We investigated the structure of ice under nanoporous confinement in periodic mesoporous organosilicas (PMOs) with different organic functionalities and pore diameters between 3.4 and 4.9 nm. X-ray scattering measurements of the system were performed at temperatures between 290 and 150 K. We report the emergence of ice I with both hexagonal and cubic characteristics in different porous materials, as well as an alteration of the lattice parameters when compared to bulk ice. This effect is dependent on the pore diameter and the surface chemistry of the respective PMO. Investigations regarding the orientation of hexagonal ice crystals relative to the pore wall using x-ray cross correlation analysis reveal one or more discrete preferred orientation in most of the samples. For a pore diameter of around 3.8 nm, stronger correlation peaks are present in more hydrophilically functionalized pores and seem to be connected to stronger shifts in the lattice parameters.

Liquid water is known to exhibit different equilibrium and dynamical properties in porous confinement compared to bulk.1–4 One particular example is the lowering of the melting point, when confined in pores with diameters smaller than 100 nm.5–8 

In addition, in its solid state, the properties of water are influenced by spatial restrictions. For instance, under confinement on a scale of nanometers, stacking-disordered ice Isd is present in a stable form.9–13 This phase, which represents the presence of both hexagonal and cubic domains, for example, is observable in micrometer-sized droplets or as a metastable phase from supercooled water.14–20 Furthermore, several studies have shown a strong presence of amorphous phases, especially pre-melted liquid water at the interface between ice and the pore wall.8,21–23

While the influence of the pore size has been extensively studied, not much is known about the effect of a modified pore wall surface chemistry on the formation of ice. In the study at hand, we want to analyze this effect, using periodic mesoporous organosilicas (PMOs). These are a class of organosilica hybrid materials with cylindrical pores, possessing organic moieties, which are an intrinsic part of the pore wall. Due to the periodic arrangement and long-range ordering of the organic moieties in the pore walls, additional (00l) reflections parallel to the pore axis appear.24,25 These organic moieties can furthermore be varied, which changes the surface chemistry and, therefore, the interactions between the pore walls and the confined material.26–28 Using the advantages of both hexagonally arranged cylindrical pores with narrow size distributions and different surface chemistries, PMOs can, therefore, be tuned to various intended applications, such as catalysis,29,30 drug delivery,31,32 or light harvesting.24,33,34 Tuning the pore–water interaction and polarity of the pore wall has an influence on the structure and dynamics of water and ice confined in PMOs,25,35,36 which is further investigated in this study.

Here, we take a closer look at the ice formed in different PMOs. We want to investigate how different pore–water interactions and a varying pore diameter influence the formation of ice inside the pores. A focus is set on the lattice parameters of the hexagonal component, when confined in PMOs with various pore diameters and surface chemistries, as well as the orientation of ice crystal in relation to the pore axis using x-ray scattering. The orientations are determined by the use of x-ray scattering with a nanofocused beam in combination with x-ray cross correlation analysis.37,38

The porous materials used in this study, as well as their porosity data and the experiment in which they were measured, are presented in Table I. The chemical structures of the PMO precursors are given in the supplementary material.

TABLE I.

List of porous materials used in the experiment. The precursors used for the PMO synthesis, the pore diameter dP (where the uncertainty is given by the half width at half maximum of the pore size distribution), the pore volume at 90 % relative pressure VP,0.9, the organic unit periodicity dorg, and the experiment in which the sample was used (1 = P02.1, 2 = P03) are shown. * Two different batches of BTEVA(3.8) were used in the two experiments, but their properties did not show any notable differences.

Precursordp (nm)VP,0.9 (cm3g−1)dorg (nm)Exp.
 MCM-41(3.9) MCM-41 3.9 ± 0.3 0.85 ⋯ 
 BTEB(3.8) BTEB 3.8 ± 1.1 1.26 0.76 
 BTEVB(3.8) BTEVB 3.8 ± 0.7 0.54 1.19 1, 2 
 BTEVFB(4.9) BTEVFB 4.9 ± 1.4 0.83 1.20 
 BTEVFB(4.4) BTEVFB 4.4 ± 0.7 1.04 1.20 
 BTEVFB(3.8) BTEVFB 3.8 ± 0.4 0.61 1.18 
 BTEVA(4.4) BTEVA 4.3 ± 0.3 0.83 1.18 
 BTEVA(3.8) BTEVA 3.8 ± 0.4 0.67 1.18 1, 2* 
 BTEVA(3.4) BTEVA 3.4 ± 0.4 0.64 1.18 
 BTEVP(3.8) BTEVP 3.8 ± 0.7 0.87 1.19 
 BTEVP(3.5) BTEVP 3.5 ± 0.8 0.63 1.19 
 BTEVP+(3.5) BTEVP+ 3.5 ± 0.5 0.47 1.18 
 BTEVP+(3.4) BTEVP+ 3.4 ± 0.6 0.60 1.18 
 BTEVCl(3.8) BTEVCl 3.8 ± 0.8 0.93 1.19 
Precursordp (nm)VP,0.9 (cm3g−1)dorg (nm)Exp.
 MCM-41(3.9) MCM-41 3.9 ± 0.3 0.85 ⋯ 
 BTEB(3.8) BTEB 3.8 ± 1.1 1.26 0.76 
 BTEVB(3.8) BTEVB 3.8 ± 0.7 0.54 1.19 1, 2 
 BTEVFB(4.9) BTEVFB 4.9 ± 1.4 0.83 1.20 
 BTEVFB(4.4) BTEVFB 4.4 ± 0.7 1.04 1.20 
 BTEVFB(3.8) BTEVFB 3.8 ± 0.4 0.61 1.18 
 BTEVA(4.4) BTEVA 4.3 ± 0.3 0.83 1.18 
 BTEVA(3.8) BTEVA 3.8 ± 0.4 0.67 1.18 1, 2* 
 BTEVA(3.4) BTEVA 3.4 ± 0.4 0.64 1.18 
 BTEVP(3.8) BTEVP 3.8 ± 0.7 0.87 1.19 
 BTEVP(3.5) BTEVP 3.5 ± 0.8 0.63 1.19 
 BTEVP+(3.5) BTEVP+ 3.5 ± 0.5 0.47 1.18 
 BTEVP+(3.4) BTEVP+ 3.4 ± 0.6 0.60 1.18 
 BTEVCl(3.8) BTEVCl 3.8 ± 0.8 0.93 1.19 

The synthesis of the porous materials was performed following the description given in a previous publication.28 The charge in BTEVP+ samples was introduced using a postsynthetic pathway. In this approach, the colorless BTEVP-PMO was exposed to a saturated iodomethane atmosphere at room temperature for two days in a sealed system. The yellowish powder was freed from iodomethane residues by keeping it open at room temperature for two days and then in vacuum (0.1 mbar) for 5 min. The synthesis parameters of the various samples are given in the supplementary material. Water was adsorbed into the pores by exposing the sample to water vapor inside a humidity chamber. The humidity was set to 90% relative humidity (RH) to ensure that no excess water is present outside the pores.

PMOs have a distinct x-ray scattering signal. Figures 1(b) and 1(c) show the small and wide angle signals of BTEVA(3.8). The peaks that are found in the small angle regime can mainly be attributed to the reflections from the distribution of the pores, i.e., (hk0), while those in the wide angle regime stem from the periodicity of the organic moieties, i.e., (00l). Note that the angle at the highest q (≈0.53 A−1) shown in Fig. 1(b) is the same as the peak at the lowest q shown in Fig. 1(c).

FIG. 1.

(a) Sketch of a PMO material. The light blue ellipsoids represent the organic moieties. The arrows indicate the directions of the scattering planes of the (hk0) and (00l) reflections. In the following, small (b) and wide (c) angle scattering signals of BTEVA(3.8) are shown as an example.

FIG. 1.

(a) Sketch of a PMO material. The light blue ellipsoids represent the organic moieties. The arrows indicate the directions of the scattering planes of the (hk0) and (00l) reflections. In the following, small (b) and wide (c) angle scattering signals of BTEVA(3.8) are shown as an example.

Close modal

The data presented here were obtained at two separate x-ray scattering experiments. The first was performed at the P02.1 beamline39 at PETRA III (DESY, Hamburg, Germany) with a beam diameter of ∼1 mm and at an energy of 60 keV. The powder samples were filled into glass capillaries with a diameter of 1.5 mm and a wall thickness of 10 μm (Hilgenberg GmbH). Scattering patterns were taken at temperatures between 290 and 150 K with an exposure time of 1 s. A Perkin Elmer XRD 1621 CN3 detector was used for capturing the patterns, which were azimuthally integrated to create the intensity curves presented later.

The second experiment, which was aimed at XCCA, was performed at the nanofocus endstation of the P03 beamline, also at PETRA III.40,41 Here, the beamsize was ∼250 × 350 nm2 with a beam energy of 17.5 keV. The images were acquired by using an Eiger X 9M detector.

In both experiments, the temperature was controlled by a nitrogen cryostream surrounding the sample capillary. We estimated the error of the temperature conservatively to be about 5 K, which is implied in all the temperature data we measured. LaB6 was used for geometry calibration in both experiments.

In order to obtain the lattice parameters of the hexagonal ice, we located the peaks of the intensity I(q) vs the momentum transfer q corresponding to the hexagonal ice by fitting them as Gaussians. We identified their Miller indices (hkl) by comparing them to bulk literature values.42 A linear regression fit corresponding to Bragg’s law was performed with the q values and the Miller indices of the hexagonal peaks,
(1)
With this, it is then possible to compute the hexagonal lattice parameters a and c. Using the width of the peaks, the crystallite size L can be calculated using the Scherrer equation,43,44
(2)
where K is the Scherrer constant, λ is the x-ray wavelength, Δ(2θ) the full width at half maximum of the peak after taking into account the instrument broadening, and θ is the Bragg angle of the diffraction peak. In the case of a cylindrical crystal, K depends on several factors, such as the aspect ratio of the cylinder and the Miller indices of the scattering plane.45,46
In order to analyze the orientation of ice crystals with respect to the pore axis, we employed x-ray cross correlation analysis (XCCA).37,38,47–50 In this, the intensity I(q1, ϕ) at q1 and azimuthal angle ϕ is correlated with I(q2, ϕ + Δ) as
(3)

If we now choose the q value related to the peaks from the PMO structure for q1 [e.g., the (00l) peaks shown in Fig. 1] and those related to the ice structure as q2 (cf. Fig. 2), the resulting correlation function C(Δ) gives us a statistical insight into common angles Δ between the scattering planes of the PMO and the ice crystallites (see discussion below).48,49

FIG. 2.

Detector image of water-filled BTEVP(3.8) at 150 K with a visualization of the XCCA process. Here, q1 is the value for the signal from the PMO at an angle ϕ1 while q2 is that of the (002) peak of the hexagonal ice at an angle ϕ2 = ϕ1 + Δ.

FIG. 2.

Detector image of water-filled BTEVP(3.8) at 150 K with a visualization of the XCCA process. Here, q1 is the value for the signal from the PMO at an angle ϕ1 while q2 is that of the (002) peak of the hexagonal ice at an angle ϕ2 = ϕ1 + Δ.

Close modal

Figure 3 shows the azimuthally integrated x-ray scattering intensity of water confined in various PMOs at temperatures between 290 and 150 K. It was obtained by subtracting the signal of an empty PMO from that of its water-filled counterpart. In some samples, namely, BTEVFB(4.9), BTEVA(4.4), BTEVA(3.8), and BTEVP(3.5), this did not fully remove the signal from the empty PMO. Here, the remaining peaks at 1.7 A−1, which stem from the periodicity of the functional groups in the pore wall, are visible. On the one hand, the reason for this were the fluctuations of the x-ray intensity during the measurement, which could not fully be compensated by normalization. On the other hand, the electron density difference is lower for water-filled pores, hence the PMO peaks are more prominent in empty (or air-filled) pores. In these cases, the (100) peak of hexagonal ice overlaps with the (003) PMO peak and was, therefore, not taken into account when determining the lattice constants discussed later.

FIG. 3.

X-ray diffraction signal of water in several different PMOs at temperatures between 290 (bottom, red) and 150 K (top, blue) in steps of 10 K.

FIG. 3.

X-ray diffraction signal of water in several different PMOs at temperatures between 290 (bottom, red) and 150 K (top, blue) in steps of 10 K.

Close modal

In most samples, characteristics of both ice Ih-like, sharp Bragg peaks and more ice Ic-like, diffuse peaks are visible. Specifically, in the regions between 1.5 and 2.0 A−1 and between 2.5 and 3.5 A−1, an overlay between a broad diffuse peak and the triplet characteristic for ice Ih is observed. This structural behavior of ice crystallization has been observed in previous simulation51,52 and experimental11,13,44 studies on water in nanopores. Figure 4 shows a separation of the diffuse and Bragg contributions, which are marked in blue and orange, respectively, for the example of BTEVA(4.4). The diffuse part also contains a contribution from liquid, non-freezing interfacial water, which is known to appear in nanopores.8,51,52 This contribution is not shown in Fig. 4 as it is difficult to meaningfully separate it from the broad cubic-like contribution. The confined water in the same pore at room temperature is also plotted to visualize the general shape of this amorphous contribution. However, as shown in a previous study by us,28 the first sharp diffraction peak of water grows and shifts to lower q values under confinement and even more during cooling, ending up closer to the first diffuse peak.

FIG. 4.

Diffuse and Bragg contributions to the integrated scattering pattern at T = 165 K are shown in blue and orange, respectively. I(q) of the confined water at 290 K is plotted for comparison (black) as well as the peak locations for bulk cubic and hexagonal ice (dark gray). The bulk hexagonal peaks are also located at the same positions as the bulk cubic peaks. Twofold labeling indicates a coincidence of peaks from different contributors. The indexing of the marked peaks can be seen in the table underneath the figure.

FIG. 4.

Diffuse and Bragg contributions to the integrated scattering pattern at T = 165 K are shown in blue and orange, respectively. I(q) of the confined water at 290 K is plotted for comparison (black) as well as the peak locations for bulk cubic and hexagonal ice (dark gray). The bulk hexagonal peaks are also located at the same positions as the bulk cubic peaks. Twofold labeling indicates a coincidence of peaks from different contributors. The indexing of the marked peaks can be seen in the table underneath the figure.

Close modal

The presence of both the diffuse and Bragg contributions suggest stacking-disordered ice I in the pore. The diffuse part implies small individual crystallites with a large number of stacking faults, while the Bragg contribution can probably be described as ice Ih with a large ratio of Φh to Φc according to Malkin et al.20 Going forward, the Bragg contribution, therefore, will be referred to as the hexagonal contribution even though it does probably not represent pure ice Ih.

In order to estimate the sizes of individual crystallites, the Scherrer equation [Eq. (2)] can be applied, leading to values of 35–50 nm with no systematic difference between the samples. The values are rather vague, as the Scherrer constant K strongly depends on various factors, as mentioned in Sec. II. In this case, cylindrical crystallites are assumed, which generally leads to Scherrer constants K > 0.9. The number, therefore, only serves as an estimate of the order of magnitude of the crystallite size, not as an exact result. A more detailed discussion is given in the supplementary material. The crystallites of the diffuse constribution were calculated to be in the range of 1–2 nm. This is in agreement with the findings of Moore et al.,51 stating that cubic ice domains in silica pores are in the range of only a couple of molecular layers. However, due to the discussed amorphous contribution, a precise determination is not possible.

Some of the studied samples stand out in this regard. BTEVFB(4.9) shows the previously discussed general structure but has much higher relative intensities of the (hexagonal) ice peaks. We connect this to its pore diameter, which is the largest of the measured samples at 4.9 nm. Therefore, the amount of ice present in the pore is larger than for the other materials, leading to a stronger scattering signal. In BTEVB(3.8) and BTEVP(3.5), one can see that the patterns differ at the five lowest temperatures. These lowest-temperature measurements were performed with a higher initial cooling rate than the standard procedure and with no equilibration steps being taken while cooling down to 180 K. In BTEVB(3.8), the (003) PMO peak at 1.7 A−1 is more visible in these temperatures while the overall structure is qualitatively the same as for the higher temperatures. In BTEVP(3.5), however, we observe no hexagonal ice peaks at those temperatures reached via the faster procedure. This suggests that the emerging ice structure is dependent on the cooling procedure. Specifically, a higher cooling rate without equilibration steps seems to hinder the formation of hexagonal ice. We also want to note that BTEVB(3.8) represents the only sample in which no hexagonal ice peaks were observed in both the standard measurement and the measurement with faster cooling.

We will now take a closer look at the hexagonal contribution to the signal with a focus on the influence of the PMO confinement on its structure. Figure 5 shows the lattice constants for the hexagonal ice contributions inside the different PMOs, as well as those of bulk ice. The bulk ice values are based on the polynomial expression described by Röttger et al.53,54 to describe the lattice constants of hexagonal ice over a wide temperature range sorted by pore size. While the measured samples follow the general trend as expected in bulk ice, some notable deviations are observed.

FIG. 5.

Plots showing the lattice parameters a and c of hexagonal ice in various porous materials, as well as their ratio c/a. The three columns show the materials with decreasing pore diameters from left to right. Hydrophilic PMO samples are plotted in a shade of red, while more hydrophobic ones are a shade of green. MCM-41 is plotted in black. The lattice parameters of bulk ice are also plotted for comparison. The bulk values were calculated according to the work by Röttger et al..53,54

FIG. 5.

Plots showing the lattice parameters a and c of hexagonal ice in various porous materials, as well as their ratio c/a. The three columns show the materials with decreasing pore diameters from left to right. Hydrophilic PMO samples are plotted in a shade of red, while more hydrophobic ones are a shade of green. MCM-41 is plotted in black. The lattice parameters of bulk ice are also plotted for comparison. The bulk values were calculated according to the work by Röttger et al..53,54

Close modal

The left panel of Fig. 5 shows ice in the largest pores with diameters ≥4.4 nm. While the more hydrophilically amine-functionalized BTEVA(4.4) closely follows the lattice parameters of bulk ice, the two samples with the BTEVFB precursor do not follow this behavior. In BTEVFB(4.4), both a and c are larger than in bulk ice. Their ratio, however, is still similar to bulk ice. This is not the case for BTEVFB(4.9), where only c differs from bulk, implying an elongated hexagonal unit cell. This trend is also observable for MCM-41(3.9) in the middle panel. Similar to BTEVFB(4.9), hexagonal ice in MCM-41(3.9) seems to be elongated along its c direction. In contrast, BTEB(3.8) gives a lower value for c and, consequently, also a lower value for the c/a ratio.

The smaller BTEVA(3.4) and BTEVP+(3.4) in the right panel show a stronger deviation from bulk than the ones previously discussed. Note that BTEVA(3.4) also particularly differs from its larger counterparts. While the ice in BTEVA(3.4) and BTEVA(3.8) structures similarly to bulk ice, in BETVA(3.4), it also shows an elongated hexagonal cell with c/a that is above that of bulk ice. This may indicate that a pore size effect only becomes relevant below 3.8 nm, at least in BTEVA-PMOs. However, it should be noted that BTEVA(3.4) has a larger error margin, potentially stemming from the lower amount of water adsorbed in the pore, which, in turn, gives a weaker scattering signal. The other sample with a pore diameter in this range, BTEVP+(3.4), supports a pore size-dependent deformation of the hexagonal structure as it shows the most elongated c parameter out of all materials. It should be noted here that due to its synthesis, a residual iodide ion is present in the BTEVP+-PMOs, which takes up additional space in the vicinity of a functional group. The c/a-ratio in BTEVP(3.5) is again more closely following that of bulk ice; however, we observe slightly larger lattice parameters for both a and c, suggesting an overall expanded unit cell, similar to BTEVFB(4.4).

The shifts in lattice parameters are most often not equal for a and c. This could be caused by a dependence of the lattice parameter shift on the orientation. Such dependence could stem from the pore wall chemistry. The interactions of water with the organic moieties could force the molecules into arrangements that would not be favorable under bulk conditions while hindering others that would. We shall now investigate the orientation of these hexagonal crystals relative to the pore axis to evaluate such dependence. In order to determine an orientational dependence, x-ray cross correlation analysis (XCCA) was conducted.37,38,47,50,55 Following Eq. (3), an angular correlation is calculated between spots at two different q values.48 We choose one q value to be the expected value for a (00l) periodicity of the functional groups of the PMO and the other that of hexagonal ice (see Fig. 2).

Figure 6 shows a selection of correlation functions in PMOs with 3.8 nm pore diameter. The correlations between the (002) peak of ice with both the (001) and (002) peaks of the PMOs are shown in the subfigures Figs. 6(a) and 6(b), respectively. The latter represent the periodicity of the functional groups in the pore walls and, therefore, the pore axis direction. Since (001)PMO and (002)PMO are parallel, both correlations should show the same qualitative features. Their equivalence can, therefore, be used as an additional indication if visible peaks are actual angular correlations or just artifacts, for example, from detector noise or background scattering. Note that the angles of the correlation peaks are statistical values that indicate a preferred orientation. Other orientations might also be present inside one pore. Therefore, the analysis is quite sensitive to the specific area where the scattering pattern was taken. In order to mitigate this, we measured at about 100 separate spots for each sample and performed background correlations, which are explained in further detail in the supplementary material.

FIG. 6.

Angular correlations between spots of the 002 signals of hexagonal ice and the 001 (panel a) and 002 (panel b) signals of various PMOs with a pore diameter of 3.8 nm.

FIG. 6.

Angular correlations between spots of the 002 signals of hexagonal ice and the 001 (panel a) and 002 (panel b) signals of various PMOs with a pore diameter of 3.8 nm.

Close modal

The correlation functions in some materials show very clear peaks, while others do not. The presence of peaks implies that some materials lead to certain angles Δ between the (00l) axis of the ice crystals and the pore axis being more common than others. The absence of peaks can either mean the absence of ice crystals in these materials or random orientations of crystals with respect to the pore axis. For the hydrophilic samples (red), BTEVP+(3.5) shows a large peak at 180°, indicating a preferred orientation of the (00l) axis of the ice parallel to the pore axis. A second large peak can be seen at about 40°. BTEVP(3.8) shows a quite large peak at about 30° and some smaller ones at ∼60°, 120°, and 150°. BTEVA(3.8) primarily shows a peak at 90°, albeit less pronounced than in BTEVP(3.8). In contrast, the more hydrophobic samples, BTEVB(3.8) also shows some quite pronounced peaks at 30°, 150°, and two peaks slightly above and below 90°, respectively. BTEVFB(3.8) only shows some weak peaks at 150°, 75°, and 30°, although the latter is only visible in the correlation with (002)PMO. BTEVCl(3.8) does not show any peaks at all. As the latter two are rather hydrophobic materials, the data shown in Fig. 6 generally suggest stronger correlations between the pore and ice crystal orientation in hydrophilic compared to hydrophobic pores, with the exception of BTEVB(3.8). However, in those samples that show strong peaks [i.e., BTEVB(3.8), BTEVA(3.8), BTEVP(3.8), and BTEVP+(3.5)], no systematic dependence of the correlation angles Δ on the material properties can be determined at these pore diameters, but it is notable that BTEVP+(3.5) shows the largest peak of all the measured materials while also having the lowest pore diameter and volume.

Note that the absence of correlation peaks in BTEVFB(3.8) and BTEVCl(3.8) does not necessarily imply that no preferred orientations occur in these samples. Instead, it is also possible that the amount of averaged spots is too small in these cases and more data would be required to reach a convergence. In any case, if preferred orientations are present, they are much more weakly pronounced in comparison to the other samples.

Figure 7 compares the lattice constants (panel a) to the angular correlation functions (panel b) for the samples measured in both experiments. A striking observation is that BTEVP+(3.4), which showed a strong unit cell elongation along the c axis, also gives a strong correlation at 180°. This suggests that the elongated cells are often oriented along the pore axis. In addition, another strong peak at about 40° and a third smaller peak at about 140° are visible. BTEVA(3.8), which closely sticks to the bulk lattice parameters, seems to be mostly oriented orthogonal to the pore axis as can be seen from its correlation peak at 90°. Smaller peaks at around 15° and 165° are also present. The correlations in BTEVB(3.8), which is the only measured PMO to show exclusively cubic ice characteristics, have two strong, symmetric correlation peaks at 30° and 150° and, additionally, two smaller peaks at about 75° and 105°, which are also symmetric. BTEVP(3.5) shows a strong peak at 30° and generally has a similar profile to BTEVP+(3.5) with no correlation at 90° and an additional small peak at around 150°, symmetric to its large peak at 30°. Both of these materials have the same functional pyridine group, but in BTEVP+, this group possesses an additional positive charge, a methyl group and the iodide counterion mentioned before.

FIG. 7.

(a) Lattice constants of materials for which XCCA was conducted. (b) Angular correlation curves for materials in panel (b). The correlations are for the angles between spots at q values identified for the (002) peak in hexagonal ice and the (002) peak of the periodicity of the organic moiety in the PMO. (c) A visualization of the most prominent angles Δ as shown in panel (b). The gray cylinder represents the pore, the black dashed line represents the pore axis, and the blue hexagonal prisms indicate the hexagonal crystallites.

FIG. 7.

(a) Lattice constants of materials for which XCCA was conducted. (b) Angular correlation curves for materials in panel (b). The correlations are for the angles between spots at q values identified for the (002) peak in hexagonal ice and the (002) peak of the periodicity of the organic moiety in the PMO. (c) A visualization of the most prominent angles Δ as shown in panel (b). The gray cylinder represents the pore, the black dashed line represents the pore axis, and the blue hexagonal prisms indicate the hexagonal crystallites.

Close modal

The obtained ice crystal orientations relative to the pore axis in these samples are shown in Fig. 7(c).

We investigated the structure of ice in periodic mesoporous organosilicas. We used x-ray scattering on powder samples in order to study confined ice with regard to its qualitative structure, as well as a more detailed analysis of the lattice constants of the hexagonal contributions. In order to analyze the orientation of the hexagonal crystallites relative to the pore axis, we used x-ray cross correlation analysis.

The overall structure, consisting of cubic, hexagonal, and amorphous contributions, which stem from the liquid layer at the pore wall,13,51 is well in accordance with the literature.8,11,13,44,51,52 Furthermore, we found indications that the structure is dependent on the way the sample is cooled. We consistently observed hexagonal contributions when lowering the temperature in a step-wise manner, while continuous cooling mostly led to pure cubic (or cubic-like) ice.

While previous studies did not report lattice constant shifts of the hexagonal phase in confinement,13 we observe that they deviate from bulk ice in several of our measured samples. This effect depends on both the pore surface chemistry and the pore size of the confining material. All the hydrophobically functionalized materials discussed in this study, i.e., BTEVFB(4.9), BTEVFB(4.4) and BTEB(3.8), show a deviation from bulk properties, while in hydrophilic materials, this effect is mostly observable for small pore diameters ≤3.8 nm. These shifts, therefore, seem to be dependent on both the pore wall chemistry and especially the pore size as stronger shifts were observed in smaller pores [i.e., BTEVP(3.7), BTEVP+(3.5), and BTEVA(3.4)]. We most commonly observe an increased c/a ratio, meaning an elongation of the unit cell (see Fig. 5).

It is not clear what causes this change in the lattice constants relative to bulk ice. An explanation could be that the highly stacking-disordered cubic-like phase leads to connections with the hexagonal ice domains that would be unfavorable under bulk conditions, leading to the observed elongated [BTEVFB(4.9), MCM-41(3.9), BTEVA(3.4), and BTEVP+(3.4)], expanded [BTEVFB(4.4) and BTEVP(3.5)], or truncated [BTEB(3.8)] hexagonal unit cells. Notably, only BTEB(3.8) leads to a c/a smaller than bulk while also being the sample with the smallest dorg at only 0.76 nm (see Table I). This length describes the distance between the silicon atoms at either end of the organic moiety. With this, dorg/c in BTEB(3.8) is close to 1, while for all other PMOs, the ratio is closer to 1.5. While there is also the interfacial water between the pore wall and the ice, this indicates that the length of the organic moieties could play an important role in the development of ice in PMOs and seems to be a major factor in the observed lattice constant shift.

Cubic or stacking-disordered ice and an amorphous non-freezing layer have consistently been reported in similar pores in various studies.9,13,44,51 The broad peaks observed in our data are in agreement with the argumentation of Morishige and Uematsu9 and Moore et al.,51 which confirmed that cubic ice consists of small crystallites with a large number of stacking faults to such a degree that it is better described as stacking-disordered ice.20 

The sharper ice Ih peaks that are observed in these systems were argued by Thangswamy et al.44 to be, in fact, not hexagonal ice inside the pore but instead ice that crept out of the pore during crystallization, forming bulk crystallites outside the pore, as suggested by a calculated crystallite size that is considerably larger than the pore diameter.44 This is also the case in our study with crystallite sizes calculated to be around 20–30 nm. However, we propose that the hexagonal contribution is, in fact, ice inside the pores. The sharpness of the corresponding peaks and the implied large crystallite size does not necessarily mean that they have to be outside the pore. Instead, they could be caused by crystallites grown along the pore axis with the crystallite size describing the length of a cylindrical crystallite. This way, it is, in principle, only limited by the length of the pore. This is supported by the fact that larger pores lead to larger hexagonal peaks, as in BTEVFB(4.9) or BTEVA(4.4) compared to smaller pores, such as BTEVP(3.5) or BTEVP+(3.4). Furthermore, we observe the previously discussed deviations in the lattice parameters of the hexagonal contributions from those of bulk ice.

X-ray cross correlation analysis suggests preferred orientations of the hexagonal contributions in several samples (see Figs. 6 and 7). For a pore diameter of about 3.8 nm, we find that stronger correlations tend to occur in more hydrophilic pores. When comparing the XCCA results to the lattice parameter shifts in specific samples (Fig. 7), more prominent correlations are found in samples that also exhibit larger lattice parameter shifts [e.g., BTEVP+(3.5)] or exclusively cubic-like ice [BTEVB(3.8)].

The supplementary material contains information on the synthesis and chemical structure of the PMOs, as well as their pore size distribution and adsorption and desorption curves. The estimation of the Scherrer constants is also discussed in further detail along with a more thorough explanation of the background correlations in the XCCA.

We acknowledge DESY (Hamburg, Germany), a member of the Helmholtz Association HGF, for the provision of experimental facilities. Parts of this research were carried out at PETRA III, and we thank Dr. Alexander Schökel and Dr. Martin Etter for their assistance in using the P02.1 beamline39 and Dr. Anton Davydok for assistance in using the nanofocus endstation at P03.40,41 Beamtime was allocated for Proposal Nos. I-20200440, I-20190201 (P02.1), and I-20220503 (P03). This research was carried out in the framework of the city of Hamburg’s state-funded research project “Control of the special properties of water in nanopores” (LFF-FV68). It was further supported by the Centre for Molecular Water Science (CMWS) in an Early Science Project and by the Cluster of Excellence Advanced Imaging of Matter of the Deutsche Forschungsgemeinschaft (DFG) (EXC 2056, Project No. 390715994).

The authors have no conflicts to disclose.

Niels C. Gießelmann: Data curation (lead); Formal analysis (lead); Investigation (equal); Software (lead); Validation (equal); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). Philip Lenz: Formal analysis (supporting); Investigation (equal); Resources (equal); Validation (equal); Visualization (equal); Writing – original draft (supporting); Writing – review & editing (equal). Sophia-Marie Meinert: Formal analysis (supporting); Investigation (equal); Validation (equal); Visualization (equal); Writing – original draft (supporting); Writing – review & editing (equal). Tamás Simon: Investigation (equal); Resources (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). Robert P. C. Bauer: Data curation (supporting); Formal analysis (supporting); Investigation (equal); Software (supporting); Writing – review & editing (equal). Wonhyuk Jo: Investigation (equal); Software (supporting); Writing – review & editing (equal). Sarah Claas: Resources (equal); Writing – review & editing (equal). Christian Köhn: Investigation (equal); Writing – review & editing (equal). Nele N. Striker: Investigation (equal); Writing – review & editing (equal). Michael Fröba: Conceptualization (equal); Funding acquisition (equal); Project administration (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal). Felix Lehmkühler: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Project administration (equal); Software (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal).

Raw data were generated at the large scale facility Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany. Derived data supporting the findings of this study are available from the corresponding author upon reasonable request.

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