ARTICLE pubs.acs.org/Langmuir
Cavitation and Pore Blocking in Nanoporous Glasses C. Reichenbach,*,† G. Kalies,† D. Enke,‡ and D. Klank§ †
Institute of Experimental Physics I, University of Leipzig, 5 Linnestrasse, D-04103 Leipzig, Germany Institute of Chemical Technology, University of Leipzig, 3 Linnestrasse, D-04103 Leipzig, Germany § Quantachrome GmbH & Co. KG, 12 Rudolf-Diesel-Strasse, D-85235 Odelzhausen, Germany ‡
ABSTRACT: In gas adsorption studies, porous glasses are frequently referred to as model materials for highly disordered mesopore systems. Numerous works suggest that an accurate interpretation of physisorption isotherms requires a complete understanding of network effects upon adsorption and desorption, respectively. The present article deals with nitrogen and argon adsorption at different temperatures (77 and 87 K) performed on a series of novel nanoporous glasses (NPG) with different mean pore widths. NPG samples contain smaller mesopores and significantly higher microporosity than porous Vycor glass or controlled pore glass. Since the mean pore width of NPG can be tuned sensitively, the evolution of adsorption characteristics with respect to a broadening pore network can be investigated starting from the narrowest nanopore width. With an increasing mean pore width, a H2-type hysteresis develops gradually which finally transforms into a H1-type. In this connection, a transition from a cavitationinduced desorption toward desorption controlled by pore blocking can be observed. Furthermore, we find concrete hints for a pore size dependence of the relative pressure of cavitation in highly disordered pore systems. By comparing nitrogen and argon adsorption, a comprehensive insight into adsorption mechanisms in novel disordered materials is provided.
1. INTRODUCTION For rigid solids, an adsorption hysteresis is mostly an indication of the presence of mesopores. Furthermore, the shape of the hysteresis loop can provide various information concerning the mesopore structure.1 A H1 hysteresis according to the IUPAC classification2 for instance gives evidence for a set of independent, cylindrical pores with uniform diameter. Here, adsorption hysteresis can be attributed to the existence of metastable states accompanying the vaporliquid phase transition inside the mesopores.35 In terms of the nonlocal density functional theory (NLDFT), capillary condensation involves the formation of liquid bridges and is thus delayed until the metastable vapor phase approaches the vapor-like spinodal.68 In contrast to that, it is assumed that desorption proceeds via a receding hemispherical meniscus. Since the hemispherical meniscus is already present at the pore entrance of a cylindrical pore open to either side, desorption is supposed to match the equilibrium conditions of the liquidvapor transition; that is, no nucleation barriers have to be overcome prior to desorption. In disordered mesopore systems, cavities of different shapes and sizes are interconnected to each other by narrowed transport paths; that is, some wider parts of the pore network have access to the bulk gas phase only via narrow constrictions. In such configurations, the hysteresis loop often exhibits a smooth adsorption branch and a steep desorption step (H2 hysteresis). In order to explain the origin of adsorption hysteresis by pore blocking effects, different simple models on the level of single ink-bottle pores have been developed.911 In ink-bottle pores, evaporation from the pore body is delayed because the connection to the bulk gas phase is obstructed by condensed liquid in the necks. The r 2011 American Chemical Society
evaporation from the whole bottle volume is then determined by the neck width and takes place at lower relative pressures. In more complex pore networks, the treatment of adsorption hysteresis requires more sophisticated network models which also take pore blocking and percolation phenomena into account.1216 The origin of hysteresis for disordered porous glasses was also explained without invoking the concept of pore blocking by long-time dynamics caused by a large number of metastabile states associated with a complex free-energy landscape.1719 Major progress in hysteresis research has been made with the synthesis of new ordered silica materials, e.g., SBA-1620 and FDU-1.21 For the first time, ideal model systems with ink-bottle pores were available for gas adsorption studies. The theoretical and experimental studies revealed that beside pore blocking a distinct mechanism called cavitation may influence the pore emptying.2227 Cavitation denotes the spinodal evaporation of the confined pore fluid once the limit of metastability of the stretched fluid is reached. In such a scenario, the pore body empties via the formation of vapor bubbles while the pore neck remains filled by condensed liquid. This mechanism has been simulated by Sarkisov and Monson.22 Comprehensive theoretical and experimental work by Ravikovitch et al. have led to the conclusion that both phenomena, pore blocking and cavitation, can take place in ordered ink-bottle pore systems depending on the neck size, the nature of adsorptive, and temperature.24 Received: May 25, 2011 Revised: July 7, 2011 Published: August 05, 2011 10699
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Langmuir In the case of a cavitation-induced pore emptying, evaporation occurs without any respect to the neck size. It has been argued that cavitation is also insensitive toward the shape and size of the blocked pore and only depends on temperature and the nature of adsorptive. This view was supported by the fact that for most disordered mesoporous solids the hysteresis in nitrogen adsorption isotherms at 77 K is forced to close in a very narrow pressure interval centered at about p/p0 = 0.42.1,28 However, if cavitation would be really insensitive toward the shape and size of the blocked pore, one should find a “universal pressure of cavitation” for a certain adsorptive at a given temperature. Instead, systematic investigations performed on ordered mesopore systems clearly revealed that there actually is a pore-size dependence of the relative pressure of cavitation.29 It was found that primal with a cavity diameter of about 11 nm the spinodal evaporation in the pore fluid coincide with the mechanisms present in macroscopic liquid droplets. For smaller cavities the relative pressure is noticeably shifted toward lower values. Yet even before this study, deviations from a “universal” pressure of cavitation have been reported and explained qualitatively.24,30,31 In spite of the ongoing controversies about the nature and origin of adsorption hysteresis, one can summarize the following (experimental) facts concerning pore blocking and cavitation in ink-bottle pores of ordered mesopore systems: (i) Cavitation takes place if the neck diameter in an ink-bottle pore falls below a critical value.23 (ii) With increasing temperature, an evaporation regulated by pore-blocking turns into a spinodal evaporation, i.e., cavitation.24 (iii) In narrow enough pores, the relative pressure of cavitation depends on the pore size. With decreasing cavity diameter, it is shifted to lower pressures.29 In the present work we want to show whether and to what extent the above facts are valid for disordered pore structures as well. A series of novel nanoporous glasses (NPG) with tunable mean pore widths is used as model system for disordered pore networks. On the basis of experimental nitrogen and argon adsorption isotherms at 77 and 87 K, we will discuss the issues (i), (ii), and (iii).
2. EXPERIMENTAL SECTION 2.1. Materials. The nanoporous glass samples (NPG) were prepared by leaching of phase separated initial glass beads with mean particle diameters between 100 and 200 μm. The basis of the manufacturing process is a miscibility gap in the ternary system SiO2Na2O B2O3 below the liquidus temperature. Depending on the initial glass composition, a thermal treatment may cause a phase separation in a sodium-borate-rich and a silica-rich phase under formation of microstructures with a mutual penetration. Leaching with hydrochloric acid removes the sodium-borate-rich phase and leaves behind a silica-rich matrix material hosting a three-dimensional disordered pore system.32 With a composition of 70 wt. % SiO2, 23 wt. % B2O3, and 7 wt. % Na2O, the initial glass contains a higher amount of silica compared to that of porous Vycor glass or controlled pore glass.3335 Since the quantity of leachable components in the initial glass is relatively low, very narrow pore networks can be realized. In addition, the spherical glass particles resist high heating/cooling rates without damage. Thus, there is no uncontrolled phase separation during the cooling and shaping process a further prerequisite for a precise tuning of the nanostructure by means of a controlled thermal treatment. A detailed description of the NPG synthesis is given in ref 36.
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Table 1. Selected Synthesis Parameters of Ten Different NPG Samples temperature
thermal
extraction in
extraction
[K]
treatment [h]
3 n HCl [h]
in NaOH
NPG-1 NPG-2
813 813
4 10
15 15
NPG-3
813
12
15
NPG-4
813
14
15
NPG-5
813
24
15
NPG-6
813
48
15
NPG-7
823
48
15
NPG-8*
813
30
15
0.1 n NaOH, 1 h
NPG-9* NPG-10*
813 823
48 48
15 15
0.5 n NaOH, 2 h 0.5 n NaOH, 2 h
sample
Selected synthesis parameters of the ten different NPG samples used in this study are listed in Table 1. The three samples marked with an asterisk were leached additionally with NaOH as a postsynthetic treatment. 2.2. Adsorption Measurements. The argon and nitrogen adsorption isotherms at 77 K were measured by an automated gas adsorption apparatus (Micromeritics) equipped with a turbo molecular pump. The pressure was detected via three pressure transducers with different measuring ranges (1, 10, and 1000 Torr). The sample cell was kept at 77 K by complete immersion into liquid nitrogen. An isothermal jacket was used to account for a falling nitrogen level throughout the adsorption measurement due to evaporation. The void volume of the sample cell was reduced by a filler rod. The free space of the sample cell was determined subsequent to the adsorption measurement by helium expansion to avoid possible falsification of the isotherm data in the low-pressure range (helium entrapment). In the low-pressure range, an incremental dosing routine was employed (3 cm3 (STP)/g). Uniform equilibrium criteria have been applied for all measurements. The argon adsorption isotherms at 87 K were measured by an Autosorb iQ (Quantachrome), also equipped with a turbo molecular pump and three pressure transducers. Furthermore, the reproducibility of all nitrogen isotherms was checked with this instrument. Prior to the adsorption experiments all samples were degassed for at least 10 h at 520 K under vacuum.
3. RESULTS AND DISCUSSION 3.1. Fine Tuning of the Mean Pore Width. First of all, it seems to be purposive to briefly describe some network characteristics of the investigated glass samples. In Figure 1, the nitrogen adsorption isotherms of the samples NPG-2, -3, -4, and -5 at 77 K are presented. The initial gas uptake in the low-pressure range accounts for the presence of micropores. The continuous, almost linear adsorption behavior in the midpressure region indicates a broad distribution of generally quite small mesopores. Once the largest mesopores are filled, the isotherms reach a plateau and no further adsorption takes place. The gas uptake is limited to 90 cm3 (STP)/g for each sample suggesting a constant total pore volume. In the order NPG-2 to NPG-5, the adsorption branches are only slightly shifted to higher relative pressures indicating that the production process enables a precise tuning of the mean mesopore width of the disordered pore network. With the generation of larger mesopores, a H2 hysteresis develops 10700
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Figure 2. Nitrogen adsorption at 77 K on NPG-6 and NPG-7 (adsorption: filled symbols; desorption: empty symbols). Figure 1. Nitrogen adsorption on NPG-2, -3, -4, and -5 at 77 K (adsorption: filled symbols; desorption: empty symbols).
progressively; that is, the hysteresis loop becomes larger with longer duration of the thermal treatment. NPG-2 was exposed to the shortest heat treatment, consequently it possesses the narrowest pore system and thus the at least developed H2 hysteresis loop. All four samples in Figure 1 show desorption first at a uniform pressure of p/p0 = 0.46, a characteristic value for a cavitation induced evaporation. The calculation of reliable pore sizes from the adsorption data is complicated since the pores of disordered NPG glasses deviate from ideal cylinder pores as assumed in many models computing pore size distributions. Since the knowledge of exact pore size distributions is not necessary for understanding the ongoing pore blocking and cavitation effects addressed in this paper, we will restrict ourselves to the discussion of the experimental isotherms. 3.2. Influence of the Mesopore Distribution on the Nitrogen Ad-/Desorption (i). For a certain adsorptive at a given temperature an increase of the neck diameter of an ink-bottle pore causes a transition from a cavitation-induced evaporation toward an evaporation controlled by pore blocking. In a complex pore network, however, we do not only have a single type of inkbottle pores. Depending on the mesopore distribution, interconnected pores with different size and shape realize various inkbottle configurations within the particle. If the evaporation from narrow pore networks initially is completely due to cavitation, a gradually increase of the mean pore width connects more and more parts of the pore system with the bulk gas phase via necks wide enough to permit evaporation by a receding meniscus. In the particular case of nitrogen desorption at 77 K this change of evaporation mechanisms can be observed in Figure 2. NPG-6 still shows a solely cavitation-induced evaporation at a relative pressure of p/p0 = 0.46. This becomes evident from the fact that the abrupt, almost vertical decrease of the isotherm is situated at the same relative pressure as in the case of NPG-2, -3, -4, and -5 in Figure 1. Another piece of evidence that desorption for NPG-6 is triggered by cavitation can be obtained by comparing the pore size distributions deduced from nitrogen and argon desorption following a procedure given by Thommes et al.34 We may conclude that the great majority of pores have access to the bulk gas phase only via necks smaller than the critical neck size. In contrast, NPG-7 already shows desorption at a relative pressure larger than p/p0 = 0.5. Additionally, desorption sets on less abrupt and is more “knee-shaped”. Such a desorption behavior
suggests a partial emptying of certain network parts controlled by pore blocking prior to the cavitation step. A post-treatment with NaOH after the acidic leaching step significantly increases the porosity and thus the gas uptake of the glass samples. Furthermore, the pore size distribution becomes shifted toward higher values by this measure, i.e., the mean pore width increases.36 The isotherm of NPG-8* is shown in Figure 3. The nitrogen desorption now clearly shows two distinct steps. The first step can be considered as the superposition of evaporation from unblocked pores and that from pore bodies delayed by pore blocking effects. Hereby, the neck size exceeds the critical neck diameter as specified in (i). Thus, the first desorption step reflects the pore and neck size distribution of the pore network. The second step can be attributed to cavitation in strongly blocked pore bodies. In that case, the neck size in a corresponding ink-bottle pore would be smaller than the critical one. For NPG-9* and -10* (see Figure 4), the adsorption and desorption branches are almost parallel (H1 hysteresis), a feature that can be explained in different ways. (1) According to the IUPAC, such a hysteresis type gives rise for unblocked cylindrical pores with uniform diameter. Here, neither cavitation nor pore blocking effects are supposed to regulate desorption. (2) The Kelvin-equation of capillary condensation in cylindrical pores relates the logarithm of the relative pressure to the inverse pore radius r37 ! p γVM ðAdsorptionÞ ln ¼ p0 rRT ! p ln p0
γVM ¼ 2 rRT
ðDesorptionÞ
with the surface tension γ, the molar volume VM of the condensed liquid, the gas constant R, and the temperature T. Due to this relation, an isotherm necessarily shows a H1-hyseresis upon increasing the mean pore width of the pore system, regardless of whether the pore size distribution is narrow or broad. For a large mean pore size, eventual pore blocking effects become invisible in the desorption branch. (3) A type H1 hysteresis was also explained by Morishige et al. by sample spanning evaporation events which empty almost the whole mesopore system at once.33 Again, such 10701
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Figure 3. Nitrogen adsorption on NPG-8* at 77 K (adsorption: filled symbols; desorption: empty symbols). Prior to the cavitation step (dashed, gray line), the slope of the desorption branch reflects the evaporation from blocked and unblocked pore bodies.
Figure 4. Nitrogen adsorption on NPG-9* and -10* at 77 K (adsorption: filled symbols; desorption: empty symbols).
an event becomes most likely in wide enough pore networks. 3.3. Influence of the Temperature on the Desorption Mechanism (ii). If Rasmussen et al. wrote that, “A decrease of the pore neck diameter has an effect similar to an increase of the temperature: it leads to the transition from the pore blocking to the cavitation regime of evaporation.”,24 a reduction of the temperature at a given neck size should lead vice versa to a transition from the cavitation regime of evaporation to pore blocking. Although we could not perform nitrogen adsorption at temperatures below 77 K, we could prove this statement by applying argon. Argon at 77 K has a significantly lower reduced temperature than nitrogen, i.e., the actual bath temperature divided by the critical temperature of the adsorptive (nitrogen: T/Tcrit. = 0.61, Tcrit. = 126.26 K; argon: T/Tcrit. = 0.51, Tcrit. = 150.86 K). Thus, the transition from cavitation to pore blocking as described in section 3.2 should occur already for smaller mean pore diameters. Figure 5 compares the argon isotherms measured on NPG-6 and NPG-7 at 77 K with the corresponding nitrogen isotherms at the same temperature. In the case of argon, desorption shows two distinct steps for both samples so that the idea of a partial emptying of certain network sections prior to cavitation becomes more convincing. As indicated by the arrows 1 and 2, the first desorption step now clearly shows a neck (respectively pore) size dependence; that is, desorption on NPG-7 takes place at higher pressures than on NPG-6. The lower closure point of the hysteresis loop is still related to cavitation in strongly blocked network parts, which causes a distinct step at a lower pressure for both glasses.
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Figure 5. Nitrogen (left) and argon (right) adsorption on NPG-6 and 7 at 77 K (adsorption: filled symbols; desorption: empty symbols). p* refers to the sublimation pressure of argon at 77 K.
In Figure 6, the way from cavitation to pore blocking is illustrated by a series of isotherms of NPG-6 at different reduced temperatures (T/Tcrit = 0.51, 0.58 and 0.61). The argon desorption from NPG-6 at 87 K is quite similar to the nitrogen desorption from NPG-7 at 77 K. This nicely proves that the reduced temperature and the pore width are conjugated influences upon desorption from mesopores. The comparison of nitrogen and argon adsorption on NPG-4 and -5 at 77 K (see Figure 7) finally answers the question about the narrowest pore network for which argon at 77 K already shows a transition from cavitation to pore blocking. Whereas evaporation on NPG-4 is cavitation-induced for both adsorptives, a change of the desorption mechanism is emerging in the argon isotherm of NPG-5. As in Figure 2, a “knee-shaped” desorption branch in the argon isotherm of NPG-5 suggests that some network parts can already empty before cavitation occurs. It should be mentioned that argon at 77 K is about 6.5 K below its triple point temperature. Thus it would solidify at a pressure of 201 Torr. Experimental investigations revealed that capillary condensation may still occur in pores with diameters below 12 nm. In such narrow pores, argon behaves like an undercooled liquid for which a saturation pressure of p0 = 229 Torr has been proposed.35 Considering this fact, the argon isotherms in Figure 7 terminate at a relative pressure of about p/p0 = 0.88. 3.4. Influence of the Pore Size on the Relative Pressure of Cavitation (iii). The lower closure point of the adsorption/ desorption hysteresis is often attributed to the limit of metastability of the confined liquid-like phase. Starting with the original argumentation given by Schofield38 it has been argued for a long time that this limit is linked to a certain pressure for a fixed temperature and adsorptive, whereas pore size and shape do not affect this pressure. Indeed, for the most micro- or mesoporous materials with disordered pore structure, a reunification of the adsorption and the desorption branch is located near the relative pressure of 0.421 for nitrogen at 77 K. Our measurements, however, point out that the pore size and the relative pressure of cavitation are noticeably correlated. In Figure 8, the nitrogen adsorption isotherms of NPG-1 and NPG5 at 77 K are compared. Referring to the end of the desorption plateau, which is directly attributed to delayed evaporation, a difference in the relative pressure of about 0.03 (p/p0 ≈ 0.43 for NPG-1; p/p0 ≈ 0.46 for NPG-5) is found. This result confirms recent studies on ordered mesoporous materials.29 In contrast to vertical cavitation steps for ordered materials, the steps in NPG isotherms are more blurred and therefore harder to interpret. Differences mainly arise from the broad pore 10702
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Figure 6. Nitrogen and argon adsorption on NPG-6 at different T/Tcrit values (adsorption: filled symbols; desorption: empty symbols). p* refers to the sublimation pressure of argon at 77 K.
Figure 7. Comparison of nitrogen and argon isotherms on NPG-4 and NPG-5 at 77 K (adsorption: filled symbols; desorption: empty symbols; for argon).
size distribution together with network effects attributed to highly disordered pore structures. A vapor bubble formed in a larger cavity, for instance, can invade neighboring smaller voids, a process which leads to ramified vapor clusters.39 Thus, one expects that a localized cavitation event taking place in a wider cavity advances the evaporation from smaller pores connected to it. The larger the mean diameter of the pore network, the farer-reaching is the influence of a localized cavitation event toward adjacent network parts. This explains why the slope of the desorption branch in a pressure range between p/p0 ≈ 0.400.44, i.e., the section following the desorption plateau, develops from a smoother one to an almost vertical one in the order NPG-2, -3, -4, and -5 (see Figure 1). The smoother slope for NPG-2 can be explained by independent cavitation events in distinct parts of the network with a relative pressure of cavitation depending on pore size. In this case, cavitation happens first in the largest pore bodies. After that, a gradually decreasing pressure induces cavitation in smaller pores. In contrast to that, the vertical cavitation step for NPG-5 speaks for a far-reaching “advanced cavitation”. A localized bubble formation taking place in a relatively large pore spreads into adjacent cavities causing an avalanche-like evaporation from large parts of the pore network. A further contribution to the sharper slope is given by the broader network itself. The larger the mean pore diameter is, the higher is the number of large mesopores which permit cavitation already at higher relative pressures. In the pressure range between p/p0 ≈ 0.400.44, the interplay of these aspects determines the exact shape of the desorption branch in a complicated manner. 3.5. Low Pressure Hysteresis. As can be seen from the isotherm of the NPG-1 sample (see Figure 8) but also from
Figure 8. Comparison of nitrogen isotherms (77 K) measured on NPG-1 and -5 (adsorption: filled symbols; desorption: empty symbols). The adsorption data for NPG-5 are offset vertically by 20 cm3 (STP)/g.
other isotherms (see Figure 1), the desorption branches do not fall back completely to the adsorption branches after the cavitation step. This result contradicts the thesis that for cavity diameters below 6 nm nitrogen adsorption at 77 K is reversible for any type of pores or pore arrangements.23 In order to explain the origin of the low pressure hysteresis, we performed adsorption runs longer than 150 h for an isotherm with very long equilibrium times per pressure point. However, no systematic changes in the shape or size of the isotherms were found, and the low pressure hysteresis remained. In a reproducible way, the low pressure hysteresis becomes more and more pronounced with decreasing mean pore size. This might be caused by extreme transport restrictions in the highly tortuous, disordered nanopores of the large spherical NPG particles (diameters between 100 and 200 μm) or even by pore blocking effects on a micropore level. It is conceivable that the concepts explaining evaporation from mesopores fail to explain an evaporation delay due to extreme confinement effects related to complex nanopore structures in larger particles.
4. SUMMARY Nitrogen and argon adsorption experiments at 77 and 87 K were performed on a series of novel nanoporous glass beads with tunable mean pore widths. The fine-tuning of the mean pore diameter allowed us to study pore blocking and cavitation effects in highly disordered networks. Recent research results concerning adsorption in well-ordered ink-bottle pores were compared with those in complex pore networks. The following differences and similarities were found: 10703
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Langmuir (i) An increase of the mean pore width of NPG leads from a cavitation-induced evaporation to a pore emptying delayed by pore-blocking effects. Due to a broad pore size distribution this transition proceeds gradually. As the network becomes broader, a growing part of the network can already empty at higher pressures while other parts remain filled until the onset of cavitation. In NPG samples, the relative pressure of evaporation controlled by pore blocking correlates sensitively to the neck sizes in the pore network, whereas the relative pressure of cavitation shows less sensitive pore size dependence. (ii) An increase of the reduced temperature (T/Tcrit) leads from the pore blocking regime back to the cavitation regime and has therewith an effect similar to a decrease of the neck size. Again, the transition occurs gradually as a result of the relatively broad pore size distribution. (iii) A pore-size dependent pressure of cavitation for disordered nanopore structures with a broad pore size distribution becomes evident. The relative pressure of cavitation is shifted toward lower values within sufficiently narrow mesopore structures. Here, however, the results are blurred due to “advanced cavitation”; that is, a vapor bubble invades adjacent pores and pore size dependent cavitation in distinct parts of the pore network. These two effects determine the slope of the desorption branch in a pressure range between p/p0 ≈ 0.400.44.
’ AUTHOR INFORMATION Corresponding Author
*Phone: 00493419732513. Fax: 00493419732549. E-mail:
[email protected].
’ ACKNOWLEDGMENT The financial support for this project by Deutsche Forschungsgemeinschaft (DFG, KA 1560/4-2 and IRTG 1056/2 “Diffusion in Porous Materials”) is gratefully acknowledged. ’ REFERENCES
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