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Micro-imaging of liquid–vapor phase transition in nano-channels
Microporous and Mesoporous Materials 214 (2015) 143e148
Contents lists available at ScienceDirect
Microporous and Mesoporous Materials journal homepage: www.elsevier.com/locate/micromeso
Micro-imaging of liquidevapor phase transition in nano-channels € rg Lenzner a, Christian Chmelik a, Alexander Lauerer a, Philipp Zeigermann a, Jo b a, * € €rger a Matthias Thommes , Rustem Valiullin , Jorg Ka a b
Faculty of Physics and Earth Sciences, University of Leipzig, Leipzig, Germany Quantachrome Instruments, Boynton Beach, FL, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 January 2015 Received in revised form 20 April 2015 Accepted 2 May 2015 Available online 11 May 2015
Mesoporous silicon accommodating structured nano-channels is employed as a host material for recording the evolution of liquidevapor phase transitions in nanoporous materials upon molecular adsorption and desorption. Analysis is based on the application of micro-imaging via IR microscopy revealing the spatial-temporal dependence of guest concentrations within the material as a function of the chosen pressure steps. In this way, phase transitions become observable in the context of their local environment and may be correlated with the pore architecture by immediate experimental evidence. © 2015 Elsevier Inc. All rights reserved.
Keywords: Phase transition Capillary condensation Sorption hysteresis Porous silicon IR microscopy
1. Introduction In addition to temperature and pressure, the phase state of mesoporous host-guest systems is well known to depend on the system's history, that is, on whether the guest pressure in the surrounding atmosphere has been attained from lower or higher values, namely via ad- or desorption. This phenomenon is referred to as sorption hysteresis and serves, since more than a century, as a basis for estimating the pore sizes of such materials [1,2]. Phase state and pore geometry are, conceptually, correlated by the Kelvin equation [3].
2gy : lnðp=p0 Þ ¼ rRT
(1)
It indicates that, given a liquid phase with a meniscus of radius r within the pore space, this phase is at equilibrium with the surrounding gas phase at already a pressure p which is smaller than the saturation pressure p0 of the bulk liquid. The terms g, y, R and T denote, respectively, surface tension, molar volume, the universal gas constant and temperature. Differences in the radius r of the meniscus at the transition from gas to liquid (capillary condensation, starting with a surface layer and, hence, an effective meniscus
* Corresponding author. E-mail address: [email protected] (R. Valiullin). http://dx.doi.org/10.1016/j.micromeso.2015.05.005 1387-1811/© 2015 Elsevier Inc. All rights reserved.
radius of twice the pore radius) and from liquid to gas (capillary evaporation, with r approaching the pore radius) are immediately seen to correspond, via Equation (1), to different pressures. Equations correlating phase transitions with pore geometry have, since this time, been subject to continuous improvement concerning both microscopic fluid structure and phase equilibrium of confined ensembles [4e7]. The availability of ordered porous materials accommodating nano-cylindrical pores [8] made them particularly useful model systems for validating theoretical developments [9,10]. In increasing detail, the influence of the local geometric environment experienced by the guest molecules during phase transition has recently become a subject of intense studies [11e14]. The option to tailor pore geometry in a desired way is provided, among others, by electro-chemically etched mesoporous silicon [15,16] allowing to produce nano-cylindrical pores with purposefully varied pore diameters [17e20]. In this way, for the first time the influence of pore hierarchies and their arrangement on phase transition could have been subject to direct investigation. Stimulated by a continuously increasing diversity of nanoporous materials, efforts to improve the correlation between pore architecture and phase transition have thus, up to date, remained a topic of intense research [21e24]. About the rate of these transitions and their intrinsic mechanisms, however, there is still little known [25e29]. This deficiency in our knowledge is mainly related to the lack of experimental data
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correlating the rate of equilibration with the pore structure. Whilst the system's response to pressure variation outside hysteresis is well-known to be governed by molecular diffusion, with equilibration over well-defined and easily predictable time scales [30], uptake and release within the range of hysteresis are found to be dramatically slowed down [20,27,31,32]. First quantitative studies of this retardation have been performed with Vycor porous glass, using the NMR signal intensity as a measure of the overall amount of guest molecules [27]. However, neither the technique of measurement nor the system under study allow, by their very nature, to directly correlate the changes thus observed with the systems pore structure. Here we report of how electro-chemically etched mesoporous silicon was successfully applied to provide exactly this information by micro-imaging via IR microscopy [33]. 2. Experimental results Fig. 1 introduces into the mesoporous host systems considered in this study. As a starting material for both systems under study, single-crystalline < 100 > oriented p-type silicon wafers were used.
By tuning the current density and the time of etching, the pore size and length of the etched channels were adjusted to give rise to the two channel geometries, represented schematically in Fig. 1a and b and, by electron microscopic images, in Fig. 1c and d. Details about the preparation procedure are contained in the Supporting Information (SI). As a precondition for micro-imaging by IR microscopy, platelets with side faces parallel to the direction of the nano-channels had to be cut out of the silicon wafers. This was accomplished by using a focused beam of Gaþ ions for wellpositioned silicon sputtering, using XeF2 for gas-assisted etching and to evacuate waste products. Subsequently, by means of a piezosteered needle (Fig. 1e), the platelets were positioned within the IR cell. IR micro-imaging was accomplished by means of a Fouriertransform IR microscope (Bruker Hyperion 3000) [34]. The use of a focal plane array (FPA) detector allowed the observation of guest distributions with a spatial and temporal resolution of about 10 mm and 90 s, respectively. Complementary measurements with improved temporal resolution were performed with a singleelement detector (SE) yielding the total amount of guest
Fig. 1. Sketch of the two silicon cuboids under investigation with their corresponding dimension. Fig. 1a shows the sample with one 5 nm pore section continued by one 10 nm pore section. Fig. 1b illustrates the sample with three 5 nm and two 10 nm pore sections arranged in an alternating fashion. In each case three channels are visualized exemplarily and idealized in a schematic way (not true to scale). The channels proceed from top to bottom and are open on both sides. As well shown are electron microscopic images depicting the side view on the silicon cuboids with two pore sections (1c) and five pore sections (1d) prepared by ion beam milling, together with zoom-in views of the etched mesoporous layers. The different layers with either 5 nm or 10 nm pores can be distinguished optically. Fig. 1e shows the view on top of a dissected porous silicon platelet attached to a piezo-driven needle within the sample chamber of the FIB (focused ion beam) setup. Subsequently, the sample was placed into an IR cell. In this view, the pores are directed perpendicular to the plane of observation.
A. Lauerer et al. / Microporous and Mesoporous Materials 214 (2015) 143e148
molecules within the sample with time resolution down to seconds. For transmissibility enhancement, the host material was kept at 450 C for several hours (heating rate 1 K/min) under pure oxygen atmosphere. By this procedure, the inner silicon surface of freshly prepared porous silicon, initially terminated by SieH or SieSi moieties, is replaced by silicon dioxide film [16] (without affecting the pore structure, see SI 2.2). Using benzene as a guest molecule, the IR signal was within the linearity range of the FPA detector throughout our measurements. Fig. 2 summarizes the results of the micro-imaging studies during benzene uptake and release within the two-channel silicon sample shown in Fig. 1a and c. The representations in the top show typical examples of the images obtained by IR microscopy by use of the focal plane array (FPA) detector. They represent the mean concentration (in observation direction, i.e. perpendicular to the xey plane) of benzene attained at equilibrium at the indicated pressures after pressure steps of 5 mbar during adsorption (a) and desorption (b), respectively. Integration of the concentrations in ydirection yields the profiles shown, for selected pressures, in Fig. 2c for adsorption and 2d for desorption. The complete file of profiles is
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given in the Supporting Information (SI 2.1). Note that the images are not extended towards the very end of the 10 nm nano-channels on the right-hand side of the silicon sample. It turned out (see SI 2.3) that, in this part, sample pretreatment did not give rise to the intended enhancement in IR transmissibility. The data shown in Fig. 2e have been obtained by use of the single element (SE) detector. Signal intensity as a function of the applied pressure yields the sorption isotherm which has been plotted after equilibration following subsequent pressure steps both upwards and downwards. In this way, the well-known distinction between an adsorption and desorption branch became visible. It was checked that the signal intensity thus determined by the SE detector was in satisfactory agreement with the integral over the concentration profiles shown in Fig. 2c and d. Application of the SE detector allows to additionally determine the time dependence of the pressure-step-induced increase or decrease in concentration towards the new equilibration value. The time constants of this process are shown in Fig. 2e, together with the sorption isotherm. Examples of the equilibration curves are shown in Fig. 2f (adsorption) and 2g (desorption).
Fig. 2. Selected FPA maps of the adsorption (2a) and desorption (2b) process of benzene in the sample containing two different pore sections with respective pressures (end of pressure step). The color scale for the relative concentrations reaches from red, corresponding to low benzene concentrations up to blue, which corresponds to high benzene concentrations. At a benzene pressure of 75 mbar the 5 nm pores, located on the left half, are almost completely filled, while the 10 nm pores on the right are still nearly empty. At 115 mbar also the 10 nm pore section is saturated with benzene. During desorption, the 5 nm pore section remains saturated down to 55 mbar, one pressure step further (at 50 mbar) a concentration gradient within the smaller pores was found, not being observed during adsorption. Fig. 2c,d shows the concentration profiles for selected pressures (data indicate final pressures after the pressure steps) of adsorption (desorption) as resulting by averaging over a selected area of the FPA maps. Note the distinct difference in the guest distributions during filling and emptying within the 5 nm pores (located at the left half). Fig. 2e shows the sorption isotherm obtained using the single element detector. It exhibits two separate hysteresis loops, easily to be attributed to the 5 and 10 nm pores, respectively. The time constants of uptake and release by each individual pressure step are as well presented. Uptake kinetics is seen to be dramatically slowed down at the onset of hysteresis, while release kinetics is slowed down upon leaving the range of hysteresis. Selected curves of uptake and release are shown in Fig. 2f and g. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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The corresponding information about the results of microimaging with the five-channel silicon sample (Fig. 1b and d) is contained in Fig. 3aef. Here IR transmissibility has been ensured over the whole of the sample. With this sample we were, moreover, able to identify a pressure step giving rise to an equilibration process slow enough for being recorded in subsequent micro-images. The resulting profiles are shown in Fig. 3f. 3. Discussion The novel type of information provided by micro-imaging of phase transitions within structured nano-channels as exemplified by Figs. 2 and 3 may be summarized as follows: (i) In addition to differences in the total amount of guest molecules during ad- and desorption as recorded in conventional hysteresis experiments, now also differences in the distribution of the guest molecules within the nanoporous host system become accessible by immediate experimental observation. In this way, the pore architecture is nicely reflected by the images of guest distribution, showing, e.g., that
saturation in narrow-channel divisions occurs at notably lower pressures than in wide-channel divisions. (ii) The rate of sample equilibration is found to be slowed down in pressure regions with the most significant changes in concentration. This is related to the well-known tendency of retardation in equilibration during phase transitions. In Refs. [27,31], guest equilibration during phase transition in stochastic pore spaces was found to occur as a concerted action of two mechanisms, with the slow mode as the direct result of disorder, rendering the phase growth to be driven by thermal activations and, thus, leading to dramatic retardation in kinetics. The same behavior is also observed in the present studies during molecular uptake where adsorption is as well seen to proceed in two steps (Fig. 2f and SI 3.3 (Fig. S7a)), with the first one too fast for being resolved and with the time constants of the second one given in Figs. 2e and 3e. There is, however, no clearly perceptible separation between these two processes during desorption, so that equilibration is reasonably well approached by a single exponential (Fig. 2g and SI 3.3 (Fig. S7b)), with the time constants given in Figs. 2e and 3e.
Fig. 3. Selected FPA maps of the adsorption (3a) and desorption (3b) process of benzene in the sample with five pore sections. At 65 mbar, the benzene concentration in the 5 nm pores is clearly seen to exceed the concentration in the 10 nm pores. At 124 mbar, also the 10 nm pore sections are saturated with benzene. Fig. 3c,d shows the concentration profiles after selected pressure steps (data represent pressures at the end of the pressure steps) during adsorption (desorption) determined by averaging over a selected area of the FPA maps, exhibiting a pronounced asymmetry in the filling of the 10 nm pores, with the pores on the left filled first and remaining filled, upon desorption, down to 80 mbar, with the big pores on the right side starting to empty at already 90 mbar. Emptying of the big pores is seen to occur with the surrounding smaller pores remaining saturated by guest molecules. Fig. 3e shows the time constants of uptake and release, jointly with the isotherms. The time constant of the one-step emptying process of the 10 nm pore section located on the left side of the sample exceeds all other time constants of both adsorption and desorption. By considering, during this interval, a small enough pressure step, we did even succeed in slowing down the desorption process to such an extent that it has become possible to record profile evolution. These data are shown in Fig. 3f. A slight change in the lab temperature (see SI 3.2) did, in addition, require a corresponding change in the pressure data actually chosen.
A. Lauerer et al. / Microporous and Mesoporous Materials 214 (2015) 143e148
(iii) It is interesting to note that the shape of the concentration profiles in the segment containing the 5 nm pores (Fig. 2c, left half of the profiles) reveals another difference between ad- and desorption: During adsorption, after each individual pressure step the concentration in this segment is found to be almost constant over the whole length, indicating that the mono- and multilayers of guest molecules emerge essentially homogenously within the channels. For desorption, however, there is a distinct exception from this pattern: Here, after the complete emptying of the large pores, in the narrow channels a striking asymmetry following a pressure step from 55 to 50 mbar is observed. This observation can be correlated with the fact that the process of wet-etching gives rise to a tiny (of the order of a few Ångstroms per mm) increase of the average pore diameter with increasing etching depth. Adsorption in these frustum-like strongly corrugated channels is controlled by the formation of liquid bridges in the pore throats, which are distributed more or less homogeneously in space. Desorption, on the other hand, occurs by the invading gas front and is, therefore, subject to stronger geometric control. It may further be altered by asymmetric boundary conditions for the mass transfer. Which of these two factors plays the dominant role for desorption shall be explored in further studies. (iv) The occurrence of two separate hysteresis loops (Fig. 2e and SI 2.2) in the sorption isotherms of the two-channel systems (Fig. 1a and c) clearly indicates the presence of two types of channels with notably different diameters. The correlation of the capillary-evaporation and condensation pressures with the pore sizes of the mesoporous silicon is, however, a difficult problem due to a strong structural disorder [35,36]. From a purely thermodynamic point of view, corresponding experiments with the five-channel sample (Fig. 1b and d) have been expected to provide similar results. By contrast, however, there is no clear distinction anymore between two loops. We have to take this as a further indication of deviations between the idealized pore structure as indicated in Fig. 1a and b and reality, emphasizing the intricacy of the pore architecture of mesoporous silicon and the difficulties with ensuring well-defined geometric properties of the pore space. In particular, we anticipate that, due to increasing of the average pore size with etching depth [37], the overlap between the pore sizes in the pore section with different average pore sizes increases. (v) In the five-channel sample (Fig. 1b and d), the 10 nm channel segments are confined by 5 nm channels. There are two possibilities that, upon desorption, a pore surrounded by narrower pores may be emptied: either only after the adjacent ones have been emptied (i.e. after the release of pore blocking) or by molecules getting out of the cage under consideration, irrespective of the fact that this cage is still surrounded by saturated ones [11]. The latter process, which appears with sufficiently small necks between adjacent cavities at sufficiently low pressures, is referred to as cavitation. In porous silicon, a phenomenon of emptying similar to cavitation, but occurring at pressures notably higher than predicted by theory, is observed [19,20]. The mechanism of this process is unknown and is under current debate. In conventional sorption studies, the decision between different emptying scenarios, namely controlled by pore blocking or occurring in two steps, cannot be based on immediate experimental evidence due to a complex structure of the material under study (mesoscalic disorder, spatial variation of porosity, etc.). Micro-imaging overcomes this deficiency by its very nature. Immediate evidence of the
147
occurrence of advanced emptying of the larger cavities is, e.g., provided by the profiles shown in Fig. 3d during desorption, after pressure steps to 75 mbar (see SI 3.1 and 3.2). Here, emptying of the wider channels is clearly seen to take place with the narrow channels still being saturated by guest molecules. (vi) Profiting from the dramatic slowing down of equilibration during emptying of the larger cavities in the ink-bottle pores, we have been able to even record the evolution of guest distributions (see Fig. 3f). As a most remarkable feature, guest profiles are seen to remain, upon desorption, symmetrical with respect to the center of the segment.
4. Conclusions To summarize, we have presented the results of micro-imaging of gaseliquid phase transitions under nanoscopic confinements. We have shown that the method used provides a most direct approach to study spatio-temporal correlations of the sorption process. In addition to its strong sensitivity to spatially-resolved phase equilibria, which may be used as contrasting mechanism for optical tomography of nano-structured materials, the potential to record the evolution of molecular distributions has shown to open new options for studying mass transfer phenomena in these materials under conditions of multi-phase equilibria. Acknowledgments Financial support by the German Science Foundation (DFG), notably within the frame of the International Research Training Group “Diffusion in Porous Materials” is gratefully acknowledged. We are deeply obliged to Prof. Dr. Kurt Binder (Mainz) for enlightening discussions. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.micromeso.2015.05.005. References [1] D.H. Everett, Adsorption Hysteresis, Marcel Dekker, Inc., New York, 1967, pp. 1055e1113. [2] M. Thommes, K.A. Cychosz, J. Int. Adsorpt. Soc. 20 (2e3) (2014) 233e250. [3] L.H. Cohan, J. Am. Chem. Soc. 66 (1) (1944) 98e105. [4] P.C. Ball, R. Evans, Langmuir 5 (3) (1989) 714e723. [5] A.V. Neimark, P.I. Ravikovitch, A. Vishnyakov, Phys. Rev. E 62 (2) (2000) 1493e1496. [6] P.A. Monson, Microporous Mesoporous Mat. 160 (2012) 47e66. [7] D. Wilms, A. Winkler, P. Virnau, K. Binder, Phys. Rev. Lett. 105 (4) (2010) 045701. [8] U. Ciesla, F. Schüth, Microporous Mesoporous Mat. 27 (2e3) (1999) 131e149. [9] K. Morishige, M. Shikimi, J. Chem. Phys. 108 (18) (1998) 7821e7824. €hn, M. Fro €ba, Appl. Surf. Sci. 196 (1e4) (2002) 239e249. [10] M. Thommes, R. Ko [11] P. Ravikovitch, A. Neimark, Langmuir 18 (25) (2002) 9830e9837. [12] B. Libby, P.A. Monson, Langmuir 20 (10) (2004) 4289e4294. [13] K. Morishige, N. Tateishi, J. Chem. Phys. 119 (4) (2003) 2301e2306. [14] G. Mistura, A. Pozzato, G. Grenci, L. Bruschi, M. Tormen, Nat. Commun. 4 (2013) article number 2966. [15] L. Canham, Handbook of Porous Silicon, Springer International Publishing, 2015. [16] M.J. Sailor, Porous Silicon in Practice, Wiley-VCH, 2012. [17] A. Khokhlov, R. Valiullin, J. K€ arger, F. Steinbach, A. Feldhoff, New. J. Phys. 9 (8) (2007) 272. [18] F. Casanova, C.E. Chiang, A.M. Ruminski, M.J. Sailor, I.K. Schuller, Langmuir 28 (17) (2012) 6832e6838. [19] A. Grosman, C. Ortega, Langmuir 27 (6) (2011) 2364e2374. [20] D. Wallacher, N. Künzner, D. Kovalev, N. Knorr, K. Knorr, Phys. Rev. Lett. 92 (19) (2004) 195704. [21] K. Morishige, M. Tateishi, F. Hirose, K. Aramaki, Langmuir 22 (22) (2006) 9220e9224.
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[22] L. Bruschi, G. Mistura, L. Liu, W. Lee, U. Gosele, B. Coasne, Langmuir 26 (14) (2010) 11894e11898. [23] O. Petrov, I. Furo, Microporous Mesoporous Mat. 138 (1e3) (2011) 221e227. [24] D. Kondrashova, R. Valiullin, Microporous Mesoporous Mat. 178 (0) (2013) 15e19. [25] L.D. Gelb, A.C. Hopkins, Nano Lett. 2 (11) (2002) 1281e1285. [26] J.W. Lee, W.G. Shim, H. Moon, Microporous Mesoporous Mat. 73 (2004) 109e119. €rger, H.J. Woo, F. Porcheron, [27] R. Valiullin, S. Naumov, P. Galvosas, J. Ka P.A. Monson, Nature 443 (7114) (2006) 965e968. [28] M. Dvoyashkin, A. Khokhlov, R. Valiullin, J. K€ arger, J. Chem. Phys. 129 (15) (2008) 154702e154706. [29] D. Schneider, R. Valiullin, P.A. Monson, Langmuir 30 (5) (2014) 1290e1294. [30] J. K€ arger, D.M. Ruthven, D. Theodorou, Diffusion in Zeolites and Other Nanoporous Materials, Wiley-VCH, Weinheim, 2012.
€rger, P.A. Monson, Magn. Reson. [31] R. Valiullin, S. Naumov, P. Galvosas, J. Ka Imaging 25 (4) (2007) 481e484. [32] H. Yanagihara, K. Yamashita, A. Endo, H. Daiguji, J. Phys. Chem. C 117 (42) (2013) 21795e21802. €rger, T. Binder, C. Chmelik, F. Hibbe, H. Krautscheid, R. Krishna, [33] J. Ka J. Weitkamp, Nat. Mater. 13 (4) (2014) 333e343. [34] C. Chmelik, L. Heinke, R. Valiullin, J. K€ arger, Chem. Ing. Tech. 82 (6) (2010) 779e804. €rger, P.A. Monson, Phys. Rev. E 78 (6) [35] S. Naumov, A. Khokhlov, R. Valiullin, J. Ka (2008) 060601e060604. [36] S. Naumov, R. Valiullin, J. K€ arger, P.A. Monson, Phys. Rev. E 80 (3) (2009) 031607. [37] A. Khokhlov, Nanoporous Silicon: Structural Characterization using NMR and Applications (Phd thesis), University of Leipzig, 2009.
Contents lists available at ScienceDirect
Microporous and Mesoporous Materials journal homepage: www.elsevier.com/locate/micromeso
Micro-imaging of liquidevapor phase transition in nano-channels € rg Lenzner a, Christian Chmelik a, Alexander Lauerer a, Philipp Zeigermann a, Jo b a, * € €rger a Matthias Thommes , Rustem Valiullin , Jorg Ka a b
Faculty of Physics and Earth Sciences, University of Leipzig, Leipzig, Germany Quantachrome Instruments, Boynton Beach, FL, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 January 2015 Received in revised form 20 April 2015 Accepted 2 May 2015 Available online 11 May 2015
Mesoporous silicon accommodating structured nano-channels is employed as a host material for recording the evolution of liquidevapor phase transitions in nanoporous materials upon molecular adsorption and desorption. Analysis is based on the application of micro-imaging via IR microscopy revealing the spatial-temporal dependence of guest concentrations within the material as a function of the chosen pressure steps. In this way, phase transitions become observable in the context of their local environment and may be correlated with the pore architecture by immediate experimental evidence. © 2015 Elsevier Inc. All rights reserved.
Keywords: Phase transition Capillary condensation Sorption hysteresis Porous silicon IR microscopy
1. Introduction In addition to temperature and pressure, the phase state of mesoporous host-guest systems is well known to depend on the system's history, that is, on whether the guest pressure in the surrounding atmosphere has been attained from lower or higher values, namely via ad- or desorption. This phenomenon is referred to as sorption hysteresis and serves, since more than a century, as a basis for estimating the pore sizes of such materials [1,2]. Phase state and pore geometry are, conceptually, correlated by the Kelvin equation [3].
2gy : lnðp=p0 Þ ¼ rRT
(1)
It indicates that, given a liquid phase with a meniscus of radius r within the pore space, this phase is at equilibrium with the surrounding gas phase at already a pressure p which is smaller than the saturation pressure p0 of the bulk liquid. The terms g, y, R and T denote, respectively, surface tension, molar volume, the universal gas constant and temperature. Differences in the radius r of the meniscus at the transition from gas to liquid (capillary condensation, starting with a surface layer and, hence, an effective meniscus
* Corresponding author. E-mail address: [email protected] (R. Valiullin). http://dx.doi.org/10.1016/j.micromeso.2015.05.005 1387-1811/© 2015 Elsevier Inc. All rights reserved.
radius of twice the pore radius) and from liquid to gas (capillary evaporation, with r approaching the pore radius) are immediately seen to correspond, via Equation (1), to different pressures. Equations correlating phase transitions with pore geometry have, since this time, been subject to continuous improvement concerning both microscopic fluid structure and phase equilibrium of confined ensembles [4e7]. The availability of ordered porous materials accommodating nano-cylindrical pores [8] made them particularly useful model systems for validating theoretical developments [9,10]. In increasing detail, the influence of the local geometric environment experienced by the guest molecules during phase transition has recently become a subject of intense studies [11e14]. The option to tailor pore geometry in a desired way is provided, among others, by electro-chemically etched mesoporous silicon [15,16] allowing to produce nano-cylindrical pores with purposefully varied pore diameters [17e20]. In this way, for the first time the influence of pore hierarchies and their arrangement on phase transition could have been subject to direct investigation. Stimulated by a continuously increasing diversity of nanoporous materials, efforts to improve the correlation between pore architecture and phase transition have thus, up to date, remained a topic of intense research [21e24]. About the rate of these transitions and their intrinsic mechanisms, however, there is still little known [25e29]. This deficiency in our knowledge is mainly related to the lack of experimental data
144
A. Lauerer et al. / Microporous and Mesoporous Materials 214 (2015) 143e148
correlating the rate of equilibration with the pore structure. Whilst the system's response to pressure variation outside hysteresis is well-known to be governed by molecular diffusion, with equilibration over well-defined and easily predictable time scales [30], uptake and release within the range of hysteresis are found to be dramatically slowed down [20,27,31,32]. First quantitative studies of this retardation have been performed with Vycor porous glass, using the NMR signal intensity as a measure of the overall amount of guest molecules [27]. However, neither the technique of measurement nor the system under study allow, by their very nature, to directly correlate the changes thus observed with the systems pore structure. Here we report of how electro-chemically etched mesoporous silicon was successfully applied to provide exactly this information by micro-imaging via IR microscopy [33]. 2. Experimental results Fig. 1 introduces into the mesoporous host systems considered in this study. As a starting material for both systems under study, single-crystalline < 100 > oriented p-type silicon wafers were used.
By tuning the current density and the time of etching, the pore size and length of the etched channels were adjusted to give rise to the two channel geometries, represented schematically in Fig. 1a and b and, by electron microscopic images, in Fig. 1c and d. Details about the preparation procedure are contained in the Supporting Information (SI). As a precondition for micro-imaging by IR microscopy, platelets with side faces parallel to the direction of the nano-channels had to be cut out of the silicon wafers. This was accomplished by using a focused beam of Gaþ ions for wellpositioned silicon sputtering, using XeF2 for gas-assisted etching and to evacuate waste products. Subsequently, by means of a piezosteered needle (Fig. 1e), the platelets were positioned within the IR cell. IR micro-imaging was accomplished by means of a Fouriertransform IR microscope (Bruker Hyperion 3000) [34]. The use of a focal plane array (FPA) detector allowed the observation of guest distributions with a spatial and temporal resolution of about 10 mm and 90 s, respectively. Complementary measurements with improved temporal resolution were performed with a singleelement detector (SE) yielding the total amount of guest
Fig. 1. Sketch of the two silicon cuboids under investigation with their corresponding dimension. Fig. 1a shows the sample with one 5 nm pore section continued by one 10 nm pore section. Fig. 1b illustrates the sample with three 5 nm and two 10 nm pore sections arranged in an alternating fashion. In each case three channels are visualized exemplarily and idealized in a schematic way (not true to scale). The channels proceed from top to bottom and are open on both sides. As well shown are electron microscopic images depicting the side view on the silicon cuboids with two pore sections (1c) and five pore sections (1d) prepared by ion beam milling, together with zoom-in views of the etched mesoporous layers. The different layers with either 5 nm or 10 nm pores can be distinguished optically. Fig. 1e shows the view on top of a dissected porous silicon platelet attached to a piezo-driven needle within the sample chamber of the FIB (focused ion beam) setup. Subsequently, the sample was placed into an IR cell. In this view, the pores are directed perpendicular to the plane of observation.
A. Lauerer et al. / Microporous and Mesoporous Materials 214 (2015) 143e148
molecules within the sample with time resolution down to seconds. For transmissibility enhancement, the host material was kept at 450 C for several hours (heating rate 1 K/min) under pure oxygen atmosphere. By this procedure, the inner silicon surface of freshly prepared porous silicon, initially terminated by SieH or SieSi moieties, is replaced by silicon dioxide film [16] (without affecting the pore structure, see SI 2.2). Using benzene as a guest molecule, the IR signal was within the linearity range of the FPA detector throughout our measurements. Fig. 2 summarizes the results of the micro-imaging studies during benzene uptake and release within the two-channel silicon sample shown in Fig. 1a and c. The representations in the top show typical examples of the images obtained by IR microscopy by use of the focal plane array (FPA) detector. They represent the mean concentration (in observation direction, i.e. perpendicular to the xey plane) of benzene attained at equilibrium at the indicated pressures after pressure steps of 5 mbar during adsorption (a) and desorption (b), respectively. Integration of the concentrations in ydirection yields the profiles shown, for selected pressures, in Fig. 2c for adsorption and 2d for desorption. The complete file of profiles is
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given in the Supporting Information (SI 2.1). Note that the images are not extended towards the very end of the 10 nm nano-channels on the right-hand side of the silicon sample. It turned out (see SI 2.3) that, in this part, sample pretreatment did not give rise to the intended enhancement in IR transmissibility. The data shown in Fig. 2e have been obtained by use of the single element (SE) detector. Signal intensity as a function of the applied pressure yields the sorption isotherm which has been plotted after equilibration following subsequent pressure steps both upwards and downwards. In this way, the well-known distinction between an adsorption and desorption branch became visible. It was checked that the signal intensity thus determined by the SE detector was in satisfactory agreement with the integral over the concentration profiles shown in Fig. 2c and d. Application of the SE detector allows to additionally determine the time dependence of the pressure-step-induced increase or decrease in concentration towards the new equilibration value. The time constants of this process are shown in Fig. 2e, together with the sorption isotherm. Examples of the equilibration curves are shown in Fig. 2f (adsorption) and 2g (desorption).
Fig. 2. Selected FPA maps of the adsorption (2a) and desorption (2b) process of benzene in the sample containing two different pore sections with respective pressures (end of pressure step). The color scale for the relative concentrations reaches from red, corresponding to low benzene concentrations up to blue, which corresponds to high benzene concentrations. At a benzene pressure of 75 mbar the 5 nm pores, located on the left half, are almost completely filled, while the 10 nm pores on the right are still nearly empty. At 115 mbar also the 10 nm pore section is saturated with benzene. During desorption, the 5 nm pore section remains saturated down to 55 mbar, one pressure step further (at 50 mbar) a concentration gradient within the smaller pores was found, not being observed during adsorption. Fig. 2c,d shows the concentration profiles for selected pressures (data indicate final pressures after the pressure steps) of adsorption (desorption) as resulting by averaging over a selected area of the FPA maps. Note the distinct difference in the guest distributions during filling and emptying within the 5 nm pores (located at the left half). Fig. 2e shows the sorption isotherm obtained using the single element detector. It exhibits two separate hysteresis loops, easily to be attributed to the 5 and 10 nm pores, respectively. The time constants of uptake and release by each individual pressure step are as well presented. Uptake kinetics is seen to be dramatically slowed down at the onset of hysteresis, while release kinetics is slowed down upon leaving the range of hysteresis. Selected curves of uptake and release are shown in Fig. 2f and g. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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The corresponding information about the results of microimaging with the five-channel silicon sample (Fig. 1b and d) is contained in Fig. 3aef. Here IR transmissibility has been ensured over the whole of the sample. With this sample we were, moreover, able to identify a pressure step giving rise to an equilibration process slow enough for being recorded in subsequent micro-images. The resulting profiles are shown in Fig. 3f. 3. Discussion The novel type of information provided by micro-imaging of phase transitions within structured nano-channels as exemplified by Figs. 2 and 3 may be summarized as follows: (i) In addition to differences in the total amount of guest molecules during ad- and desorption as recorded in conventional hysteresis experiments, now also differences in the distribution of the guest molecules within the nanoporous host system become accessible by immediate experimental observation. In this way, the pore architecture is nicely reflected by the images of guest distribution, showing, e.g., that
saturation in narrow-channel divisions occurs at notably lower pressures than in wide-channel divisions. (ii) The rate of sample equilibration is found to be slowed down in pressure regions with the most significant changes in concentration. This is related to the well-known tendency of retardation in equilibration during phase transitions. In Refs. [27,31], guest equilibration during phase transition in stochastic pore spaces was found to occur as a concerted action of two mechanisms, with the slow mode as the direct result of disorder, rendering the phase growth to be driven by thermal activations and, thus, leading to dramatic retardation in kinetics. The same behavior is also observed in the present studies during molecular uptake where adsorption is as well seen to proceed in two steps (Fig. 2f and SI 3.3 (Fig. S7a)), with the first one too fast for being resolved and with the time constants of the second one given in Figs. 2e and 3e. There is, however, no clearly perceptible separation between these two processes during desorption, so that equilibration is reasonably well approached by a single exponential (Fig. 2g and SI 3.3 (Fig. S7b)), with the time constants given in Figs. 2e and 3e.
Fig. 3. Selected FPA maps of the adsorption (3a) and desorption (3b) process of benzene in the sample with five pore sections. At 65 mbar, the benzene concentration in the 5 nm pores is clearly seen to exceed the concentration in the 10 nm pores. At 124 mbar, also the 10 nm pore sections are saturated with benzene. Fig. 3c,d shows the concentration profiles after selected pressure steps (data represent pressures at the end of the pressure steps) during adsorption (desorption) determined by averaging over a selected area of the FPA maps, exhibiting a pronounced asymmetry in the filling of the 10 nm pores, with the pores on the left filled first and remaining filled, upon desorption, down to 80 mbar, with the big pores on the right side starting to empty at already 90 mbar. Emptying of the big pores is seen to occur with the surrounding smaller pores remaining saturated by guest molecules. Fig. 3e shows the time constants of uptake and release, jointly with the isotherms. The time constant of the one-step emptying process of the 10 nm pore section located on the left side of the sample exceeds all other time constants of both adsorption and desorption. By considering, during this interval, a small enough pressure step, we did even succeed in slowing down the desorption process to such an extent that it has become possible to record profile evolution. These data are shown in Fig. 3f. A slight change in the lab temperature (see SI 3.2) did, in addition, require a corresponding change in the pressure data actually chosen.
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(iii) It is interesting to note that the shape of the concentration profiles in the segment containing the 5 nm pores (Fig. 2c, left half of the profiles) reveals another difference between ad- and desorption: During adsorption, after each individual pressure step the concentration in this segment is found to be almost constant over the whole length, indicating that the mono- and multilayers of guest molecules emerge essentially homogenously within the channels. For desorption, however, there is a distinct exception from this pattern: Here, after the complete emptying of the large pores, in the narrow channels a striking asymmetry following a pressure step from 55 to 50 mbar is observed. This observation can be correlated with the fact that the process of wet-etching gives rise to a tiny (of the order of a few Ångstroms per mm) increase of the average pore diameter with increasing etching depth. Adsorption in these frustum-like strongly corrugated channels is controlled by the formation of liquid bridges in the pore throats, which are distributed more or less homogeneously in space. Desorption, on the other hand, occurs by the invading gas front and is, therefore, subject to stronger geometric control. It may further be altered by asymmetric boundary conditions for the mass transfer. Which of these two factors plays the dominant role for desorption shall be explored in further studies. (iv) The occurrence of two separate hysteresis loops (Fig. 2e and SI 2.2) in the sorption isotherms of the two-channel systems (Fig. 1a and c) clearly indicates the presence of two types of channels with notably different diameters. The correlation of the capillary-evaporation and condensation pressures with the pore sizes of the mesoporous silicon is, however, a difficult problem due to a strong structural disorder [35,36]. From a purely thermodynamic point of view, corresponding experiments with the five-channel sample (Fig. 1b and d) have been expected to provide similar results. By contrast, however, there is no clear distinction anymore between two loops. We have to take this as a further indication of deviations between the idealized pore structure as indicated in Fig. 1a and b and reality, emphasizing the intricacy of the pore architecture of mesoporous silicon and the difficulties with ensuring well-defined geometric properties of the pore space. In particular, we anticipate that, due to increasing of the average pore size with etching depth [37], the overlap between the pore sizes in the pore section with different average pore sizes increases. (v) In the five-channel sample (Fig. 1b and d), the 10 nm channel segments are confined by 5 nm channels. There are two possibilities that, upon desorption, a pore surrounded by narrower pores may be emptied: either only after the adjacent ones have been emptied (i.e. after the release of pore blocking) or by molecules getting out of the cage under consideration, irrespective of the fact that this cage is still surrounded by saturated ones [11]. The latter process, which appears with sufficiently small necks between adjacent cavities at sufficiently low pressures, is referred to as cavitation. In porous silicon, a phenomenon of emptying similar to cavitation, but occurring at pressures notably higher than predicted by theory, is observed [19,20]. The mechanism of this process is unknown and is under current debate. In conventional sorption studies, the decision between different emptying scenarios, namely controlled by pore blocking or occurring in two steps, cannot be based on immediate experimental evidence due to a complex structure of the material under study (mesoscalic disorder, spatial variation of porosity, etc.). Micro-imaging overcomes this deficiency by its very nature. Immediate evidence of the
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occurrence of advanced emptying of the larger cavities is, e.g., provided by the profiles shown in Fig. 3d during desorption, after pressure steps to 75 mbar (see SI 3.1 and 3.2). Here, emptying of the wider channels is clearly seen to take place with the narrow channels still being saturated by guest molecules. (vi) Profiting from the dramatic slowing down of equilibration during emptying of the larger cavities in the ink-bottle pores, we have been able to even record the evolution of guest distributions (see Fig. 3f). As a most remarkable feature, guest profiles are seen to remain, upon desorption, symmetrical with respect to the center of the segment.
4. Conclusions To summarize, we have presented the results of micro-imaging of gaseliquid phase transitions under nanoscopic confinements. We have shown that the method used provides a most direct approach to study spatio-temporal correlations of the sorption process. In addition to its strong sensitivity to spatially-resolved phase equilibria, which may be used as contrasting mechanism for optical tomography of nano-structured materials, the potential to record the evolution of molecular distributions has shown to open new options for studying mass transfer phenomena in these materials under conditions of multi-phase equilibria. Acknowledgments Financial support by the German Science Foundation (DFG), notably within the frame of the International Research Training Group “Diffusion in Porous Materials” is gratefully acknowledged. We are deeply obliged to Prof. Dr. Kurt Binder (Mainz) for enlightening discussions. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.micromeso.2015.05.005. References [1] D.H. Everett, Adsorption Hysteresis, Marcel Dekker, Inc., New York, 1967, pp. 1055e1113. [2] M. Thommes, K.A. Cychosz, J. Int. Adsorpt. Soc. 20 (2e3) (2014) 233e250. [3] L.H. Cohan, J. Am. Chem. Soc. 66 (1) (1944) 98e105. [4] P.C. Ball, R. Evans, Langmuir 5 (3) (1989) 714e723. [5] A.V. Neimark, P.I. Ravikovitch, A. Vishnyakov, Phys. Rev. E 62 (2) (2000) 1493e1496. [6] P.A. Monson, Microporous Mesoporous Mat. 160 (2012) 47e66. [7] D. Wilms, A. Winkler, P. Virnau, K. Binder, Phys. Rev. Lett. 105 (4) (2010) 045701. [8] U. Ciesla, F. Schüth, Microporous Mesoporous Mat. 27 (2e3) (1999) 131e149. [9] K. Morishige, M. Shikimi, J. Chem. Phys. 108 (18) (1998) 7821e7824. €hn, M. Fro €ba, Appl. Surf. Sci. 196 (1e4) (2002) 239e249. [10] M. Thommes, R. Ko [11] P. Ravikovitch, A. Neimark, Langmuir 18 (25) (2002) 9830e9837. [12] B. Libby, P.A. Monson, Langmuir 20 (10) (2004) 4289e4294. [13] K. Morishige, N. Tateishi, J. Chem. Phys. 119 (4) (2003) 2301e2306. [14] G. Mistura, A. Pozzato, G. Grenci, L. Bruschi, M. Tormen, Nat. Commun. 4 (2013) article number 2966. [15] L. Canham, Handbook of Porous Silicon, Springer International Publishing, 2015. [16] M.J. Sailor, Porous Silicon in Practice, Wiley-VCH, 2012. [17] A. Khokhlov, R. Valiullin, J. K€ arger, F. Steinbach, A. Feldhoff, New. J. Phys. 9 (8) (2007) 272. [18] F. Casanova, C.E. Chiang, A.M. Ruminski, M.J. Sailor, I.K. Schuller, Langmuir 28 (17) (2012) 6832e6838. [19] A. Grosman, C. Ortega, Langmuir 27 (6) (2011) 2364e2374. [20] D. Wallacher, N. Künzner, D. Kovalev, N. Knorr, K. Knorr, Phys. Rev. Lett. 92 (19) (2004) 195704. [21] K. Morishige, M. Tateishi, F. Hirose, K. Aramaki, Langmuir 22 (22) (2006) 9220e9224.
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