Evaporation from an Ink-Bottle Pore: Mechanisms of Adsorption and

Mar 3, 2014 - We present a molecular simulation study of argon adsorption and desorption in ink-bottle pores in order to investigate the effects of po...
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Evaporation from an Ink-Bottle Pore: Mechanisms of Adsorption and Desorption Yonghong Zeng,† Chunyan Fan,‡ D. D. Do,*,† and D. Nicholson† †

School of Chemical Engineering, University of Queensland, St. Lucia, QLD 4072, Australia Department of Chemical Engineering, Curtin University, Perth, WA 6845, Australia

‡

S Supporting Information *

ABSTRACT: We present a molecular simulation study of argon adsorption and desorption in ink-bottle pores in order to investigate the effects of pore width, length, and temperature on the form of the hysteresis loop, with particular emphasis on the pressure at which evaporation occurs. We show that intrinsic cavitation occurs only in an ink-bottle pore with a sufficiently long and narrow neck. The tension in the condensed fluid is characterized by the average value of the shortest distance between molecules, and when this reaches a critical value, cavitation occurs. As the neck width is increased or the neck length is decreased, the evaporation mechanism in the cavity switches from cavitation to evaporation at higher pressure than the cavitation pressure (which we call cavitation-like pore opening). For cavitation-like pore opening, the evaporation pressure is greater than the intrinsic cavitation pressure and the tensile strength just prior to evaporation is less than the critical tension. For a given temperature, the reduced pressure of cavitation, (P/P0)cav, is always lower than the cavitation-like pore opening reduced pressure, and (P/P0)cav follows a linear dependence on the temperature. The intersection between the cavitation curve and the cavitationlike pore opening curve for a given neck size is the transition temperature, Ttrans: for T < Ttrans, cavitation-like pore opening is the operating mechanism, while cavitation occurs for T > Ttrans.

1. INTRODUCTION Adsorption of simple gases such as argon in mesoporous solids is extensively used to characterize porous structure1−3 since characterization of a porous solid is an essential step in the application of adsorbents to separation or purification process.4−9 For adsorption of a given adsorbate in a mesoporous solid of a given pore size, the condensation pressure is not the same as the evaporation pressure for temperatures less than the critical hysteresis temperature (Tch), resulting in a hysteresis loop whose size, shape, and position are complex functions of the adsorbate−solid pair and the temperature.10 Consequently, Tch is a function of the adsorbate−solid pair and the pore geometry. Experimental observations have shown that Tch increases with increasing pore width, and therefore, at a given temperature there is a critical pore size below which adsorption is reversible and the adsorption follows a micropore filling mechanism. Since the hysteresis loop, particularly the pressure dependence of its adsorption and desorption boundaries, is widely used in the calculation of pore size distributions (PSDs), many studies have been carried out to understand the microscopic origin of the hysteresis, particularly its functional dependence on pore size, in order to derive the structural properties of a porous solid. This functional dependence is different for adsorption and desorption, which gives rise to different hysteresis loop shapes, and for this reason attempts have been made to classify the loop shapes observed experimentally. Four types have been identified by IUPAC: H1 to H4.11,12 Among these, type H2, which has a gradually increasing adsorption branch and a characteristically steep desorption branch (associated with the cavity),3 is commonly found for disordered solids. The desorption pressure is generally found to be independent of © XXXX American Chemical Society

the cavity size, and as such, it cannot be used to determine the PSD. For example, the characteristic reduced pressure of cavitation for nitrogen at 77 K, (P/P0)cav (where P0 is the saturation vapor pressure), is invariably found experimentally to occur at about 0.42.12,13 Interconnected network structures in which large cavities are surrounded by smaller necks connected to the bulk gas (commonly described as ink-bottle pores) have been proposed as a possible explanation of this phenomenon.14 Desorption from filled ink-bottle pores has been shown to occur via two possible mechanisms: pore blocking and cavitation.15−17 The pore blocking mechanism is a process in which a meniscus formed at the mouth of the neck recedes into the pore interior until the cavity is gradually emptied; cavitation occurs when the neck is so small that the condensed fluid in the cavity is stretched to the limit of its mechanical stability, at which point the interior of the cavity empties while the neck remains (partially) filled. Recent simulation studies have shown that the desorption mechanism of a given gas can switch from pore blocking to cavitation when the necks are smaller than a critical size at a given temperature, when the temperature is increased for a given neck size, or when the adsorbate species is altered.16,18 Molecular simulation studies have helped to uncover the underlying mechanism of the cavitation phenomenon: for example, an investigation of adsorption and desorption in pores Special Issue: Alirio Rodrigues Festschrift Received: January 15, 2014 Revised: February 27, 2014 Accepted: March 3, 2014

A

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Figure 1. Schematic diagram of three slit-shaped pores: (a) ink-bottle pore; (b) closed pore; (c) open-end pore. A closed pore is defined as one that is not open to the surrounding gas. Periodic boundary conditions were applied in the x direction.

each point on the isotherm, 50 000 cycles were run in both the equilibration and sampling stages. Each cycle consisted of 1000 attempted displacements, insertions, or deletions with equal probability. The cutoff radius was set as half of the simulation box length. In the equilibration stage, the maximum displacement step length was initially set as half of the box length and was adjusted during the equilibration stage to achieve an acceptance ratio for displacement of 20%.26 The final step length used in the sampling stage was chosen to give this acceptance ratio. The pore density, ρ, is defined as the number of particles per unit accessible volume and was calculated using the following equation:

without connectivity, using molecular dynamics (MD) and Monte Carlo (MC) methods, led Sarkisov and Monson19 to question the validity of the network percolation theory. Ravikovitch and Neimark,20 using nonlocal density functional theory (NLDFT), showed that the desorption mechanism changes from pore blocking to cavitation when the neck of an ink-bottle pore is smaller than a certain value. Using local compressibility as a measure of the cohesiveness of the adsorbate, Fan et al.21 proposed that the difference in the compressibility of the fluid in the neck and the cavity is a critical indicator to distinguish cavitation from pore blocking. In previous work,10 we comprehensively examined the evaporation mechanism in cylindrical ink-bottle pores by grand canonical Monte Carlo (GCMC) simulations. Our simulation results confirmed the existence of two mechanisms for evaporation in addition to conventional cavitation and pore blocking: cavitation-like pore opening and advanced evaporation from the cavity. In the present study, we have extended this work to slitlike ink-bottle pores with silica surfaces and confirmed the existence of these two phenomena. We focused our attention on the evaporation pressure and obtained the functional dependence of the evaporation pressure on the neck dimensions and temperature.

ρ=

g (r ) =

⟨{ΔN } NK ⟩ 4 π[(r 3

+ Δr )3 − r 3]⟨ρK ⟩

(4)

(1/NK)∑j N= K1ΔNj(r

where {ΔN}NK = → r + Δr), NK is the number of particles in core region K, ΔNj(r → r + Δr) is the number of particles in the spherical bin bounded by r and r + Δr and centered on particle j, and ρK is the mean density of particles in core region K.

(1)

with molecular parameters σff = 0.3405 nm and εff/kB = 119.8 K. The pore model consisted of three planar homogeneous silica layers that were finite in the y direction and infinite in the x direction. The solid−fluid (SF) interaction was modeled by the Bojan−Steele (BS) potential:22−24

3. RESULTS AND DISCUSSION 3.1. Adsorption in an Ink-Bottle Pore with a Narrow Neck. Evaporation from the cavity by cavitation is identified by a steep decrease in the adsorbed density at the so-called cavitation pressure20 and is observed for an ink-bottle pore having a neck size smaller than a critical value. To better understand the contributions from the cavity and neck sections of an ink-bottle pore, we compared the simulation results for the three pore models shown in Figure 1. Model (a) is an inkbottle model with cavity dimensions W1 = L1 = 7 nm and neck dimensions W2 = 1.63 nm and L2 = 10 nm. The other two models are (b) a closed pore and (c) an open-end pore with dimensions the same as the cavity and neck in (a), respectively. Simulated adsorption isotherms for argon at 87 K in the inkbottle pore are shown in the top panel of Figure 2. There are two distinct hysteresis loops, corresponding to pore filling and emptying of the neck and the cavity. The adsorption and

φf,S = 2πρS εSf σSf 2{[φrep(z , y+ ) − φrep(z , y− )] − [φatt(z , y+ ) − φatt(z , y− )]}

(3)

where ⟨N⟩ is the ensemble average of the number of particles in the simulation box and Vacc is the accessible volume of the pore, where the solid−fluid potential is nonpositive. The radial distribution function (RDF) in core region K of the pore, g(r), is defined as the probability of finding the center of a molecule at a radial distance r from the center of any given molecule:

2. THEORY 2.1. Fluid−Fluid and Solid−Fluid Potentials. Argon was modeled as a spherical molecule, with the interaction between two argon molecules, φff(r), given by the 12−6 Lennard-Jones equation, ⎡⎛ σ ⎞12 ⎛ σ ⎞6 ⎤ φff (r ) = 4εff ⎢⎜ ff ⎟ − ⎜ ff ⎟ ⎥ ⎝r ⎠⎦ ⎣⎝ r ⎠

⟨N ⟩ Vacc

(2)

where z is the shortest distance between an adsorbate atom and the surface, ρS is the surface density of silica, and σSf and εSf are the solid−fluid molecular parameters. The molecular parameters for the silica surface are ρSεSf/kB =2620 K/nm2 and σSf = 0.30 nm.25 The variables y+ and y− are defined in the Supporting Information. 2.2. Monte Carlo Simulations. The simulated adsorption isotherms were obtained in the grand canonical ensemble. For B

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Figure 4. Adsorption isotherms for argon at 87 K in closed pores with square cross sections (W = L) and different cavity sizes.

Figure 2. Adsorption isotherms for argon at 87 K in the ink-bottle pore and the corresponding unit pores. Solid symbols represent adsorption branches and open symbols desorption branches.

end pore, which are shown in the bottom two panels of Figure 2. During the first stage of adsorption in the ink-bottle pore, molecular layering occurs on the pore walls of both the cavity and the neck. Condensation first occurs in the neck at a reduced pressure of 0.1 (marked as A in Figure 2) which is the same as for the corresponding open-end pore (A′) because before condensation occurs the neck behaves like an open-end pore. Once the neck has been filled, the cavity behaves as a closed pore, and therefore, the adsorption in the ink-bottle pore should then be the same as that in a closed pore. As the pressure is increased, more layers build up on the walls of the cavity until the gaslike core is small enough for the attraction between adsorbate layers from opposite surfaces to induce condensation in the cavity at point C. Upon desorption from the filled ink-bottle pore, the evaporation of the condensed fluid in the cavity is delayed compared with a uniform pore (either open at both ends or closed at one end) having the same size as the cavity. As the pressure is reduced, the fluid in the cavity is stretched until the limit of mechanical stability of the condensed fluid is reached, and bubbles then form spontaneously by cavitation, resulting in a very steep drop along the desorption branch of the isotherm at a reduced pressure of 0.27 (point D). This cavitation pressure is identical to that in the closed pore (point D′). Once cavitation has occurred in the cavity, the neck behaves as an open-end pore

Figure 3. Radial distribution functions for Ar at 87 K at the center of the 7 nm closed pore. The first peaks are shown on an enlarged scale, and the full distribution functions are shown in the inset. The dashed lines are at the distances 0.370 nm and 0.374 nm discussed in the text. The lines are labeled as in Figure 2.

desorption processes can be elucidated by comparing this isotherm with the isotherms of the closed pore and the openC

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The mean distance between neighboring molecules is a measure of the extent of stretching in the condensed fluid, and it can be estimated from the position of the first maximum in the radial distribution function. Figure 3 shows RDFs for the argon adsorbate inside a 1 nm cubic region at the center of the 7 nm square closed pore. At pressures above the cavitation pressure, the RDF maximum is at a separation of 0.37 nm, and just before the cavitation this distance increases to 0.374 nm, which just exceeds the mean distance between molecules in liquid argon at 87 K;27 the adsorbate fluid is therefore under tension, and cavitation occurs. 3.2. Effect of Cavity Size. Although cavity formation is primarily dependent on the tensile strength of the bulk fluid, it is also modified by the presence of the adsorbent field, which is intensified as the cavity size is reduced as a result of potential overlap.15 Therefore, the evaporation pressure is reduced below the intrinsic value of 0.27 in order to stretch the fluid to the critical separation distance of 0.374 nm. To illustrate this, in Figure 4 we show isotherms for closed pores with square cross sections of various dimensions [model (b) in Figure 1]. The smallest pore (3 nm) has a hysteresis loop that is significantly smaller that those in the larger pores, with both the condensation and evaporation pressures shifted to lower values. In the pores with larger cavities (9 and 11 nm), the size of the hysteresis loop increases with pore size, mainly because a shift in the condensation pressure to higher values is necessary to build up the adsorbed layers to a thickness where the gaslike core is small enough for condensation to occur while the reduced pressure at evaporation, which is due to the tension of argon at 87 K, remains at 0.27. 3.3. Effect of Neck Width. Our earlier studies of ink-bottle pores showed that the desorption mechanism passes from cavitation to pore blocking as the neck width increases.28 This is confirmed in Figure 5 for a wide range of neck widths. For pores with neck widths less than the critical size, which is 2.30 nm for argon adsorption at 87 K, the isotherms show either double hysteresis loops or a fused hysteresis loop. For pores having neck widths greater than the critical size, desorption proceeds by pore blocking, in which a meniscus formed at the mouth of the neck recedes into the pore interior until the cavity is emptied by a sharp evaporation of the residual concave lens at a single reduced pressure. This process results in a characteristic knee in the desorption branch of the isotherm, with evaporation from the cavity occurring at a pressure higher than the intrinsic cavitation pressure. This phenomenon is better described by the term cavitation-like pore opening10 because of the sequential processes of meniscus withdrawal from the neck and the sharp evaporation from the cavity and the neck. In this mechanism, the onset of evaporation is associated with the tension of the condensed fluid in the cavity and the extent of filling in the neck. As the pressure is decreased, the amount of adsorbate filling the neck is reduced when the meniscus recedes and at the same time the condensed fluid in the cavity is stretched. When the meniscus is close to the junction between the neck and the cavity, the condensed fluid in the cavity evaporates at a pressure higher than the cavitation pressure. It should be emphasized that the process of cavitation-like pore opening does not involve bubble formation in the interior, as distinct from cavitation, where bubble formation is an essential part of the mechanism. For those ink-bottle pores having small necks, the adsorption branch shows two steps, with the first condensation step being shifted to higher pressures as the neck size is increased because

Figure 5. Adsorption isotherms for argon at 87 K in ink-bottle pores with different neck widths. The cavity size is 9 nm × 9 nm (W1 = L1 = 9 nm), and the neck length is L2 = 10 nm.

Figure 6. Adsorption isotherms for argon at 87 K in ink-bottle pores with neck widths of 2.3 nm and different neck lengths.

with both ends of the neck exposed to the gas phase. Evaporation from the neck then occurs at a lower pressure (B), corresponding to the evaporation from the open-end pore (B′). We can conclude that it is sufficient to use a closed pore model to study cavitation microscopically. D

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Figure 7. Snapshots of argon at 87 K in ink-bottle pores with 2.3 nm wide necks just before and just after evaporation. The neck lengths for (a, a′), (b, b′), and (c, c′) are 10, 5, and 2 nm, respectively.

proceeds by the advance of a meniscus (formed at the closed end) toward the neck, which induces filling of the neck at a lower pressure than in an open-end pore of the same width. This can be described as advanced condensation in the neck. Interestingly, the neck size for advanced condensation is larger than the critical neck size for cavitation. 3.4. Effect of Neck Length. The neck length also has a significant effect on the evaporation pressure since the forces holding the adsorbate are weaker for shorter necks. The effects of the neck length were studied by keeping the neck width at 2.3 nm, which is the critical neck width at 87 K, and the simulated isotherms are shown in Figure 6. When the neck length is reduced, there is a competition between two processes for the desorption of adsorbate from the cavity: (1) evaporation followed by bubble formation in the cavity occurs when the limit of the tensile strength of the condensed fluid is reached; (2) desorption starts from the junction between the cavity and the neck (when the neck has been emptied), and this process is similar to that in a closed-end pore. Both processes are associated with steep evaporation, but it should be noted that when emptying of the cavity is dominated by the second process, the corresponding evaporation pressure is higher than the cavitation pressure. Figure 7 shows snapshots of the adsorbate just before and just after evaporation in the cavity. In the pore with an extralong neck (10 nm), the desorption mechanism is cavitation, which occurs at a reduced pressure of 0.27 as discussed earlier. In this case, desorption from the cavity is hindered by the constriction of the neck, and the metastable fluid in the cavity is stretched because of the reduction in pressure. When the pressure is further decreased, the condensed fluid is stretched to its limit of mechanical stability, at which point the fluid in the center of the cavity empties instantly, leaving a gas-like bubble, while the neck remains (partially) filled. When the neck is shorter (5 nm), a phenomenon termed advanced evaporation10 is observed in the neck, which occurs at the cavitation pressure (i.e., the condensed fluids in the cavity and the neck evaporate at the same time). This occurs because when the condensed fluid in the cavity evaporates at the cavitation pressure, Pcav, the neck changes its status from that of a closed-end pore to that of an open-end pore, and since the evaporation pressure of the neck having open ends is lower than the cavitation pressure, the fluid in the neck also evaporates as soon as cavitation occurs in the cavity. For pores having even shorter necks (less than 2 nm), desorption is controlled by cavitation-like pore opening in the cavity because the weaker adsorbent field at the neck does not hinder the removal of adsorbate, and the cavity therefore

Figure 8. Radial distribution functions from a cubic core region at the cavity center for argon at 87 K in ink bottle pores with different neck lengths. The vertical dashed line is drawn at the position of the equilibrium separation (0.374 nm).

Figure 9. Temperature dependence of the evaporation pressure of argon from ink-bottle pores and a closed pore. The ink-bottle cavity has dimensions 9 × 9 nm and a neck length of 3 nm. The saturation vapor pressure for argon at different temperature was calculated from ref.29

a higher pressure is required for condensation to occur in the larger necks. When the neck is wide enough, adsorption E

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Figure 10. Evolution of condensation and evaporation mechanism in ink-bottle pores. All of the isotherms shown can be obtained by increasing the neck width or reducing the neck length.

behaves like a closed-end pore, in which the sole mechanism for desorption is pore blocking. Thus, evaporation from a cavity depends on the adjoining neck length, and the evaporation pressure is shifted to higher values as the neck length is reduced. To gain further insight into how molecules behave microscopically, the radial distribution functions shown in Figure 8 were obtained for ink-bottle pores with various neck lengths inside a 1 nm cube at the center of the cavity at pressures just before evaporation. For neck lengths longer than 2 nm, the maxima in the first peaks are located at 0.374 nm, indicating that the fluid is under full tension and that evaporation will occur via a cavitation mechanism. On the other hand, for neck lengths shorter than 2 nm, the maximum is at 0.37 nm, which implies that bubble formation does not occur in the pore interior and that emptying of the pore is controlled by a cavitation-like pore opening process. 3.5. Effects of Temperature. We also investigated the effect of temperature on evaporation in a closed pore, where cavitation is the only mechanism of evaporation, and in an inkbottle pore with a relatively wide neck, where evaporation proceeds via cavitation-like pore opening. When the evaporation reduced pressure (P/P0) is plotted against reduced temperature (Figure 9), a number of interesting points may be noted:

2. Desorption from the ink-bottle pore is controlled by cavitation-like pore opening at low temperatures, but the mechanism switches to cavitation at some transition temperature. 3. The transition temperature is dependent on the pore dimensions.

4. SUMMARY OF CONDENSATION AND EVAPORATION MECHANISMS In Figure 10, we summarize the evolution of isotherms obtained for an ink-bottle pore and the corresponding condensation and evaporation mechanisms. For condensation, there are two possible mechanisms: (1) Condensation in the neck followed by condensation in the cavity occurs, resulting in a double loop or fused loop hysteresis (see the adsorption branches of the top four isotherms in Figure 10). This typically occurs with narrow necks and at high temperatures. (2) A meniscus is formed at the closed end of the cavity and advances to the junction of the cavity with the neck when advanced condensation in the neck occurs. This typically occurs for larger necks and low temperatures. For evaporation, we identify four mechanisms, depending on the neck dimensions: (1) When the neck is smaller than a critical size and sufficiently long, the desorption branch occurs in two steps. The first step is associated with the cavitation of

1. The reduced pressures of evaporation from both pores shift to higher values as the temperature increases. F

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the condensed fluid in the cavity and the second step (at a lower pressure) with the evaporation from the neck, which behaves as an open-end pore prior to evaporation. This is shown in the desorption branches of the top two isotherms. (2) When the neck is reduced in length or increased in width, evaporation in the neck is induced by cavitation in the cavity, resulting in a single-step evaporation. We refer to this as advanced evaporation in the neck. This is shown in the third isotherm. (3) When the neck is larger than the critical size, the evaporation mechanism is cavitation-like pore opening, which can be distinguished by a knee shape in the desorption branch and an evaporation pressure higher than the cavitation pressure. This is shown in the fourth and fifth isotherms. (4) In pore blocking, desorption is controlled by recession of the meniscus from the pore mouth to the closed end. This is observed only when the neck width is equal to the cavity size as illustrated in the last isotherm.

(3) Everett, D. H. Adsorption Hysteresis. In The Solid−Gas Interface; Flood, E. A., Ed.; Marcel Dekker: New York, 1967; Vol. 2, pp 1055− 1113. (4) Asadi, T.; Ehsani, M. R.; Ribeiro, A. M.; Loureiro, J. M.; Rodrigues, A. E. CO2/CH4 Separation by Adsorption Using Nanoporous Metal Organic Framework Copper−Benzene-1,3,5Tricarboxylate Tablet. Chem. Eng. Technol. 2013, 36, 1231−1239. (5) Dantas, T. L. P.; Luna, F. M. T.; Silva, I. J., Jr.; de Azevedo, D. C. S.; Grande, C. A.; Rodrigues, A. E.; Moreira, R. F. P. M. Carbon Dioxide−Nitrogen Separation through Adsorption on Activated Carbon in a Fixed Bed. Chem. Eng. J. 2011, 169, 11−19. (6) Shen, C.; Yu, J.; Li, P.; Grande, C.; Rodrigues, A. Capture of CO2 from Flue Gas by Vacuum Pressure Swing Adsorption Using Activated Carbon Beads. Adsorption 2011, 17, 179−188. (7) Lopes, F. V. S.; Grande, C. A.; Rodrigues, A. E. Activated Carbon for Hydrogen Purification by Pressure Swing Adsorption: Multicomponent Breakthrough Curves and PSA Performance. Chem. Eng. Sci. 2011, 66, 303−317. (8) Grande, C. A.; Gascon, J.; Kapteijn, F.; Rodrigues, A. E. Propane/ Propylene Separation with Li-Exchanged Zeolite 13X. Chem. Eng. J. 2010, 160, 207−214. (9) Silva, M. S. P.; Moreira, M. A.; Ferreira, A. F. P.; Santos, J. C.; Silva, V. M. T. M.; Sá Gomes, P.; Minceva, M.; Mota, J. P. B.; Rodrigues, A. E. Adsorbent Evaluation Based on Experimental Breakthrough Curves: Separation of p-Xylene from C8 Isomers. Chem. Eng. Technol. 2012, 35, 1777−1785. (10) Nguyen, P. T. M.; Fan, C.; Do, D. D.; Nicholson, D. On the Cavitation-Like Pore Blocking in Ink-Bottle Pore: Evolution of Hysteresis Loop with Neck Size. J. Phys. Chem. C 2013, 117, 5475− 5484. (11) Sing, K. S. W.; Everett, D. H.; Haul, R. A. W.; Moscou, L.; Pierotti, R. A.; Rouquerol, J.; Siemieniewska, T. Reporting Physisorption Data for Gas/Solid Systems with Special Reference to the Determination of Surface Area and Porosity (Recommendations 1984). Pure Appl. Chem. 1985, 57, 603−619. (12) Sing, K. S. W.; Williams, R. T. Physisorption Hysteresis Loops and the Characterization of Nanoporous Materials. Adsorpt. Sci. Technol. 2004, 22, 773−782. (13) Thommes, M.; Smarsly, B.; Groenewolt, M.; Ravikovitch, P. I.; Neimark, A. V. Adsorption Hysteresis of Nitrogen and Argon in Pore Networks and Characterization of Novel Micro- and Mesoporous Silicas. Langmuir 2006, 22, 756−764. (14) McBain, J. W. An Explanation of Hysteresis in the Hydration and Dehydration of Gels. J. Am. Chem. Soc. 1935, 57, 699−700. (15) Rasmussen, C. J.; Vishnyakov, A.; Thommes, M.; Smarsly, B. M.; Kleitz, F.; Neimark, A. V. Cavitation in Metastable Liquid Nitrogen Confined to Nanoscale Pores. Langmuir 2010, 26, 10147− 10157. (16) Ravikovitch, P. I.; Neimark, A. V. Density Functional Theory of Adsorption in Spherical Cavities and Pore Size Characterization of Templated Nanoporous Silicas with Cubic and Three-Dimensional Hexagonal Structures. Langmuir 2002, 18, 1550−1560. (17) Neimark, A. V.; Vishnyakov, A. The Birth of a Bubble: A Molecular Simulation Study. J. Chem. Phys. 2005, 122, No. 054707. (18) Morishige, K.; Tateishi, N.; Hirose, F.; Aramaki, K. Change in Desorption Mechanism from Pore Blocking to Cavitation with Temperature for Nitrogen in Ordered Silica with Cagelike Pores. Langmuir 2006, 22, 9920−9924. (19) Sarkisov, L.; Monson, P. A. Lattice Model of Adsorption in Disordered Porous Materials: Mean-Field Density Functional Theory and Monte Carlo Simulations. Phys. Rev. E 2001, 65, No. 011202. (20) Ravikovitch, P. I.; Neimark, A. V. Experimental Confirmation of Different Mechanisms of Evaporation from Ink-Bottle Type Pores: Equilibrium, Pore Blocking, and Cavitation. Langmuir 2002, 18, 9830−9837. (21) Fan, C.; Do, D. D.; Nicholson, D. On the Cavitation and Pore Blocking in Slit-Shaped Ink-Bottle Pores. Langmuir 2011, 27, 3511− 3526.

5. CONCLUSIONS We have carried out a detailed GCMC simulation study of argon adsorption in ink-bottle pores and in closed pores to explore the effects of the neck dimensions and temperature on the evaporation of argon. From our microscopic analysis, we found the following: (1) the average distance between molecules in the condensed fluid expands to a critical value (0.374 nm) just before cavitation at 87 K; (2) besides the usual mechanisms of evaporation (cavitation and pore blocking), desorption in an ink-bottle pore can be governed by another mechanism, cavitation-like pore opening, which depends on the neck dimensions and temperature; and (3) the reduced pressure at cavitation has a linear dependence on the reduced temperature and is always lower than that for cavitation-like pore opening when temperature is less than a threshold value.

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ASSOCIATED CONTENT

S Supporting Information *

Bojan−Steele equation and its limit for small z. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS ́ E. This paper is a contribution in honor of Professor Alirio Rodrigues of the University of Porto on the occasion of his 70th birthday. This project was supported by the Australian Research Council.

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REFERENCES

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H

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