Formation of Periodically Arranged Nanobubbles in Mesopores

Mar 4, 2016 - Within the mean-field model of Saam and Cole for vapor condensation in cylindrical pores, a nitrogen and C5F12 sorption isotherm is well...
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Formation of Periodically Arranged Nanobubbles in Mesopores: Capillary Bridge Formation and Cavitation during Sorption and Solidification in an Hierarchical Porous SBA-15 Matrix Tommy Hofmann,*,† Dirk Wallacher,† Jan Perlich,§ Sarathlal Koyiloth Vayalil,§ and Patrick Huber*,∥ †

Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, D-12489 Berlin, Germany Deutsches Elektronen Synchrotron, D-22607 Hamburg, Germany ∥ Technische Universität Hamburg, D-21073 Hamburg, Germany §

ABSTRACT: We report synchrotron-based small-angle X-ray scattering experiments on a template-grown porous silica matrix (Santa Barbara Amorphous-15) upon in situ sorption of fluorinated pentane C5F12 along with volumetric gas sorption isotherm measurements. Within the mean-field model of Saam and Cole for vapor condensation in cylindrical pores, a nitrogen and C5F12 sorption isotherm is well described by a bimodal pore radius distribution dominated by meso- and micropores with 3.4 and 1.6 nm mean radius, respectively. In the scattering experiments, two different periodicities become evident. One of them (d1 = 11.5 nm) reflects the next nearest neighbor distance in a 2D-hexagonal lattice of tubular mesopores. A second periodicity (d2 = 11.4 nm) found during in situ sorption and freezing experiments is traced back to a superstructure along the cylindrical mesopores. It is compatible with periodic pore corrugations found in electron tomograms of empty SBA-15 by Gommes et al. (Chem. Mater. 2009, 21, 1311−1317). A Rayleigh−Plateau instability occurring at the cylindrical blockcopolymer micelles characteristic of the SBA-15 templating process quantitatively accounts for the superstructure and thus the spatial periodicity of the pore wall corrugation. The consequences of this peculiar morphological feature on the spatial arrangement of C5F12, in particular the formation of periodically arranged nanobubbles (or voids) upon adsorption, desorption, and freezing of liquids, are discussed in terms of capillary bridge formation and cavitation in tubular but periodically corrugated pores.

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INTRODUCTION Mesoporous substrates provide a natural environment to study condensed matter on nanometer sized length scales.2−21 A multitude of techniques can be utilized to elucidate static and dynamical characteristics of liquids and solids upon confinement in pores only a few nanometer across. The variety of successfully employed experimental probes includes elastic and inelastic scattering techniques, SQUID measurements, calorimetric studies, sorption and flow experiments, and dielectric characterization. Mesoporous substrates are available with different and often tailorable morphological characteristics to suit different experimental demands. Complex polydisperse pore networks (Vycor, sol−gel glasses, nanoporous metals) come along with more monodisperse ordered systems (porous silicon, MCM-41, SBA-15) and responsive hosts, such as metal−organic frameworks.9,22,23 Originally mostly considered as inert and rigid substrates that provide only a geometrical confinement for the guest molecules of interest, recent studies also focused on the direct response of substrates on liquid and solid infiltration and tailored functionalized materials for technical, biological, or medical applications.23−35 In the material class of ordered mesoporous substrates, the silicate SBA-15 is arguably the most prominent example. This © XXXX American Chemical Society

template-grown glass matrix has been the focus of interest for several years since its synthesis was first described in 1998.36 To list only a few fields of applications, it has been rigorously employed as a host material to probe nanoscale adsorption and wetting,12,22,37−40 it served as template for the growth of nanowires,41,42 and it was functionalized to facilitate drug delivery.43 SBA-15 initially attracted attention as a model system for experimental and theoretical studies because of its supposedly simple internal structure. At first glance, characterized by fairly monodisperse cylindrical pores arranged on a 2D-hexagonal lattice, it triggered the hope to reconcile theoretical predictions with experiments that often appear at odds in substrates, which exhibit irregularly shaped pores with wider size distributions in complex networks. However, carefully analyzed scattering and sorption studies hinted fairly early toward a complex internal structure,12,37,44 which influences static and dynamic behavior of pore condensates in unexpected but intriguing ways. Scattering experiments and wetting studies appear very sensitive to the exact morphology of the utilized nanostructured Received: December 14, 2015 Revised: March 2, 2016

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Subsequently, a sol gel process was triggered by adding 8.8 g of tetra-ethyl-ortho-silicate as silica source to the solution and stirring for 20 h at constant temperature T. The solid deposit was recovered and dried after additional aging at 80°C for 12 h. Calcination of the template polymers under oxygen atmosphere at 500° for 6 h left only the stable silica skeleton and concluded the SBA-15 synthesis.

substrates. As such they are not only perfectly suited to probe theoretical concepts of nanoscale wetting.45 They also provide a reliable metrology to ascertain the morphological characteristics of the substrates as an indisputable prerequisite to understand experiments concerning fundamental but also applied scientific aspects.46 Here, we present detailed sorption/wetting studies on liquid nitrogen (N2) and fluorinated pentane (C5F12) in SBA-15 in combination with synchrotron-based small-angle scattering experiments. Our paper goes beyond the established characterization of SBA-15 in terms of meso- and microporosity.44 It discusses, in particular, the existence of periodic pore-wall corrugations along the tubular pore axis and their influence on sorption processes such as capillary condensation and evaporation as well as freezing. Capillary bridging and cavitation are identified as mechanisms that cause the formation of nanobubbles upon liquid filling, evaporation, and solidification along the corrugated pores.

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ISOTHERMS Sorption isotherms are a standard tool to characterize nanoand mesoporous substrates with respect to pore size distribution (PSD), porosity (Φ) and effective surface area (A).52 At constant temperature T, volumetric measurements relate the uptake f = N/N0 of liquid in the pores to the relative vapor pressure Prel = P/P0 of the coexisting gas phase and therefore to the chemical potential difference Δμ = kBTln(Prel) < 0 between bulk system and pore confined liquid. The main quantities of interest in these measurements are the number of physisorbed liquid molecules N, the number of molecules required to fill the pore space completely N0, the pressure of the coexisting vapor P and the vapor pressure P0 of the bulk system. Different theoretical approaches as BET- or FHHanalysis,53,54 Saam-Cole modeling,55 or more sophisticated density functional calculations,56 allow inferring microscopic characteristics of porous materials from these quantities. Two sorption isotherms were measured in our experiments. A nitrogen isotherm in SBA-15 was recorded at T = 77 K (Figure 2). It provides an initial characterization of the porous

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SBA-15: SYNTHESIS SBA-15 is a template-grown, powdery silicate matrix with tubular pores that are arranged by design on a hexagonal 2D lattice.36 Its synthesis commonly encompasses three subprocesses: templating process, sol−gel process and calcination. A multitude of different synthesis routes36,43,47 allows tailoring pore diameters, pore−pore distances36 or surface functionality43 in powdery and monolithic substrates.48 In the sequence of subprocesses, the morphology of the initially formed micelles molds readily the morphology of the final SBA-15 silica sample. As the shape of these micelles is not only determined by screening hydrophobic polymer blocks in an aqueous solution, which results in regular spherical and cylindrical geometries, but rather is subject to thermally driven, hydrodynamic instabilities like Rayleigh-Plateau, it can be expected that the final silica product reflects morphological artifacts of these instabilities (Figure 1).49−51 The synthesis of our sample followed a standard recipe of Zhao et al.36 to obtain a fine grained powder (1 μm) with tubular mesopores roughly 7 nm across and 11 nm apart. The templating process constituted of dissolving of 4 g of the micelles forming triblockcopolymer EO20PO70EO20 at T = 35°C in 30 g water and 80 g of 2 M hydrochloric acid.

Figure 2. Comparison between the measured nitrogen isotherm (symbols) and the prediction of the Saam−Cole model (red line) at T = 77 K. The inset depicts the bimodal pore size distribution employed in the Saam-Cole calculations.

substrate in terms of micro- and mesoporosity within the IUPAC classification. A C5F12 isotherm was measured at T = 240 K (Figure 3). It serves as a testing ground for the morphological features of SBA-15 as predicted by the aforementioned N2 isotherm. Further, it illustrates the in situ sample preparation for the scattering experiments, and it relates the scattering data to the filling fraction and thermodynamic state of the pore condensate. Contrast matching upon filling is caused by the small difference in electron density (ρSiO2/ ρC5F12(T = 240 K) = 1.27, ρSiO2/ρC5F12(T = 150 K) < 1.1) between silica and fluoropentane inferred from the bulk mass densities.57 It facilitates detailed scattering studies on the morphological features of SBA-15.

Figure 1. Proposed templating process of SBA-15 and envisioned wetting sequence in periodically corrugated nanochannels: (1) Rayleigh−Plateau instabilities in micelles during the templating process cause periodically corrugated mesopores upon calcination. (2) Upon liquid condensation and liquid evaporation, nanobubbles form along the tubular pores through liquid bridging and cavitation. B

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constant of H = 3.28 × 10−20 J.61 Surface tension and density of liquid nitrogen are other parameters of the model and taken from the known bulk properties57 (σ = 8.84 mJm−2, ρ = 0.808 gcm−3). A bimodal PSD accounts straightforward for micropores and mesopores. The experimental N2 isotherm is well described with a bimodal PSD, which is composed of two Gaussian terms. One is centered around 3.4 nm with a FWHM value of 0.24 nm. It accounts for the mesopores that cause the steep increase in de nitrogen uptake at characteristic pressures Pad rel and Prel. The second Gaussian term centers around an average pore radius of 1.6 nm with a FWHM of 1.4 nm. It accounts for broad size distribution of micropores, which are caused in the template process during synthesis. Attempts to describe the isotherm with a monomodal PSD and the discussed parameters expectedly failed. C5F12−Isotherm. A theoretical description of the isotherm follows the same approach as discussed for the nitrogen isotherm. Saam-Cole calculations employ a Hamaker constant of H = 3.02 × 10−20 J as predicted by the Lifshitz theory,62 a bulk surface tension57 of σ = 15.4 mJm−2 and a bulk density57 of ρ = 1.804 gcm−3 to predict the adsorption−desorption cycle in SBA-15. The PSD obtained from the nitrogen isotherm has only to be altered with respect to two points to achieve an acceptable degree of agreement between theory and experiment. Slightly larger pore radii were assumed at 240 K than at 77 K but are not a source of major concern as thermal expansion should cause a small increase in diameter and a difference of less than 10% must be considered to lie well within the error margin of a standard PSD. The total pore volume estimate from the fluoropentane isotherm is smaller than for the nitrogen isotherm. The kinetic diameters of C5F12 in longitudinal and transversal directions are with 0.44 and 1.08 nm notably larger than the average value of 0.34 nm obtained for N2.63 Consequently, the large C5F12 molecules cannot access all micropores and we consider only 40% of the micropores as accessible for fluoropentane. For the fluoropentane isotherm as well as for the nitrogen isotherm, the model fails to describe the steep part of the ad,SC ad,SC adsorption branch (Pad is defined rel < Prel ). The pressure Prel as the upper spinodal point for a liquid film on a clylindrical pore wall with average pore Radius of R = 3.4 nm. As such it only represents an upper limit for the transition pressure from liquid film on the pore wall to capillary condensate in the pore center. In comparison with the experiment, it cannot be more ad ad,SC holds. expected as that the inequality Pde rel < Prel ≤ Prel Small-angle X-ray diffraction upon in situ C5F12 sorption. Figure 4 displays the small-angle X-ray scattering signal of pure SBA-15 in the Q-range between 0.3 nm−1 and 1.5 nm−1. The eminent Bragg reflections are caused by the 2D hexagonal lattice of tubular mesopores. Positions of the Bragg reflections translate directly into a pore−pore distance of d1 = 11.5 nm. Peak intensities contain information about the microporous roughness as well as mesoporous morphology of SBA-15.12,37 An analysis following the approach of Hofmann et al.37 readily implies that mesopores with a radius of Rxray = 4.4 nm are surrounded by a microporous corona with an estimated width of 2δ ≈ 1.6 nm. In this model the actual mesopore radius is given by Rxray − δ ≈ 3.6 nm, a value which agrees fairly well with the desorption data presented above. A slight asymmetry of the (10)-reflection on the low-Q site hints toward additional features, which are hidden underneath

Figure 3. Fluoropentane isotherm measured at T = 240 K. The inset depicts the pore size distribution within the Saam−Cole model.

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X-RAY SCATTERING Scattering experiments were performed at synchrotron facilities DORIS III and PETRA III of DESY in Hamburg, Germany. We employed small-angle scattering beamlines BW4 and P03 to study structural characteristics of SBA-15 as well as the geometric distributions of nanoconfined liquids in SBA-15 upon adsorption, desorption and freezing. With wavelengths of λP03 = 0.95 Å and λBW4 = 1.38 Å and sample to detector distances of lBW4 = 1380 mm and lP03 = 3500 mm it was readily possible to probe wavevector transfers Q between 0.2 nm−1 and 2.5 nm−1. This Q-range reveals structural informations on length scales between 31 and 2.5 nm. Different detectors were used at different instruments. That are a Princeton Roper CCD Detector at BW4 and Pilatus Detector at P03. More detailed information about the instrument designs can be found in prominent references.58−60 A closed cycle cryostat with stainless steal capillary, a gas distribution unit with various pressure gauges and a Beryllium sample cell allowed combining sorption measurements and Xray scattering experiments. Parametric measurements in the temperature range between 240 K and 60 K were readily possible for porous SBA-15 filled with controlled amounts (0 < f < 1) of C5F12.

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SBA-15: MORPHOLOGY N2−Isotherm. It is not possible to provide a IUPAC classification of the measured nitrogen isotherm (Figure 2) considering only micropores or only mesopores. The coexistence of micropores and mesopores in SBA-15 defines the pressure dependence of the filling fraction f upon adsorption and desorption. We follow the approach of Moerz et al.61 to describe the N2 isotherm at T = 77K within the Saam−Cole Model.55 Here, adsorption in independent, cylindrical pores of infinite length starts with a liquid film on the pore walls at low pressures and concludes with capillary condensation in the pore center at a spinodal pressure Pad,SC rel . The desorption branch is similarly defined by the existence of a wall film at Prel < Pde,SC and the rel equilibrium coexistence of wall film and capillary condensate at de,SC Prel . The complete hysteretic sorption−desorption cycle (Pde,SC < Pad,SC rel rel ) is defined by liquid−substrate, liquid−liquid interactions and pore radius. In the calculations, the van der Waals interactions between nitrogen and silicate scale with an earlier reported Hamaker C

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Figure 4. Scattering intensity I(Q) of pure SBA-15 as a function of wavevector transfer Q. The first three Bragg reflections of the hexagonal pore lattice are shown.

Figure 6. Contribution of the APS to the scattering signal depending on filling fraction as inferred from nonlinear least-squares fitting of the intensities.

the strong Bragg reflections. We interpret the small shoulder of the (10) reflections as additional periodic structure (APS) inside the SBA-15 grains. It is not the first time, that such an feature has been observed, but it has been rarely discussed.12 The APS becomes more prominent in the scattering data upon partial filling of the pore space with fluorinated contrast matching pentane (Figure 5). It appears most pronounced above f = 90%. Its Q-value translates in a periodicity of 11.4 nm slightly smaller than the pore−pore distance of 11.5 nm. Figure 6 depicts quantitatively the f-dependent contribution of the APS to the scattering signal for adsorption and desorption as inferred from nonlinear least-squares fitting of the intensities. In the filling regime, between 60% and 95% the intensity appears to be almost constant, but it decreases rapidly

in the postfilling regime as the hysteresis loop in the isotherm closes. Below 60% it was not possible to extract reliable intensities, as the neighboring (10)-SBA-15 reflex dominates the scattering signal. Interestingly, a similar superstructure becomes evident in the case that the pores were completely filled with C5F12 at T = 240 K and subsequently cooled down. Figure 7 clearly indicates this reappearance of the APS close to 140 K, which is well below the bulk freezing point57 of 148 K. Figure 5 shows the APS in the solid phase at T = 82 K.

Figure 7. Scattering signal as a function of temperature upon cooling the initially completely filled SBA-15 sample. Provided temperatures are averaged over the time of data collection (i.e., 120 s per pattern) while simultaneously cooling with a rate of 0.5 K/min.

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FORMATION OF PERIODICALLY ARRANGED NANOBUBBLES DURING SORPTION AND FREEZING SBA-15 Bragg reflections change upon filling with fluorinated pentane with respect to their absolute intensity as well as their relative intensities. X-ray adsorption, contrast variations between pore space and silica matrix and changes in the geometric formfactor of the pores upon filling are main causes for this intensity variations and a thorough guide to analyze such variations is given in the manuscripts of Hofmann et al. and Zickler et al.12,37 or more recently Gommes.64 Here, we try to elucidate the origin of the found morphological feature, i.e. the APS as revealed in the scattering data and to ascertain its

Figure 5. The APS signal in the liquid state at a temperature of 240 K and a filling fraction f = 0.90 (a, c) and in the solid state at a temperature of 82 K obtained by cooling a completely filled SBA-15 sample (b, c). The inset illustrates a quasi-Bragg reflection caused by a periodic chain of spheres with finite size in a powder average. D

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representative for a minority of periodically corrugated pores. In adsorption the microporous corona of the SBA-15 walls is filled first. At a critical pressure capillary condensate forms in the pore center. This capillary condensate is characterized by a multitude of periodically arranged voids or nanobubbles along the corrugated pore axis.67 As the pressure is increased further these voids are also filled and the APS signal vanishes. In desorption equilibrium or near equilibrium cavitation cause the reappearance of the voids and the capillary bridging configuration, before at decreasing pressure capillary condensate and micropore filling retreat.3,6,68−71 Found pore corrugations of roughly d2 = 11.4 nm lie well within the predicted Λ range that separates the two wetting regimes A and B.4 In particular, it is significantly larger than the annealing length for thin films (ΛH ≈ 1−2 nm), which favors smooth wall coating and uniform capillary condensation. As outlined in Reference,4 the envisioned wetting scenario in such a corrugated tubular geometry puts strict boundaries on the free energies of liquid film state and capillary bridge state upon adsorption and desorption. In adsorption the liquid film must become unstable at pressures below the spinodal point of the bridge configuration, whereas in desorption the filled configuration must become unstable with respect to the bridged state before the liquid film represents the lowest energy configuration at lowest pressures. Detailed and demanding numerical simulations would be required to quantitatively predict the wetting sequence as well as the scattering amplitude from empty, respectively, partially filled SBA-15 with periodically corrugated pores. This approach is far beyond the scope of our experimental study. But a few semiquantitative arguments explain how a powder of quasi onedimensional chains of periodic voids along tubular nanochannels cause an additional reflection in the scattering signal. The origin of the APS signal relates readily to the formfactor of a single chain, if one assumes periodic bubble configurations, which are not omnipresent in and along each pore, but rather appear as elusive minority species in otherwise uniformly with liquid filled pores.72 Starting from a single, periodic onedimensional assembly of objects of finite size, e.g., nanobubbles along a z-direction, the Bragg condition is fulfilled on equally spaced planes in reciprocal space Δ = 2π/d apart. The scattering intensity I(Q) ∝ ∑i ∞= −∞δ(Qz − iΔ) × |F(Q)|2 for wave vector transfers Q residing in these planes varies according the geometric formfactor F(Q) squared of the scattering objects and particularly decreases as Q increases. In a powder average, each plane and its inherent signal modulation give rise to a quasi-Bragg reflection (Figure 5) as the spacing Δ defines a low Q cutoff of the scattering intensities and the formfactor causes decaying intensities toward higher Q values. In its origin and appearance, this scattering scenario bears a striking resemblance to the well-known Warren shape of peak profiles observed in two-dimensional structures.73,74 The simplified calculation as shown in Figure 5 represents the integrated intensity of a powder line due to spherically shaped bubbles with a radius of R = 3.4 nm at an average distance of 11.4 nm with a small but finite distance variation. A rigorous treatment would rely on similar arguments but take into account more realistic ”bubble” geometries and Debye−Waller factors due to irregularities along the chains, and properly account for the electron density of SBA-15 and C5F12, to name only a few aspects to consider. It constitutes another, independent experimental evidence for the hypothesis outlined above that, upon cooling a

influence on the wetting sequence upon liquid uptake and removal. In a series of recently published manuscripts,1,4,65 Gommes studied the morphology of SBA-15 mesopores and predicted theoretically its influence on sorption processes in the tubular channels. He convincingly illustrated deviations from a perfectly cylindrical pore shape in SBA-15 by means of 3D electron tomography1 and identified corrugations along the main pore axis with well-defined correlation lengths up to several nanometer. These insights motivate translating the Q position of the APS into an axial correlation length of periodic pore corrugations of roughly d2 = 11.4 nm whose origin becomes apparent if we consider the SBA-15 synthesis process as outlined above. The templating process encompasses 2D hexagonally arranged, cylindrical blockcopolymer (BCP) micelles embedded in a silica glass matrix.66 In the ideal case, the micelles act as perfectly smooth and cylindrical templates for the SBA-15 mesopores after polymer removal by calcination. As any soft matter structure the micelles are susceptible to thermally excited fluctuations, most prominently thermally activated, radial capillary undulations. They can trigger the transformation of a cylindrical micelle into a sequence of micellar drops, the well-known Rayleigh−Plateau instability.49 It is now remarkable, that the characteristic pore corrugation length inferred from our experiments is in excellent agreement with the periodicity, which theory predicts for a chain of touching, spherical micelles that results from a cylindrical BCP micelle undergoing a Rayleigh−Plateau instability,50,51 d2 = ΛRP = 3.89 RBCP = 11.4 nm, where RBCP = 2.93 nm, the radius of the cylindrical micelle is slightly smaller than the mean pore radius of the silica mesopores of our SBA-15 matrix R = 3.4 nm: see Figure 1. Thus, the correlation length observed in the sorption and freezing experiment can readily be traced back to a hydrodynamically driven shape transformation of the BCP template during the SBA-15 synthesis. As will be outlined below with regard to the f-dependent scattering characteristics of the APS signal, not the entire cylindrical micelle population undergoes this transition and, presumably, this fraction sensitively depends on the processing parameters, in particular the thermal history of the micelles. In the present sample, only a small fraction of the cylindrical BCP micelles transformed to chains of BCP droplets and hence acts as templates for tubular, but periodically corrugated silica pores after the calcination process; see Figure 1. In theoretical simulations based on the Derjaguin−Broekhoff−de Boer model, the correlation length Λ appeared as the defining parameter for the wetting sequence upon liquid uptake and removal.4 In particular, two wetting regimes A and B could be identified depending on the magnitude of Λ. At small correlation lengths Λ, the liquid film smooths out corrugations of the pore wall at small pressures before capillary condensation occurs uniformly along the pore axis at larger pressures (regime A). At sufficiently large Λ capillary bridging in adsorption and equilibrium cavitation4 in desorption can cause liquid configurations characterized by an alternating sequence of vapor voids and liquid filled segments along the tubular pore as sketched in Figure 1 (regime B). In the theoretical limit of large Λ, the dependence of the APS signal upon sorption is readily explained by periodically arranged voids along the tubular pores if the following wetting sequence applies and keeping in mind that f represents a global average over the ensemble of pores and might not be E

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Langmuir completely filled substrate, the APS signal recovers significantly below the bulk freezing point (see Figure 7) of 148 K, likely marking the solidification of the confined liquid. Decreasing the density of the liquid or, respectively, solid while cooling and freezing allows forming voids in the initially filled pore space, with a correlation length of ∼11 to 12 nm, in which the periodic capillary bridge configuration returns in the corrugated pores. The stability of this configuration of bubbles was tested on time scales of a few hours; however, the APS might disappear with time in a very slow recondensation process of C5F12 from the coexisting vapor phase that fills the voids. A more mundane explanation of the APS signal could simply resort to a multimodal pore size distribution in SBA-15. For instance, a small fraction of SBA-15 grains could also exhibit tubular pores with slightly larger pores and larger pore−pore distance than the majority of SBA-15 grains. These grains would only be filled upon adsorption at higher pressures and become readily visible in Figure 6 close to the postfilling regime after filling the smaller, dominating fraction of pores. In this scenario, the APS signal would represent an additional (10) reflection of an multimodal SBA-15 size distribution. However, the question arises why no other reflections, such as (21) and (20), can be found, although the data should provide the possibility to ascertain such reflections. Moreover, the observation of an APS signal upon solidification appears at odds with a secondary phase of SBA-15 with wider pores. From optical transmission measurements on partially filled porous Vycor glass, it could be unambiguously interfered that confined liquids migrate from segments with smaller to larger pores upon cooling and solidification.75 A similar scenario expected here would render the secondary phase invisible in the scattering experiment due to contrast matching between condensate and glass matrix. One can also raise the tempting question whether the observed APS is caused by a Rayleigh−Plateau instability of the liquid C5F12 itself. Confined in cylindrical, uncorrugated pores, it might be subject to thermally driven undulations, as reported earlier for poly(methyl methacrylate) and polystyrene in up to several hundred nanometer wide pores of anodized alumina membranes (AAM),76,77 resulting in the formation of periodic vacancies along the pores. As such, the observed phenomena would become an intrinsic property of the confined liquid and one might expect to find it also for other liquid−porous material combinations. However, X-ray scattering experiments on C5F12 in smooth 10 nm wide AAM pores did not show any signs of an APS upon sorption. Further, recent theoretical studies predict for solids confined in rigid, cylindrical cavities significantly larger characteristic wavelengths for instabilities to occur at78 than observed in our cooling experiments.

pecularities of the nanobubble formation upon freezing of the liquid in the nanochannels. Sorption isotherms and Saam-Cole modeling readily confirmed the morphological characterization of SBA-15 in terms of micro- and mesopores. Overcoming the inherent limitations of Saam-Cole modeling of experimental isotherms, combined sorption and X-ray scattering experiments with contrast-matching C5F12 in a SBA-15 silica substrate proofed to be very effective in revealing subtle details of the silica nanochannels microscopic structure like additional hidden periodicities along the tubular channels as well as in ascertaining a detailed wetting sequence upon adsorption and desorption of liquids in the pores. At low relative vapor pressure condensation in the micropores or the fractal folding of the walls contribute significantly to the filling fraction as readily inferred from SaamCole modeling of sorption isotherms. At higher pressures capillary condensation occurs and fills the mesopores at almost constant P (see Saam-Cole). In the pressure range between Pad < P/P0 < 1 inter grain condensation of liquid occurs in the powdery sample. The desorption process follows a similar although hysteretic path. For filling fractions above roughly 65%, scattering experiments suggest the existence of periodically arranged nanobubbles that nucleate between necks along the pore axis with a spacing of roughly 11.4 nm. Theoretically, this observation of nanobubbles can be traced back to the coherence length of pore-wall corrugations as proposed by Gommes et al.4 To be more precise, the formation of periodic voids in the condensed liquids upon filling reflects capillary bridging as defining mechanism for the liquid distribution along the pore, whereas in desorption cavitation triggers a similar liquid distribution as in adsorption. Since in previous studies this phenomenon was rather inferred indirectly from the shape of sorption isotherms, this finding constitutes, to the best of our knowledge, the first direct experimental evidence of cavitation in mesopores. Whereas cavitation in liquids is a well-known phenomenon, the formation of voids in solids as observed here upon liquid solidification is still under active investigation, in particular with regard to fracture formation under mechanical tensile loads.79 We do not claim, that our SBA-15 sample is representative for all SBA-15 samples. The synthesis routes for SBA-15 are manifold, and small deviations in the recipes can cause significant differences in the morphology e.g. microporosity, pore size and corrugation length. This comment in particular applies to recent results of other groups. Samples studied by Gommes4 exhibit a coherence length smaller than the threshold that allows cavitation effects in desorption and Morishige2 rules out periodic corrugations in his samples by an elaborate set of sorption studies. Our study shows that thermodynamically stable nanobubbles can be reversibly formed and removed in mesoporous solids with pore wall corrugations. Thus, it contributes to the ongoing discussion on the interplay of vapor nucleation and pore blocking effects upon capillary evaporation in mesoporous materials.68,80 An extension of the study of the thermodynamics and stability of these equilibrium nanostructures may also be of value for a better understanding of metastable, long-living nanobubbles at planar surfaces, where the rather complex nucleation and stability mechanisms are still under very active research.81

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CONCLUSION Combined sorption and X-ray scattering experiments identified a novel morphological feature, the APS with well-defined periodicity in the microscopic structure of SBA-15. Its origin convincingly traces back to hydrodynamic Rayleigh-Plateau instabilities in micelles during the templating process of SBA15, which lead to periodic corrugations along the tubular nanochannels. These corrugations are apparently responsible for a complex wetting behavior upon liquid sorption in SBA-15, which exhibits the formation of nanobubbles through liquid bridging in adsorptions and cavitation effects in desorption. An alternative explanation of the APS in terms of multimodal pore size distribution was discussed but finally failed to explain F

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Parts of this research were carried out at synchrotron light sources DORIS III and PETRA III of Deutsche Elektronensynchrotron (DESY, Hamburg, Germany), a member of the Helmholtz Association (HGF). This work has been supported by the German Science Foundation (DFG) within the Collaborative Research Initiative SFB 986, ”Tailor-Made Multi-Scale Materials Systems”, project B7, Hamburg.

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