated and the MS-signal returned to its initial level. When the injector was pushed back (t ≈ 124 s), the ethanol molecules desorbed from the ice surface and the signal increased and then again returned to its initial level after 15 s. Similar experiments were conducted over a temperature range 193 -223 K and for gas phase concentrations of ethanol varying from 6.4×10 11 to 1.2×10 13 molecule cm -3 .

In the temperature range of 203-223 K and for concentrations mentioned above, the integrated areas of the adsorption and desorption peaks were found to be the same, within experimental errors, so that adsorption of ethanol on ice could be considered reversible. At 193 K and for concentrations larger than 7×10 12 molecules cm -3 , the desorption peak was significantly smaller than the adsorption peak. As observed for the uptake of many species on ice surfaces 17,18 , unlimited gas-phase uptake can occur at low temperature and high gas phase concentrations due to a mechanism of surface adlayer growth via a flux of both ethanol and water vapor to the ice surface to generate a liquid solution or amorphous supercooled mixture. The missing ethanol will then be trapped either inside the generated solution or under this latter in the first solid layers.

Surface coverage

The number of ethanol molecules adsorbed on the ice surface was determined from the integrated area of the adsorption peak (in molecule s cm -3 ) and the total flow rate in the flow tube (cm 3 s -1 ). The surface coverage N (in molecule cm -2 ) of ethanol on ice was then calculated from the exposed ice surface S ice (in cm -2 ) according to N = N ads /S ice where N ads is the number of ethanol molecules adsorbed on the exposed ice surface. Our experimental ice surface areas are considered equal to the geometric areas of pyrex.

The experiments were performed using 5 different diluted mixtures and 8 newly generated ice surfaces in order to verify the reproducibility of the data. A typical example of ice film is shown in figure 3. The plot of surface coverage N versus the gas phase concentration at 223 K is shown in figure 4, together with the results obtained by Sokolov and Abbatt 11 . The relative errors on the gas phase concentrations (horizontal error bars) calculated from the possible uncertainties on each flow, total pressure etc. range between 2 and 25 %. The quoted errors on N (vertical error bars) arise from uncertainties made on the total flow rate, on the exposed ice area, on the concentration in the gas phase. They also include a systematic error of 2 % that corresponds to the error on the integrated area of adsorption peak. The resulting error on N varies between 6 and 20 %.

Isotherms

In this work, the data have been fitted by using B.E.T. isotherm theory where the surface is considered uniform so that all sites are equivalent and the ability of a molecule to adsorb at a given site is independent of the neighbouring sites. The choice for this quite simple model has been a posteriori justified by the very good comparison between the results issued from these experiments and those issued from molecular dynamics simulations (see the theoretical part of this paper). In B.E.T. model, the initial adsorbed layer can act as a substrate for further adsorption. In this case, for all layer except the first, the heat of adsorption is equal to the molar heat of condensation L.

The most convenient form of the BET equation for application to experimental data is given by the following equation:

0 M M 0 0 p p C N 1 C C N 1 )) p / p ( 1 ( N p p Y ⋅ ⋅ - + ⋅ = - = ( 1
)
where Y is the BET function [START_REF] Gregg | Adsorption, Surface Area and Porosity[END_REF] , p and p 0 are respectively the partial pressure of the compound in the flow tube and its saturation pressure (Torr) and C is the BET constant (no unit). The values of the saturation pressures p 0 were calculated from the Antoine equation:

c T b a p log 0 + - = (2)
The Antoine parameters available in the literature for ethanol are a = 5.372, b = 1670.41 and c = -40.19 20 . The saturation vapour pressures of ethanol are then the following (in Torr):

2.07×10 -3 (193 K); 9.71×10 -3 (203 K); 3.81×10 -2 (213 K); 1.29×10 -1 (223 K).
The plot of Y against p/p 0 gives a straight line with a slope s = (C-1) / N M C and an intercept i = 1 / N M C. The BET plot is linear for relative pressures higher than 7.5×10 -4 as shown in figure 5. The values of N M and C determined from a combination of the slope and intercept (N M = 1/(s+i) ; C = s/i + 1) are reported in table I. The B.E.T. constant is then used to derive the enthalpy of adsorption from the following expression:

(T) H lnC RT (T) H vap ads ∆ + - = ∆ (3)
The enthalpy of adsorption is independent of temperature between 193 and 223 K and the average value is ∆H ads = -57 ± 8 kJ mol -1 . Even if the values of N M seem to be slightly higher for the lowest temperature (193 K), the average monolayer capacity corresponding to the adsorption of ethanol on ice surfaces is N M = (2.8 ± 0.8)×10 14 molecules cm -2 . For either ∆H ads or N M , the quoted uncertainties were taken as the mean of the four individual errors at each temperature.

Comparison with previous studies

Our results are reported in the table II together with previously reported data for primary The same authors have shown that the monolayer capacity of a primary alcohol on ice do not change within the experimental errors (N M = 3.1×10 14 molecules cm -2 ) when the alkyl chain increases. They concluded that it was probably an indication that when the surface is saturated, the molecules are oriented in a similar manner with the hydroxyl group binding to the ice surface and the alkyl chain at right angles to the surface. They have also found that the adsorption enthalpy decreases in absolute value when the alkyl chain was shorter. Indeed, the value of ∆H ads = -61.8 ± 3.3 kJ mol -1 for ethanol is smaller in absolute value than that for 1butanol (∆H ads = -67.3 ± 7.5 kJ mol -1 ), itself lower than that obtained for 1-pentanol (∆H ads = -71.5 ± 3.3 kJ mol -1 ) 11 . This is consistent with the both determinations of ∆H ads for methanol: ∆H ads = -51 ± 10 kJ mol -1 12 and ∆H ads = -45 kJ mol -1 13 .

Molecular dynamics calculations

Interaction potential

The intermolecular potentials used in the present study to describe the interaction between water and ethanol molecules consist of site-site potentials which contain coulombic and Lennard-Jones contributions. These potentials are written as

) r ( V ij                 σ -         σ ε + = 6 ij ij 12 ij ij ij 2 ij j i ij r r 4 e r q q ) r ( V (4)
where is the distance between the ith and jth sites of the interacting molecules. q ij r i e is a point charge located at the ith site, and σ ε, are the usual Lennard-Jones parameters. For the lateral interaction V between the ethanol molecules, we use the model proposed by Briggs et al. eth eth- [START_REF] Briggs | [END_REF] in which charges and dispersion-repulsion centers are located on the atoms of the hydroxyl group and on the C atom of the alkyl groups, that are treated as single sites centred on the carbon atom. TIP4P model is used for water-water interaction 22 ( ) and the parameters for the interaction V between ethanol and water are obtained by using the usual Lorentz-Berthelot combining rules, defined as follows:

w w V - w eth- j i ij ε ε ε = (5) and 2 j i ij σ σ σ + = (6)
The various potential parameters are summarized in Table III. In the simulation, all interactions between sites are damped through a switching function S(R) (where R is the centers of mass separation between molecules) which is defined such as, at the boundaries of the switching region, the potential energy is continuous and the switching function first and second derivatives are zero 15 .

Details of the simulation

We consider adsorption on the (0001) basal plane of proton disordered hexagonal ice.

The simulation box is a parallelepiped of sizes L x = 35.914 Å and L y = 38.878 Å along the x and y directions perpendicular to the c axis of ice. It contains six bilayers of moving water molecules which form a slab of 21.99 Å thick. These moving water molecules are placed on a slab consisting of four bilayers of fixed water molecules. To simulate an infinite surface, periodic boundary conditions are imposed by replicating the simulation box along (x,y). This box contains a total of 1600 water molecules, 960 of them being moving molecules. The initial configuration of the water molecules 23 obeys the ice rules [START_REF] Eisenberg | The Structure and Properties of Water[END_REF] and has no net charges and no net dipole moment. In order to check the influence of the proton ordering on the simulation results, we have also considered adsorption on proton ordered hexagonal ice. In this case, the simulation box is a parallelepided of sizes The simulation box also contains a certain number of moving ethanol molecules that is determined from experimental results. In the experiments, the averaged maximum number of adsorbed ethanol molecules in a monolayer is equal to (2.8 ± 0.8)×10 14 molecules.cm -2 (see experimental section). This corresponds to 45 predictor-corrector method based on the quaternion representation of the molecular orientations is used for the orientational equations χ θ ϕ , , [START_REF] Allen | Computer Simulations of Liquids[END_REF] . Every run involved an equilibration period of 60000 steps (132 ps), followed by a production run of 40000 steps (88 ps). The initial linear and angular velocities for each moving molecule are taken from a Boltzmann distribution corresponding to the desired simulation temperature. The simulations are performed in the NVT ensemble using a Berendsen thermostat. The potential cut-off in the calculations of the acetone-acetone, acetone-water and water-water interactions is handled through three different neighbor lists [START_REF] Allen | Computer Simulations of Liquids[END_REF] , with the same radial cutoff (15 Å) in the direct space.

Due to this large cut-off, the calculations of the electrostatic interactions through the Ewald scheme were not necessary [START_REF] Spohr | [END_REF] . Simulations are performed at 193 and 223 K, i.e. the boundaries of the temperature range considered in the experiments.

Theoretical Results

Geometry of the admolecules

We first characterize in our calculations the translational ordering of the ethanol molecules along the z axis, perpendicular to the ice surface, in order to determine the maximum coverage corresponding to the formation of one complete monolayer above the ice surface. Indeed, this information can be directly compared to the experimental data.

As an example, the distribution functions p(z) of the distances between the molecular centers of mass of the moving molecules (water + ethanol) and the origin of the absolute frame is given in Fig. 7a for a coverage of 49 ethanol molecules, at both 193 and 223 K. The double peaks correspond to the hexagonal arrangement of the water molecules, which is preserved at these low temperatures, although a certain disorder is evidenced for the surface layer of the ice crystal. Note that these distribution functions for the water molecules are very similar to those obtained by Kroes in molecular dynamics simulations of the surface melting of the (0001) face of TIP4P ice (i.e. using the same potential than in the present simulations) 27 , indicating that the ethanol adsorption between 193 and 223 K does not significantly modify the ice surface characteristics. At the surface of our ice crystal, the single peak around 36.0 Å corresponds to the monolayer arrangement of the 49 ethanol molecules.

This peak does not shift significantly when the temperature increases from 193 to 223 K, although it slightly broadens due to the thermal fluctuations (Fig. 7a).

The distribution functions p(z) at 193 K for the ethanol molecules only are also shown in indicating the formation of a single ethanol layer above the ice surface. However, it is interesting to note that, in the simulation with 64 molecules (i.e. the number of molecules corresponding to the monolayer completion in the simulation with 98 molecules), only 55 molecules out 64 are arranged in a first layer, the remaining molecules being adsorbed in an upper layer (Fig. 7b). This difference is due to the fact that, in a simulation with 98 molecules, the 34 excess molecules in the upper layer act as a cover that prevents the 64 molecules in the lower layer from escaping.

On the basis of these results, we can conclude that, from a theoretical point of view, the monolayer contains between 49 and 55 molecules, i.e. between 3.0 and molecules.cm the ethanol molecules. However, a careful analysis of the data shows that the molecular orientations still correspond to a configuration where the OH groups are closer to the ice surface than the alkyl chains (see Fig. 9).

°150 = θ

The distribution function p (not shown) is much less structured than and ) (ϕ

) ( p θ ) ( p χ
and tends to spread over the whole angular range. This feature is connected to the proton disordering at the ice surface and to the optimization of the lateral interactions between ethanol molecules. Very similar results are obtained at 223 K, although the corresponding peaks in the orientational distribution functions are wider due to larger thermal fluctuations. By contrast, more pronounced preferred orientations are obtained on proton ordered ice (not shown), due to the periodic arrangement of the dangling OH bonds at the ice surface.

formation of hydrogen bonds. The integrated intensity of the first peak in g , up to the first minimum, gives the number of Y atoms in the first shell of the X atom. The present results for and g indicate that 55 % of the ethanol molecules act as a proton donors, whereas 42 % of these molecules acts as proton acceptors, the remaining molecules (around 3 %) being not involved in such bonding with the ice surface. For the third function (

), the integrated intensity of the first peak indicates that, in average, 43 % of the ethanol molecules are also bound via lateral hydrogen-bonds. Note that some ethanol molecules form hydrogen-bonds both with the ice surface and with a nearest neighbour ethanol molecule, as shown on the snapshot issued from the simulation at 193 K and at monolayer coverage (49 molecules, Fig. 9).

Conclusion

The present paper reports the first combined experiments/theory study of the interactions between ethanol and ice. In the experiments, the adsorption of ethanol on ice has been characterized between 193 and 223 K, and is found to be (almost) fully reversible in this temperature range. The enthalpy of adsorption is independent of temperature between 193 and 223 K, and the average value is ∆H ads = -57 ± 8 kJ mol -1 . Even if the values of N M seem to be slightly higher for the lowest temperature (193 K), the average monolayer capacity corresponding to the adsorption of ethanol on ice surfaces is N M = (2.8 ± 0.8)×10 14 molecules cm -2 . These values are in good agreement with previous experimental data 11 . From a theoretical point of view, molecular dynamics simulations have been used to investigate, at a molecular level, the details of the adsorption characteristics of ethanol on ice, in the same temperature range as in the experiments, and with a number of ethanol molecules in the simulation box that reproduces the experimental amount of adsorbed molecules. At first sight, it seems quite difficult to compare the theoretical results with the experimental data because the simulations are performed on a perfect ice crystal, and correspond to equilibrium situations. Nevertheless, the energy values obtained in our simulations are in very good agreement with the measured values, and this indicates that the potential used in the present study is accurate enough to describe the ethanol/ice interactions. This also justifies a posteriori our analysis of the experimental data with the BET theory. Note that no other theoretical study is available in the literature for the ethanol/ice system. The calculated saturation coverage (3.2×10 14 molecules.cm -2 ) is also in good agreement with the values issued from the BET analysis of the experimental data, and is similar to that deduced from experimental and theoretical studies of other systems such as methanol or acetone adsorbed on ice [11][12][13]15,16 . The main advantage of the simulations is that they provide additional information on the structure of the adsorbate, and on the competition between ethanol-ice and ethanol-ethanol interactions. In particular, the theoretical results evidence the formation of hydrogen bonds in the simulated system, and a relatively strong influence of the intraadsorbate interactions on the structuration of the ethanol molecules on ice. Finally, the present simulations indicate that the ethanol molecules are oriented with their alkyl chain directed away from the ice surface (Fig. 9), in agreement with the trends inferred from experiments on alcohols of different sizes adsorbed on ice 11 .

Figure captions

  Similar reversible adsorptions on ice were already observed for acetone, methanol and formaldehyde byWinkler et al. (2001) 12 or for C 2 -C 6 n-alcohols bySokolov et al. (2002) 11 .

alcohols RCH 2

 2 OH (where R = H, CH 3 , C 2 H 5 , n-C 3 H 7 ).Sokolov and Abbatt (2002) 11 have studied the adsorption of ethanol on ice surfaces between 218 and 233 K in the concentration range of 3.01×10 11 -2.73×10 13 molecules cm -3 , using a Coated Wall Flow Tube coupled to a mass spectrometer. Under their experimental conditions, the adsorption was always found reversible. In the figure4, our measurements of N (molecules cm -2 ) plotted versus the concentration of ethanol at 223 K, are in good agreement with those determined by Sokolov and Abbatt. In the same way, our values of N M and ∆H ads are also consistent with those derived by these authors with Langmuir model: N M = 2.9×10 14 molecules cm -2 , ∆H ads = -61.8 ± 3.3 kJ mol -1 .

  unit cell contains 8 water molecules. Periodic boundary conditions are imposed by replicating the unit cell along the x and y directions, and the simulation box contains 960 moving molecules forming a slab of thickness (along the z direction), adsorbed on 640 fixed water molecules (Fig.

13 ±

 13 molecules in our simulation box. Thus simulations have been performed at low (9 ethanol molecules), medium (25 and 49 ethanol molecules) and high coverages (64 and 98 ethanol molecules). At the beginning of the simulations (initial conditions), the ethanol molecules are randomly distributed above the surface, in a single plane (9, 25, 49 and 64 molecules) or in two planes (98 molecules) because, on the basis of the experimental results, this latter coverage would correspond to the formation of more than one monolayer above the ice surface. Each molecule is treated as a rigid rotor, and six external coordinates are used to describe the translation of the center of mass (x,y,z) and the orientation of the molecule ( ) with respect to an absolute frame tied to the bottom of the simulation box. The translational equations of motion are solved with a time step of 2.2 fs using the Verlet algorithm, and a

Fig. 7b in

  Fig. 7b in order to study the influence of the ethanol coverage on the translational ordering of the adsorbed molecules. In this figure, it is cleary evidenced that two layers are formed for the highest coverage (98 molecules) since two peaks are obtained in the corresponding p(z) function. The integrals of these peaks indicate that the layer close to the ice surface contains 64 ethanol molecules, whereas the 34 remaining molecules arrange themselves in a second layer. Lower ethanol coverages lead to the occurrence of only one peak in p(z) (Fig. 7b),

- 2 .

 2 Similar results are obtained when considering the proton-ordered ice crystal. Additional information concerning the orientations of the ethanol molecules can be obtained from the simulations, through the study of the angular distribution functions ) the orientation of the molecule in an absolute frame. defines the orientation of the C-C axis with respect to the z axis perpendicular to the ice surface, is the angle made between the projection of this C-C axis in the (x,y) plane and the y axis, and the internal rotation of the ethanol molecule around its C-C axis is characterized by . The angular distribution functions are given in Fig. 8 for two typical situations corresponding to submonolayer (9 molecules) and (nearly) monolayer (49 molecules) coverages, at 193 K. At submonolayer coverage, the distribution exhibits a single large peak around 115°, with a full width at medium height (FWMH) equal to about 30°. This value corresponds to a tilted orientation of the C-C axis of the ethanol molecules, the methyl group being away from the ice surface. Note that the large value of the FWMH indicates large angular fluctuations around the mean value, due to the thermal motions at the temperature of the simulation. In the same way, characterized by one single large peak centered around a mean value of 300° which corresponds to an orientation of the OH group directed toward the ice surface, compatible with the formation of hydrogen bonds with the water molecules. At full monolayer coverage, additional peaks are evidenced in ) ( p θ and due to lateral interactions which tend to flatten down ( ) ( p χ °= θ 83 ) or to lift up ( )

Figure 1 :

 1 Figure 1: Schematic illustration of the vertical coated wall flow tube.

Figure 2 :

 2 Figure 2: Ethanol concentration in the gas phase as a function of time during the adsorption of ethanol on ice surfaces at 213 K with [ethanol] =4.6×10 12 molecule cm -3 .

Figure 3 :

 3 Figure 3: Digital picture of a typical ice film (74 µm). Note that the stripes correspond to the winding of the resistance around the warming and sliding injector (in white).

Figure 4 :

 4 Figure 4: Surface coverage of ethanol versus its gas phase concentration at 223 K. Our data are compared with those obtained by Sokolov and Abatt (2002). Our quoted errors are detailed in the text.

Figure 5 :

 5 Figure 5: Plot of Y versus the relative pressure (p/p 0 ) according to the B.E.T. model (see eq.

1 )

 1 for the four studied temperature i.e. 193, 203, 213 and 223 K. The dashed line represents the lower limit under which B.E.T. analysis is not valid i.e. for p/p 0 < 7.5×10 -4 while the solid lines correspond to the plots obtained according to eq. 1. The quoted errors are detailed in the text.

Figure 6 :

 6 Figure 6: Snapshot of the ice crystal (side view of the simulation box) at T = 193 K, showing the six mobile layers of proton disordered ice adsorbed on four rigid ice layers.

Figure 7 :

 7 Figure 7: (a) Distribution functions p(z) (in arbitrary unit) of the distance z (Å) of the water and ethanol molecular centers of mass from the bottom of the simulation box at 193 and 223 K for a coverage equal to 49 ethanol molecules; (b) distribution functions p(z) of ethanol molecules only, for different coverages at 193 K, and for proton disordered ice.

Figure 8 :

 8 Figure 8: Angular distribution functions for the ethanol molecules on proton disordered ice at 193 K and for two typical coverages : nearly isolated molecules (9 molecules -dotted curve) and monolayer (49 molecules -full curves): (a) angle θ; (b) angle χ. The angles are in degrees, and the distribution functions are given in arbitrary units.

Figure 9 :

 9 Figure 9: Snapshot issued from the simulation of 49 ethanol molecules adsorbed on proton disordered ice ((a) top view; (b) side view showing only the top layers of the system) at 193 K. The water molecules are represented by small sticks for clarity.

Figure 10 :

 10 Figure 10: Radial distribution functions g(r) for the distances between the oxygen atom of the ethanol molecule and the H atoms of the water molecules ( ) or the H atom of the OH group of the neighboring ethanol molecules ( g ), and between the hydrogen atom of the OH group of the ethanol molecule and the O atom of water ( g ), at 193 K and for a coverage corresponding to 49 ethanol molecules on proton-disordered ice.

  Figure 2

Figure 3 [Figure 5 Figure 6

 356 Figure 3

  Figure 8

Table I :

 I Fit parameters for B.E.T. Isotherms corresponding to adsorption of ethanol on ice surfaces. The errors bars are given at 2σ levels (see text). in molecule cm -2 ; b in cm 3 molecule -1 ; c in kJ mol -1 .

	T	a N M (×10 14 )	b C (×10 2 )	c ∆H vap	c ∆H ads
	193	3.30 ± 0.66	3.13 ± 1.42	-47.17	-56.4 ± 8.4
	203	2.62 ± 0.26	3.31 ± 0.62	-46.84	-56.6 ± 3.7
	213	2.51 ± 0.44	6.39 ± 1.87	-46.48	-57.9 ± 6.7
	223	2.67 ± 1.67	4.83 ± 3.02	-46.10	-57.6 ± 14.3

a

Table II :

 II Adsorption of ethanol on ice surfaces: comparison with previous works.

	Compound	T range	∆H ads	N M (10 14 )	Technique	reference
		K	kJ mol -1	molecule cm -2
	Methanol	198-223	-51 ± 10	3.2 ± 1.0	CWFT a
	Methanol	< 180	-45	-
	Ethanol	193-223	-57 ± 8	2.8 ± 0.8	CWFT a	This work
	Ethanol	218-233	-61.8 ± 3.3	3.1 ± 0.3	CWFT a
	1-butanol		-67.3 ± 7.5
	1-pentanol		-71.5 ± 3.3

Table III :

 III Parameters for the potentials used in the simulations. The coordinates of the different sites are given with respect to the molecular frame located at the center of mass.

	Site		coordinates (Å)		q (e)		ε (kJ mol -1 )	σ (Å)
			(x,y,z)
	Water
	O		( 0.000; 0.000; -0.0650)	-		0.592		3.152
	H		( 0.757; 0.000; 0.5208)	0.52		-		-
	H		(-0.757; 0.000; 0.5208)	0.52		-		-
	site elec.		( 0.000; 0.000; 0.0845)	-1.04		-		-
	Ethanol
	H (OH)	0	( 0.0000; 0.872; 1.694) 50	100	0.435	150	-	200	-	250
	O (OH)		( 0.0013; 0.880; 0.752)		-0.700 time (s)		0.709		3.07
	C (C-OH)	(-0.0030;-0.479; 0.311)		0.265		0.492		3.905
	H (CH 2 )		( 0.8970;-0.977; 0.738)		-		-		-
	H (CH 2 )		(-0.9090;-0.969; 0.733)	-		-		-
	C (CH 3 )		( 0.0000;-0.515;-1.212)		-		0.730		3.905
	H (CH 3 )		( 0.0000;-1.565;-1.585)	-		-		-
	H (CH 3 )		( 0.9050;-0.008;-1.621)	-		-		-
	H (CH 3 )		(-0.8980;-0.004;-1.626)	-		-		-

a CWFT : Coated Wall Flow Tube.

Acknowledgement

This work was supported by EC (project CUT-ICE, EVK2-CT1999-00005) and by CNRS (program PNCA). This is the EOST contribution n° 2004.XXX-UMR7517.

Energy of the admolecules

The different contributions to the total energy for the system ethanol-proton disordered ice are given in Table IV. At 193 K, and low coverage (9 ethanol molecules), the lateral interactions between ethanol molecules ( ) are negligible, and the total potential energy (about -67 kJ mol

) mainly comes from the electrostatic interaction between ethanol and water molecules. When the coverage is increased up to the completion of one monolayer (between 49 and 64 ethanol molecules), increases from 8% (25 ethanol molecules) to 26 % (49 ethanol molecules) and 35 % (64 ethanol molecules) of the total potential energy.

Note that the ethanol-ice interaction ( V ) decreases (in absolute value) when increasing the ethanol coverage due to the influence of the lateral interactions on the geometry of the adsorbed ethanol molecules. This leads to a strong decrease of the total energy when a second layer of ethanol is formed above the ice surface (98 ethanol molecules).

Taking into account the kinetic energy, the total energy per ethanol molecule ranges from -47.2 to -68.9 kJ mol -1 for the various coverages and temperatures considered in the present simulations.

Very similar trends are obtained when considering adsorption on proton-ordered ice crystal. Indeed, around monolayer coverage, the total energy at 193 K increases from -53.0 to -51.7 kJ mol -1 when the coverage is increased from 49 to 64 ethanol molecules in the simulation box, respectively.

Characterization of hydrogen bonds

In order to characterize the hydrogen bonding between ethanol molecules and ice, and