How CO₂ gas accelerates water nucleation at low temperature

The issue of homogeneous binary nucleation of H₂O and CO₂ at low temperatures as opposed to heterogeneous nucleation has been discussed in the context of low temperature natural gas separation and CO₂ capture technologies, the formation of H₂O and CO₂ clouds in the Martian atmosphere, and, more recently, the influence of CO₂ on the formation of H₂O clouds in the Earth’s atmosphere.^1–10 In supersonic gas separators, condensable gases are first converted into droplets or particles by rapid gas expansion and then removed from the gas phase by centrifugal separation.² The performance of these devices depends on their design, for which an accurate knowledge of nucleation and subsequent droplet and particle growth is crucial but is still one of the biggest limitations. The same lack of detailed knowledge about the mechanisms of the very first steps in cloud formation on Mars makes it difficult to assess the role of homogeneous nucleation processes in its atmosphere. It is currently assumed that heterogeneous nucleation, i.e., nucleation triggered by existing condensation nuclei, is more likely than homogeneous nucleation.^6–9,11,12

As we have shown in our previous publication on the nucleation of toluene in the presence of CO₂,¹³ homogeneous binary nucleation can be governed by subtle effects that are challenging to observe directly in an experiment. We found that the mere presence of CO₂ gas significantly accelerates toluene nucleation via the formation of short-lived toluene–CO₂ dimers. We refer to these dimers as chaperone complexes,^14,15 and we still refer to this process as homogeneous binary nucleation or homogeneous co-nucleation, although only pure toluene clusters are formed, i.e., this catalytic process does not lead to co-condensation of CO₂ gas. Our study of nucleation at the molecular level shows that such multicomponent effects in homogeneous nucleation, which have so far not been visible in most experiments and have not been considered in most simulations, could change current assessments of the relevance of homogeneous nucleation mechanisms in atmospheric and industrial processes. We would like to note that the effects investigated here, which are due to weak intermolecular interactions, differ in their character from the amplification effects in systems with strongly bound, reactive nucleating clusters.^16–18 

In the present study, we investigated whether similar acceleration phenomena occur in the homogeneous binary nucleation of H₂O–CO₂ at temperatures of 57 and 75 K and pressures of ∼40 and 70 Pa, respectively, and we compare the results with our previous toluene–CO₂ study.¹³ Both homogeneous unary H₂O and CO₂ nucleation have been studied over a wide range of conditions.^4,19–29 However, we are only aware of one study by Campagna et al.,¹⁰ which deals with the nucleation of water in the presence of CO₂, although at much higher pressures and temperatures of ∼1 bar and 240 K, respectively. It reports higher nucleation rates for water nucleation in the presence of CO₂ gas and attributes this to a reduction in water surface tension due to CO₂. This study does not provide cluster-size resolved (molecular-level) experimental data, and it probes a very different nucleation regime, i.e., nucleation in the presence of a substantial free energy barrier, while our conditions reach the regime of vanishing nucleation barrier. At present, a direct comparison of the two studies does not appear to be possible, but it is conceivable that the accelerated nucleation could have a similar molecular origin.

To obtain information about the rate-determining nucleation step at the molecular level, we combine supersonic expansion generated by Laval nozzles with mass spectrometric detection of clusters.^26–33 This provides direct experimental information on the temporal evolution of the number and type of molecules that make up the nucleating clusters, as well as their number concentration. This allows us to determine nucleation rates and propose nucleation mechanisms based on information at the molecular level. Laval expansions combined with a range of different characterization methods have been used for a long time by several research groups to study chemical kinetics at low temperatures.^{19,20,34–41} Our experimental setup is optimized for the observation of the first rate-determining nucleation step, where cluster concentrations are so low that monomer depletion and coagulation are negligible. Nevertheless, our experiments also provide information on the initial growth of clusters (early cluster growth), which allows us to also report first data on the influence of CO₂ gas on the early growth of water clusters directly after nucleation.

The nucleation and growth experiments were carried out with our Laval setup (see Fig. 1 and refs. for details).^{26,27,29–33} Gas mixtures of H₂O (Dest, Supelco chromatography grade) and CO₂ were mixed with a Ar–N₂ (PanGas 5.0) carrier gas mixture and expanded from the stagnation volume (p₀ and T₀ are the stagnation pressure and temperature, respectively) through a De-Laval nozzle (see Tables T1–T4). H₂O was supplied via a liquid flow meter (LFM; Bronkhorst) and vaporized in a controlled evaporator mixer (CEM; Bronkhorst) (not shown). All gas flows were regulated with mass flow controllers (GM50; MKS). The ratio of Ar and N₂ in the carrier gas mixture was adjusted so that two different flow temperatures of T = 57 and 75 K were achieved (see Tables T1–T4). The total static pressures in the nucleation region were 42 ± 1 and 69 ± 1 Pa, respectively, where the H₂O and CO₂ contents varied between 0.08%–0.4% and 0%–10%, respectively (see Tables T1–T4). The natural logarithm of the supersaturation S with respect to H₂O varied between about 60 and 85 (see Tables T1–T4).

The supersonic expansion generated a uniform flow at the Laval nozzle exit that was extended into the postnozzle flow region by matching the background pressure in the expansion chamber to the static pressure p in the flow. This postnozzle flow corresponds to a wall-less flow reactor that enables nucleation studies at constant p, T, and supersaturation S. The flow speed v, the Mach number M, and the flow temperature T were determined from pressure measurements with a Pitot tube in the flow downstream of the nozzle using a modified Rayleigh–Pitot equation.^{26,30,31,33,42,43} The central part of the postnozzle flow was sampled into the time-of-flight mass spectrometer (TOF-MS) with a 1 mm skimmer. The nozzle-to-skimmer distance L_NS can be adjusted (up to about 160 mm in steps of 1 mm) by moving the Laval nozzle on an axial translation stage. An increase in L_NS corresponds to an increase in the nucleation time t, given by the relationship t = L_NS/v. Nucleation times up to a few hundred microseconds can be achieved with a time resolution of ∼2 µs (determined by the spot size of the ionizing laser).

The clusters in the gas flow were photoionized in the TOF chamber with an vacuum ultraviolet (VUV) light of 13.8 eV, i.e., with photon energies close to the lowest ionization energy of H₂O. The VUV light was produced by four-wave mixing in a supersonic krypton expansion (not shown).⁴⁴ Single-photon VUV ionization just above the threshold has been shown to be a soft ionization method for weakly bound clusters.^45–48 Because fast intra-cluster proton transfer takes place in H₂O clusters,^46,48 protonated water cluster cations are detected in the mass spectra.^26,27 The cluster cations were accelerated in a six-plate Wiley–McClaren type extractor at voltages of up to 30 kV to ensure quantitative detection of relative cluster ion intensities by a microchannel plate detector (MCP, Photonics).²⁶ The intensities of the H₂O monomer ion (and also the CO₂ monomer ion) in the mass spectra were 3–4 orders of magnitude larger than the intensities of the H₂O cluster ions. To avoid saturation effects due to monomers when measuring cluster ion mass spectra, the monomer ions were deflected in those measurements (and, thus, not detected) by a voltage pulse applied to a mass gate located just in front of the MCP detector.^26,27,31 We intentionally worked under conditions where the monomer intensities are much higher than the cluster intensities to avoid depletion of monomers during nucleation and early growth so that p, T, and S remain constant.

We performed H₂O nucleation experiments at 57 and 75 K at different nucleation times t up to 200 µs for CO₂ to H₂O ratios between ∼10 and 160 (Tables T2 and T4). Figure 2 compares example mass spectra for binary nucleation at 75 K for a CO₂ to H₂O ratio of ∼20 (red) with unary H₂O nucleation experiments (black) under the same conditions, i.e., the same p, T, and H₂O saturation S. Two important findings emerge from this following comparison: (i) Only homo-molecular (H₂O)_i clusters are observed in the mass spectra, even in the binary case. There are no hetero-molecular (H₂O)_i(CO₂)_k clusters [and no pure (CO₂)_k clusters] visible in the spectra. (ii) Binary H₂O nucleation is accelerated in the presence of CO₂. This can be seen from the fact that binary nucleation starts earlier than unary nucleation and that at any time t the number concentration of (H₂O)_i clusters is significantly higher in the binary case. The same behavior was observed for all other CO₂ to H₂O ratios (not shown). The comparison of measurements with different CO₂ to H₂O ratios also shows that (iii) a higher CO₂ content increases the acceleration in the binary case.

To quantify and compare the acceleration in the presence of CO₂ gas, we determined experimental nucleation rates J^exp from the mass spectra as described in Sec. III A [Eq. (2)]. The corresponding experimental data points (blue circles) are summarized in Fig. 3, shown is $J exp / C 1 H 2 O 2$ as a function of $C 1 C O 2 / C 1 H 2 O$ [see Eq. (4)]. The red squares indicate the corresponding average values for the unary case, i.e., the average unary rate constant k_1,1 [Sec. III B, Eq. (3)]. This figure illustrates clearly that the presence of CO₂ gas accelerates H₂O nucleation and that the acceleration increases with increasing CO₂ content [points (ii) and (iii) above].

The experimental data points in Fig. 3 are consistent with a linear dependence of the nucleation rates on the CO₂ monomer concentration, in line with the kinetic model proposed in Eq. (4). Fitting $J model / C 1 H 2 O 2$ [Eq. (4), Sec. III B] to the experimental data points yields the rate constant for the hetero-dimer formation β [reaction (R2)] in Table I. A comparison of the data in Table I reveals for both temperatures that β is smaller than the homo-molecular rate constant k_1,1 and that β decreases with increasing temperature. The decrease in β with T is a consequence of the higher collision energy between a H₂O and a CO₂ molecule at 75 K (∼940 J/mol for one relative translational and two relative rotational degrees of freedom) compared with 57 K (∼710 J/mol). Higher collision energies—and to some extent also the higher internal energy of the molecules—reduce the lifetime of the excited H₂O–CO₂ Chaperon complexes formed in the collision and, thus, lead to smaller β. Campagna et al.¹⁰ recently reported a similar acceleration effect in the nucleation of water by CO₂ gas, but at much higher pressures (∼1 bar) and temperatures (∼240 K), where nucleation is controlled by a free energy barrier. The acceleration was explained by a reduction in the macroscopic surface tension caused by CO₂ gas. It remains unclear whether processes similar to those proposed here would explain this behavior at the molecular level.

The fact that at a given temperature β is smaller than k_1,1 seems at first glance to contradict our statement that CO₂ accelerates H₂O nucleation. However, since the CO₂ concentration exceeds the H₂O concentration, the contribution of the hetero-molecular pathway [reactions (R2) and (R3)] to the nucleation rate [Eq. (4)] easily exceeds the contribution of the homo-molecular pathway [reaction (R1)]. For the studied CO₂ to H₂O ratios between ∼10 and 110, the hetero-molecular pathways increase the value of J^exp by factors between ∼2 and 6 at 75 K and factors between ∼3 and 14 at 57 K compared with purely unary nucleation. A further increase in the CO₂ concentration further accelerates nucleation; e.g., a CO₂ to H₂O ratio of ∼160 at 57 K accelerates the nucleation rate by a factor of ∼25 (see the last line in Table T4). At these higher CO₂ concentrations, however, we began to see hetero-molecular CO₂–H₂O clusters in the mass spectra (see Fig. S2), implying that alternative pathways involving different hetero-molecular clusters are opening up in addition to reactions (R2) and (R3). Since the analysis would require less well-defined, more complex reaction schemes, we excluded such data from the analysis. In a simple picture, the values of k_1,1 and β are determined by the efficiency of formation of the metastable excited dimers [excited (H₂O)₂ for k_1,1 and excited (H₂O)(CO₂) for β] and their lifetimes. Longer lifetimes increase the efficiency of energy dissipation to the bath gas and, thus, the efficiency of the formation of relaxed, bound dimers. Both a higher capture efficiency and a longer lifetime thus lead to higher values for k_1,1 and β, and both are governed by the intermolecular interactions. This simple picture explains qualitatively why k_1,1 is greater than β. Because of the long-range dipole–dipole interaction, it is plausible that the capture efficiency for the (H₂O)₂ dimer formation is higher than for the (H₂O)(CO₂) dimer formation without dipole–dipole interaction. For the same reason, the relaxed ground state (H₂O)₂ dimer should be more strongly bound than the relaxed ground state (H₂O)(CO₂) dimer. Quantum chemical calculations confirm that the binding energy of the homo-dimer is ∼4 kJ/mol higher than that of the hetero-dimer (Sec. S4). A deeper binding energy potential generally implies a longer lifetime of the excited dimers (resonance states above the dissociation limit), which indicates a longer lifetime of (H₂O)₂ than of (H₂O)(CO₂). Thus, both capture efficiency and the efficiency of energy redistribution are in agreement with higher values of k_1,1 than of β. This is also consistent with the fact that only H₂O clusters (i.e., long-lived clusters) are visible in the mass spectra but no hetero-molecular clusters. The lifetime of the latter is obviously too short to form relaxed, bound (H₂O)(CO₂). However, as explained above, this transient hetero-dimer is the key species for accelerating water nucleation.

In a recent publication,¹³ we reported on the acceleration of toluene nucleation in the presence of CO₂ gas. Figure 4(a) shows the same plots as Fig. 3, but for the toluene–CO₂ system, and Table I compares the rate constants obtained for the toluene–CO₂ system at 55 K with those of the H₂O–CO₂ system at 57 K. The values of k_1,1 and β are both substantially higher for the toluene system than for the H₂O system. The acceleration of toluene nucleation by CO₂ exceeds the one for H₂O by almost a factor of 20. The higher rate constants for toluene are likely mainly an effect of the larger numbers of degrees of freedom of the excited toluene–CO₂ Chaperon complex (48 degrees of freedom) compared with the H₂O–CO₂ Chaperon complex (6 degrees of freedom). A higher number of degrees of freedom leads to a longer lifetime of the transient excited dimers as the energy redistribution within the cluster becomes more efficient. This in turn increases the efficiency of the energy transfer to the bath gas and, thus, the rate constant for the formation of the bound dimer. The efficiency of energy redistribution depends on the density of states, which in turn increases exponentially with the number of degrees of freedom of a molecule. Consequently, even a small increase in the number of degrees of freedom has a strong influence on the lifetime. (Quantitative data for cluster systems can be found in Ref. 44.) Differences in intermolecular interaction between the toluene–CO₂ system and the H₂O–CO₂ systems (Table T5) also contribute to the differences in the rate constants, but it is plausible that the degrees of freedom play a dominant role here.

The presence of CO₂ might influence not only the nucleation step, i.e., the rate liming step, but also the subsequent growth of H₂O clusters. To quantify this effect, we determined rate constants k_1,i for monomer association, assuming that this is the dominant process for cluster growth (Sec. III C). Representative values of k_1,i are listed in Table T5 of the supplementary material. They are in the range 10⁻¹⁰–10⁻⁹ s⁻¹ cm³, as expected, significantly higher than the dimerization rates (Table I). A comparison between experimental and simulated early cluster growth is provided in Fig. S3.

Figure 5 shows the cluster growth enhancement factors η_1,i for (H₂O)_i clusters with up to i ∼ 25 molecules [Eq. (7)]. Binary CO₂–H₂O enhancement factors for different CO₂ to H₂O ratios (legend) are represented by symbols, and unary H₂O enhancement factors are indicated by the purple dashed line. η_1,i indicates how much faster the association of a water monomer with a water cluster consisting of i molecules proceeds compared with the hypothetical monomer association assuming hard-sphere collisions [Eq. (6)]. All values of η_1,i are above 1 (Fig. 5). For the unary case, this reflects the fact that intermolecular interaction between the water monomer and the cluster exceeds the hard sphere rate because of intermolecular interactions, i.e., electrostatic, induction, and dispersion forces. In the presence of CO₂ (binary case), η_1,i additionally represents the influence of CO₂ on the water association to water clusters. A larger value of η_1,i in the binary compared with the unary case implies faster water association in the binary case due to the presence of CO₂. Figure 5(b) shows that η_1,i for the binary and the unary cases are essentially identical at a temperature of 75 K. This shows that CO₂ has no additional influence on early cluster growth, in contrast to nucleation, where it has a dominant influence (Sec. IV A). The same holds for monomer association at 57 K for the larger clusters with more than about 20 molecules [i > 20 in Fig. 5(a)]. For smaller water clusters at 57 K, however, η_1,i is considerably larger in the binary than in the unary case. This indicates that the presence of CO₂ gas does not only accelerate nucleation but also the growth of small clusters. It is conceivable that this enhancement is again mediated by the formation of transient hetero-molecular CO₂–H₂O clusters, similar to reactions (R2) and (R3), thus providing alternative pathways for faster energy dissipation compared with the unary case. However, a closer look at Fig. 5(a) reveals an unexpected trend. For the two lowest CO₂/H₂O ratios, η_1,i is slightly higher for the higher ratio. This is what one would expect. However, this trend is reversed at the higher CO₂/H₂O ratios: η_1,i decreases here with increasing CO₂/H₂O ratio. At first glance, this seems counterintuitive. However, we believe that this is an artifact due to the way in which the association rates of the monomers are determined and the fact that small amounts of stable, mixed (H₂O)_n(CO₂)_m clusters are already present, which lie below our detection limit in the mass spectra (∼10⁸–10⁹ cm⁻³). η_1,i is determined from the number concentration of pure (H₂O)_i clusters, which is obtained by integration of the corresponding mass peaks (Sec. III C). The presence of more and more mixed (H₂O)_n(CO₂)_m clusters with increasing CO₂/H₂O ratio, whose intensities are below the detection limit, leads to a reduction of the mass signal of the pure (H₂O)_i clusters and, thus, to an apparent decrease in η_1,i. For cases where mixed (H₂O)_n(CO₂)_m clusters below the detection limit are formed, η_1,i as determined here is thus not representative of the acceleration of early cluster growth. A quantitative description of such cases would require the knowledge of the number concentration of mixed (H₂O)_n(CO₂)_m clusters.

For comparison, Fig. 4(b) shows the enhancement factors η_1,i for early cluster growth for the toluene–CO₂ system at 57 K. The comparison of the binary with the unary case indicates that the presence of CO₂ also accelerates the growth of clusters. Because of the limited data quality, no clear trend as a function of the toluene/H₂O ratio is visible. η_1,i seems to be less cluster size-dependent than in the H₂O–CO₂ case at 57 K [Fig. 5(a)]: The values for η_1,i of the smallest clusters tend to be higher for the H₂O–CO₂ case, while the opposite holds for the largest clusters. At the current stage, this behavior remains unexplained, but it illustrates the complexity of early cluster growth.

We have determined nucleation rate constants for homogeneous water vapor nucleation without (unary nucleation) and with (binary nucleation) carbon dioxide gas from experimental data obtained with a setup that combines Laval expansion with mass spectrometric detection. The latter allows us to record cluster number concentrations as a function of cluster size (number of molecules per cluster) and cluster composition. In both unary and binary nucleation, only homomolecular water clusters were observed, but no mixed water–carbon dioxide clusters. However, the presence of CO₂ gas led to a considerable increase in the nucleation rate. At a CO₂ concentration that is about ten times higher than the H₂O concentration, the rates are approximately double in comparison to unary nucleation. At a CO₂ concentration about 100 times higher than the H₂O concentration, a ∼6-fold higher rate was observed at 75 K, which increased to a ∼20-fold higher rate at 57 K. We attribute this increase in the nucleation rate to the formation of short-lived mixed H₂O–CO₂ dimers, which provide an alternative catalytic pathway that enables efficient energy dissipation and, thus, accelerates water nucleation. We had already observed the same phenomenon in the nucleation of toluene in the presence of CO₂,¹³ but to a greater extent than in the H₂O–CO₂ system. We attribute the higher acceleration in the case of toluene to the larger number of degrees of freedom of the toluene–CO₂ chaperone complex compared with the H₂O–CO₂ complex. We have also found that the presence of CO₂ can accelerate the subsequent growth of water clusters. The underlying mechanisms are likely to be complex, and a better understanding would require large-scale molecular dynamic simulations^1,21 and advanced simulation approaches, such as the ab initio transition state theory based on master equation approaches; see e.g., Bourgalais et al.²⁰ 

The data obtained in this study are relevant for the separation of natural gas using supersonic gas separators.^1,2,4,10 They contribute to a better understanding of the complex intermolecular effects that determine nucleation and growth in gas separation processes, and they provide benchmark data to test corresponding molecular dynamics simulations.¹ It is less clear whether the observed catalytic pathway via the formation of a Chaperone complex is relevant for the formation of H₂O and CO₂ clouds on Mars, where relevant temperatures are higher (∼100 to 200 K) and CO₂ dominates the atmospheric gas composition (∼96%) at pressures that are about ten times higher than in the present study.⁵² Earlier simulations indicated a clear preference for heterogeneous over homogeneous nucleation in the Martian atmosphere.^5–9 However, as detailed simulations of energy redistribution and transfer representative of conditions on Mars remain a major challenge, the influence of chaperone-like mechanisms cannot yet be fully assessed. Surprisingly, additional experiments (not reported here) we have conducted at higher CO₂ content (up to 100% CO₂) and higher temperatures (up to 155 K) showed saturation-like features in the mass spectra, which might indicate excessive CO₂ condensation.

The supplementary material encompasses tables containing experimental conditions and nucleation rates for unary and binary nucleation experiments. A figure visualizing the determination of experimental nucleation rates. A figure visualizing the appearance of hetero-molecular water–carbon dioxide clusters. A table with calculated binding energies for dimers. A table containing monomer association rate constants. A figure comparing experimental and simulated early growth data.

We thank Philipp Albrecht, Markus Steger, and Egor Chasovskikh for their technical support. The financial support was provided by the Swiss National Science Foundation (SNSF: Project No. 200020_200306) and the ETH Zurich.

The authors have no conflicts to disclose.

F.G. and J.K. contributed equally to this work.

Stefan Feusi: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (supporting); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (supporting). Felix Graber: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (supporting); Software (equal); Validation (equal); Visualization (equal); Writing – review & editing (supporting). Jai Khatri: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (supporting); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (supporting); Writing – review & editing (supporting). Chenxi Li: Formal analysis (equal); Investigation (equal); Methodology (supporting); Supervision (supporting); Validation (equal); Writing – review & editing (supporting). Ruth Signorell: Conceptualization (lead); Data curation (supporting); Formal analysis (equal); Funding acquisition (lead); Methodology (equal); Project administration (lead); Resources (lead); Supervision (lead); Validation (equal); Writing – original draft (equal); Writing – review & editing (lead).

The data that support the findings of this study are openly available in the ETH Research Collection at http://hdl.handle.net/20.500.11850/689030.