Adsorption on Nanopores of Different Cross Sections Made by

Article Cite This: Langmuir XXXX, XXX, XXX−XXX

pubs.acs.org/Langmuir

Adsorption on Nanopores of Different Cross Sections Made by Electron Beam Nanolithography Lorenzo Bruschi,† Giampaolo Mistura,*,† Luisa Prasetyo,‡ Duong D. Do,‡ Michele Dipalo,*,§ and Francesco De Angelis§ †

Dipartimento di Fisica e Astronomia G. Galilei, Università di Padova, via Marzolo 8, 35131 Padova, Italy School of Chemical Engineering, University of Queensland, St. Lucia, Queensland 4072, Australia § Istituto Italiano di Tecnologia, via Morego 30, 16163 Genova, Italy ‡

S Supporting Information *

ABSTRACT: Adsorption on nanoporous matrices is characterized by a pronounced hysteresis loop in the adsorption isotherm, when the substrate is loaded and unloaded with adsorbate, the origin of which is a matter of immense debate in the literature. In this work, we report a study of argon adsorption at 85 K on nonconnecting nanopores with one end closed to the surrounding where the effects of different pore cross sections fabricated by electron beam lithography (EBL) are investigated. A polymethylmethacrylate (PMMA) resist is deposited on the electrodes of a sensitive quartz crystal microbalance without degradation of the resonance quality factor or the long-term and short-term stabilities of the device even at cryogenic temperatures. Four different pores’ cross sections: circular, square, rectangular, and triangular, are produced from EBL, and the isotherms for these pore shapes exhibit pronounced hysteresis loops whose adsorption and desorption branches are nearly vertical and have almost the same slopes. No difference is observed in the hysteresis loops of the isotherms for the pores with triangular and square cross sections, whereas the hysteresis loop for the pore with circular cross sections is much narrower, suggesting that they are more regular than the other pores. All of these observations suggest that the hysteresis behavior resulted mainly from microscopic geometric irregularities present in these porous matrices.

■

INTRODUCTION The realization of new functional materials often relies on the templates of regular porous structure.1−3 Advances in nanotechnology allow patterning-extended surface areas with ordered arrays of straight, unconnected pores with a characteristic size ranging from a few to a couple of hundred nanometers.4 Examples of such materials include porous silicon,5,6 porous silica,7,8 and porous alumina.9,10 These bottom-up approaches present many advantages: they are robust, relatively simple, and easy to implement in an industrial process. However, the main drawback of these self-assembling processes is that the morphology of the porous network (e.g., pores’ cross section, size, and density) cannot be easily varied. Advanced nanolithography techniques, such as electron beam lithography (EBL) and the focussed ion beam, can overcome some of these limitations at the expense of patterning only very small areas on the order of a few hundred micrometer-square or less. Here, we present the first adsorption study on an array of nanoscopic pits of different cross sections fabricated by EBL. The total pores volume accessible to the adsorbate, on the order of 10−8 cc, is below the sensitivity of standard techniques such as the adsorption volumetry and ellipsometry. The torsional microbalance, successfully employed in our previous study of porous alumina,11 is also not sensitive enough. To this © XXXX American Chemical Society

end, we have then adopted the much more sensitive quartz crystal microbalance (QCM).12 It consists of a small quartz disk whose principal faces are optically polished and covered by two metallic films acting as electrodes, above which a porous layer is prepared. By applying a sinusoidal voltage across the two electrodes, it is possible to drive the crystal to its own mechanical resonance with the two parallel faces oscillating in a transverse shear motion, characteristic of the AT cut. Because the quality factors of these modes are usually very large, on the order of 104 or higher, the QCM is a very sensitive probe. A change in the inertia of the sensor caused by adsorption gives rise to a decrease in the resonance frequency proportional to the mass of the adsorbate. Considering a frequency stability of 0.1 Hz for a typical resonance of 5 MHz, the resulting mass sensitivity is on the order of nanograms or better. With this technique, we study the hysteresis phenomenon which is generally observed in experimental adsorption isotherms of many porous materials.13−15 These isotherms represent the mass of the gas, typically N2 or Ar at liquid nitrogen temperature, adsorbed onto a substrate as a function Received: October 25, 2017 Revised: December 4, 2017 Published: December 6, 2017 A

DOI: 10.1021/acs.langmuir.7b03695 Langmuir XXXX, XXX, XXX−XXX

Article

Langmuir

oscillating frequencies on the order of 5 MHz.44 To promote the adhesion of the PMMA layer, a thin layer (7 nm) of chrome is deposited on the gold surface of the quartz crystal by sputtering deposition. Furthermore, small areas of 5 × 5 μm2 are left without nanopores to enhance the adhesion of the PMMA layer to the QCM electrodes. Finally, the pores are sculpted with an interpore distance of 1 μm. The thickness of the PMMA resist layer is set around 400 nm, which is the pore length at the end of the lithographic process. The PMMA thickness is chosen as high as possible to increase the total volume of the nanopores; however, an upper limit is set by the aspect ratio of the pore depth to the diameter, which degrades for a thick resist owing to the electron scattering that broadens the beam. After the development of exposed PMMA with the developer methyl isobutyl ketone (MIBK)/isopropanol (1:3), the samples are treated with a mild oxygen plasma to remove any residues of PMMA at the bottom of the pores. Owing to the large areas of the QCM electrodes to be patterned (a circle of diameter 4 mm) and the high density of nanopores, a relatively high electron beam current of approximately 250− 350 pA is used to reduce the total exposure time for each substrate. Actually, even with such a relatively high beam current, the complete EBL exposure of one QCM requires approximately 20−30 h corresponding to the opening of about 10 million pores. Higher beam currents certainly decrease the exposure time but also produce more irregularities, particularly at the edges of square and triangular pores. Preliminary tests have indicated that limiting the beam currents to 350 pA is a good compromise that guarantees acceptable exposure times and preserves the sharp features of square and triangular pores. With these exposure parameters, we also observe very small deviations of the actual pore size from the nominal values set during the pattern design; on an average, the discrepancy between nominal and actual dimensions is below 10 nm. Another factor that contributes to the irregularities of the nanopores’ shape is the initial surface condition of the QCM gold electrodes evaporated onto the quartz blanks. Indeed, the electrodes present a rougher surface [approximately 10 nm rms roughness, see atomic force microscopy (AFM) data in the Supporting Information] than chemomechanically polished wafers normally used for high-resolution EBL. Moreover, the typical surface of the QCM presents defects and impurities that make it difficult to obtain a very smooth spin coating of the PMMA resist (see dark-field optical images in the Supporting Information). For this study, pores of different cross sections: circular, triangular, square, and rectangular, are prepared. Figure 1 shows various SEM images of the nanopores produced with EBL taken at different magnifications, including cross-sectional images of the pores in the axial direction. These images are taken after evaporating a thin gold layer (thickness 10 nm) on the porous PMMA. Accordingly, they underestimate the pore sizes by about 10 nm. The thin gold coating for SEM imaging is also responsible for the high surface roughness observable in Figure 1c. Since the gold coating is deposited after the hysteresis measurements, the resulting roughness does not play any role in the observed adsorption behavior. Adsorption Measurements. Adsorption isotherms of argon at T = 85 K are measured with a QCM. Compared to the torsional microbalance used in our studies on the porous alumina,11 the mass resolution of QCM is 1000 times better. Nanoelectromechanical systems (NEMS) allow the detection of masses as small as 1 MDa,45,46 which, in principle, would be

of the equilibrium pressure of the surrounding vapor. In the case of porous materials having pores of tens of nanometers in size, they always exhibit two main features: (i) a sharp increase in the adsorbed amount at a pressure well below the liquid− vapor coexistence pressure P0 of the bulk adsorbate, which is explained in terms of the capillary condensation in small pores13,16 and (ii) an hysteresis loop between the adsorption (gas is added to the sample cell) and desorption (gas is removed from the sample cell) branches, with the condensation pressure, Pads, greater than the evaporation pressure, Pdes. As the pore size increases, both these pressures approach P0. For cylindrical pores whose two ends are open to the surrounding gas, the hysteresis phenomenon was originally explained in terms of the different shape of the meniscus of the interface, separating the gas and adsorbed phases, during adsorption (adsorbate is added to the pore) and desorption (adsorbate is removed from the pore).17 It follows that in a closed-bottom cylindrical pore, a continuous transition is expected because the meniscus nucleates at the closed end and will be the same in both adsorption and desorption. Classical theories, 18−21 mean field density functional theory,22−24 simulations of diffusive mass transfer into model pores,25,26 and grand canonical lattice model Monte Carlo simulations23,27,28 support this macroscopic argument. However, in stark contrast to these simulation studies, experiments with ordered mesoporous matrices consisting of straight unconnected pores show that adsorption is always characterized by pronounced hysteresis loops irrespective of whether the pores are open at one or at both ends.15,29−37 Recent simulations with closed-end pores whose diameters ,< = Dp ± σ, which is in substantial agreement with the value Dp = 76 ± 6 nm derived from the real-space images of the pores coated with a gold film. If we extend this analysis to the other pores, we get Dp = 94 ± 8 nm, Dp = 94 ± 11 nm, and Dp = 104 ± 10 nm for the triangular, square, and rectangular cross sections, respectively, which represent the equivalent diameter of the circles of these pore cross sections. As a comparison, the values derived from the SEM images are: triangular pore side L = 104 ± 6 nm, square pore side L = 102 ± 6 nm, and rectangular pore with sides L1 = 106 ± 6 nm and L2 = 130 ± 12 nm. No other significant differences in adsorption are observed and the normalized loops exhibit essentially the same shape, considering the much enlarged scale of the graph and the simplicity of the normalization procedure. This conclusion agrees with recent computer simulations of Ar adsorption in the open pores of nanometer size (∼10 nm) and with circular or triangular cross sections.51 The basis chosen for a quantitative comparison between pores of different shape is that they have the same surface area per unit volume. At low pressures, the adsorption isotherms look different and the adsorbed mass on open triangular pores is larger than that on open circular pores. In the open triangular pore, the molecules initially adsorb along the three junctions at very low loadings. As the pressure is increased, the atoms continue to accumulate along the strong adsorption sites at the junctions until these are filled with a single line of adsorbed atoms. When the pressure is further increased, the atoms are adsorbed by spreading over the three walls. Numerical simulations carried out on pores of different cross sections with one end closed confirm these results (see Simulation Results section). However, such differences cannot be detected in our QCM experiment because they occur at very low pressures, below ∼1 Torr, and become less pronounced as the pore size increases. As the pressure is further increased, multiple adsorbate layers are formed on the surfaces of all pores leaving a low density core which reduces in size and approaches a cylindrical shape to minimize the free energy by reducing the interfacial area per unit volume. Because the solid−fluid interaction decays approximately as the inverse third power of the distance from the surface and becomes negligible at distances of about two collision diameters, the process of filling the gaslike core (condensation) is governed mainly by the fluid−fluid interactions and the interface curvature. As a consequence, condensation and evaporation are not significantly affected by the shape of the pore as observed in Figure 4 and reported in other numerical studies.52,53 Finally, Figure 4 shows that the hysteresis loop of the circular pores is somewhat narrower than the others, indicating a higher order degree of the pores probably because of the lack of sharp angles which are difficult to reproduce in the EBL process with sizes below 100 nm and with high beam currents. We have then studied in more detail the adsorption in circular pores made by slightly changing the fabrication protocol. The results are

Figure 4. Normalized hysteresis loops of Ar adsorption isotherms measured at 85 K in closed-bottom pores of different cross sections: rectangular, square, triangular, and circular. The adsorption data are normalized to the values of the plateaus observed after capillary condensation. The snapshots are SEM micrographs of representative pores.

normalized adsorption data for the four geometries investigated. The data are normalized for the adsorbed amount of the hysteresis loop, that is, a value of zero and unity represent the beginning and the end of the loop. The horizontal shifts of these normalized plots suggest that the effective pore size Dp is different for the four specimens. Actually, assuming pores of “equivalent” cylindrical shape, the position of the evaporation branches of Figure 4 is analyzed in terms of the macroscopic Kelvin equation50 P γ 4 ln h = − P0 nlkBT Dp where the liquid Ar surface tension is γ = 13.1 erg/cm2 and its number density nl = 2.1 × 1022 atoms/cm3, both evaluated at a D


Langmuir

■

Article

SIMULATION RESULTS Our simulation results in Figure 6 confirm that the condensation is not affected by the shape of the pore cross

summarized in Figure 5, where the hysteresis loops observed in these circular pores are compared with those measured for the

Figure 5. Normalized hysteresis loops of Ar adsorption isotherms measured at 85 K in closed-bottom pores of circular cross sections C1−C4 made by EBL. The adsorption data are normalized to the values of the plateaus observed after capillary condensation. The curves are compared with previously published adsorption isotherms in mesoporous alumina (AAO)36 and nanopits etched in silicon (Si).41

Figure 6. Adsorption isotherms of argon at 87 K on graphitic rectangular and triangular pores with one end closed. Points T1, T2, and T3 and R1, R2, and R3 correspond to the snapshots shown in Figure 7.

closed-bottom AAO pores36 and in chemically etched silicon pits presenting bottlenecks formed by re-entrant planes (111̅) and (111) sample labeled δ3 in ref 41. Sample C1 was the first one exhibiting a resonance at low temperatures and providing a detectable adsorption signal. Its hysteresis loop is the widest one among those of Figure 5. According to the analysis introduced in ref 36, this wide loop is indicative of irregularities in the pores. A detailed analysis of the pores cross sections is obviously impossible. We have then proceeded with a study of the pore shapes by analyzing with the software ImageJ top-view SEM images of a large number of nanopores (typically more than 1500 pores, see the Supporting Information for further details). By exploiting the “Analyze Particles” function, it is possible to automatically evaluate the percentage of nanopores with the predefined parameters of size and circularity. As a result, sample C1 has a percentage of only 15% of regular circular nanopores, whereas for sample C2, which exhibits a very narrow loop, this percentage rises to near 100%. The remaining samples C2−C4 present circular pores having slightly different diameter, whereas the hysteresis loops look practically the same, also consistent with their real-space SEM analysis. These loops are somewhat narrower than those observed in self-ordered porous alumina,36 a result that could have been anticipated considering the very large aspect ratio of the AAO pores (diameter 83 nm, length 60 μm) and that the anodization process produces a variation in the pore diameter along its axis of about 1 nm. More interestingly, these loops are also narrower than that found with pits etched in silicon presenting very smooth inner walls and bottlenecks,41 suggesting that the EBL process guarantees a good surface finish. Although we are not aware of specific studies dealing with the surface finish of inner sidewalls produced by EBL on PMMA, given the polymeric composition of the material and the slow chemical development in diluted MIBK, it is plausible to suggest that those sidewalls present smoother surfaces in comparison with dry etched silicon.

section, as shown in the same reduced pressure at which the condensation occurs for the two pores. Although the condensation is not affected, the behavior of the isotherm at low loading depends on the shape of the pore cross section. Actually, the Henry constant derived from the adsorption branch of the isotherm for the triangular pore is 1.6 times greater than that of the square cross section.54 This is because the adsorbate molecules at the junctions between adjacent surfaces interact with a larger number of the neighboring surface atoms in the case of triangular cross sections. As expected, the snapshots of Figure 7 show that as the pressure is increased, atoms progressively accumulate along the strong adsorption sites at the junctions and the closed end until these are filled with a single line of adsorbed atoms.

■

CONCLUSIONS This work presents a new methodology to fabricate pores of nanometric size and different cross sections by writing with the EBL technique a pattern on a PMMA resist deposited on the electrodes of a QCM. The exposed PMMA layer does not degrade the quality factor or the long-term and short-term stabilities of the device even at cryogenic temperatures. Argon adsorption isotherms at 85 K exhibit pronounced hysteresis loops. No difference is observed in the hysteresis loops between triangular and square pores, as expected considering their size. The circular pores show very narrow loops suggesting that they are more regular than the other pores. All of these observations confirm that the main cause of hysteresis relies on the pore irregularities of the porous matrix. It would be interesting to extend these measurements to much narrower pores where differences arising from the pores’ cross section may be detected. However, this kind of study is challenging because of the difficulties of fabricating very dense and large arrays of smaller nanostructures with high aspect ratios (pores 250 nm depth). These nanopores could be produced by EBL, focussed ion beam milling, though with E


Article

Langmuir

Figure 7. continued

F


Article

Langmuir

Figure 7. (a) Snapshots of argon adsorption at 87 K for triangular pores at different pressures labeled in Figure 6. (b) Snapshots of argon adsorption at 87 K for rectangular pores at different pressures labeled in Figure 6.

for resolutions below 20 nm.55 Alternatively, given the regular periodicity of the nanopore patterns, interference UV

extremely long fabrication times, or with hot-tip writing nanolithography, in which an AFM tip is used as writing tool G


Article

Langmuir

(10) Lee, W.; Ji, R.; Gösele, U.; Nielsch, K. Fast fabrication of longrange ordered porous alumina membranes by hard anodization. Nat. Mater. 2006, 5, 741−747. (11) Bruschi, L.; Carlin, A.; Mistura, G. Wetting on a geometrically structured substrate. J. Chem. Phys. 2001, 115, 6200−6203. (12) Rodahl, M.; Höök, F.; Krozer, A.; Brzezinski, P.; Kasemo, B. Quartz crystal microbalance setup for frequency and Q-factor measurements in gaseous and liquid environments. Rev. Sci. Instrum. 1995, 66, 3924−3930. (13) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity; Academic Press: London, 1982. (14) Morishige, K. Adsorption hysteresis in ordered mesoporous silicas. Adsorption 2008, 14, 157−163. (15) Mistura, G.; Bruschi, L.; Lee, W. Adsorption on highly ordered porous alumina. J. Low Temp. Phys. 2016, 185, 138−160. (16) Horikawa, T.; Do, D. D.; Nicholson, D. Capillary condensation of adsorbates in porous materials. Adv. Colloid Interface Sci. 2011, 169, 40−58. (17) Cohan, L. H. Sorption hysteresis and the vapor pressure of concave surfaces. J. Am. Chem. Soc. 1938, 60, 433−435. (18) Parry, A. O.; Rascón, C.; Wilding, N. B.; Evans, R. Condensation in a capped capillary is a continuous critical phenomenon. Phys. Rev. Lett. 2007, 98, 226101. (19) Roth, R.; Parry, A. O. Drying in a capped capillary. Mol. Phys. 2011, 109, 1159−1167. (20) Parry, A. O.; Rascón, C. Scaling properties of fluid adsorption near the base of a cylinder. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2012, 85, 031606. (21) Parry, A. O.; Rascón, C. Fluid adsorption at the base of a cylinder. Phys. Rev. Lett. 2011, 107, 206104. (22) Marconi, U. M. B.; Van Swol, F. Microscopic model for hysteresis and phase equilibria of fluids confined between parallel plates. Phys. Rev. A: At., Mol., Opt. Phys. 1989, 39, 4109−4116. (23) Libby, B.; Monson, P. A. Adsorption/desorption hysteresis in inkbottle pores: a density functional theory and Monte Carlo simulation study. Langmuir 2004, 20, 4289−4294. (24) Monson, P. A. Understanding adsorption/desorption hysteresis for fluids in mesoporous materials using simple molecular models and classical density functional theory. Microporous Mesoporous Mater. 2012, 160, 47−66. (25) Sarkisov, L.; Monson, P. A. Modeling of adsorption and desorption in pores of simple geometry using molecular dynamics. Langmuir 2001, 17, 7600−7604. (26) Schneider, D.; Valiullin, R.; Monson, P. A. Filling dynamics of closed end nanocapillaries. Langmuir 2014, 30, 1290−1294. (27) Gelb, L. D. The ins and outs of capillary condensation in cylindrical pores. Mol. Phys. 2002, 100, 2049−2057. (28) Zeng, Y.; Prasetyo, L.; Tan, S. J.; Fan, C.; Do, D. D.; Nicholson, D. On the hysteresis of adsorption and desorption of simple gases in open end and closed end pores. Chem. Eng. Sci. 2017, 158, 462−479. (29) Coasne, B.; Grosman, A.; Ortega, C.; Simon, M. Adsorption in noninterconnected pores open at one or at both ends: a reconsideration of the origin of the hysteresis phenomenon. Phys. Rev. Lett. 2002, 88, 256102. (30) Morishige, K.; Ito, M. Capillary condensation of nitrogen in MCM-41 and SBA-15. J. Chem. Phys. 2002, 117, 8036−8041. (31) Wallacher, D.; Künzner, N.; Kovalev, D.; Knorr, N.; Knorr, K. Capillary condensation in linear mesopores of different shape. Phys. Rev. Lett. 2004, 92, 195704. (32) Bruschi, L.; Fois, G.; Mistura, G.; Sklarek, K.; Hillebrand, R.; Steinhart, M.; Gö sele, U. Adsorption hysteresis in self-ordered nanoporous alumina. Langmuir 2008, 24, 10936−10941. (33) Casanova, F.; Chiang, C. E.; Li, C.-P.; Roshchin, I. V.; Ruminski, A. M.; Sailor, M. J.; Schuller, I. K. Gas adsorption and capillary condensation in nanoporous alumina films. Nanotechnology 2008, 19, 315709. (34) Casanova, F.; Chiang, C. E.; Li, C.-P.; Roshchin, I. V.; Ruminski, A. M.; Sailor, M. J.; Schuller, I. K. Effect of surface interactions on the

lithography may be used to produce masters that can be exploited for nanoimprinting.56 We conclude by pointing out that QCM with tailored porous layers can find useful applications in gas sensing where enhanced sensitivities are required. The possibility to customize the porous patterns presents advantages with respect to simply replacing the conventional gold electrodes with porous gold electrodes made by selectively leaching out silver from the ingots of the Ag−Au alloy.57

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.7b03695. Example of particle analysis performed with ImageJ on sample C1 and C3; dark-field optical image of a silicon wafer surface and a QCM gold electrode; and AFM surface map of a QCM (PDF)

■

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (G.M.). *E-mail: [email protected] (M.D.). ORCID

Giampaolo Mistura: 0000-0002-3426-5475 Duong D. Do: 0000-0003-4222-489X Michele Dipalo: 0000-0002-1823-8231 Francesco De Angelis: 0000-0001-6053-2488 Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Jin, M.; Feng, X.; Feng, L.; Sun, T.; Zhai, J.; Li, T.; Jiang, L. Superhydrophobic aligned polystyrene nanotube films with high adhesive force. Adv. Mater. 2005, 17, 1977−1981. (2) Lee, W.; Han, H.; Lotnyk, A.; Schubert, M. A.; Senz, S.; Alexe, M.; Hesse, D.; Baik, S.; Gösele, U. Individually addressable epitaxial ferroelectric nanocapacitor arrays with near Tb inch-2 density. Nat. Nanotechnol. 2008, 3, 402−407. (3) Yao, X.; Hu, Y.; Grinthal, A.; Wong, T.-S.; Mahadevan, L.; Aizenberg, J. Adaptive fluid-infused porous films with tunable transparency and wettability. Nat. Mater. 2013, 12, 529−534. (4) Hoa, M. L. K.; Lu, M.; Zhang, Y. Preparation of porous materials with ordered hole structure. Adv. Colloid Interface Sci. 2006, 121, 9−23. (5) Beale, M. I. J.; Benjamin, J. D.; Uren, M. J.; Chew, N. G.; Cullis, A. G. An experimental and theoretical study of the formation and microstructure of porous silicon. J. Cryst. Growth 1985, 73, 622−636. (6) Herino, R.; Bomchil, G.; Barla, K.; Bertrand, C.; Ginoux, J. L. Porosity and pore size distributions of porous silicon layers. J. Electrochem. Soc. 1987, 134, 1994. (7) Zhao, D.; Feng, J.; Huo, Q.; Melosh, N.; Fredrickson, G. H.; Chmelka, B. F.; Stucky, G. D. Triblock copolymer syntheses of mesoporous silica with periodic 50 to 300 angstrom pores. Science 1998, 279, 548−552. (8) Beck, J. S.; Vartuli, J. C.; Roth, W. J.; Leonowicz, M. E.; Kresge, C. T.; Schmitt, K. D.; Chu, C. T. W.; Olson, D. H.; Sheppard, E. W.; McCullen, S. B.; Higgins, J. B.; Schlenker, J. L. A new family of mesoporous molecular sieves prepared with liquid crystal templates. J. Am. Chem. Soc. 1992, 114, 10834−10843. (9) Masuda, H.; Fukuda, K. Ordered Metal Nanohole Arrays Made by a Two-Step Replication of Honeycomb Structures of Anodic Alumina. Science 1995, 268, 1466−1468. H


Article

Langmuir hysteresis of capillary condensation in nanopores. Europhys. Lett. 2008, 81, 26003. (35) Grosman, A.; Ortega, C. Capillary condensation in porous materials. Hysteresis and interaction mechanism without pore blocking/percolation process. Langmuir 2008, 24, 3977−3986. (36) Bruschi, L.; Mistura, G.; Nguyen, P. T. M.; Do, D. D.; Nicholson, D.; Park, S.-J.; Lee, W. Adsorption in alumina pores open at one and at both ends. Nanoscale 2015, 7, 2587−2596. (37) Grosman, A.; Puibasset, J.; Rolley, E. Adsorption-induced strain of a nanoscale silicon honeycomb. Europhys. Lett. 2015, 109, 56002. (38) Ancilotto, F.; Da Re, M.; Grubišić, S.; Hernando, A.; Silvestrelli, P. L.; Toigo, F. Grand Canonical Monte Carlo study of argon adsorption in aluminium nanopores. Mol. Phys. 2011, 109, 2787− 2796. (39) Malijevský, A. Does adsorption in a single nanogroove exhibit hysteresis? J. Chem. Phys. 2012, 137, 214704. (40) Paul, R.; Rieger, H. Condensation phenomena in nanopores: A Monte Carlo study. J. Chem. Phys. 2005, 123, 024708. (41) Mistura, G.; Pozzato, A.; Grenci, G.; Bruschi, L.; Tormen, M. Continuous adsorption in highly ordered porous matrices made by nanolithography. Nat. Commun. 2013, 4, 2966. (42) Saeed, A.; Panaro, S.; Zaccaria, R. P.; Raja, W.; Liberale, C.; Dipalo, M.; Messina, G. C.; Wang, H.; De Angelis, F.; Toma, A. Stacked optical antennas for plasmon propagation in a 5 nm-confined cavity. Sci. Rep. 2015, 5, 11237. (43) Vieu, C.; Carcenac, F.; Pépin, A.; Chen, Y.; Mejias, M.; Lebib, A.; Manin-Ferlazzo, L.; Couraud, L.; Launois, H. Electron beam lithography: resolution limits and applications. Appl. Surf. Sci. 2000, 164, 111−117. (44) Pierno, M.; Bruschi, L.; Mistura, G.; Boragno, C.; de Mongeot, F. B.; Valbusa, U.; Martella, C. Nanofriction of adsorbed monolayers on superconducting lead. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 035448. (45) Jensen, K.; Kim, K.; Zettl, A. An atomic-resolution nanomechanical mass sensor. Nat. Nanotechnol. 2008, 3, 533−537. (46) Hanay, M. S.; Kelber, S.; Naik, A. K.; Chi, D.; Hentz, S.; Bullard, E. C.; Colinet, E.; Duraffourg, L.; Roukes, M. L. Single-protein nanomechanical mass spectrometry in real time. Nat. Nanotechnol. 2012, 7, 602−608. (47) Bruschi, L.; Mistura, G. Measurement of the friction of thin films by means of a quartz microbalance in the presence of a finite vapor pressure. Phys. Rev. B: Condens. Matter Mater. Phys. 2001, 63, 235411. (48) Morishige, K. Nature of adsorption hysteresis in cylindrical pores: effect of pore corrugation. J. Phys. Chem. C 2016, 120, 22508− 22514. (49) Grosman, A.; Ortega, C. Cavitation in metastable fluids confined to linear mesopores. Langmuir 2011, 27, 2364−2374. (50) Evans, R.; Marconi, U. M. B.; Tarazona, P. Capillary condensation and adsorption in cylindrical and slit-like pores. J. Chem. Soc., Faraday Trans. 2 1986, 82, 1763−1787. (51) Wang, Y.; Do, D. D.; Herrera, L. F.; Nicholson, D. On the condensation/evaporation pressures and isosteric heats for argon adsorption in pores of different cross-sections. Colloids Surf., A 2013, 420, 96−102. (52) Malanoski, A. P.; van Swol, F. Lattice density functional theory investigation of pore shape effects. I. Adsorption in single nonperiodic pores. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2002, 66, 041602. (53) Ustinov, E. A. Modeling of N2 Adsorption in MCM-41 materials: hexagonal pores versus cylindrical pores. Langmuir 2009, 25, 7450−7456. (54) Do, D. D.; Nicholson, D.; Do, H. D. On the Henry constant and isosteric heat at zero loading in gas phase adsorption. J. Colloid Interface Sci. 2008, 324, 15−24. (55) Seniutinas, G.; Balčytis, A.; Reklaitis, I.; Chen, F.; Davis, J.; David, C.; Juodkazis, S. Tipping solutions: emerging 3D nanofabrication/-imaging technologies. Nanophotonics 2017, 6, 923−941. (56) Li, W.; Marconi, M. C. Extreme ultraviolet Talbot interference lithography. Opt. Express 2015, 23, 25532−25538.

(57) Hieda, M.; Garcia, R.; Dixon, M.; Daniel, T.; Allara, D.; Chan, M. H. W. Ultrasensitive quartz crystal microbalance with porous gold electrodes. Appl. Phys. Lett. 2004, 84, 628−630.

I


Adsorption on Nanopores of Different Cross Sections Made by

Recommend Documents