Water and formic acid aggregates: A molecular dynamics study Delphine Vardanega and Sylvain Picaud Citation: The Journal of Chemical Physics 141, 104701 (2014); doi: 10.1063/1.4894658 View online: http://dx.doi.org/10.1063/1.4894658 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/141/10?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Multi-species nucleation rates in CLOUD AIP Conf. Proc. 1527, 326 (2013); 10.1063/1.4803269 General approach to the formulation and solution of the multi-parameter inverse problems of atmospheric remote sensing AIP Conf. Proc. 1531, 240 (2013); 10.1063/1.4804751 MIPAS: 10 years of spectroscopic measurements for investigating atmospheric composition AIP Conf. Proc. 1531, 23 (2013); 10.1063/1.4804698 Modelling of HNO3-mediated laser-induced condensation: A parametric study J. Chem. Phys. 135, 134703 (2011); 10.1063/1.3644591 Aggregation of water molecules: Atmospheric implications J. Chem. Phys. 113, 6652 (2000); 10.1063/1.1310601
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THE JOURNAL OF CHEMICAL PHYSICS 141, 104701 (2014)
Water and formic acid aggregates: A molecular dynamics study Delphine Vardanega and Sylvain Picauda) Institut UTINAM – UMR 6213 CNRS, Université de Franche-Comté, 16 route de Gray, F-25030 Besançon Cedex, France
(Received 18 July 2014; accepted 24 August 2014; published online 8 September 2014) Water adsorption around a formic acid aggregate has been studied by means of molecular dynamics simulations in a large temperature range including tropospheric conditions. Systems of different water contents have been considered and a large number of simulations has allowed us to determine the behavior of the corresponding binary formic acid–water systems as a function of temperature and humidity. The results clearly evidence a threshold temperature below which the system consists of water molecules adsorbed on a large formic acid grain. Above this temperature, formation of liquidlike mixed aggregates is obtained. This threshold temperature depends on the water content and may influence the ability of formic acid grains to act as cloud condensation nuclei in the Troposphere. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4894658] I. INTRODUCTION
Organic material is ubiquitous in the Earth’s atmosphere, coming from both natural sources and anthropogenic activities. The interactions between water and organic molecules are thus currently investigated in the context of atmospheric chemistry because liquid droplets and ice particles may scavenge some of these organic molecules from the atmosphere, thus modifying the atmospheric composition and chemistry.1–3 Moreover, upon aggregation, either directly or after various oxidation processes, volatile organic compounds (VOCs) may form particles of different sizes, contributing to the aerosol formation. Thus, organic matter represents an important fraction of the fine aerosol mass4 which comes also from sea salt, mineral dust, black carbon, sulfates, and nitrate ammonium whose relative abundance depends on, e.g., location, time, and meteorological conditions.5 The atmospheric aerosol plays a central role on current atmospheric research, because it affects the climate system via different physical mechanisms.5–7 Indeed, the aerosol particles have a direct effect on climate not only by scattering and absorbing solar radiation but also by scattering, absorbing, and emitting thermal radiation. Moreover, these particles may have an indirect effect by acting as cloud condensation (CCN) and ice (IN) nuclei, depending on temperature and on their affinity for water molecules. Indeed, the composition, the size, and the concentration of the aerosol particles impact on the number, concentration, and size of the CCN and/or IN that may be formed. As a consequence, they may strongly influence the formation of droplets and/or ice particles in the resulting clouds, thus modifying the cloud properties such as light scattering. They may also impact on the cloud lifetimes and on the precipitation rates.7 For all these reasons, a detailed description of the processes governing the ability of aerosol to act as condensation nuclei for water, either in the liquid (CCN) or in the solid a) Author to whom correspondence should be addressed. Electronic mail:
[email protected] 0021-9606/2014/141(10)/104701/8/$30.00
(IN) state, is strongly needed, based on a better understanding of the underlying interactions between water molecules and aerosol particles. However, the corresponding aerosol+water systems are very complex, because aerosols are usually mixtures of compounds, the properties of which strongly depend on their way of production. Owing to this complexity, modeling ideal systems by computer simulations is, in a first step, an interesting way to better understand the water-aerosol interactions at the molecular scale. However, due to the size of the corresponding models which have to consist of, at least, hundreds of different molecules, calculations based on a rigorous quantum description of these interactions will be certainly not feasible before long. In contrast, classical approaches based on a simplified description of the aerosol–water interactions are of great interest, as long as the empiric parameters used in the classical interaction models can correctly reproduce experimental observations. This is indeed the case for a wide variety of atmospherically relevant organic compounds for which the accuracy of the interaction models with water has been tested in recent years, on the basis of classical molecular dynamics and Monte Carlo simulations aiming at investigating VOC adsorption on, i.e., ice surfaces.8–18 A few molecular dynamics simulation studies have thus been recently devoted to a detailed investigation of the behavior of large droplets made of water and organic molecules used as surrogates for organic aerosols. Either big water droplets coated by various organic molecules19–24 or the reverse situation, i.e., large organic aggregates interacting with surrounding water molecules25, 26 have been considered in the corresponding theoretical works, as a function of temperature. These two approaches showed however some similar results especially regarding the state of mixture of the aerosol particles. Indeed, water and organic molecules have been found to form either mixed or separate phases depending on temperature, concentration, and also on the types of the organic molecules. Moreover, some of these results have been tentatively related to the conclusions of a recent experimental work by Shill and Tolbert27 who tried to provide a simple parametrization of
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organic ice nucleation efficacy by using the O:C ratio as a proxy for characterizing the organic aerosol hydrophilicity. However, the theoretical results showed that not only the O:C ratio should be considered but also the internal conformation of the organic molecules.25, 26 This unfortunately indicates that a systematic study of various organic molecules should be undertaken before any global conclusion can be drawn. As a consequence, we complement our previous work on oxalic and malonic acids25, 26 by considering here the case of formic acid (HCOOH), the smallest monoacid molecule, for which entropic effects related to internal conformation changes with temperature are minimized. In Sec. II, we present the protocol of our simulations and the technical details of data processing. Then, in Sec. III, we present the analysis of the simulation results for binary formic acid/water mixtures, as a function of temperature and water composition. Finally, in Sec. IV, the main conclusions of this study are summarized. II. COMPUTATIONAL DETAILS
Molecular dynamics simulations were performed using the GROMACS program package (version 4.5.4)28 to study the formation and stability of formic acid aggregates together with water molecules at five different compositions, corresponding to 0, 50, 66, 75, and 83 mol. % water concentrations. The initial geometry of the formic acid molecule and the corresponding force field between acid molecules have been taken from the literature.29 This intermolecular potential is a combination of electrostatic interactions between point charges located on appropriate sites of the molecules and of Lennard-Jones contributions. The interactions between water molecules were described by the five-site TIP5P model.30 In this model, a 12-6 Lennard-Jones site is located on the oxygen atom and the charge distribution of the water molecule is represented by two positive charges placed on the H atoms and two negative-charge sites that are located in the tetrahedral direction of the two lone pairs, at a distance of 0.70 Å away from the oxygen. In this model, the OH length and HOH bond angles are set to the experimental gas phase values, i.e., 0.9572 Å and 104.52◦ . In a similar way, the acid-water interaction has been calculated as a sum of pairwise dispersion-repulsion and Coulomb contributions between atoms and partial charges. The dispersion-repulsion terms were represented by the Lennard-Jones potential, the parameters of which are being obtained from the ε, σ values of the individual atoms according to the Lorentz-Berthelot rules.31 The Lennard-Jones potential was truncated at the cut-off radius of 14 Å. The longrange part of the electrostatic interactions was evaluated by the particle Mesh Ewald (PME) method32 with the same cutoff value. Bond, angle, and torsion flexibility was allowed for the formic acid and the water molecules. First, to create a formic acid aggregate, 120 formic acid molecules have been randomly placed in a large cubic simulation box having an edge length of 80 Å. This initial system was equilibrated during 1 ns on the (N,V,T) ensemble at 100 K. During this simulation, formic acid molecules aggregated to form a single big aerosol particle containing the 120
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molecules. Once this aggregate was formed, a production run of 5 ns was performed in the same conditions for data analysis. Such formic acid aggregate was shown to be stable upon temperature increase (at least up to 250 K, see below). This equilibrated aggregate was then used as model aerosol particle to investigate water adsorption. Then, four different compositions have been chosen to investigate the adsorption of water on the aerosol and to analyse the behavior of the resulting binary systems at different temperatures in the range of 100-250 K. Note that temperature values much lower than those encountered in the Troposphere have been considered because, in molecular dynamics simulations, the temperature at which a phase transition occurs may strongly depend on the interaction potential used in the calculations (see for instance, the discussion of melting temperatures for various water models in Vega et al.33 ). Because the characteristics of the water-formic acid potential used here was not known a priori, we thus choose to consider a rather large range of temperatures to investigate possible structural and thermodynamic evolutions in the molecular systems under study. As detailed below, important changes in the aerosol mixing state have been indeed evidenced at quite low temperatures that needed to be characterized in details. The stabilized formic acid aggregate has been placed in the middle of an empty cubic simulation box having the edge length of 80 Å and then, 120, 240, 360, and 640 water molecules, respectively, have been randomly placed in the box, modeling thus roughly 50, 66, 75, and 83 mol. % water contents. These systems have been equilibrated primarily on the canonical (N,V,T) ensemble for 5 ns at 100 K. These pre-equilibrated systems have then been further equilibrated for 1 ns on the isothermal-isobaric (N,p,T) ensemble at various temperatures, including atmospherically relevant values. During these simulations, pressure has been kept constant to 1 atm. Each of these simulations has been followed by a 1 ns long production run, performed under the same conditions, during which 1000 equilibrium configurations, separated by 1 ps long trajectories each have been saved for data analyses. For all these simulations, a time step of 0.1 fs was used. The temperature and pressure of the systems were controlled by means of the weak coupling method of Berendsen et al.34 Indeed, this method allows for exponential decay of instantaneous value of temperature and/or pressure to the target value and thus converges relatively quickly. It is thus useful for stabilizing systems that may be far from equilibrium such as the aerosol particles modeled here. Moreover, this method usually yields correct results for most calculated properties provided that large systems of hundreds of atoms/molecules are considered. Periodic boundary conditions were applied during the simulations. A total number of 40 simulations have thus been performed to analyse the temperature behavior of the binary formic acid-water system. In such binary mixtures, the structural characteristics are well visible by looking at equilibrium snapshots, or as a more quantitative approach, they might be investigated by means of detailed cluster analysis. We have thus calculated the size distribution P(n) of the clusters formed in the binary water+formic acid systems, together with that of the
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formic acid clusters disregarding the water molecules and that of the water clusters without the formic acid molecules for all the temperatures considered at four compositions. During the course of this analysis two formic acid molecules have been regarded to be bonded if the distance from any of their hydroxylic hydrogen to any of the carbonylic or hydroxylic oxygen atoms of the other formic acid molecule was smaller than a cut-off distance of 2.10 Å or 3.90 Å, respectively. A water and a formic acid molecule have been considered to be connected if the H(acid)–O(water) cut-off distances turned out to be smaller than the cut-off value of 2.10 Å. In the same way, two water molecules have been considered to be nearest neighbors if the distance between their oxygen and hydrogen atoms did not exceed the value of 2.55 Å. The cut-off values listed above have been obtained as the first minimum position of the corresponding partial pair correlation functions. Moreover, to get a deeper insight into the energetic changes that occur during and as a result of the structural changes, and furthermore, to shed light on the energetic reasons underlying these changes when temperature increases, we have calculated the distributions of the binding energy between a formic acid molecule and all the other formic acids in b ), between a water molecule and all the the system (Eacid−acid b ), and between a formic acid molecule other waters (Ewat−wat b ). These binding energy and all the water molecules (Eacid−wat distributions are also useful tools to provide us with information about the hydrogen bonded network of the aerosol and can thus be related to the size distributions mentioned above.
III. RESULTS AND DISCUSSION A. Structure of pure aerosol particles
Simulation of the pure aerosol phase of 120 formic acid molecules resulted in the formation of one single big aerosol particle irrespective of the temperature in the 100–250 K range. A snapshot of this aggregate is shown in Fig. 1 (top) for different temperatures. This conclusion has been also supported by statistically relevant quantitative results based on the size distribution P(n) of the clusters formed by the formic acid molecules (Fig. 2, top) at various temperatures. In a general way, P(n) is characterized by two main peaks that are broader for higher temperature values due to larger thermal motions. The first peak, obtained at large n values corresponds to the formation of a large, more or less structured, big formic acid aggregate in the simulation box. The second one, obtained at very low n values, originates from formic acid molecules that are in fact slightly beyond the distance criterion defined for the cluster analysis (2.10 Å, see Sec. II) and not from molecules completely isolated in the box. This is confirmed by a detailed analysis of the snapshots and by additional cluster analysis using a larger value for this distance criterion. Indeed, Fig. 3 shows the P(n) distribution for increasing values of this distance criterion from 2.10 to 2.70 Å at, for instance, 100 K. It clearly appears that when using the larger distance criterion all the formic acid molecules belong to a single big aggregate, leading to a single peak in P(n) located at the value n = 120. However, in the following, the results are presented for a distance criterion equal to 2.10 Å, i.e.,
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FIG. 1. Equilibrium snapshots of formic acid aggregates at 100, 150, and 200 K (left, middle, and right) and for 0, 50, 66, and 83 mol. % water concentrations (from top to bottom).
for the value determined from the analysis of the pair radial distribution functions (see Sec. II). Note that a detailed analysis of the snapshots and of the hydrogen bonding network formed between the formic acid molecules (see below) shows some local ordering in the acid aggregate that is however difficult to compare with that of the formic acid crystal. Indeed, the quite small number of acid molecules considered here and the finite size of the resulting aggregate certainly prevents the formation of a well-ordered crystal structure. In addition, because it has been observed previously for malonic acid molecules that the size of the aerosol may depend on the initial density of acid molecules in the simulation box,26 the present simulations have been repeated with a system of double density, consisting of 240 formic acid molecules randomly placed in the same simulation box. The corresponding results show that for the double density we obtained a stable aerosol of formic acid molecules twice as big as for the lower density case, i.e., this particle consisted of 240 formic acid molecules. It thus appears that formic acid molecules, such as the malonic ones, have a strong tendency to form large aggregates. Nevertheless, the above mentioned aggregate of 120 formic acid molecules appeared as a good compromise between the relevance and the time cost of the corresponding simulations and it has thus been used for further simulations when considering addition of water molecules in the simulation box. Note, however, that in this case, some additional simulations have also been performed by considering a bigger acid aggregate (240 molecules) and water molecules in the simulation box that lead to results very similar to those presented here with the smaller aggregate.
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FIG. 2. Cluster size distributions P(n) of formic acid molecules in the formic acid-water binary aerosols for 0, 50, 66, and 83 mol. % water concentrations (from top to bottom) and at temperatures of 100 K (left), 150 K (middle), and 200 K (right).
B. Behavior of the binary aerosol
We have analysed the temperature behavior of the binary formic acid-water system at four different compositions, cor-
FIG. 3. Cluster size distributions P(n) of formic acid aggregates at the temperatures of 100 K for cut-off values of 2.1 Å (top left), 2.3 Å (top right), 2.5 Å (bottom left), and 2.7 Å (bottom right).
responding to 50, 66, 75, and 83 mol. % water concentrations. In all cases, it turned out to be possible to differentiate unambiguously between the appearing situations by simply looking at the equilibrium snapshots taken from the simulations corresponding to temperatures in the range of 100–250 K. Some of these snapshots are given in Fig. 1 for different temperatures and water contents. At 100 K, the analysis of these snapshots indicates that formic acid molecules tend to form a big aggregate surrounded by adsorbed water molecules, irrespective of the water content. When the temperature increases, more intensive thermal motion of the formic acid molecules initiates the formation of relatively big and flexible voids within the core of the aggregate, allowing water molecules to penetrate into the core of the aggregate and fill the voids. At high water content and above 200 K (Fig. 1, bottom right), a total dissolution of the formic acid cluster is even evidenced. These conclusions have been also supported by statistically relevant quantitative results based on the size distribution P(n) of the clusters formed by the formic acid molecules. These cluster size distributions are shown in Fig. 2 for three temperatures and for the formic acid–water systems of three compositions (50, 66, and 83 mol. % water concentrations) Indeed, no significant difference has been obtained between 75 and 83 mol. % water concentrations and thus only the results for the latter case are given here. At 100 K, P(n) is characterized by two main peaks. The first one, corresponding to large n values, originates from the formation of a large formic acid aggregate in the simulation box. As already mentioned above, the second peak, obtained at very low n values,
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corresponds in fact to formic acid molecules that are slightly beyond the distance criterion defined for the cluster analysis and not from molecules isolated in the box. Again, this has been confirmed by a detailed analysis of the snapshots and by additional cluster analysis using a larger value of this distance criterion. At 150 K, the position of the first peak is shifted to lower n values indicating that the average size of the aggregate slightly decreases by about 30 molecules between 100 and 150 K. Indeed, larger thermal motions lead to increased fluctuations of distances between formic acid molecules and, as a consequence, the number of formic acid separated by more than 2.10 Å increases. In addition, these larger motions allow water molecules to penetrate deeper in the internal structure of the acid aggregate, thus initiating its dissociation. This analysis is confirmed at higher temperature (200 K) where only a single, quite high intensity peak is seen at small aggregation number values, indicating the complete dissolution of the formic acid aggregate. It can thus be concluded that the qualitative picture suggested by the equilibrium snapshots, which states that in case of formic acid–water mixtures, the formic acid aggregates dissociate at high temperatures, is supported by the formic acid cluster size distribution. As a consequence, the formic acid-water mixtures are thus characterized by two main situations. At low temperatures formic acid forms a single big aggregate, on which water molecules are absorbed, while for higher temperatures a mixing of the two species is seen. This conclusion seems valid for all the water concentrations considered here, as illustrated on the equilibrium snapshots in Fig. 1, where we may clearly identify the demixed state of the formic acid–water system for the low temperature and the mixed situation observed at high temperatures for all concentrations. To better characterize the transition between the demixed and mixed situations, we have represented in Fig. 4 the average cluster size of the largest formic acid aerosol formed at various water contents as a function of the temperature. This average cluster size has been calculated on the basis of the peaks obtained in the corresponding P(n) functions (Fig. 2). We have also added in this figure the corresponding analysis for the pure formic acid aerosol (i.e., system at 0 mol. % of water), for comparison. It can thus be easily seen that, without any water in the simulation box, the average size of the formic acid aggregate slightly decreases when temperature is increased, as already mentioned before. In contrast, when water molecules are added, the temperature has a strong influence on the size of the formic acid aggregate. Indeed, at low temperature (typically less than 120–130 K depending on the water content) and low water contents (50 and 66 mol. % of water) the average size of the formic acid aggregate remains nearly constant, indicating the formation of a large formic acid aggregate in the simulation box. This situation typically corresponds to a pure demixed system (i.e., a segregation of the different types of molecules is obtained). Note however that at high water contents (75 and 83 mol. % of water), we did not obtain any plateau in the average cluster size curve even at the lowest temperature considered here, suggesting a partial formic acid–water mixing even at 100 K. Note that an
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FIG. 4. Average cluster size of the formic acid aggregates formed in the formic acid-water systems corresponding to 0, 50, 66, 75, and 83 mol. % water contents (black circles, red triangles, green squares, yellow diamonds, and blue triangles, respectively), as a function of the temperature.
additional simulation at 50 K for the 83 mol. % water content actually indicated the formation of the demixed system at this very low temperature, but we did not perform any systematic search for a possible plateau in P(n) between 50 and 100 K, because these temperatures are anyway much lower than those encountered in the Troposphere. When the temperature is increased, the average size of the formic acid aggregate progressively decreases up to the complete deliquescence obtained above 200 K, irrespective of the water content. It should be however emphasized that, even at these temperatures, we still observed the formation of a big mixed aggregate in the simulation box, as shown in the snapshots given in Fig. 1 (right) and as indicated by the single peak obtained at large n values in the size distribution of the clusters formed by the formic acid+water molecules (not shown). Note that these conclusions remain valid when increasing the size criterion used to define the formic acid aggregate formation. As an illustration, Fig. 5 shows the results obtained for two different size criteria for the system containing 50 mol. % of water molecules. It clearly appears on this figure that whereas the size criterion may influence the size of the formic acid aggregate (i.e., the average number of formic acid molecules included in the aggregate), it does not change the shape of the corresponding curves nor the threshold temperature for which the deliquescence of this aggregate starts. It should be emphasized that the mixing mechanism suggested simply by looking at the distribution of aggregate sizes and snapshots has to be confirmed by a careful investigation of the energetic background to get a justification, and to have an at least semi-quantitative picture of the processes underlying the transitions between mixed and demixed situations.
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FIG. 5. Average cluster size of the pure formic acid aerosol in the formic acid–water system corresponding to 50 mol. % of water and for cut-off values of 2.1 Å (red triangles) and 2.7 Å (yellow diamands), as a function of the temperature.
C. Energetic background
The binding energy Eb distributions calculated for the formic acid–water mixed aerosols are presented in Fig. 6 to-
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gether with those calculated for the formic acid system without water, for comparison. Note that the term “binding energy” means the total interaction energy of a certain molecule (formic acid or water) with all the molecules of a certain kind in the system. In other words, this is the energy cost of bringing this molecule at infinite distance from the other molecules considered in the energy calculations. The left, middle, and right panels of Fig. 6 show the distribution of the binding energy of a formic acid molecule with all the other formic acids in the system, that of a formic acid molecule with all the waters, and that of a water molecule with the other waters in the system. The amount of water molecules in the system is increased from top to bottom of Fig. 6. First of all, binding energies strongly depend on the temperature but they are not strongly modified by the water content of the binary water+acid systems, with the exception of the water-water binding energy distribution that (as expected) depends on the water concentration. As a consequence, we just analyse here the results obtained for the higher water content in detail, i.e., for a system containing 120 formic acid and 640 water molecules (Fig. 6, bottom). Looking first at the water–water binding energy distributions (Fig. 6, bottom right), we can see several peaks for each temperature that can be tentatively related to hydrogen bonding. For instance, the four peaks clearly evidenced at 100 K could correspond to arrangements in which one water molecule forms (in average) around 4, 3, 2, and 1 hydrogen-bonds with other water
FIG. 6. Binding energy distributions of formic acid water binary aerosols for 0, 50, 66, and 83 mol. % water content (from top to bottom) at the temperatures of 100 K (black lines), 150 K (red lines), and 200 K (blue lines). Left panels: binding energy of a formic acid molecule with all the other formic acid molecules; middle panels: binding energy between a formic acid molecule and all the water molecules; and right panels: binding energy of a water molecule with all the other waters in the system.
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molecules, assuming that the average energy of a single hydrogen bond is around −25 kJ mol−1 when using the TIP5P interaction potential.30 Note that the number of H-bonds given this way is indication only, because calculating the exact numbers of hydrogen bonds per water molecule would, of course, require a more rigorous definition of these H-bonds based on a combination of energy and geometric criteria. The relative intensity of the peaks in the Eb distribution between water molecules varies significantly upon increasing the temperature suggesting some rearrangements in the hydrogen bond network when changing temperature. Stronger evolutions are seen for the formic acid–formic acid binding energy distribution. Thus, at 100 K, three main peaks are observed which roughly correspond to 4, 3, and 2 hydrogen bonds, in accordance with the formation of a large formic acid aggregate in the simulation box. When temperab is shifted towards ture increases, the peak position in Eacid−acid higher energy values (i.e., less negative values) indicating that, in the mixed acid-water system, formic acid molecules tend to lose their hydrogen bonded formic acid neighbors. In contrast, in the formic acid–water binding energy distribub , the positions of the peaks shifts towards lower tions Eacid−wat energy values as a consequence of the formation of an increased number of hydrogen bonds between formic acid and water molecules when the temperature is increased. The concomitant decrease of the formic acid–water binding energy and loss of hydrogen bonds between formic acid neighbours fully supports the existence of a transition from a demixed to a mixed situation of the binary formic acid+water systems upon temperature increase, as already suggested by the analyses of the snapshots and cluster size distributions. D. Discussions
The present results can be, at least qualitatively, compared to those recently obtained on formic acid particles using infrared spectroscopy, although the temperature of the experiments was much lower and the particle much bigger than those considered here.35 Indeed, at 78 K, large formic acid particles are characterized by hydrogen-bonded chains leading to an overall crystalline structure. When adding more and more water, this crystalline structure disappears and water and formic acid molecules tend to mix on a molecular level. The corresponding process is however shown to depend on the amount of water molecules added to the formic acid grain. These conclusions are in agreement with the results of our simulations indicating that the hydrogen bond network of pure formic acid grains is strongly modified upon water adsorption. They also agree with our findings showing that the formic acid–water mixing depends on the water content and is partially present for high water contents even at temperatures as low as 100 K. In addition, it is interesting to compare the present results with those previously obtained for the oxalic acid molecule25 which is, as the formic one, characterized by a O:C ratio equal to 2. Indeed, it has been recently suggested to use this ratio as a proxy for characterizing organic aerosol hydrophilicity, although this conclusion was based on experiments considering
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monocarboxylic acids only.27 At low temperature, it has been shown that water adsorbed on large oxalic acid aggregates irrespective of the water concentrations, as obtained here for formic acid at very low temperature. In contrast, different behavior were evidenced for the water–oxalic acid systems at higher temperatures that consist either of mixed droplets or of oxalic acid molecules adsorbed on water aggregates, depending on the water contents. In the present simulations, only large mixed droplets of formic acid and water molecules have been found at temperatures relevant for Tropospheric conditions, a behavior that is thus rather similar to that obtained for the malonic acid (O:C = 4/3)—water systems.21, 26 The comparison between these three acid molecules thus indicates that, unfortunately, using the O:C ratio for predicting the ability of carboxylic acids to act as water nuclei might be not as straightforward as previously inferred.27 At least, it seems that this conclusion cannot be generalized to mono and dicarboxylic acids because the affinity of these molecules for water depends not only on the O:C ratio, but also on the number of carboxylic groups and of the internal geometry of the acid molecules. It is also interesting to discuss the interfacial properties of the particles studied here in terms of water accommodation which is related to the water vapor condensational growth of the particle. The present results show that formic acid molecules tend to form stable aggregates at tropospheric temperatures that can trap surrounding water molecules by hydrogen bonding. At high water content, formic acid molecules tend to dissolve into water above typically 160–180 K. Although our simulations have been limited to an upper value of 83 mol. % water content, we can infer from our results that the surface of mixed formic acid-water particles is thus essentially water in tropospheric conditions, in agreement with the conclusions of recent molecular dynamics simulations of malonic acid coated aerosol.21 As a consequence, a mixed formic acid–water aerosol particle would thus behave like a pure water droplet in the Troposphere, resulting in a water vapor accommodation factor equal to unity. These conclusions (initial formation of nanosized clusters and subsequent growth) could be, at least qualitatively, related to results of direct observations of atmospheric aerosol nucleation.36 IV. SUMMARY AND CONCLUSIONS
The water adsorption around small formic acid aggregates has been studied by means of molecular dynamics simulations in the temperature range of 100–250 K, thus including temperatures relevant for the Troposphere. Systems of various compositions, corresponding to different water contents have been considered and a total number of 40 simulations have been performed, allowing us to characterize a “phase diagram-like” (Fig. 4) of the binary formic acid–water systems. In this diagram, both the temperature and the water content have a strong influence on the behavior of the system. Two situations are thus evidenced for the formic acid–water aggregates, corresponding either to water adsorption on large formic acid grains at very low temperatures, or to the formation of mixed droplets consisting of formic acid and water molecules at higher temperatures. At moderate temperatures,
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an intermediate situation is obtained here, characterized by a partial deliquescence of the acid aggregate. Note that it cannot be totally excluded that the temperature range corresponding to this partial deliquescence depends on the duration of the simulations and, as a consequence, much longer simulations could result in a more abrupt transition between the two extreme situations (mixed and demixed systems). Anyway, this would not change the present conclusion that formic acid and water molecules formed mixed droplets at temperatures relevant for tropospheric conditions, irrespective of water concentration. In addition, the comparison between the present results and those previously obtained for oxalic and malonic acids indicates that, unfortunately, using the O:C ratio for predicting the ability of carboxylic acids to act as water nuclei might be not as straightforward as previously inferred.27 At least, it seems that the affinity of these acid molecules for water depends not only on the O:C ratio, but also on their number of carboxylic groups and of their internal geometry. The present results cannot be directly compared to any field measurements. However, they represent an additional step towards modeling of organic cloud condensation nuclei, leading to a deeper understanding of the complicated and environmentally relevant problem of heterogeneous nucleation of water. In particular, the present simulation results, together with those previously published on dicarboxylic acids25, 26 point out the complex effect of both temperature and humidity on the behavior of organic aerosols. They emphasize the need for further experimental and simulation works in this field. ACKNOWLEDGMENTS
The authors gratefully thank Dr. Maria Darvas for help in setting up some data files for the molecular simulation runs. Simulations have been executed on Institut UTINAM’s computers supported by the Region de Franche-Comté and the CNRS (Institut des Sciences de l’Univers – INSU) and also using the computing resources of the Mésocentre de Calcul, a Regional Computing Center at Université de Franche-Comté. 1 J.
H. Seinfeld and S. N. Pandis, Atmospheric Chemistry and Physics, 2nd ed. (Wiley, New York, 2006). 2 C. E. Kolb, R. A. Cox, J. P. D. Abbatt, M. Ammann, E. J. Davis, D. J. Donaldson, B. C. Garrett, C. George, P. T. Griffiths, D. R. Hanson, M. Kulmala, G. McFiggans, U. Pöschl, I. Riipinen, M. J. Rossi, Y. Rudich, P. E. Wagner, P. M. Winkler, D. R. Worsnop, and C. D. O’Dowd, Atmos. Chem. Phys. 10, 10561 (2010). 3 V. F. McNeill, A. M. Grannas, J. P. D. Abbatt, M. Ammann, P. Ariya, T. Bartels-Rausch, F. Dominé, D. J. Donaldson, M. I. Guzman, D. Heger, T. F. Kahan, P. Klán, S. Masclin, C. Toubin, and D. Voisin, Atmos. Chem. Phys. 12, 9653 (2012). 4 A. I. Calvo, C. Alves, A. Castro, V. Pont, A. M. Vicente, and R. Fraile, Atmos. Res. 120-121, 1 (2013).
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Kanakidou, J. H. Seinfeld, S. N. Pandis, I. Barnes, F. J. Dentener, M. C. Facchini, R. Van Dingenen, B. Ervens, A. Nenes, C. J. Nielsen, E. Swietlicki, J. P. Putaud, Y. Balkanski, S. Fuzzi, J. Horth, G. K. Moortgat, R. Winterhalter, C. E. L. Myhre, K. Tsigaridis, E. Vignati, E. G. Stephanou, and J. Wilson, Atmos. Chem. Phys. 5, 1053 (2005). 6 S. K. Satheesh and K. Krishna Moorthy, Atmos. Environ. 39, 2089 (2005). 7 U. Lohmann and J. Feichter, Atmos. Chem. Phys. 5, 715 (2005). 8 S. Picaud and P. N. M. Hoang, J. Chem. Phys. 112, 9898 (2000). 9 B. Collignon and S. Picaud, Chem. Phys. Lett. 393, 457 (2004). 10 N. Peybernès, S. Le Calvé, P. Mirabel, S. Picaud, and P. N. M. Hoang, J. Phys. Chem. B 108, 17425 (2004). 11 S. Picaud, P. N. M. Hoang, N. Peybernès, S. Le Calvé, and Ph. Mirabel, J. Chem. Phys. 122, 194707 (2005). 12 P. Jedlovszky, L. B. Partay, P. N. M. Hoang, S. Picaud, Ph. van Hessberg, and J. N. Crowley, J. Am. Chem. Soc. 128, 15300 (2006). 13 G. Hantal, P. Jedlovszky, P. N. M. Hoang, and S. Picaud, J. Phys. Chem. C 111, 14170 (2007). 14 G. Hantal, P. Jedlovszky, P. N. M. Hoang, and S. Picaud, Phys. Chem. Chem. Phys. 10, 6369 (2008). 15 P. Jedlovszky, G. Hantal, K. Neurohr, S. Picaud, P. N. M. Hoang, Ph. von Hessberg, and J. N. Crowley, J. Phys. Chem. C 112, 8976 (2008). 16 M. Darvas, S. Picaud, and P. Jedlovszky, ChemPhysChem 11, 3971 (2010). 17 M. Petitjean, M. Darvas, S. Le Calvé, P. Jedlovszky, and S. Picaud, ChemPhysChem 11, 3921 (2010). 18 M. Darvas, J. Lasne, C. Laffon, Ph. Parent, S. Picaud, and P. Jedlovszky, Langmuir 28, 4198 (2012). 19 X. Li, T. Hede, Y. Tu, C. Leck, and H. Ågren, J. Phys. Chem. Lett. 1, 769 (2010). 20 T. Hede, X. Li, C. Leck, Y. Tu, and H. Ågren, Atmos. Chem. Phys. 11, 6549 (2011). 21 X. Ma, P. Chakraborty, B. J. Henz, and M. R. Zachariah, Phys. Chem. Chem. Phys. 13, 9374 (2011). 22 L. Sun, X. Li, T. Hede, Y. Tu, C. Leck, and H. Ågren, J. Phys. Chem. B 116, 3198 (2012). 23 X. Li, T. Hede, Y. Tu, C. Leck, and H. Ågren, Tellus, Ser. B 65, 20476 (2013). 24 L. Sun, T. Hede, Y. Tu, C. Leck, and H. Ågren, J. Phys. Chem. A 117, 10746 (2013). 25 M. Darvas, S. Picaud, and P. Jedlovszky, Phys. Chem. Chem. Phys. 13, 19830 (2011). 26 M. Darvas, S. Picaud, and P. Jedlovszky, Phys. Chem. Chem. Phys. 15, 10942 (2013). 27 G. P. Schill and M. A. Tolbert, J. Phys. Chem. A 116, 6817 (2012). 28 D. van der Spoel, E. Lindahl, B. Hess, A. R. van Buuren, E. Apol, P. J. Meulenhoff, D. P. Tieleman, A. L. T. M. Sijbers, K. A. Feenstra, R. van Drunen, and H. J. C. Berendsen, GROMACS User Manual version 4.5.4, 2010, see www.gromacs.org. 29 P. Jedlovszky and L. Turi, J. Phys. Chem. A 101, 2662 (1997); Corrigendum, J. Phys. Chem. A 103, 3796 (1999). 30 M. W. Mahoney and W. L. Jorgensen, J. Chem. Phys. 112, 8910 (2000). 31 M. P. Allen and D. J. Tildesley, Computer Simulations of Liquids (Clarendon Press, Oxford, 1987). 32 U. Essmann, L. Perera, M. L. Berkowitz, T. Darden, H. Lee, and L. G. Pedersen, J. Chem. Phys. 103, 8577 (1995). 33 C. Vega, J. L. F. Abascal, M. M. Conde, and J. L. Aragones, Faraday Discuss. 141, 251 (2009). 34 H. J. C. Berendsen, J. P. M. Postma, A. DiNola, and J. R. Haak, J. Chem. Phys. 81, 3684 (1984). 35 M. Gadermann, D. Vollmar, and R. Signorell, Phys. Chem. Chem. Phys. 9, 4535 (2007). 36 M. Kulmala, J. Kontkanen, H. Junninen, K. Lehtipalo, H. E. Manninen, T. Nieminen et al., Science 339, 943 (2013).
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THE JOURNAL OF CHEMICAL PHYSICS 141, 104701 (2014)
Water and formic acid aggregates: A molecular dynamics study Delphine Vardanega and Sylvain Picauda) Institut UTINAM – UMR 6213 CNRS, Université de Franche-Comté, 16 route de Gray, F-25030 Besançon Cedex, France
(Received 18 July 2014; accepted 24 August 2014; published online 8 September 2014) Water adsorption around a formic acid aggregate has been studied by means of molecular dynamics simulations in a large temperature range including tropospheric conditions. Systems of different water contents have been considered and a large number of simulations has allowed us to determine the behavior of the corresponding binary formic acid–water systems as a function of temperature and humidity. The results clearly evidence a threshold temperature below which the system consists of water molecules adsorbed on a large formic acid grain. Above this temperature, formation of liquidlike mixed aggregates is obtained. This threshold temperature depends on the water content and may influence the ability of formic acid grains to act as cloud condensation nuclei in the Troposphere. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4894658] I. INTRODUCTION
Organic material is ubiquitous in the Earth’s atmosphere, coming from both natural sources and anthropogenic activities. The interactions between water and organic molecules are thus currently investigated in the context of atmospheric chemistry because liquid droplets and ice particles may scavenge some of these organic molecules from the atmosphere, thus modifying the atmospheric composition and chemistry.1–3 Moreover, upon aggregation, either directly or after various oxidation processes, volatile organic compounds (VOCs) may form particles of different sizes, contributing to the aerosol formation. Thus, organic matter represents an important fraction of the fine aerosol mass4 which comes also from sea salt, mineral dust, black carbon, sulfates, and nitrate ammonium whose relative abundance depends on, e.g., location, time, and meteorological conditions.5 The atmospheric aerosol plays a central role on current atmospheric research, because it affects the climate system via different physical mechanisms.5–7 Indeed, the aerosol particles have a direct effect on climate not only by scattering and absorbing solar radiation but also by scattering, absorbing, and emitting thermal radiation. Moreover, these particles may have an indirect effect by acting as cloud condensation (CCN) and ice (IN) nuclei, depending on temperature and on their affinity for water molecules. Indeed, the composition, the size, and the concentration of the aerosol particles impact on the number, concentration, and size of the CCN and/or IN that may be formed. As a consequence, they may strongly influence the formation of droplets and/or ice particles in the resulting clouds, thus modifying the cloud properties such as light scattering. They may also impact on the cloud lifetimes and on the precipitation rates.7 For all these reasons, a detailed description of the processes governing the ability of aerosol to act as condensation nuclei for water, either in the liquid (CCN) or in the solid a) Author to whom correspondence should be addressed. Electronic mail:
[email protected] 0021-9606/2014/141(10)/104701/8/$30.00
(IN) state, is strongly needed, based on a better understanding of the underlying interactions between water molecules and aerosol particles. However, the corresponding aerosol+water systems are very complex, because aerosols are usually mixtures of compounds, the properties of which strongly depend on their way of production. Owing to this complexity, modeling ideal systems by computer simulations is, in a first step, an interesting way to better understand the water-aerosol interactions at the molecular scale. However, due to the size of the corresponding models which have to consist of, at least, hundreds of different molecules, calculations based on a rigorous quantum description of these interactions will be certainly not feasible before long. In contrast, classical approaches based on a simplified description of the aerosol–water interactions are of great interest, as long as the empiric parameters used in the classical interaction models can correctly reproduce experimental observations. This is indeed the case for a wide variety of atmospherically relevant organic compounds for which the accuracy of the interaction models with water has been tested in recent years, on the basis of classical molecular dynamics and Monte Carlo simulations aiming at investigating VOC adsorption on, i.e., ice surfaces.8–18 A few molecular dynamics simulation studies have thus been recently devoted to a detailed investigation of the behavior of large droplets made of water and organic molecules used as surrogates for organic aerosols. Either big water droplets coated by various organic molecules19–24 or the reverse situation, i.e., large organic aggregates interacting with surrounding water molecules25, 26 have been considered in the corresponding theoretical works, as a function of temperature. These two approaches showed however some similar results especially regarding the state of mixture of the aerosol particles. Indeed, water and organic molecules have been found to form either mixed or separate phases depending on temperature, concentration, and also on the types of the organic molecules. Moreover, some of these results have been tentatively related to the conclusions of a recent experimental work by Shill and Tolbert27 who tried to provide a simple parametrization of
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organic ice nucleation efficacy by using the O:C ratio as a proxy for characterizing the organic aerosol hydrophilicity. However, the theoretical results showed that not only the O:C ratio should be considered but also the internal conformation of the organic molecules.25, 26 This unfortunately indicates that a systematic study of various organic molecules should be undertaken before any global conclusion can be drawn. As a consequence, we complement our previous work on oxalic and malonic acids25, 26 by considering here the case of formic acid (HCOOH), the smallest monoacid molecule, for which entropic effects related to internal conformation changes with temperature are minimized. In Sec. II, we present the protocol of our simulations and the technical details of data processing. Then, in Sec. III, we present the analysis of the simulation results for binary formic acid/water mixtures, as a function of temperature and water composition. Finally, in Sec. IV, the main conclusions of this study are summarized. II. COMPUTATIONAL DETAILS
Molecular dynamics simulations were performed using the GROMACS program package (version 4.5.4)28 to study the formation and stability of formic acid aggregates together with water molecules at five different compositions, corresponding to 0, 50, 66, 75, and 83 mol. % water concentrations. The initial geometry of the formic acid molecule and the corresponding force field between acid molecules have been taken from the literature.29 This intermolecular potential is a combination of electrostatic interactions between point charges located on appropriate sites of the molecules and of Lennard-Jones contributions. The interactions between water molecules were described by the five-site TIP5P model.30 In this model, a 12-6 Lennard-Jones site is located on the oxygen atom and the charge distribution of the water molecule is represented by two positive charges placed on the H atoms and two negative-charge sites that are located in the tetrahedral direction of the two lone pairs, at a distance of 0.70 Å away from the oxygen. In this model, the OH length and HOH bond angles are set to the experimental gas phase values, i.e., 0.9572 Å and 104.52◦ . In a similar way, the acid-water interaction has been calculated as a sum of pairwise dispersion-repulsion and Coulomb contributions between atoms and partial charges. The dispersion-repulsion terms were represented by the Lennard-Jones potential, the parameters of which are being obtained from the ε, σ values of the individual atoms according to the Lorentz-Berthelot rules.31 The Lennard-Jones potential was truncated at the cut-off radius of 14 Å. The longrange part of the electrostatic interactions was evaluated by the particle Mesh Ewald (PME) method32 with the same cutoff value. Bond, angle, and torsion flexibility was allowed for the formic acid and the water molecules. First, to create a formic acid aggregate, 120 formic acid molecules have been randomly placed in a large cubic simulation box having an edge length of 80 Å. This initial system was equilibrated during 1 ns on the (N,V,T) ensemble at 100 K. During this simulation, formic acid molecules aggregated to form a single big aerosol particle containing the 120
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molecules. Once this aggregate was formed, a production run of 5 ns was performed in the same conditions for data analysis. Such formic acid aggregate was shown to be stable upon temperature increase (at least up to 250 K, see below). This equilibrated aggregate was then used as model aerosol particle to investigate water adsorption. Then, four different compositions have been chosen to investigate the adsorption of water on the aerosol and to analyse the behavior of the resulting binary systems at different temperatures in the range of 100-250 K. Note that temperature values much lower than those encountered in the Troposphere have been considered because, in molecular dynamics simulations, the temperature at which a phase transition occurs may strongly depend on the interaction potential used in the calculations (see for instance, the discussion of melting temperatures for various water models in Vega et al.33 ). Because the characteristics of the water-formic acid potential used here was not known a priori, we thus choose to consider a rather large range of temperatures to investigate possible structural and thermodynamic evolutions in the molecular systems under study. As detailed below, important changes in the aerosol mixing state have been indeed evidenced at quite low temperatures that needed to be characterized in details. The stabilized formic acid aggregate has been placed in the middle of an empty cubic simulation box having the edge length of 80 Å and then, 120, 240, 360, and 640 water molecules, respectively, have been randomly placed in the box, modeling thus roughly 50, 66, 75, and 83 mol. % water contents. These systems have been equilibrated primarily on the canonical (N,V,T) ensemble for 5 ns at 100 K. These pre-equilibrated systems have then been further equilibrated for 1 ns on the isothermal-isobaric (N,p,T) ensemble at various temperatures, including atmospherically relevant values. During these simulations, pressure has been kept constant to 1 atm. Each of these simulations has been followed by a 1 ns long production run, performed under the same conditions, during which 1000 equilibrium configurations, separated by 1 ps long trajectories each have been saved for data analyses. For all these simulations, a time step of 0.1 fs was used. The temperature and pressure of the systems were controlled by means of the weak coupling method of Berendsen et al.34 Indeed, this method allows for exponential decay of instantaneous value of temperature and/or pressure to the target value and thus converges relatively quickly. It is thus useful for stabilizing systems that may be far from equilibrium such as the aerosol particles modeled here. Moreover, this method usually yields correct results for most calculated properties provided that large systems of hundreds of atoms/molecules are considered. Periodic boundary conditions were applied during the simulations. A total number of 40 simulations have thus been performed to analyse the temperature behavior of the binary formic acid-water system. In such binary mixtures, the structural characteristics are well visible by looking at equilibrium snapshots, or as a more quantitative approach, they might be investigated by means of detailed cluster analysis. We have thus calculated the size distribution P(n) of the clusters formed in the binary water+formic acid systems, together with that of the
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formic acid clusters disregarding the water molecules and that of the water clusters without the formic acid molecules for all the temperatures considered at four compositions. During the course of this analysis two formic acid molecules have been regarded to be bonded if the distance from any of their hydroxylic hydrogen to any of the carbonylic or hydroxylic oxygen atoms of the other formic acid molecule was smaller than a cut-off distance of 2.10 Å or 3.90 Å, respectively. A water and a formic acid molecule have been considered to be connected if the H(acid)–O(water) cut-off distances turned out to be smaller than the cut-off value of 2.10 Å. In the same way, two water molecules have been considered to be nearest neighbors if the distance between their oxygen and hydrogen atoms did not exceed the value of 2.55 Å. The cut-off values listed above have been obtained as the first minimum position of the corresponding partial pair correlation functions. Moreover, to get a deeper insight into the energetic changes that occur during and as a result of the structural changes, and furthermore, to shed light on the energetic reasons underlying these changes when temperature increases, we have calculated the distributions of the binding energy between a formic acid molecule and all the other formic acids in b ), between a water molecule and all the the system (Eacid−acid b ), and between a formic acid molecule other waters (Ewat−wat b ). These binding energy and all the water molecules (Eacid−wat distributions are also useful tools to provide us with information about the hydrogen bonded network of the aerosol and can thus be related to the size distributions mentioned above.
III. RESULTS AND DISCUSSION A. Structure of pure aerosol particles
Simulation of the pure aerosol phase of 120 formic acid molecules resulted in the formation of one single big aerosol particle irrespective of the temperature in the 100–250 K range. A snapshot of this aggregate is shown in Fig. 1 (top) for different temperatures. This conclusion has been also supported by statistically relevant quantitative results based on the size distribution P(n) of the clusters formed by the formic acid molecules (Fig. 2, top) at various temperatures. In a general way, P(n) is characterized by two main peaks that are broader for higher temperature values due to larger thermal motions. The first peak, obtained at large n values corresponds to the formation of a large, more or less structured, big formic acid aggregate in the simulation box. The second one, obtained at very low n values, originates from formic acid molecules that are in fact slightly beyond the distance criterion defined for the cluster analysis (2.10 Å, see Sec. II) and not from molecules completely isolated in the box. This is confirmed by a detailed analysis of the snapshots and by additional cluster analysis using a larger value for this distance criterion. Indeed, Fig. 3 shows the P(n) distribution for increasing values of this distance criterion from 2.10 to 2.70 Å at, for instance, 100 K. It clearly appears that when using the larger distance criterion all the formic acid molecules belong to a single big aggregate, leading to a single peak in P(n) located at the value n = 120. However, in the following, the results are presented for a distance criterion equal to 2.10 Å, i.e.,
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FIG. 1. Equilibrium snapshots of formic acid aggregates at 100, 150, and 200 K (left, middle, and right) and for 0, 50, 66, and 83 mol. % water concentrations (from top to bottom).
for the value determined from the analysis of the pair radial distribution functions (see Sec. II). Note that a detailed analysis of the snapshots and of the hydrogen bonding network formed between the formic acid molecules (see below) shows some local ordering in the acid aggregate that is however difficult to compare with that of the formic acid crystal. Indeed, the quite small number of acid molecules considered here and the finite size of the resulting aggregate certainly prevents the formation of a well-ordered crystal structure. In addition, because it has been observed previously for malonic acid molecules that the size of the aerosol may depend on the initial density of acid molecules in the simulation box,26 the present simulations have been repeated with a system of double density, consisting of 240 formic acid molecules randomly placed in the same simulation box. The corresponding results show that for the double density we obtained a stable aerosol of formic acid molecules twice as big as for the lower density case, i.e., this particle consisted of 240 formic acid molecules. It thus appears that formic acid molecules, such as the malonic ones, have a strong tendency to form large aggregates. Nevertheless, the above mentioned aggregate of 120 formic acid molecules appeared as a good compromise between the relevance and the time cost of the corresponding simulations and it has thus been used for further simulations when considering addition of water molecules in the simulation box. Note, however, that in this case, some additional simulations have also been performed by considering a bigger acid aggregate (240 molecules) and water molecules in the simulation box that lead to results very similar to those presented here with the smaller aggregate.
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FIG. 2. Cluster size distributions P(n) of formic acid molecules in the formic acid-water binary aerosols for 0, 50, 66, and 83 mol. % water concentrations (from top to bottom) and at temperatures of 100 K (left), 150 K (middle), and 200 K (right).
B. Behavior of the binary aerosol
We have analysed the temperature behavior of the binary formic acid-water system at four different compositions, cor-
FIG. 3. Cluster size distributions P(n) of formic acid aggregates at the temperatures of 100 K for cut-off values of 2.1 Å (top left), 2.3 Å (top right), 2.5 Å (bottom left), and 2.7 Å (bottom right).
responding to 50, 66, 75, and 83 mol. % water concentrations. In all cases, it turned out to be possible to differentiate unambiguously between the appearing situations by simply looking at the equilibrium snapshots taken from the simulations corresponding to temperatures in the range of 100–250 K. Some of these snapshots are given in Fig. 1 for different temperatures and water contents. At 100 K, the analysis of these snapshots indicates that formic acid molecules tend to form a big aggregate surrounded by adsorbed water molecules, irrespective of the water content. When the temperature increases, more intensive thermal motion of the formic acid molecules initiates the formation of relatively big and flexible voids within the core of the aggregate, allowing water molecules to penetrate into the core of the aggregate and fill the voids. At high water content and above 200 K (Fig. 1, bottom right), a total dissolution of the formic acid cluster is even evidenced. These conclusions have been also supported by statistically relevant quantitative results based on the size distribution P(n) of the clusters formed by the formic acid molecules. These cluster size distributions are shown in Fig. 2 for three temperatures and for the formic acid–water systems of three compositions (50, 66, and 83 mol. % water concentrations) Indeed, no significant difference has been obtained between 75 and 83 mol. % water concentrations and thus only the results for the latter case are given here. At 100 K, P(n) is characterized by two main peaks. The first one, corresponding to large n values, originates from the formation of a large formic acid aggregate in the simulation box. As already mentioned above, the second peak, obtained at very low n values,
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corresponds in fact to formic acid molecules that are slightly beyond the distance criterion defined for the cluster analysis and not from molecules isolated in the box. Again, this has been confirmed by a detailed analysis of the snapshots and by additional cluster analysis using a larger value of this distance criterion. At 150 K, the position of the first peak is shifted to lower n values indicating that the average size of the aggregate slightly decreases by about 30 molecules between 100 and 150 K. Indeed, larger thermal motions lead to increased fluctuations of distances between formic acid molecules and, as a consequence, the number of formic acid separated by more than 2.10 Å increases. In addition, these larger motions allow water molecules to penetrate deeper in the internal structure of the acid aggregate, thus initiating its dissociation. This analysis is confirmed at higher temperature (200 K) where only a single, quite high intensity peak is seen at small aggregation number values, indicating the complete dissolution of the formic acid aggregate. It can thus be concluded that the qualitative picture suggested by the equilibrium snapshots, which states that in case of formic acid–water mixtures, the formic acid aggregates dissociate at high temperatures, is supported by the formic acid cluster size distribution. As a consequence, the formic acid-water mixtures are thus characterized by two main situations. At low temperatures formic acid forms a single big aggregate, on which water molecules are absorbed, while for higher temperatures a mixing of the two species is seen. This conclusion seems valid for all the water concentrations considered here, as illustrated on the equilibrium snapshots in Fig. 1, where we may clearly identify the demixed state of the formic acid–water system for the low temperature and the mixed situation observed at high temperatures for all concentrations. To better characterize the transition between the demixed and mixed situations, we have represented in Fig. 4 the average cluster size of the largest formic acid aerosol formed at various water contents as a function of the temperature. This average cluster size has been calculated on the basis of the peaks obtained in the corresponding P(n) functions (Fig. 2). We have also added in this figure the corresponding analysis for the pure formic acid aerosol (i.e., system at 0 mol. % of water), for comparison. It can thus be easily seen that, without any water in the simulation box, the average size of the formic acid aggregate slightly decreases when temperature is increased, as already mentioned before. In contrast, when water molecules are added, the temperature has a strong influence on the size of the formic acid aggregate. Indeed, at low temperature (typically less than 120–130 K depending on the water content) and low water contents (50 and 66 mol. % of water) the average size of the formic acid aggregate remains nearly constant, indicating the formation of a large formic acid aggregate in the simulation box. This situation typically corresponds to a pure demixed system (i.e., a segregation of the different types of molecules is obtained). Note however that at high water contents (75 and 83 mol. % of water), we did not obtain any plateau in the average cluster size curve even at the lowest temperature considered here, suggesting a partial formic acid–water mixing even at 100 K. Note that an
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FIG. 4. Average cluster size of the formic acid aggregates formed in the formic acid-water systems corresponding to 0, 50, 66, 75, and 83 mol. % water contents (black circles, red triangles, green squares, yellow diamonds, and blue triangles, respectively), as a function of the temperature.
additional simulation at 50 K for the 83 mol. % water content actually indicated the formation of the demixed system at this very low temperature, but we did not perform any systematic search for a possible plateau in P(n) between 50 and 100 K, because these temperatures are anyway much lower than those encountered in the Troposphere. When the temperature is increased, the average size of the formic acid aggregate progressively decreases up to the complete deliquescence obtained above 200 K, irrespective of the water content. It should be however emphasized that, even at these temperatures, we still observed the formation of a big mixed aggregate in the simulation box, as shown in the snapshots given in Fig. 1 (right) and as indicated by the single peak obtained at large n values in the size distribution of the clusters formed by the formic acid+water molecules (not shown). Note that these conclusions remain valid when increasing the size criterion used to define the formic acid aggregate formation. As an illustration, Fig. 5 shows the results obtained for two different size criteria for the system containing 50 mol. % of water molecules. It clearly appears on this figure that whereas the size criterion may influence the size of the formic acid aggregate (i.e., the average number of formic acid molecules included in the aggregate), it does not change the shape of the corresponding curves nor the threshold temperature for which the deliquescence of this aggregate starts. It should be emphasized that the mixing mechanism suggested simply by looking at the distribution of aggregate sizes and snapshots has to be confirmed by a careful investigation of the energetic background to get a justification, and to have an at least semi-quantitative picture of the processes underlying the transitions between mixed and demixed situations.
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FIG. 5. Average cluster size of the pure formic acid aerosol in the formic acid–water system corresponding to 50 mol. % of water and for cut-off values of 2.1 Å (red triangles) and 2.7 Å (yellow diamands), as a function of the temperature.
C. Energetic background
The binding energy Eb distributions calculated for the formic acid–water mixed aerosols are presented in Fig. 6 to-
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gether with those calculated for the formic acid system without water, for comparison. Note that the term “binding energy” means the total interaction energy of a certain molecule (formic acid or water) with all the molecules of a certain kind in the system. In other words, this is the energy cost of bringing this molecule at infinite distance from the other molecules considered in the energy calculations. The left, middle, and right panels of Fig. 6 show the distribution of the binding energy of a formic acid molecule with all the other formic acids in the system, that of a formic acid molecule with all the waters, and that of a water molecule with the other waters in the system. The amount of water molecules in the system is increased from top to bottom of Fig. 6. First of all, binding energies strongly depend on the temperature but they are not strongly modified by the water content of the binary water+acid systems, with the exception of the water-water binding energy distribution that (as expected) depends on the water concentration. As a consequence, we just analyse here the results obtained for the higher water content in detail, i.e., for a system containing 120 formic acid and 640 water molecules (Fig. 6, bottom). Looking first at the water–water binding energy distributions (Fig. 6, bottom right), we can see several peaks for each temperature that can be tentatively related to hydrogen bonding. For instance, the four peaks clearly evidenced at 100 K could correspond to arrangements in which one water molecule forms (in average) around 4, 3, 2, and 1 hydrogen-bonds with other water
FIG. 6. Binding energy distributions of formic acid water binary aerosols for 0, 50, 66, and 83 mol. % water content (from top to bottom) at the temperatures of 100 K (black lines), 150 K (red lines), and 200 K (blue lines). Left panels: binding energy of a formic acid molecule with all the other formic acid molecules; middle panels: binding energy between a formic acid molecule and all the water molecules; and right panels: binding energy of a water molecule with all the other waters in the system.
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molecules, assuming that the average energy of a single hydrogen bond is around −25 kJ mol−1 when using the TIP5P interaction potential.30 Note that the number of H-bonds given this way is indication only, because calculating the exact numbers of hydrogen bonds per water molecule would, of course, require a more rigorous definition of these H-bonds based on a combination of energy and geometric criteria. The relative intensity of the peaks in the Eb distribution between water molecules varies significantly upon increasing the temperature suggesting some rearrangements in the hydrogen bond network when changing temperature. Stronger evolutions are seen for the formic acid–formic acid binding energy distribution. Thus, at 100 K, three main peaks are observed which roughly correspond to 4, 3, and 2 hydrogen bonds, in accordance with the formation of a large formic acid aggregate in the simulation box. When temperab is shifted towards ture increases, the peak position in Eacid−acid higher energy values (i.e., less negative values) indicating that, in the mixed acid-water system, formic acid molecules tend to lose their hydrogen bonded formic acid neighbors. In contrast, in the formic acid–water binding energy distribub , the positions of the peaks shifts towards lower tions Eacid−wat energy values as a consequence of the formation of an increased number of hydrogen bonds between formic acid and water molecules when the temperature is increased. The concomitant decrease of the formic acid–water binding energy and loss of hydrogen bonds between formic acid neighbours fully supports the existence of a transition from a demixed to a mixed situation of the binary formic acid+water systems upon temperature increase, as already suggested by the analyses of the snapshots and cluster size distributions. D. Discussions
The present results can be, at least qualitatively, compared to those recently obtained on formic acid particles using infrared spectroscopy, although the temperature of the experiments was much lower and the particle much bigger than those considered here.35 Indeed, at 78 K, large formic acid particles are characterized by hydrogen-bonded chains leading to an overall crystalline structure. When adding more and more water, this crystalline structure disappears and water and formic acid molecules tend to mix on a molecular level. The corresponding process is however shown to depend on the amount of water molecules added to the formic acid grain. These conclusions are in agreement with the results of our simulations indicating that the hydrogen bond network of pure formic acid grains is strongly modified upon water adsorption. They also agree with our findings showing that the formic acid–water mixing depends on the water content and is partially present for high water contents even at temperatures as low as 100 K. In addition, it is interesting to compare the present results with those previously obtained for the oxalic acid molecule25 which is, as the formic one, characterized by a O:C ratio equal to 2. Indeed, it has been recently suggested to use this ratio as a proxy for characterizing organic aerosol hydrophilicity, although this conclusion was based on experiments considering
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monocarboxylic acids only.27 At low temperature, it has been shown that water adsorbed on large oxalic acid aggregates irrespective of the water concentrations, as obtained here for formic acid at very low temperature. In contrast, different behavior were evidenced for the water–oxalic acid systems at higher temperatures that consist either of mixed droplets or of oxalic acid molecules adsorbed on water aggregates, depending on the water contents. In the present simulations, only large mixed droplets of formic acid and water molecules have been found at temperatures relevant for Tropospheric conditions, a behavior that is thus rather similar to that obtained for the malonic acid (O:C = 4/3)—water systems.21, 26 The comparison between these three acid molecules thus indicates that, unfortunately, using the O:C ratio for predicting the ability of carboxylic acids to act as water nuclei might be not as straightforward as previously inferred.27 At least, it seems that this conclusion cannot be generalized to mono and dicarboxylic acids because the affinity of these molecules for water depends not only on the O:C ratio, but also on the number of carboxylic groups and of the internal geometry of the acid molecules. It is also interesting to discuss the interfacial properties of the particles studied here in terms of water accommodation which is related to the water vapor condensational growth of the particle. The present results show that formic acid molecules tend to form stable aggregates at tropospheric temperatures that can trap surrounding water molecules by hydrogen bonding. At high water content, formic acid molecules tend to dissolve into water above typically 160–180 K. Although our simulations have been limited to an upper value of 83 mol. % water content, we can infer from our results that the surface of mixed formic acid-water particles is thus essentially water in tropospheric conditions, in agreement with the conclusions of recent molecular dynamics simulations of malonic acid coated aerosol.21 As a consequence, a mixed formic acid–water aerosol particle would thus behave like a pure water droplet in the Troposphere, resulting in a water vapor accommodation factor equal to unity. These conclusions (initial formation of nanosized clusters and subsequent growth) could be, at least qualitatively, related to results of direct observations of atmospheric aerosol nucleation.36 IV. SUMMARY AND CONCLUSIONS
The water adsorption around small formic acid aggregates has been studied by means of molecular dynamics simulations in the temperature range of 100–250 K, thus including temperatures relevant for the Troposphere. Systems of various compositions, corresponding to different water contents have been considered and a total number of 40 simulations have been performed, allowing us to characterize a “phase diagram-like” (Fig. 4) of the binary formic acid–water systems. In this diagram, both the temperature and the water content have a strong influence on the behavior of the system. Two situations are thus evidenced for the formic acid–water aggregates, corresponding either to water adsorption on large formic acid grains at very low temperatures, or to the formation of mixed droplets consisting of formic acid and water molecules at higher temperatures. At moderate temperatures,
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an intermediate situation is obtained here, characterized by a partial deliquescence of the acid aggregate. Note that it cannot be totally excluded that the temperature range corresponding to this partial deliquescence depends on the duration of the simulations and, as a consequence, much longer simulations could result in a more abrupt transition between the two extreme situations (mixed and demixed systems). Anyway, this would not change the present conclusion that formic acid and water molecules formed mixed droplets at temperatures relevant for tropospheric conditions, irrespective of water concentration. In addition, the comparison between the present results and those previously obtained for oxalic and malonic acids indicates that, unfortunately, using the O:C ratio for predicting the ability of carboxylic acids to act as water nuclei might be not as straightforward as previously inferred.27 At least, it seems that the affinity of these acid molecules for water depends not only on the O:C ratio, but also on their number of carboxylic groups and of their internal geometry. The present results cannot be directly compared to any field measurements. However, they represent an additional step towards modeling of organic cloud condensation nuclei, leading to a deeper understanding of the complicated and environmentally relevant problem of heterogeneous nucleation of water. In particular, the present simulation results, together with those previously published on dicarboxylic acids25, 26 point out the complex effect of both temperature and humidity on the behavior of organic aerosols. They emphasize the need for further experimental and simulation works in this field. ACKNOWLEDGMENTS
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