Adsorption Hysteresis in Self-Ordered Nanoporous Alumina

Transcription

1 10936 Langmuir 2008, 24, Adsorption Hysteresis in Self-Ordered Nanoporous Alumina Lorenzo Bruschi, Giovanni Fois, Giampaolo Mistura,*, Kornelia Sklarek, Reinald Hillebrand, Martin Steinhart,*, and Ulrich Gösele Dipartimento di Fisica G.Galilei and CNISM, UniVersità di PadoVa, Via Marzolo 8, PadoVa, Italy and Max Planck Institute of Microstructure Physics, Weinberg 2, Halle, Germany ReceiVed May 19, ReVised Manuscript ReceiVed July 12, 2008 We performed systematic adsorption studies using self-ordered nanoporous anodic aluminum oxide (AAO) in an extended range of mean pore diameters and with different pore topologies. These matrices were characterized by straight cylindrical pores having a narrow pore size distribution and no interconnections. Pronounced hysteresis loops between adsorption and desorption cycles were observed even in the case of pores closed at one end. These results are in contrast with macroscopic theoretical models and detailed numerical simulations of the adsorption in a single pore. Extensive measurements involving adsorption isotherms, reversal curves, and subloops carried out in closedbottom pores suggest that the pores do not desorb independently from one another. Introduction Porous solids represent a broad class of materials that finds many applications in a variety of different fields, ranging from catalysis to oil extraction, from mixture separation to pollution control. 1,2 They all share a complicated pore connectivity and broad distribution of pore sizes whose mean values range from nanometer to micrometer size depending on the fabrication method. The consequent large exposed surface area and the possibility to tailor in some way the average pore diameter, D, have made the porous solids the ideal playground to study fundamental issues related to phase separation 3 and superfluidity in confined systems 4 as well as the loss of ordering of liquid crystals 5 and the appearance of a supersolid phase of 4 He. 6 The morphology of a porous matrix is commonly characterized by the determination of adsorption isotherms. 1,2 These curves represent the mass of the gas, typically N 2 or Ar at liquid nitrogen temperature, adsorbed onto a substrate as a function of the equilibrium vapor pressure of the surrounding vapor. In the case of porous materials, they typically exhibit two main features: (i) a sharp increase in the amount of adsorbed gas well below the liquid-vapor coexistence pressure P 0 of the bulk adsorbate, which is explained in terms of capillary condensation in the small pores, and (ii) a hysteresis loop between the adsorption (gas is added to the sample cell) and the desorption (gas is removed from the sample cell) branches. Condensation occurs at a pressure P ads larger than the pressure of evaporation P des.asd increases, P ads moves closer to P 0. From the shape of this loop it is possible to derive information about the pore size distribution and connectivity. Despite its commonplace occurrence, the origin of the hysteresis phenomenon is still a matter of debate. According to macroscopic * To whom correspondence should be addressed. G.M.: mistura@ padova.infm.it. M.S.: steinhart@mpi-halle.de. Università di Padova. Max Planck Institute of Microstructure Physics. (1) Gregg, S. J.; Sing, K. S. W. Adsorption, surface area and porosity; Academic Press: New York, (2) Everett, D. H. In The solid gas interface; Flood, E. A., Ed.; Marcel Dekker: New York, 1967; Vol. 2. (3) Gelb, L. D.; Gubbins, K. E.; Radhakrishnan, R.; Sliwinska-Bartkowiak, M. Rep. Prog. Phys. 1999, 62, (4) Chan, M. H. W.; Mulders, N.; Reppy, J. Phys. Today 1996, 49(8), 30, Part 1. (5) Bellini, T.; Radzihovsky, L.; Toner, J.; Clark, N. L. A. Science 2001, 294, (6) Kim, E.; Chan, M. H. W. Nature 2004, 427, 225. thermodynamic arguments, hysteresis is usually explained in terms of the different shape of the vapor/adsorbate interface during adsorption and desorption in a pore open at both ends. 1,7 As first suggested by Cohan, during adsorption in a cylindrical pore, the meniscus is nucleated on the walls of the pore and has a cylindrical shape. However, evaporation from the full pore takes place from the hemispherical menisci at each end of the cylinder. Since the curvatures of the menisci are different, the Kelvin equation implies that condensation and evaporation occur at different relative pressures, which gives rise to hysteresis (see section III for further details). Using similar considerations, no hysteresis is expected in the case of a regular cylindrical pore with only one open end or of a rectangular well because the meniscus nucleates at the bottom corners and is the same both in adsorption and in desorption. As a development of such ideas, the hysteresis was associated to the stability of multilayers adsorbed in cylindrical pores. 8 Mean density functional theory, 9 molecular dynamics simulations of adsorption and desorption by diffusive mass transfer into model pores, 10 and grand canonical Monte Carlo simulations 11 confirmed this classical picture of adsorption in a single pore. To test these ideas, experiments were performed on mesoporous silicon characterized by a trivial topology consisting of straight and not interconnected pores In contrast to theoretical predictions, adsorption of N 2 and Ar in these silicon matrices was characterized by pronounced hysteresis loops independent of whether the pores were open at one or both ends. The disagreement with Cohan s argument was attributed to the presence of a thick film covering the porous layer that connected the pores during desorption 12 or quenched disorder imposed by some variation of the pore diameter along the pores. 13 In this latter approach, the pores are modeled as an ensemble of segments with different diameters. 13 Cavities and constrictions in this system are nonindependent domains as the condensation and evaporation (7) Cohan, L. H. J. Am. Chem. Soc. 1938, 60, 433. (8) Saam, W. F.; Cole, M. W. Phys. ReV. B1975, 11, (9) Bettolo Marini Marconi, U.; van Swol, F. Europhys. Lett. 1989, 8, 531. (10) Sarkisov, L.; Monson, P. A. Langmuir 2001, 17, (11) Gelb, L. D. Mol. Phys. 2002, 100, (12) Coasne, B.; Grosman, A.; Ortega, C.; Simon, M. Phys. ReV. Lett. 2002, 88, (13) Wallacher, D.; Kujnzner, N.; Kovalev, D.; Knorr, N.; Knorr, K. Phys. ReV. Lett. 2004, 92, (14) Grosman, A.; Ortega, C. Langmuir 2008, 24, /la801493b CCC: $ American Chemical Society Published on Web 08/27/2008

2 Adsorption Hysteresis in Nanoporous Alumina Langmuir, Vol. 24, No. 19, Figure 1. SEM top-view images of AAOs with D ) (a) 400 and (d) 25 nm; (b and e) corresponding distributions of the apparent pore areas; (c and f) PDFs of the center-to-center distances in the pore arrays. pressures are influenced by the neighbor domains. 15 More recently, adsorption experiments were carried out in ordered mesoporous SBA-15 silica. This material presents straight and parallel pores that have a narrower size distribution than mesoporous silicon obtained by electrochemical etching, which was used for the above-mentioned experiments. A detailed capillary study showed that also in SBA-15 the open pores, with a mean D value of less than 10 nm, did not empty independently of each other and hysteresis was again found. 16,17 Investigation of the temperature dependence of capillary condensation and evaporation for nitrogen in SBA-15 further indicated that evaporation did not take place at equilibrium. 18 However, the analysis was complicated by the rough pore walls and the presence of a significant number of disordered micropores located in the walls separating the mesopores. 19 Thus, we have chosen to perform systematic adsorption studies using self-ordered nanoporous anodic aluminum oxide (AAO), a material that does not suffer the drawbacks of porous silicon and SBA-15 silica, in an ample interval of nominal pore diameters of 25, 60, and 400 nm. (15) Coasne, B.; Pellenq, R. J. M. J. Chem. Phys. 2004, 121, (16) Esparza, J. M; Ojieda, M. L.; Campero, A.; Dominguez, A.; Rojas, F.; Vidales, A. M.; Lopez, R. H.; Zgrablich, G. Colloids Surf. A: Physicochem. Eng. Aspects 2004, 241, 35. (17) Grosman, A.; Ortega, C. Langmuir 2005, 21, (18) Morishige, K.; Ito, M. J. Chem. Phys. 2002, 117, (19) Hofmann, T.; Wallacher, D.; Huber, P.; Birringer, R.; Knorr, K.; Schreiber, A.; Findenegg, G. H. Phys. ReV. B2005, 72, The pores had a depth of 100 µm and were either open at both ends or had closed bottoms. Experimental Section The nanoporous AAO samples were obtained with sulfuric acid, 20 oxalic acid, 21 and phosphoric acid 22 as electrolytes. After anodization, the AAO layer had hemispherical pore bottoms and was attached to an underlying aluminum substrate. Selective wet-chemical etching steps allow successively removing the Al and, to open the pore bottoms, the hemispherical barrier oxide initially separating the pores and the Al substrate. 23 Nanoporous alumina grown under selfordering regimes is characterized by a regular arrangement of the pores, narrow pore size distribution, and uniform pore depth as well as solid pore walls without micropores ,24 Real-space image analysis of SEM (scanning electron microscopy) top-view images of AAOs with D values of 400 and 25 nm (Figure 1a and 1d) revealed sharp, monomodal distributions of the apparent pore areas (Figure 1b and 1e). Although their absolute peak positions depend to a large extent on the imaging conditions and thresholding procedure, the shapes and widths of the pore size distributions are meaningful. (20) Masuda, H.; Hasegawa, F.; Ono, S. J. Electrochem. Soc. 1997, 144, L127. (21) Masuda, H.; Fukuda, F. Science 1995, 268, (22) Masuda, H.; Yada, K.; Osaka, A. Jpn. J. Appl. Phys., Part 2: Lett. 1998, 37, L1340. (23) Kriha, O.; Zhao, L.; Pippel, E.; Gösele, U.; Wehrspohn, R. B.; Wendorff, J. H.; Steinhart, M; Greiner, A. AdV. Funct. Mater. 2007, 17, (24) Nielsch, K.; Choi, J.; Schwirn, K.; Wehrspohn, R. B.; Gösele, U. Nano Lett. 2002, 2, 677.

3 10938 Langmuir, Vol. 24, No. 19, 2008 Bruschi et al. Figure 2. Cross-sectional SEM image of self-ordered porous alumina with a pore diameter of 60 nm. The dispersity of the pore diameter distribution, defined as the standard deviation divided by the mean pore diameter, amounts to about 8%. As a comparison, the porous silicon used in a recent adsorption study had a dispersity of about 50%. 12 The D values resulting from the anodization regimes applied here were previously determined by transmission electron microscopy. 24 The pair distribution functions (PDFs) of the center-to-center distances in the pore arrays show patterns typical of hexagonal lattices. The positions of the nearest neighbor peaks, which are not affected by imaging conditions and thresholding, appear at 500 nm for D ) 400 nm (Figure 1c; full width at half-maximum, fwhm 53 nm) and 66 nm for D ) 25 nm (Figure 1f; fwhm 8.6 nm). In contrast to mesoporous silica and disordered porous materials, the pores are strictly separated, i.e., no junctions and no micropores penetrating through the pore walls are present, as clearly shown by the cross-sectional SEM image of self-ordered porous alumina with a pore diameter of 60 nm (etched with oxalic acid) displayed in Figure 2. The straight cylindrical nature of the nanopores was exploited to prepare nanowires and nanotubes with uniform diameter over their entire length. 25,26 The absence of connections between the pores was also evidenced by the occurrence of homogeneous nucleation in polymeric nanofibers confined to self-ordered porous alumina. 27 The AAO samples were square pieces or disks (characteristic size about 1 cm) cut out of aluminum foils or alumina membranes with thickness of 400 and 100 µm, respectively. They were attached to the extremity of a hardened steel rod and driven to the torsional resonant frequency of the system by means of a piezoelectric crystal acting onto the extremity of a stainless steel arm hard soldered to the torsion rod. The oscillations were detected by a similar piezoelectric crystal mounted in a symmetric way with respect to the other one. As the AAOs were exposed to a vapor, the resonance frequency decreased because of an increase in the total moment of inertia I. Assuming that under equilibrium conditions a homogeneous film covers the substrate, the relative change of I is then proportional to the film mass m film. Therefore, apart from a multiplicative constant, the mass of the adsorbed film is proportional to the relative frequency shift. 28 The microbalance was mounted inside a double-wall copper cell to reduce thermal gradients. The temperature stability was better than 1 mk. With a thermostatted high-sensitivity commercial pressure gauge, the pressure reading was maintained stable within (0.05 Torr for several days. The saturated pressure P 0 was determined with an accuracy of (0.10 Torr as that pressure above which no variation is detected after further dosing of gas into the sample cell. (25) Routkevitch, D.; Bigioni, T.; Moskovits, M.; Xu, J. M. J. Phys. Chem. 1996, 100, (26) Steinhart, M.; Wehrspohn, R. B.; Gösele, U.; Wendorff, J. H. Angew. Chem., Int. Ed. 2004, 43, (27) Steinhart, M.; Göring, P.; Dernaika, H.; Prabhukaran, M.; Gösele, U.; Hempel, E.; Thurn-Albrecht, T. Phys. ReV. Lett. 2006, 97, (28) Bruschi, L.; Carlin, A.; Mistura, G. Phys. ReV. Lett. 2002, 89, Figure 3. Adsorption isotherms of Ar taken at T ) 85 K on AAOs with closed pore bottoms and different D values. We believe that the bulk liquid formed also on the microbalance because after each dosing at P 0 the resonance frequency f decreased. If the condensation had only occurred elsewhere in the sample cell, f would have hardly changed after each dosing. With this setup we measured the adsorption of liquid Ar films at a constant temperature of 85 K. We selected Ar as adsorbate because it completely wets most solid surfaces thanks to its low polarizability. It is also very pure, characterized by simple van der Waals interactions, and easy to thermocontrol using a conventional liquid nitrogen cryostat. Results and Discussion Figure 3 summarizes the main results of our adsorption study obtained from AAOs with closed pore bottoms. It shows the vapor-corrected frequency shifts 29 normalized to the total adsorption close to saturation as a function of the relative vapor pressure P/P 0. In contradiction with Cohan s predictions, there are pronounced hysteresis loops for D ) 25 and 60 nm (for D ) 400 nm, see also Figure 7). Their shape resembles that of type H1 in the IUPAC classification (e.g., a hysteresis loop with parallel adsorption and desorption branches), which is generally associated to capillary condensation and evaporation in ordered mesoporous materials with cylindrical pores open at both ends. Adsorption isotherms measured in AAOs with open pores of the same nominal diameters show slightly wider hysteresis loops but of the same type H1 (see below). For an assembly of independent cylindrical pores open at both ends, a hysteresis loop with nearly parallel adsorption and desorption branches similar to those we found is predicted whose slope reflects the pore size distribution. 30,31 If the pores are instead closed at one end, no hysteresis is expected, in contrast to the results of Figure 3. The presence of hysteresis agrees with previous investigations on porous silicon and SBA-15, characterized by pores open at both ends and by closed pore bottoms and with diameters smaller than 15 nm and depths inferior to 20 µm. However, the H1 shape of the loops in Figure 3 contrasts with the loops of type H2 found in closed pore bottoms etched in porous silicon Hysteresis loops of type H2 are typically observed in disordered porous materials like Vycor and present an asymmetrical shape with an evaporation branch much steeper than the adsorption (29) Bruschi, L.; Carlin, A.; Parry, A. O.; Mistura, G. Phys. ReV. E2003, 68, (30) Ball, R. P.; Evans, R. Langmuir 1989, 5, 714. (31) Coasne, B.; Gubbins, K. E.; Pellenq, R. J. M. Phys. ReV. B2005, 72,

4 Adsorption Hysteresis in Nanoporous Alumina Langmuir, Vol. 24, No. 19, Figure 4. Enlargement of adsorption isotherms of Ar taken at T ) 85 K on AAO with D ) 60 nm. Samples A and B refer to AAO with closed pore bottoms. Figure 5. Hysteresis loop on AAO (pore bottoms closed) with D ) 25 branch. 1 The origin of such loops was explained in terms of quenched disorder due to some variations in the pore diameters along the pores, 13,32 and their appearance was taken as an indication that the pores in silicon and SBA-15 matrices do not empty independently of one another. 12,14,17 It is evident from Figure 3 the dependence of the hysteresis loop on D. As the pore size increases, the condensation pressure moves closer to P 0, the loop gets narrower, and the two branches become more parallel and much steeper. For D ) 25 nm, condensation occurs in the interval P < ) 0.86 e P/P 0 e 0.92 ) P >. If we analyze this branch in terms of the Kelvin equation, ln(p/p 0 ) is proportional to the inverse of the radius of curvature of the meniscus, which can be roughly assumed to be equal to the pore radius. Accordingly, the ratio between the maximum and the minimum pore diameters can be estimated as D > /D < ln(p < /P 0 )/ln(p > /P 0 ) along either branches of the hysteresis loop, a conclusion that is consistent with the width of the pore size distribution extracted from scanning electron micrographs, which yielded a mean diameter D ) 25 nm and a dispersion σ ) 8%D if we assume that D g D + 3σ and D e D - 3σ. The ratios derived from the slopes of the other hysteresis branches observed in this study were comprised between 1.4 and 2, values which are in substantial agreement with the result of about 1.6 deduced from the real space image analysis of the pores if we consider the crudity of the thermodynamic model employed. Again, this conclusion contrasts with that reached in the case of porous silicon, where the pore size distribution deduced from the Kelvin equation was about 10 times narrower than that derived from transmission electron micrographs. 33 Figure 4 shows an enlargement of the isotherms near capillary condensation measured on AAO with D ) 60 nm. In particular, the data of the pores open at one end refer to two samples prepared in separate times and with different geometry: two rectangular pieces glued together, sample A, and a circular disk, sample B. The very good agreement between these two curves is indicative of a very controlled fabrication process and of an accurate measurement methodology. Comparing the hysteresis loops of pores with closed and opened pore bottoms, three features appear evident: (i) the shape of the loops is very similar; (ii) the width of the loop observed with the open pore bottoms is larger than (32) Kierlik, E.; Monson, P. A.; Rosinberg, M. L.; Sarkisov, L.; Tarjus, G. Phys. ReV. Lett. 2001, 87, (33) Coasne, B.; Grosman, A.; Dupont-Pavlosky, N.; Ortega, C.; Simon, M. Phys. Chem. Chem. Phys. 2001, 3, nm. Also shown, a primary descending scanning curve and two subloops. The inset shows a comparison of the two subloops. that corresponding to the pores closed at one end; (iii) desorption in the pores closed at one end occurs at a relative pressure close to the desorption in the pores with opened bottoms. Observation iii is in agreement with Cohan s macroscopic argument (see below). It also suggests that the filling of these pores occurs from the bottom to the top without formation of intermediate bridges; otherwise, the condensation branches of closed and open pores of the same diameter would be superimposed. 17 To better understand the origin of the hysteresis loop, we performed a detailed adsorption study on AAO with D values of 25 nm. Figure 5 shows the corresponding results for closedbottom pores. If the pores behaved independently from one to another, a primary descending scanning curve (PDSC) initiated at a point I on the condensation branch should follow the reversible path schematically indicated in Figure 5 which ends at point F on the desorption curve. 2,16,17,31 The experimental PDSC instead deviates significantly from this line and meets the desorption branch only at the closure of the loop. We also compared the shape of two subloops, one starting from the condensation branch and the other from the desorption branch, between the same relative pressure end points 2 indicated by the two vertical dashed lines in Figure 5. The two subloops have been replotted in the inset of the same figure, which clearly shows that they have different slopes. Similar behavior is displayed by the pores open at both ends of the same nominal diameter as shown in Figure 6. We first notice that for this sample the hysteresis loop is shifted to a higher relative pressure than that observed for the closed-bottom pores, as clearly evinced by the location of the desorption branch. Such a behavior, which contrasts with that found for the larger pores, is likely related to sample fabrication. In fact, opening of the pore bottoms by treatment of AAO membranes with phosphoric acid may also result in a slight widening of the pores. Hence, it can be assumed that the pores with opened bottoms have slightly larger diameters and that this effect is most pronounced in the case of the narrowest pores. If we now focus onto the scanning curves, again we see that the PDSC meets the desorption branch only at the closure of the loop. The two subloops show a pronounced hysteresis although, as seen in the inset of Figure 6, they look nearly congruent, i.e., they can be superimposed on top of each other by a translation along the ordinate axis. While the shapes of the PDSC lines are consistent

5 10940 Langmuir, Vol. 24, No. 19, 2008 Bruschi et al. isotherm found for pores open at both ends of the same nominal diameter shows a much wider H1 hysteresis loop (width at halfstep is 0.001) with the desorption branch lying, at least initially, very close to the corresponding branch measured with the pores closed at the bottom. We compared the midpoints of the hysteresis branches with the predictions of Cohan s model. 1,12 Condensation in a cylindrical pore open at both ends is predicted to occur at a pressure P open given by an equation similar to the classical Kelvin formula where the curvature of the meniscus is that of a cylinder of radius D/2 - t(p open ) Figure 6. Hysteresis loop in D ) 25 nm pores open at both ends. Also shown, a primary descending scanning curve and two subloops. The inset shows a comparison of the two subloops. Figure 7. Hysteresis loops on AAOs with D ) 400 nm. with recent studies on SBA-15 of different quality characterized by pores open at both ends with a diameter smaller than 10 nm 16,17 and on porous silicon with closed pores having D ) 13 ( 6 and 26 ( 14 nm, 14 the shape of the subloops are different, and their implications will be discussed in the final section. Arguably, one of the most interesting results of this work is related to adsorption on the largest pores where Cohan s macroscopic arguments should be valid. Figure 7 displays, on a very expanded scale, the isotherms measured in the 400 nm pore matrices. The two curves show the same general behavior as that already discussed for the 60 nm pores. We do not know why the slopes of the two loops are different. It would be interesting to compare our results with detailed numerical studies. The curve corresponding to the pores closed at the bottom presents a desorption branch parallel to the adsorption branch and slightly separated from this latter one by , equivalent to a pressure difference of 0.2 Torr. Detailed tests of the response of our capacitance gauge to variations in the ambient pressure yielded an uncertainty of about (0.05 Torr in the pressure measurement, which translates in error bars that are practically coincident with the size of the symbols used in Figure 7. In other words, the hysteresis loop is certainly very narrow but its origin cannot be accounted for as a mere instrumental artifact. In comparison, the ln P open )- γv l 1 P 0 K B T D 2-t(P open ) where γ is the liquid argon surface tension, V l the liquid specific volume, T the temperature, and t(p open ) the thickness of the adsorbed layer corresponding to P open. For a cylindrical pore closed at one end, the meniscus is expected to have a hemispherical shape so that condensation occurs at a pressure P closed ln P closed )- γv l 2 P 0 K B T D 2-t(P closed ) Evaporation of the fluids instead proceeds through the same hemispherical meniscus in both cases, i.e., at pressure P closed as found in Figure 4. Calculation of P open and P closed requires explicit determination of the dependence of the adsorbed film thickness on gas pressure t(p). Considering the unavoidable large uncertainty on t(p) caused by the many assumptions one has to make 12 and the fact that for large pores this correction becomes less important, we neglected this term in our analysis. In the case of D ) 400 nm and open pore bottoms, condensation is predicted to occur at a relative pressure of ( and evaporation at ( , the uncertainty being estimated from the maximum dispersion of the pore size distribution function, instead of the experimental values ( and ( Even for these large pores, Cohan s argument provides only a fairly accurate description of the observed hysteresis. As expected, larger discrepancies are found for the smaller pores investigated in this study and in the filling of a room temperature solvent in an AAO membrane with D ) 20 nm. 34,35 In Table 1 of the Supporting Information we compare the positions of the condensation and evaporation branches of the various samples investigated with the predictions of Cohan s model. The adsorption data presented here are not apt to a unique, unambigous interpretation. For instance, the shape of the hysteresis loops observed with the 25 nm pores (see Figures 5 and 6) resembles the curves calculated for an assembly of independent cylindrical pores having a regular cross-section and a Gaussian pore size distribution function centered about D ) 7.2 nm and with dispersion of 1.4 nm, 30,31 although the dispersity of our samples is about twice smaller. In particular, the slope of the adsorption branch is slightly larger than that of the desorption branch. Furthermore, the scanning curves are either reversible, if we assume that the very weak irreversibility of the lowest subloop in Figure 5 falls within the error bar, or congruent, suggesting that the pores are independent. On the other hand, the primary descending scanning curves meet the hysteresis loops at their closure points, indicating that the porous domains are nonindependent. 2,14,16,17,31 In the case of N 2 adsorption in SBA- (34) Alvine, K. J.; Shpyrko, O. G.; Pershan, P. S.; Shin, K.; Russell, T. P. Phys. ReV. Lett. 2006, 97, Alvine, K. J.; Shpyrko, O. G.; Pershan, P. S.; Shin, K.; Russell, T. P. Phys. ReV. Lett. 2007, 98, (35) Caupin, F. Phys. ReV. Lett. 2007, 98,

6 Adsorption Hysteresis in Nanoporous Alumina Langmuir, Vol. 24, No. 19, , density functional theory calculations suggest that the experimental scanning curves are caused by undulated pores, so that each pore is made up of nonidependent adsorption domains. 16,31 Regarding the alumina samples used in this study, it is well known that the pore walls in AAO are homogeneous on mesoscopic length scales and do not exhibit constrictions or similar features. 36 However, they consist of amorphous alumina incorporating electrolyte anions and defects on a molecular scale. Thus, possible inhomogeneities on a subnanometer scale, either of geometrical 13,31,32 or chemical 37 nature, may also contribute to the observed results. If we then assume that the pores are weakly disordered, we can explain the hysteresis found in both pores open at one end and at both ends because Cohan s argument applies only to regular cylindrical pores and the shape of the PDSC. On the other hand, the pores are probably not disordered enough, so that some features of the independent domain behavior are observed. Needless to say, detailed calculations and further experiments should be carried out to confirm such a speculative interpretation. Conclusions We studied the adsorption of self-ordered porous alumina using a torsional oscillator, which demonstrates that this simple microbalance can be a powerful and flexible technique to study adsorption phenomena in very small porous substrates having different shapes and thicknesses. The pores investigated, open at both ends or only at one, were parallel, noninterconnected cylinders with nominal mean diameters ranging from 25 to 400 nm and a depth of 100 µm. In spite of the absence of connections between the pores in these matrices, we always found hysteresis (36) Sulka G. D. In Nanostructured Materials in Electrochemistry; Eftekhari, A., Ed.; Wiley-VCH: Weinheim, (37) Puibasset, J. J. Phys. Chem. B 2005, 109, loops, even for the largest pores closed at one end. The shape of these loops resembles that of type H1 regardless of the topology of the single pores and reminds us of that calculated for an array of independent cylindrical pores open at both ends having a Gaussian pore size distribution. 15,30 A simple analysis based on the Kelvin equation of the condensation and evaporation branches yielded a pore size variation consistent with the pore size distribution derived from scanning electron micrographs. However, the presence of hysteresis in pores closed at one end is in contrast with the predictions of the macroscopic Cohan model and recent simulations based on the adsorption in a single regular pore. 7,9-11 Extensive adsorption scanning curves indicate that the pores are not independent of one another, possibly because of the presence of pore inhomogeneities. However, the shapes of adsorption cycles within the main hysteresis loop contrast with those observed in other mesoporous materials with not interconnected pores 12-14,16,17 and suggest that self-ordered porous alumina matrices might be affected by less disorder. It is our hope that this work will stimulate new models and calculations that deal explicitly with the adsorption in regular arrays of parallel, not interconnected cylindrical pores closed at one end whose inner walls present a weak disorder, both chemical and morphological. Acknowledgment. We thank Francesco Ancilotto for many clarifying discussions. This work was partially supported by Padua University through project CPDA077281/07. Supporting Information Available: Table 1 compares the positions of the condensation and evaporation branches of the various samples investigated with the predictions of Cohan s model. This material is available free of charge via the Internet at LA801493B