The MCM-41 (see Fig. 1a and b) particles were synthesized following Beck et al. (1992), where: NH4OH (121 mL, 28 %, Sigma-Aldrich), deionized water (300 mL) and ethanol (500 mL, 99.8 %, Sigma-Aldrich) were stirred for 5 min in a 1 L polypropylene beaker. For the synthesis of materials with 2.8 or 3.3 nm pores, C16TMABr (hexadecyltrimethylammonium bromide, 1.74 g, 99 %, Acros) was subsequently added and stirred for 15 min before TEOS (tetraethoxysilane, 4.5 mL, 20.2 mmol, 98 %, Sigma-Aldrich) was quickly dropped into the reaction mixture. For 2.5 nm pores, a mixture of C16TMABr (0.871 g, 99 %) and C14TMABr (tetradecyltrimethylammonium bromide, 0.804 g, 99 %, Sigma-Aldrich) was used. After a few minutes, silica started to precipitate. The reaction was stirred at room temperature for 2 h before filtering (Sartorius^® 393). The filter cake was subsequently washed twice with 50 mL of deionized water, dried at T=80 ∘C for approximately 1 h and finally ground in methanol for 3 min. To obtain 3.3 nm pores, the dried particles were transferred into a Teflon-lined acid digestion vessel (Parr 4748), suspended in deionized water (80 mL), aged (80 ∘C, 24 h), subsequently filtered (Sartorius^® 393), dried and ground in methanol (99 %, Sigma-Aldrich). After drying again (80 ∘C, ≥1 h), the particles were calcined at 550 ∘C for 12 h.

To obtain larger pore diameters (∼9 nm), SBA-15 particles (see Fig. 1c and d) were synthesized similarly to Linton et al. (2009b) where Pluronic^® P104 (1.25 g, BASF) was dissolved under vigorous stirring in a hydrochloric acid solution (200 mL, 1.6 mol L-1) at 60 ∘C and TMOS (tetramethoxysilane, 8 mL, 99 %, Sigma-Aldrich) was added quickly under vigorous stirring. After 1 min (approximate hydrolysis time, Linton et al., 2009a) the stirring rate was lowered to moderate stirring. After another 1 min, the reaction mixture was diluted with a hydrochloric acid solution (200 mL, 1.6 mol L-1), leading to precipitation of the silica. The reaction mixture was further stirred at 60 ∘C for 24 h. The resulting suspension was centrifuged and washed with deionized water (200 mL) twice, and the product was transferred to the Teflon-lined acid digestion vessel. The wet particles were dispersed in deionized water (60 mL), and the pH was adjusted to 9 by the addition of NH4OH (1.05 mL, 28 %). The mixture was aged in quiescent conditions at 80 ∘C for 15 h. The suspension was centrifuged and washed with deionized water (200 mL) twice and once with ethanol (70 %). The white powder was dried (80 ∘C, ≥1 h) before it was ground in methanol (99 %) for 3 min. After drying again (80 ∘C, ≥1 h), the particles were calcined at 550 ∘C for 12 h.

In order to investigate the impact of water contact angle on the ability of porous particles to nucleate ice via PCF, particles of similar pore diameters were functionalized with trimethyl and hydroxyl groups after calcination. We will focus on ice nucleation experiments with particles functionalized with trimethyl and hydroxyl groups rather than just calcined ones, as their water contact angle was observed to change with aging in air (Muster et al., 2001). A batch of 2.8 nm pore samples was calcined at 550 ∘C and then separated into three parts, with one part unmodified, one part hydroxylated and the remaining part methylated. A summary of the particles investigated in this study is provided in Table 1. Hydroxylation and methylation were conducted as follows:

Silanol surface (hydroxylation): a calcined sample (1.0 g) was suspended in toluene (200 mL) and heated to 60 ∘C before a calculated amount of water was added (Eq. A1 of Appendix A1) in order to achieve a concentration of 4.6 silanol groups nm-2 (Zhuravlev, 2000). The particles were then suspended for 60 min through vigorous stirring and occasional sonication, before the suspension was filtered and washed with deionized water (80 mL) and dried (120 ∘C, 20 mbar) overnight.

Particle surface area (SBET) and pore diameters were determined by nitrogen adsorption (Quantachrome, NOVA 3000e). The nitrogen isotherms were obtained by measuring >10 m2 of dried (80 ∘C) sample, and the SBET was obtained from the relative pressure range where multilayer adsorption takes place (0.05–0.30) and applying the Brunauer, Emmett and Teller (BET) gas adsorption theory (Brunauer et al., 1938). The average pore diameter (dDFT) was obtained using the NLDFT (nonlocal density functional theory) method (Landers et al., 2013) applied to the N2 sorption measurements.

Diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) was used to characterize the functionalized particles and estimate the concentration of hydroxyl and methyl groups on the silica particles. The samples were prepared by combining 6 mg of dried sample (80 ∘C, >1 h) with 194 mg of dry potassium bromide (KBr) to produce a 3 % (w/w) mixture. The mixture was ground vigorously for over a minute (Hamadeh et al., 1984) before being filled in the sample holder, where the sample was flattened with a spatula. A scan resolution of 4 cm-1 was chosen, and background scans with pure KBr were performed; each sample was corrected accordingly. The mixtures were scanned immediately after grinding to avoid the adsorption of water vapor. The background-corrected scans were averaged and then normalized to the BET surface area of the sample instead of using the traditional method of normalizing based on the Si–O asymmetric stretching peak in the vicinity of 1100 cm-1 (Muster et al., 2001). Normalization to the BET surface is more appropriate considering the porous nature of the samples.

Water sorption isotherms were obtained using dynamic vapor sorption (DVS; TA Instruments, VTI-SA+), where the water uptake is determined gravimetrically. Each isotherm was obtained using approximately 10 mg of sample dried at 120 ∘C in a pure nitrogen atmosphere for 1 h before the reference mass was determined in order to evaporate any pre-adsorbed water. The DVS cell was then cooled to the temperature (T=25 ∘C) at which the sorption measurements were performed. The adsorption isotherms were obtained by continuously measuring the sample mass while increasing the humidity from 0 % to 90 % in steps of 5 % RHw. The water uptake reported here denotes quasi equilibrium values at each RHw step defined as a mass change rate less than 0.008 % over the course of 5 min. The water contact angle of the sample surface was then determined from the sorption isotherm using the Cohan–Kelvin equation (Kocherbitov and Alfredsson, 2007): 4rnldft-tads=-2γ(T)cos⁡θvl(T)RTln⁡(p/p0). Here tads is the statistical thickness of adsorbed water, rnldft is the pore radius as determined by NLDFT (dDFT/2), and p/p0 is the water saturation ratio or RHw/100. The statistical thickness in cylindrical pores is calculated by subtracting the volume of the adsorbate (Vads) from the full pore volume (Vtot) and can be rewritten as 5rnldft-tads=rnldftVtotVtot-Vads. By substituting Eq. (5) into Eq. (4), the Cohan–Kelvin equation for cylindrical pores can be written as 6rnldft=-VtotVtot-Vads⋅2γ(T)cos⁡θvl(T)RTln⁡(p/p0). And when solving for θ becomes 7θ=arccosrnldft(RTln⁡p/p0)-VtotVtot-Vads2γ(T)vl(T)π180. For water in confinement at 25 ∘C, the values of γ(T) and vl(T) are 71.69 mN m-1 and 20.5 m3 mol-1, respectively (Kocherbitov and Alfredsson, 2007). When deriving θ, p/p0 is identified as the saturation ratio where the pore condensation step of the DVS measurement is the steepest.

Nitrogen adsorption and NLDFT provide particle surface area (SBET) and average pore diameter (dDFT), respectively, and are summarized in Table 1 for each sample. The sample naming is such that the initial number represents the average pore diameter in nanometers followed by a C, M or H to represent whether the sample was calcined, methylated or hydroxylated, respectively. The numbers 1 or 2 after the letter indicate whether the samples are independent synthesis batches or several batches that have been combined and then separated and functionalized in different ways, respectively. An overview of the pore size distributions of the samples is shown in Fig. 2. As evident from Fig. 2a, the methylation of the 2.8 nm sample led to a decrease in mean pore diameter by 0.1 nm (2.7M2). The presence of trimethylsilyl groups is confirmed by our DRIFTS measurements (see Sect. 3.1.2), indicating that the methylation was successful. However, we cannot quantify the exact coverage and distribution of the trimethylsilyl groups. The addition of hydroxyl groups to the silica does not produce a difference in the pore size relative to the calcined sample (Fig. 2a). This suggests that the OH groups do not detectably reduce the pore width or that the pore surface of the calcined sample is already sufficiently hydroxylated, as discussed below.

The pore size distributions of the hydroxylated samples are shown in Fig. 2b. The 2.8 nm samples, 2.8H1 and 2.8H2, are quite similar; however 2.8H1 has a larger fraction of 2.6 nm pores. 2.5H1 has the narrowest pore size distribution and the lowest total pore volume of the hydroxylated samples as shown in Table 1. Meanwhile, 3.3H1 has the broadest pore size distribution with pores ranging from 2.7 to 4.5 nm. The methylated samples show a similar trend with a broadening of pore size distribution with increasing average pore diameter (see Fig. 2c). Consistent with functionalization, the methylated samples have lower pore volumes than the corresponding hydroxylated samples (see VPtot in Table 1). This provides additional evidence that the methylation procedure was effective. The SBA samples (9.1H2 and 9.0M2) show a similar trend with a slight decrease in pore diameter upon methylation (Fig. 2d). As shown in Table 1, there is no relationship between the total BET surface area and pore diameter except when comparing the MCM-41 to the SBA-15 samples which have approximately half of the specific surface area due to their differing morphology and pore structure.

When comparing the impact of functionalization on the same initial bulk sample (2.8C2), the difference between hydroxylation (2.8H2) and methylation (2.7M2) is visible in the DRIFTS spectra (Fig. 3a). The intensity in the O–H stretching region, 3200–3800 cm-1 is much larger for the hydroxylated sample (2.8H2) than the calcined (2.8C2) and methylated (2.7M2) samples, consistent with the addition of hydroxyl groups during the hydroxylation process. The broad absorption band peaking at about 3450 cm-1 (3000–3700 cm-1) in the calcined, hydroxylated and methylated samples is indicative of water adsorbed on the silica surface and residual silanol groups (Chen et al., 1996). Previous studies have shown that calcining silica particles at temperatures above 200 ∘C, as is the case for our calcined samples, removes all free water (Muster et al., 2001; Zhuravlev, 2000). However, here the DRIFTS cell was operated at ambient conditions, allowing for water to (re-)adsorb to the particle surface and contributing to the broad absorption in the range 3000–3700 cm-1 (Muster et al., 2001). Indeed, when exposing a silica sample calcined at 200 ∘C to ambient conditions, the increase in mass due to adsorbed water is visible using thermogravimetric analysis (not shown). The methylated sample (2.7M2) has the weakest absorbance in the OH stretching region (3000–3700 cm-1; see Fig. 3a). Furthermore, the methylated sample shows a peak associated with the C–H stretching band around 2960 cm-1, indicating the presence of trimethylsilyl groups bonded to the silica surface. However, the presence of isolated and geminal silanol groups, as shown by the peak at 3750 cm-1, indicates that the methylation is incomplete (Bergna, 1994; Muster et al., 2001). The increase in the C–H stretching band due to the methylation (at 2960 cm-1), roughly corresponds to the decrease in the isolated silanol/geminal silanol peak for the 2.8 nm samples (Fig. 3a). The calcined sample (2.8C2) has the highest concentration of isolated and geminal silanol groups. This is expected as during hydroxylation (2.8C2 transitioning to 2.8H2) the concentration of silanol groups increases and becomes sufficiently dense for chains of hydrogen bonds to form between individual silanol groups, decreasing the number of isolated silanol groups and thereby shifting the peak at 3750 to ∼3660 cm-1 (Muster et al., 2001).

When comparing the DRIFTS results of the different hydroxylated and methylated samples (Fig. 3b and c), it is clear that the SBA-15 particles (9.1H2 and 9.0M2) also show absorbance in the OH (3200–3800 cm-1) and CH (∼2960 cm-1) stretching region of the spectra, respectively, demonstrating that the functionalization was successful. Differing peak intensities between particle types could be due to the differing densities of silanol and siloxanes on the surface of the particles. Although the clear peak in the C–H stretch region of the DRIFTS (Fig. 3c) shows that the methylation process on the SBA-15 particles (9.1H2 functionalization to 9.0M2) was successful, methylation is far from complete since the peak arising from isolated/geminal silanol stretching vibrations (3750 cm-1) is still visible in all methylated samples (Fig. 3c). The concentration of hydroxyl groups on the hydroxylated samples is independent of pore size (Fig. 3). Rather, the intensity in the O–H stretching region likely depends on the age and exposure of the calcined samples to ambient water vapor. The methylated samples show much less spread in the amount of adsorbed water, suggesting that they are more resistant to hydroxylation and more stable over time (Fig. 3c).

Two water vapor sorption cycles were obtained for the samples 2.4M1, 2.5H1, 3.3M1, 3.3H1, 9.1H2 and 9.0M2, and the resultant isotherms are shown in Fig. 4. The sorption isotherms have been classified following the recommendation by the International Union of Pure and Applied Chemistry (IUPAC; Sing, 2009; Thommes et al., 2015). The hydroxylated samples (2.5H1, 3.3H1 and 9.1H2) show Type IV isotherms, characterized by an initial monolayer-multilayer adsorption occurring on the pore wall followed by a steep, almost step-like increase in water mass known as the condensation step at the p/p0 or RH associated with pore filling. This is consistent with previous observations for mesoporous silica (Kittaka et al., 2011). The methylated samples, 2.4M1, 3.3M1 and 9.0M2 show similar isotherms but lack an initial monolayer adsorption along the uptake curves. This is consistent with a Type V isotherm and provides direct evidence that the methylation was successful in making the particles more hydrophobic. It should be highlighted that in the second sorption cycle, the methylated samples have Type IV isotherms that are more similar to the isotherms of the hydroxylated samples, independent of the pore size. This transition suggests that the exposure to high concentrations of water vapor during the first sorption cycle increases the number of silanol groups on the surface of the methylated samples. Indeed, the second sorption cycle of the methylated samples shows that the condensation step shifts close to the RH of the hydroxylated sample during the first sorption cycle. This indicates that the water contact angle of the methylated sample becomes closer to that of the hydroxylated sample.

Similarly, the shift in the condensation step to lower humidities for the hydroxylated samples suggests a decrease in water contact angle. The relative mass of the hydroxylated samples does not return to zero after the desorption cycle (Fig. 4a and b), indicating that water remains adsorbed on the particles. This strongly adsorbed water is expected to lower the water contact angle between water and the wall surface to nearly zero. Moreover, multilayers of adsorbed water narrow the effective diameter for pore filling (Broekhoff and de Boer, 1967; Kruk et al., 1997; Miyahara et al., 2000). Both effects explain the observed shift of the condensation step to lower humidities. Furthermore, it is visible from Fig. 4 that the hydroxylated samples adsorb relatively more water than the methylated samples even though they have very similar pore diameters (see dDFT in Table 1). However, the samples have differing total pore volumes (VPtot), and thus, it is expected that the absolute amount of condensed water differs.

The water contact angle of the samples is obtained by inserting the RH of the condensation step in the first water sorption cycle into Eq. (7) (see Table 1). The water contact angles for the MCM-41 particles ranged between 41–45∘ and 75–80∘, for the hydroxylated and methylated samples, respectively, based on the observed value and uncertainty in the measured dDFT. Conversely, the SBA-15-type samples have significantly lower water contact angles of 15 and 60∘ for the hydroxylated (9.1H2) and methylated (9.0M2) samples, respectively. However, these values may be due to the large spread in the pore diameters within the sample. As can be seen from Fig. 2, the pore size distribution is significantly wider for the SBA-15 samples than for the MCM-41 particles (ranges from ∼7 to 16 nm with a clear maximum in the size distribution at 9 nm). Therefore, it is difficult to properly assign the correct pore diameter responsible for the initial pore condensation observed from the sorption measurements based on the uncertainty in dDFT alone (±1.1 nm). If 7 nm is used as the pore diameter instead of 9.1 or 9.0 nm and the RH of the initial uptake in pore water from the sorption measurements is used, the water contact angles for 9.1H2 and 9.0M2 become 37 and 71∘, respectively.

Upon cooling of a sample prepared as a slurry in the DSC, the exterior water freezes first followed by the freezing of pore water due to the decrease in temperature required for water in confinement to freeze (Deschamps et al., 2010; Janssen et al., 2004; Jelassi et al., 2010; Kittaka et al., 2011; Marcolli, 2014; Moore et al., 2012; Morishige and Uematsu, 2005). This can most clearly be seen in the freezing of 3.3M1 shown in Fig. 5a where the initial release of latent heat (peak) centered around 255 K is due to the freezing of the exterior bulk water followed by the second peak starting at 234 K due to the freezing of the pore water. Tap water was used for the experiments with the SBA-15 samples to shift the freezing of exterior water to higher temperatures so that the freezing of pore water is observable (Fig. 4c). Also shown in Fig. 5 are the expected critical pore diameters Dp calculated following Eqs. (2) and (3), yielding a direct comparison of the theoretical predictions of pore freezing to the experimentally determined onset of ice formation (peaks in thermograms). Since previous MDS and X-ray diffraction studies have shown ice in confinement to be typically stacking disordered or cubic (Moore et al., 2010, 2012; Morishige et al., 2009) two parameterizations from literature (Murray et al., 2010; Zobrist et al., 2007) were used to calculate Dp, assuming either cubic (Fig. 5a and b) or hexagonal ice (Fig. 5c). As can be seen in Fig. 5, the parameterization assuming cubic ice is more accurate at predicting the observed freezing temperature for narrow mesopores (2.8 and 3.3 nm samples) where the freezing temperatures are around 230 K. In contrast, the freezing temperature of the 9.1 nm pore samples (9.1H2 and 9.0M2; Fig. 4c) of approximately 261 K is better predicted assuming that the ice is hexagonal. These results are consistent with studies that have shown that cubic ice occurs more readily at colder temperatures (Kuhs et al., 2012; Malkin et al., 2015).

The DSC thermograms of the SBA-15 samples (9.1H2 and 9.0M2) show a bimodal peak associated with the freezing of pore water (see Fig. 5c), with a pronounced peak around 258 K and a shoulder towards higher T. This indicates that there is a bimodal distribution of pore sizes that contribute differing fractions of pore volume to the samples. Indeed, the pore size distributions show that the SBA-15 samples have a clear shoulder in the distribution at 11 nm followed by a main peak at 9.1 nm (see Fig. 2d). Thus the bimodal freezing signal is likely due to the freezing of pore water in pores larger than 11.0 nm followed by the release of heat from the freezing in the smaller, more abundant 9.1 nm, remaining pores.

Deschamps et al. (2010) showed that highly hydrophobic pore surfaces had lower melting and freezing temperatures than hydrophilic pores of the same diameter. They associated the depressed freezing temperatures with a decrease in mobility of water molecules in hydrophobic mesopores. However, as the pore size exceeded 3 nm, the dependence on pore hydrophobicity of the freezing point depression disappeared (Deschamps et al., 2010; Jähnert et al., 2008; Schreiber et al., 2001). In agreement with a loss of the dependence on hydrophobicity for pores larger than 3 nm, Moore et al. (2012) showed that the melting temperature in a 4 nm diameter silica pore was the same regardless of hydrophobicity using MDS. The DSC thermographs in Fig. 5 show that there is no detectable difference in the onset freezing temperatures for the SBA-15 samples depending on functionalization (9.1H2 and 9.0M2; Fig. 5c). However, in contrast to the results of Deschamps et al. (2010), the 2.8 nm (Fig. 5b) samples also show no detectable difference in freezing onset. This indifference may stem from the fact that the observed freezing onsets occur due to the ice growth in the largest detectable pores of a sample. As can be seen from Fig. 2, both 2.8H2 and 2.7M2 contain a fraction of pores larger than 3 nm. Therefore, the observed freezing onsets in the thermograms may be due to pore diameters that are wide enough for growing ice to not be impacted by the water contact angle of the pore wall (Moore et al., 2012).

Pore diameter has no impact on the humidity required for the hydroxylated samples to reach an AF0.05 below the HFT (Fig. 7, dashed back line), the only exception being at 233 K, where ice formation starts well below water saturation for the 9.1H2 sample, while the smaller pore size samples reach an AF0.05 only close to water saturation. This is indeed expected for pores up to 3.3 nm, when considering that the water contact angle of the pore surface is rather low for the hydroxylated samples (41–45∘; see Sect. 3.1.3), such that the pores are expected to fill already below ice saturation. Assuming that 9.1H2 has a similar water contact angle as the other hydroxylated samples, the 9.1 nm pores would require a RHi of ∼123 % and 118 % at 223 and 228 K, respectively, for pore filling to occur. However, based on the water sorption measurements (see Fig. 4c) the estimated water contact angle of 9.1H2 is approximately 15∘. Furthermore, when examining the pore size distribution shown in Fig. 2d, more than 5 % of the pores are smaller than 9.1 nm (between 7 and 9 nm), and thus, a lower humidity for pore filling is required for these pores. Based on the lower water contact angle alone, the 9.1 nm pores are expected to fill at ∼114 % and 109 % RHi at 223 and 228 K, respectively. Therefore, no significant dependence of the AF0.05 is expected for the investigated samples at 223 and 228 K due to the ice growth limitations in ZINC, as discussed above.

At 233 K the AF0.05 RHi shifts to water saturation for all samples except for 9.1H2 (Fig. 7). The DSC experiments with 3.3M1 show that ice freezes within the pores only below 233 K (Fig. 5a). Therefore the inability of 5 % of the particles to freeze up to water saturation for these samples is consistent with PCF.

In contrast, the pore diameters in the 9.1H2 sample are wide enough to host ice at 233 K (see DSC experiments, Fig. 5c). Yet, nucleation rates at this temperature are too low for pore water to freeze within the residence time of ZINC. However, the strong increase in the AF at about 108 % RHi together with the decrease starting from 125 % RHi (see Fig. A1c) can be explained by the dependence of nucleation rates on pressure (Marcolli, 2020). At 233 K, the pressure-dependent version of the Murray et al. (2010) parameterization of CNT (Marcolli, 2020) predicts a nucleation rate of 9×1010 cm-3 s-1 at water saturation (P=0.1 MPa), which increases to 2×1016 cm-3 s-1 at the RHi of pore filling (∼108 % RHi, P=-32 MPa). Thus, the water in a pore of 9.1 nm diameter should freeze at 108 % RHi within about 1.6 s. At water saturation, it takes one pore 4×105 s to freeze, implying that most pores should freeze at 108 % RHi within the residence time of ZINC and that the AF decreases when water saturation is approached as can be seen in Fig. A1c.

At 238 K only the 2.8H1 sample reached an AF0.05 (Fig. 7). However, all of the other hydroxylated samples with the exception of 9.1H2, have a similar increase in the AF near water saturation, reaching values just below the AF0.05 threshold (Fig. A1d). This indicates that there are active sites located on the external particle surface that nucleate ice through immersion or condensation freezing rather than PCF. Considering that pores are closely spaced, the outer surface is cladded in pore openings, providing a nanoscale pattern that might influence the ice nucleation activity in immersion and condensation mode.

The SBA-15 sample 9.1H2 also showed an increase in the AF near water saturation, albeit the increase was about an order of magnitude lower than for the MCM-41 samples (Fig. A1d). Thus, the 9.1H2 surface seems to be less efficient at nucleating ice than the one of the MCM-41 samples, indicating that the synthesis procedure for SBA-15 particles (see Sect. 2.1.1 and 2.1.2) generates less active sites than the one for MCM-41 samples. This is especially true when considering that the pores in the MCM-41 samples are too narrow to host the critical ice embryo, and therefore, the surface area is significantly smaller than for the 9.1H2 sample. In experiments performed at 243 K the ability of the hydroxylated samples to nucleate ice approached the detection limit of ZINC and are therefore not shown.

Unlike the hydroxylated samples, the methylated samples show a dependence of onset humidity on pore diameter. At 223 and 228 K, the samples with 2.4 nm pore diameters had the lowest AF0.05 RHi and the 3.3 nm particles the highest. The 2.6, 2.7 and 9.0 nm samples are in between and overlap (Fig. 8). This indicates that due to the higher water contact angles after methylation (60–71∘ compared with 15–37∘ for the hydroxylated samples), PCF is limited by pore filling. Thus, the increase in RHi required for filling of increasing pore diameters is observable within ZINC for methylated samples. The similar AF0.05 RHi of 9.0M2 at 223 and 228 K compared with the methylated MCM-41 samples can be explained by its lower water contact angle (60∘ vs. 78∘; see Table 1), suggesting a more hydrophilic surface of 9.0M2 compared with MCM-41. The 9.0M2 is less active than the 9.1H2 sample (see Figs. 6 and 7), indicating that the methylation and associated increase in water contact angle decreased the ice nucleation ability.

Unlike the hydroxylated samples at 233 K, which showed a clear increase in the AF at ∼105 % RHi (Fig. A1c), the methylated samples (except 9.0M2) show only a weak and continuous increase in the AF up to approximately 0.01 before water saturation is reached and homogeneous freezing of bulk water sets in (see Fig. A2c). This difference is likely due to the higher humidity required for pore filling of the methylated samples. The pore water experiences just a moderately negative pressure of at most -26 MPa at pore filling conditions, which enhances nucleation rates to a level that is able to induce freezing in only very few pores that also need to be wide enough to host ice. The reduction in the AF below water saturation of the methylated compared with the hydroxylated samples is consistent with previous observations that alkylation of silanol groups suppressed ice nucleation below water saturation at 233 K (Kanji et al., 2008).

The AF0.05 of 9.0M2 is close to the predicted pore filling line for θ=78∘ at 233 K (Fig. 8), while at 223 and 228 K, it is much below the predicted line even for θ=60∘. This freezing activity is attributed to either nonuniform methylation, which led to variations in water contact angle, or the presence of pore-like imperfections on the rough surface of the 9.0M2 particles that are narrower than the measured pore diameters and remained undetected in the pore-size distribution (Fig. 2) due to their extremely small volumes. At 233 K, the onset humidity of the 2.7M2 shifts close to water saturation in accordance with the DSC results in Fig. 5 showing that ice only freezes close to or below 233 K for pores narrower than 3.3 nm (see Fig. A2). A clear onset RHi where the bulk of the 9.0M2 particles nucleate ice is absent (Fig. A2c) as is observed with 9.1H2 in Fig. A1c, indicating that pores of 9.0M2 continuously fill and freeze while RH increases. Indeed, the measured pore diameters by N2 sorption (see Fig. 2d) show a wide pore size distribution for 9.0M2 and 9.1H2. Water uptake reaching 1 wt % only above 90 % RHw for 9.0M2 (Fig. 4) is in accordance with AF exceeding 0.05 only for RHi>130 %, further supporting that ice nucleation on 9.0M2 is limited by pore filling. Since homogeneous nucleation rates close to water saturation at 233 K are rather too low to induce freezing of water in 9.0M2 pores, ice nucleation sites for immersion freezing within the pores might be responsible for the observed AF. The assumption of nucleation sites on the 9.0M2 is further supported by its ice nucleation activity persisting above the HFT (Fig. A2d).

The methylated MCM-41 samples have a very weak increase in the AF around water saturation at 238 K (Fig. A2d), reaching a similar AF as at 233 K below water saturation. The increase in the AF for MCM-41 samples at 238 K is lower than the one observed for the hydroxylated MCM-41 samples at the same temperatures and relative humidities, consistent with the notion that methylation decreases the ice nucleation activity of a surface (Kanji et al., 2008).

At 238 K, the 9.0M2 sample shows a distinct and continuous increase in the AF below water saturation. Since the temperature is too high for homogeneous ice nucleation within pores, this is a clear indication of active sites present in pores resulting in immersion freezing as soon as the pores fill with water. Interestingly, the AF is higher in 9.0M2 compared with 9.1H2 (Figs. A2d and A1d, respectively), showing that the density of hydroxyl groups is not always a good predictor for ice nucleation ability. Indeed, it has been shown that methylated amorphous silica has an enhanced nucleation ability relative to hydroxylated silica due to the condensation of water on a hydrophilic Si–OH group surrounded by methylated groups (Bassett et al., 1970; Salazar and Sepúlveda, 1983). Salazar and Sepúlveda (1983) postulated that adsorption on islands of silanol groups followed by multilayer growth similar to condensation of water would nucleate ice when water molecules come in contact with the neighboring methyl groups. However, it is important to note that hydroxylation and methylation had an opposite effect on the heterogeneous ice nucleation ability at 238 K of MCM-41 and SBA-15 particles, making generalization in terms of dependence on water contact angle and degree of hydroxylation difficult. The MCM-41 samples are spherical (Fig. 1a and b), and the pore entrances are evenly distributed over the entire particle surface. Meanwhile, the SBA-15 samples are hexagonal and consist of a 2-D network of pores oriented along the long axis of their geometry (Fig. 1c and d) and, thus, potentially have six pore-free faces where the interaction between silanol islands and surrounding trimethylsilyl groups is possible. Thus, the potential presence of nonporous faces on the SBA-15 samples could explain the difference in the role of methylation and hydroxylation on the heterogeneous freezing abilities of the sample types at 238 K.