Correlation between the Sorption-Induced Deformation of Nanoporous

Article pubs.acs.org/Langmuir

Correlation between the Sorption-Induced Deformation of Nanoporous Glass and the Continuous Freezing of Adsorbed Argon Klaus Schappert,* Nicolas Reiplinger, and Rolf Pelster* FR 7.2 Experimentalphysik, Universität des Saarlandes, 66123 Saarbrücken, Germany

ABSTRACT: In this article we study the dependence of the sorption-induced deformation of nanoporous glass on the liquid− solid phase transition of adsorbed argon. During cooling we observe a continuous reduction of the expansion of the porous glass matrix caused by the adsorbate. The contraction is attended by a likewise continuous change of the adsorbed argon’s phase state from liquid to solid. This simultaneous behavior evidences that the liquid−solid phase transition leads to a reduction of the pressure the adsorbate exerts on the pore walls. Furthermore, the study shows that small temperature changes can temporarily cause strong deformations of the porous material that decay in long time intervals of up to 1 week. We expect that our observations for the model system of argon and porous glass can be generalized to other systems. Consequently, this study will have implications when considering porous materials for applications, e.g., as a medium for storage.

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INTRODUCTION Adsorption in pores is a ubiquitous phenomenon both in nature as well as in numerous applications. Nanoporous materials can, e.g., be used for the storage of substances like methane in the automobile industry.1 The high concentration of carbon dioxide in the atmosphere has led to the study of possibilities of a geological storage of CO2.2,3 An effect that is of special interest in this connection is the deformation of a porous matrix in consequence of the adsorption of a substance.3−28 This sorption-induced deformation depends on the elasticity of the pore system.4−6,10,24 Adsorbates exert a pressure on the pore walls and the porous matrix expands in consequence of a change of the surface free energy, respectively of the surface stress.5,25,27,29 Within a thermodynamic approach, the deformation can be explained as a result of the so-called solvation pressure pS.4,5,29 The formation of concave menisci between the adsorbate and the vapor counteracts the expansion because the strong curvature of such a meniscus is related to a high contracting Laplace pressure (see, e.g., refs 4 and 5). The deformation depends on the interaction between the adsorbate and the pore surface, the pore size distribution, and the packing of the molecules (see, e.g., refs 18 and 30−33). Thus, porous matrices expand and contract during the filling process (the same holds for draining), and even abrupt changes can occur at fillings where capillary bridges form or vanish.12 © 2016 American Chemical Society

The study of sorption-induced deformation and of the factors influencing the extent of this effect are of great importance for a number of applications. Sorption-induced deformation plays a major role for the recovery of methane from porous rocks,8,9 but also in the geological storage of CO2.2,3 The influence of temperature changes and of the adsorbate’s solidification on the deformation is of particular interest, also because the exertion of high pressures on adsorbates can lead to changes of its phase state. Both liquid−solid phase transitions in nanopores34,35 and the influence of these phase transitions (or also glass transitions) on the deformation of porous samples7,28,36−45 have been intensively explored. Many of these studies addressed the anomalous adsorbate water, also because of its relevance in concret, rocks, or soils.7,37,39−45 Length changes of the porous materials during temperature cycles were among others attributed to the freezing of the adsorbate, to its migration between sample and sample cell as well as to changes of the adsorbate’s menisci.7,36,38,39 In this Article we present a combined study of the temperature-dependent sorption-induced deformation and the elasticity of the adsorbate. With this combination we reveal a Received: April 22, 2016 Revised: July 8, 2016 Published: July 11, 2016 7741

DOI: 10.1021/acs.langmuir.6b01533 Langmuir 2016, 32, 7741−7746

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Figure 1. Elongation Δl of the porous glass in consequence of the adsorbed argon as a function of temperature for (a) the full sample and (b) the sample with one adsorbed argon layer. During cooling the dilatation of the sample caused by the adsorbed argon decreases continuously below T ≈ 76 K for the full sample (see panel a). For one surface layer, the decrease is particularly strong for temperatures below ≈35 K. (c,d) Temperature K K = 6.37 GPa, G43 = 6.62 GPa). The dependence of the effective shear modulus G scaled to the shear modulus of the empty sample, G0 (G86 0 0 continuous increase of G/G0 indicates a continuous freezing of the adsorbed argon (for the full sample below T ≈ 76 K). (e,f) Fraction xfr of solid argon as a function of temperature. A reduction of temperature below the onset of freezing causes a continuous increase of xfr, i.e., the lower the temperature, the smaller the amount of liquid argon. These measurements are very time-consuming, e.g., for the full sample a waiting time of about 4 days was necessary to reach a stable value for the height of the sample after a temperature change from 55 to 50 K (see also discussion). This slow equilibration resulted in measurement times of several weeks. A faster conduct of the experiment would have considerably influenced the measured deformation and could result in the interpretation of nonequilibrium states. The filling of the sample with liquid argon was undertaken at 86 K via the gas phase. The molar amount of adsorbed argon, nads,total, and its volume Vads,total, was calculated via the ideal gas equation (cp. ref 12). During one measurement, the pores of the Vycor sample were completely filled, i.e., the volume filling fraction f = Vads,total/Vpores = 1 and during the other experiment the filling corresponded to approximately one adsorbed argon layer (with a thickness u ≈ 0.34 nm on the pore walls, i.e., f = (r2P − (rP − u)2)/r2P ≈ 0.18). The measurement with f = 1 was performed at the vapor pressure of bulk argon, p0. During this measurement, there was additional condensed argon in the sample cell to ensure a complete filling of the pores during cooling. For the measurement with a partial pore filling the sample was initially filled with a filling fraction of f ≈ 0.11 at 86 K, corresponding to an incomplete coverage of the pore walls (relative pressure of p/p0 = 0.09). During cooling, argon vapor from the sample cell condensed into the pores until, at temperatures below 65 K, a nearly constant filling of the pores with f ≈ 0.18, i.e. a monolayer, was reached. For lower temperatures, the vapor pressure of argon and hence the amount of argon vapor in the sample cell is negligible. Simultaneously to the deformation we performed ultrasonic measurements. The effective shear modulus G was determined with

direct correlation between the deformation caused by the adsorbate and its composition of (coexisting) liquid and solid.

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EXPERIMENTAL DETAILS

The influence of the adsorbed argon on the deformation of a nanoporous Vycor glass sample (average pore radius rP = 3.7 nm, porosity ϕ = 27%) was measured with a capacitative distance sensor, which was mounted a few micrometers above the upper surface of the sample. Any change of the height l of the sample modifies the measured distance d between the sample’s surface and the sensor. The experimental setup for the measurements is described in more detail in ref 12. We estimate the error in the measured deformation to be ≤0.06 μm. The temperature dependence of the sorption-induced length change Δl(T) = d0(T) − df(T) is determined from the difference between the measured distance during a temperature cycle with the empty sample, d0(T), and the temperature-dependent distance with the (partially) filled sample, df(T). Consequently, the length changes Δl depicted in this paper display directly the contribution of the adsorbed argon on the expansion of the porous sample at different temperatures. The temperature dependence of the deformation of the empty sample due to its thermal contraction is excluded, while any temperature dependent influence of the adsorbed argon on the deformation is disclosed. However, the thermal expansion coefficient of porous glass is typical rather small (≈ 8 × 10−7 K−1),28 i.e., the height of the sample l0(T) can be regarded as almost constant during the measurements. The length of the sample at room temperature is l0 ≈ 2.66 mm. 7742

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Langmuir the aid of the measured velocity of the ultrasonic shear waves propagating through the sample, ct, and the effective density ρ via the relation G = c2t ρ. The effective density ρ = ρ0(1 + nads,totalm/M0) was calculated from the density of the empty sample ρ0 and its mass M0, the molar amount of adsorbed argon, nads,total, and the molar mass of argon m = 39.948 g/mol. The effective shear modulus G depends on the shear modulus of the empty sample, G0, the shear modulus of quartz glass, GQ, i.e., the material of the porous matrix, and the shear modulus of the pore filling, Gpore (cp. refs 46−48):

⎛ G ⎞ G = G0 + ⎜⎜1 − 0 ⎟⎟ · Gpore GQ ⎠ ⎝

modulus G remains almost equal to the shear modulus of the empty sample, G0, until T ≈ 76 K, i.e., the adsorbed argon does not contribute to the effective shear modulus G. The observation of G/G0 ≈ 1 for temperatures above ≈76 K signifies that the adsorbed argon behaves liquidlike as inviscid liquids cannot sustain shear stress.52 Below a temperature of T ≈ 76 K, we observe a continuous and almost linear increase of the effective shear modulus with decreasing temperature, i.e., the process of freezing starts. In comparison to bulk argon, this corresponds to a reduction of the freezing temperature in the pores by about 8 K (Tfr,bulk = 84 K),53 which is typical for nanoporous glass with rP ≈ 4 nm (cp. refs 48 and 53). The increase of G/G0 signifies a continuous freezing of the adsorbed argon. A reduction of the temperature causes an increase in the amount of solid argon (volume Vads,fr) and a concurrent decrease of the liquid argon in the pores, which becomes noticeable in an increase of the fraction of solid argon, xfr = Vads,fr/Vads,total, displayed in Figure 1e. Our previous ultrasonic studies on the elasticity of argon in porous Vycor glass revealed similar values for the fraction of solid argon during cooling and heating (over a broad temperature range between ≈12 K and ≈75 K),48 i.e., the system containing coexistent liquid and solid argon is obviously in equilibrium. The heterogeneity of the pore surface of porous Vycor glass disturbs the crystallization of the adsorbed argon. Since surface layers were shown to freeze at lower temperatures, we can assume that “freezing starts in the center of the pores and, with decreasing temperature, the thickness of the liquid layer between the solid core in the center of the pores and the pore walls decreases”48 (cp. also Section 3.3 in ref 46). Our measurement with approximately one adsorbed argon layer on the pore walls shows a behavior that is similar to the measurement with the full sample. During cooling, the elongation Δl falls continuously; however, the decrease is particularly strong for T ≲ 35 K (see Figure 1b). The decrease of Δl is accompanied by a continuous increase of the effective shear modulus G and the fraction of solid argon, xfr (see Figure 1d,f). The change of elasticity signifies a continuous freezing of the surface layer, similar to that of the full sample (cp. refs 47,48).54 Also, here previous cooling and heating cycles on similar samples showed that the fraction of solid argon, xfr, is in equilibrium with the liquid argon at different temperatures (cp. Figure 7 in ref 47). The main difference to the behavior of the full pores is that one monolayer needs lower temperatures to achieve the solid state (cp. Figure 1; note the different temperature ranges). Thus, the decrease of the expansion caused by the adsorbed argon comes along with an increase of the fraction of solid argon, xfr , for both spatial configurations. The direct comparison between the extension caused by the adsorbed argon and the fraction of solid argon is shown in Figure 2. It reveals the direct relation between the continuous freezing of the adsorbed argon and the simultaneous continuous reduction of the elongation Δl caused by the adsorbed argon (see Figure 2). Obviously, solid argon induces a smaller expansion of the porous matrix than liquid argon. In consequence of the continuous crystallization of the adsorbate on cooling, the mobility of the adsorbed argon is reduced. In addition, during crystallization liquid/solid interfaces form and are continuously altered. Obviously, this has an impact on the pressure on the porous matrix, which is the reason for the observed deformation. The deforming solvation pressure pS is related 1 to the deformation ΔV/V0 or Δl /l0 = 3 ΔV /V0 via an elastic

(1)

Liquid argon in the pores does not contribute to the effective shear modulus because inviscid liquids cannot sustain shear stress, i.e., ≈ 0 GPa.47,49 However, as soon as solid argon forms upon GAr,liquid pore cooling, the effective shear modulus of the (partially) filled sample is increased.47 The shear modulus of the solid fraction of the adsorbed argon in porous Vycor glass (pore radius rP ≈ 3.8−4 nm) is almost equal to the shear modulus of bulk argon, GAr,bulk, and it holds

Gpore =

Vads,fr Vpores

·GAr,bulk =

Vads,fr Vads,total Vads,total Vpores    x fr

f

·GAr,bulk (2)

with the volume of adsorbed solid argon, Vads,fr, the volume of the pores Vpores, and the total volume of liquid and solid adsorbed argon, Vads,total.47,48 Consequently, we can evaluate the fraction of frozen argon xfr = Vads,fr/Vads,total from the measured effective shear moduli, the filling fraction f, and the literature values for the shear modulus of bulk argon, GAr,bulk, via eqs 1 and 2. For the shear modulus of bulk argon, GAr,bulk, we have used a polynomial fit of the temperaturedependent values determined in ref 50. More details on the ultrasonic method can be found in refs 12 and 49.

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MEASUREMENTS AND ANALYSIS It is known that the adsorption of argon in nanoporous glass causes a deformation of the matrix, whereas its extent depends decisively on the amount of adsorbate.12 The strongest expansion is observed for a full sample at the saturation vapor pressure, because at this pressure the menisci at the pore ends are flat, and the contracting Laplace pressure tends to zero.12 In the following we are going to study the temperature dependence of the adsorption-induced deformation of the porous glass for two different spatial configurations of adsorbed argon: for approximately one adsorbed argon layer on the pore walls (f ≈ 0.18 for T ≤ 65 K, thickness u ≈ 0.34 nm) and for completely filled pores ( f = 1 with additional adsorbate in the sample cell). At 86 K for the completely filled sample the adsorbed argon causes an expansion Δl ≈ 0.9 μm of the sample with a length of l0 ≈ 2.66 mm. This elongation caused by the adsorbed liquid argon remains almost constant during cooling for T > 76 K (see Figure 1a). A reduction of the temperature below T ≈ 76 K is accompanied by a continuous decrease of Δl. Thus, at low temperatures the adsorbed argon causes a smaller elongation of the length of the sample (cp. the definition of Δl above). The slope of the decrease of Δl diminishes when the temperature is reduced, and below ≈50 K the deformation caused by the adsorbed argon is almost constant.51 We can compare this deformation behavior with the simultaneously measured effective elastic properties of the filled sample (see Figure 1c). During cooling the effective shear 7743

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Figure 2. Elongation of the nanoporous glass caused by adsorbed argon, Δl, as a function of the fraction of solid argon, xfr (solid circles: full sample; open circles: 1 surface layer). An increase of the amount of solid argon and the simultaneous decrease of the amount of liquid argon causes a continuous reduction of the extension in consequence of the adsorbate.

modulus MPL: pS = MPL·Δl/l0 (cp. refs 4, 5, and 10).55 The socalled pore-load modulus, MPL, relating the solvation pressure to the deformation, is usually regarded as independent of the elasticity of the pore filling.10,24 Thus, the observed continuous reduction of Δl corresponds to a continuous diminution of the solvation pressure (l0 is basically constant), i.e., for solid adsorbed argon the solvation pressure is considerably smaller than for liquid argon. Furthermore, our temperature-dependent deformation measurements for the full sample reveal significant differences between the expansion for the nonequilibrated and the final equilibrated state. For the full sample, the equilibration of the measured elongation required very long waiting times, in particular at low temperatures (see Figure 3a,b). Initially during the temperature step, the adsorbate’s contribution to the elongation of the sample diminishes very strongly. For the temperature step from 55 to 50 K it is almost reduced to the size of the empty sample, i.e., Δl = 0 μm (see Figure 3b). Then an expansion process starts, and at 50 K it takes about 4 days to reach a stable value for the elongation caused by the adsorbed argon. (For the temperature step from 50 to 43 K, even a waiting time of 1 week was necessary to reach a reasonably stable value for Δl.) At higher temperatures the equilibration is considerably faster (see Figure 3a for a temperature step from 75 to 74 K), and the initial contraction is somewhat smaller. In contrast to the equilibration of the length of the full sample, the measurements with approximately one adsorbed argon layer on the pore surface do not exhibit a temporary contraction and subsequent expansion of Δl after a temperature step (cp. Figure 3c, for T = 32 K → T = 27 K). Here the sample reaches a constant length almost as soon as the new temperature is reached (after 50 min). The observed effect of an initial contraction after a reduction of the temperature of the full sample can be explained as a consequence of the formation of vapor voids in the pores during cooling. Because of the temperature dependence of the density of adsorbed argon, a reduction of temperature reduces the volume of the adsorbed argon, and thus bubbles can form in the pores. For example, cooling of bulk argon from 86 to 40 K results in an increase of density by Δρ/ρ = 0.24 (ρ86K liquid ≈ 3 56,57 1.401 g/cm3, ρ40K ≈ 1.737 g/cm ) and thus to a decrease solid in volume by 24%. The creation of vapor bubbles goes along with the formation of concave menisci between the condensed

Figure 3. Equilibration of the length of the sample after different temperature steps. During cooling of the full sample [for (a) 75 to 74 K and (b) 55 to 50 K], the increasing density of the adsorbed argon results in the formation of small vapor voids in the pores, which are associated with a contracting Laplace pressure. The voids can be filled with argon from the sample cell; however, such a filling process is very slow, particularly at low temperatures. By contrast, the length of the sample with one argon monolayer on the pore surface reaches a stable value as soon as the new temperature is reached (see panel c for 32 to 27 K).

argon and the vapor, which cause a high contracting (negative) Laplace pressure. Additional argon from the sample cell can fill these voids via spatial rearrangement of the adsorbate; however, at low temperatures the filling proceeds very slowly.58 Thus, the contracting pressure is reduced and the porous matrix expands again slowly. In addition, there may be a second mechanism responsible for the slow expansion following the initial contraction: there are pressure differences in the filled pore regions due to curved liquid/solid interfaces, which can cause a liquid flow (e.g., via the liquid/premelted film near the pore surface), subsequent freezing and an expansion of the porous matrix (similar to cryosuction; see Chapter 9.3 in ref 59). However, the measurements do not give us insight into such microscopic processes. The differences in the extent of the initial contraction and in the equilibration time between the two temperature steps (Figures 3a,b) probably depend on both the size of the temperature step as well as on the fraction of solid argon (for 75 K → 74 K: xfr → 0.10, and for 55 K → 50 K: xfr → 0.68). For the sample with one adsorbed argon layer, the center of the pores is only filled with argon vapor, i.e., no new vapor voids can form upon cooling. Consequently, during 7744

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(6) Gor, G. Y.; Paris, O.; Prass, J.; Russo, P. A.; Ribeiro Carrott, M. M. L.; Neimark, A. V. Adsorption of n-Pentane on Mesoporous Silica and Adsorbent Deformation. Langmuir 2013, 29, 8601−8608. (7) Erko, M.; Wallacher, D.; Paris, O. Deformation mechanism of nanoporous materials upon water freezing and melting. Appl. Phys. Lett. 2012, 101, 181905. (8) Yang, K.; Lu, X.; Lin, Y.; Neimark, A. V. Deformation of Coal Induced by Methane Adsorption at Geological Conditions. Energy Fuels 2010, 24, 5955−5964. (9) Brochard, L.; Vandamme, M.; Pellenq, R. J.-M.; Fen-Chong, T. Adsorption-Induced Deformation of Microporous Materials: Coal Swelling Induced by CO2−CH4 Competitive Adsorption. Langmuir 2012, 28, 2659−2670. (10) Prass, J.; Müter, D.; Fratzl, P.; Paris, O. Capillarity-driven deformation of ordered nanoporous silica. Appl. Phys. Lett. 2009, 95, 083121. (11) Günther, G.; Prass, J.; Paris, O.; Schoen, M. Novel Insights into Nanopore Deformation Caused by Capillary Condensation. Phys. Rev. Lett. 2008, 101, 086104. (12) Schappert, K.; Pelster, R. Unexpected Sorption-Induced Deformation of Nanoporous Glass: Evidence for Spatial Rearrangement of Adsorbed Argon. Langmuir 2014, 30, 14004−14013. (13) Schappert, K.; Pelster, R. Influence of the Laplace pressure on the elasticity of argon in nanopores. EPL 2014, 105, 56001. (14) Grosman, A.; Puibasset, J.; Rolley, E. Adsorption-induced strain of a nanoscale silicon honeycomb. EPL 2015, 109, 56002. (15) Zickler, G. A.; Jähnert, S.; Funari, S. S.; Findenegg, G. H.; Paris, O. Pore lattice deformation in ordered mesoporous silica studied by in situ small-angle X-ray diffraction. J. Appl. Crystallogr. 2007, 40, s522− s526. (16) Vandamme, M.; Brochard, L.; Lecampion, B.; Coussy, O. Adsorption and strain: The CO2-induced swelling of coal. J. Mech. Phys. Solids 2010, 58, 1489−1505. (17) Kowalczyk, P.; Furmaniak, S.; Gauden, P. A.; Terzyk, A. P. Methane-Induced Deformation of Porous Carbons: From Normal to High-Pressure Operating Conditions. J. Phys. Chem. C 2012, 116, 1740−1747. (18) Balzer, C.; Braxmeier, S.; Neimark, A. V.; Reichenauer, G. Deformation of Microporous Carbon during Adsorption of Nitrogen, Argon, Carbon Dioxide, and Water Studied by in Situ Dilatometry. Langmuir 2015, 31, 12512−12519. (19) Balzer, C.; Wildhage, T.; Braxmeier, S.; Reichenauer, G.; Olivier, J. P. Deformation of Porous Carbons upon Adsorption. Langmuir 2011, 27, 2553−2560. (20) Herman, T.; Day, J.; Beamish, J. Deformation of silica aerogel during fluid adsorption. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 73, 094127. (21) Dourdain, S.; Britton, D. T.; Reichert, H.; Gibaud, A. Determination of the elastic modulus of mesoporous silica thin films by x-ray reflectivity via capillary condensation of water. Appl. Phys. Lett. 2008, 93, 183108. (22) Amberg, C. H.; McIntosh, R. A Study of Adsorption Hysteresis by Means of Length Changes of a Rod of Porous Glass. Can. J. Chem. 1952, 30, 1012−1032. (23) Dolino, G.; Bellet, D.; Faivre, C. Adsorption strains in porous silicon. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 17919− 17929. (24) Gor, G. Y.; Bertinetti, L.; Bernstein, N.; Hofmann, T.; Fratzl, P.; Huber, P. Elastic response of mesoporous silicon to capillary pressures in the pores. Appl. Phys. Lett. 2015, 106, 261901. (25) Bangham, D. H.; Fakhoury, N. The Expansion of Charcoal accompanying Sorption of Gases and Vapours. Nature 1928, 122, 681−682. (26) Bangham, D. H.; Fakhoury, N. The Swelling of Charcoal. Part I.-Preliminary Experiments with Water Vapour, Carbon Dioxide, Ammonia, and Sulphur Dioxide. Proc. R. Soc. London, Ser. A 1930, 130, 81−89. (27) Bangham, D. H.; Fakhoury, N.; Mohamed, A. F. The Swelling of Charcoal. Part II.- Some Factors Controlling the Expansion Caused by

cooling the elongation of the sample reaches a constant value as soon as the new temperature is reached (see Figure 3c).

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CONCLUSIONS AND OUTLOOK Through a comparison of the simultaneously measured deformation and the elasticity of nanoporous glass filled with argon, we have evidenced the correlation between the elongation of the porous matrix caused by the adsorbate and its phase state. The continuous crystallization of the adsorbed argon with reducing temperature results in a continuous reduction of the deformation caused by the adsorbate. This hints at a continuous diminution of the solvation pressure pS in consequence of the continuous crystallization. Further research will help to determine how the solvation pressure pS depends not only on the fraction of solid argon, but also on the spatial arrangement of coexisting liquid and solid argon as well as on the filling fraction. It is known that the interaction between adsorbate and adsorbent decisively influences the liquid−solid phase behavior of the adsorbate, e.g., for argon (or alkanes) adsorbed on graphite, the existence of a near surface solid monolayer that melts only above the melting temperature of the bulk substances is known60−63 (in contrast to our observations for argon in porous Vycor; see Figure 1e,f and refs 46−48). Thus, studies with different adsorbates (and porous systems) might help to reveal the influence of the strength of molecular interactions and its temperature dependence on the extent of the expansion of porous materials. The extremely slow equilibration that we observed for argon (cp. Figure 3) shows that long waiting times are necessary between individual temperature steps, probably because of the slow migration of adsorbate. Therefore, a fast conduct of an experiment can lead to nonequilibrium states, a multitude of configurations, and related misinterpretations. On the other hand, the slow equilibration and the appearance of nonequilibrium configurations shows that a small change of temperature can temporarily provoke considerable deformations (cp. Figure 3). Also in technical applications, such significant influences on the deformation in consequence of seemingly insignificant temperature changes should be taken into consideration.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Makal, T. A.; Li, J.-R.; Lu, W.; Zhou, H.-C. Methane storage in advanced porous materials. Chem. Soc. Rev. 2012, 41, 7761−7779. (2) White, C. M.; Smith, D. H.; Jones, K. L.; Goodman, A. L.; Jikich, S. A.; LaCount, R. B.; DuBose, S. B.; Ozdemir, E.; Morsi, B. I.; Schroeder, K. T. Sequestration of Carbon Dioxide in Coal with Enhanced Coalbed Methane Recovery - A Review. Energy Fuels 2005, 19, 659−724. (3) Karacan, C. O. Heterogeneous Sorption and Swelling in a Confined and Stressed Coal during CO2 Injection. Energy Fuels 2003, 17, 1595−1608. (4) Gor, G. Y.; Neimark, A. V. Adsorption-Induced Deformation of Mesoporous Solids: Macroscopic Approach and Density Functional Theory. Langmuir 2011, 27, 6926−6931. (5) Gor, G. Y.; Neimark, A. V. Adsorption-Induced Deformation of Mesoporous Solids. Langmuir 2010, 26, 13021−13027. 7745

DOI: 10.1021/acs.langmuir.6b01533 Langmuir 2016, 32, 7741−7746

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(52) More complex substances (like heptane and nonane) may also contribute to the effective shear modulus above the melting temperature.64 (53) Molz, E.; Wong, A. P. Y.; Chan, M. H. W.; Beamish, J. R. Freezing and melting of fluids in porous glasses. Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 48, 5741−5750. (54) In Figure 1b, the behavior with one surface layer is only shown for temperatures below T ≈ 65 K because at higher temperatures a change of temperature significantly influences the filling fraction f. For higher temperatures, a reduction of temperature causes an increase of the filling fraction because vapor from the sample cell is adsorbed by the sample. Below T ≈ 60−65 K there remains only a negligible amount of argon in the vapor because of the low vapor pressure of argon at these temperatures (cp., e.g., Figure 5 in ref 47). (55) Actually, the solvation pressure pS must be corrected by the pressure existing already for the empty sample (cp. refs 4 and 5). (56) Goldman, K.; Scrase, N. Densities of saturated liquid argon. Physica 1969, 45, 1−11. (57) Dobbs, E. R.; Figgins, B. F.; Jones, G. O.; Piercey, D. C.; Riley, D. P. Density and Expansivity of Solid Argon. Nature 1956, 178, 483. (58) During the measurement of sorption isotherms with argon at low temperatures we have observed similarly slow equilibration processes (cp. ref 47). (59) Coussy, O. Mechanics and Physics of Porous Solids; John Wiley & Sons, Inc.: Chichester, UK, 2010. (60) Larese, J. Z. Multilayer Argon Films on Graphite: Structural and Melting Properties. Acc. Chem. Res. 1993, 26, 353−360. (61) Larese, J. Z.; Zhang, Q. M. Layer-by-Layer Melting of Argon Films on Graphite: A Neutron-Diffraction Study. Phys. Rev. Lett. 1990, 64, 922−925. (62) Larese, J. Z.; Zhang, Q. M.; Passell, L.; Hastings, J. M.; Dennison, J. R.; Taub, H. Layer-by-layer growth of solid argon films on graphite as studied by neutron diffraction. Phys. Rev. B: Condens. Matter Mater. Phys. 1989, 40, 4271−4275. (63) Castro, M. A.; Clarke, S. M.; Inaba, A.; Arnold, T.; Thomas, R. K. Competitive Adsorption of Simple Linear Alkane Mixtures onto Graphite. J. Phys. Chem. B 1998, 102, 10528−10534. (64) Schappert, K.; Gemmel, L.; Meisberger, D.; Pelster, R. Elasticity and phase behaviour of n-heptane and n-nonane in nanopores. EPL 2015, 111, 56003.

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DOI: 10.1021/acs.langmuir.6b01533 Langmuir 2016, 32, 7741−7746