Desorption Hysteresis

Article pubs.acs.org/Langmuir

Restricted Access: On the Nature of Adsorption/Desorption Hysteresis in Amorphous, Microporous Polymeric Materials Jekaterina Jeromenok and Jens Weber* Department of Colloid Chemistry, Max Planck Institute of Colloids and Interfaces, Science Park Golm, D-14424 Potsdam, Germany S Supporting Information *

ABSTRACT: The phenomenon of low-pressure adsorption/ desorption hysteresis, which is commonly observed in microporous polymers, is investigated by detailed gas adsorption studies. Diffusional limitations by pore blocking effects, which arise as a consequence of the micropore morphology and connectivity, are discussed as the origin of the hysteresis rather than swelling effects, which have been suggested previously. Micropores with narrow openings, which cannot be filled easily, are expected to be present next to open pores. Those pores are termed restricted-access pores and are only filled in the course of the adsorption process as a consequence of the increasing solvation pressure exhibited from already filled micropores. As a consequence of the results presented here, it is suggested to use the desorption branch in addition to the adsorption branch for the extraction of the porosity characteristics, such as specific surface area, pore volume, and pore size distribution. The magnitude of the low-pressure hysteresis might hence give an idea of the micropore connectivity, which is important information for potential applications.

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INTRODUCTION Soft microporous materials, i.e., polymeric and other purely organic materials having permanent pores with sizes smaller than 2 nm, have often fascinated the scientific community throughout the last years, and a vast amount of synthetic routines have been developed.1−4 The fascination arises from the fact that the advantages of classic inorganic materials such as high surface area can be combined with all of the functionalities provided by organic polymer chemistry (lightweight, tunable optoelectronic properties, processability, etc.). Most microporous polymers are of an amorphous nature and their characterization is mainly done by gas adsorption in analogy to classic microporous materials. Some trends came to our attention, which deserve further investigation. A significant number of microporous polymers, among them soluble PIMs but also cross-linked systems such as CMPs or CTFs,5−16 show a pronounced hysteresis upon desorption down to very low relative pressures; that is, the desorption branch of the isotherm does not follow adsorption, when being analyzed by nitrogen adsorption/desorption at 77.4 K (see Scheme 1). This effect is often discussed as the swelling/deformation phenomenon,17,18 but no detailed understanding has been achieved so far. No clear answers can however be expected from application of the classical micropore analysis methods of gas adsorption isotherms (e.g., density functional theory models,19 such as NLDFT20−23 and QSDFT,24,25 or semiempirical methods such as the Horvarth-Kawazoe26 (HK) method and others27,28) as long as the origin of the hysteresis is not understood. The hysteresis effect is hence expected to have strong implications © 2013 American Chemical Society

on the calculation of pore size distribution (PSD), specific surface area, and the micropore volume. These are the most important characterization parameters of amorphous microporous polymers and they are typically also used to explain the performance of microporous materials in various applications. Given their importance it becomes clear that a better understanding of the phenomenon is indeed needed.14 Two examples are presented and discussed within this study, which demonstrate that the hysteresis effect cannot be attributed to swelling only, but that it is most probably mainly related to diffusional aspects, which arise as a consequence of the micropore topology. The two possibilities (swelling or restricted filling of preexisting pores) are depicted schematically in Scheme 1. The term swelling is used in this paper in the connotation of rubber-swelling (volume-swelling), which means creation of new pores/voids by interaction with solvents. This is different to adsorption-induced deformations, which have been known in the adsorption community also as swelling based on the early works of Meehan, Bangham, and others.29−31 Both effects result in macroscopic volume changes, which are usually however of different magnitudes as will be discussed later. Received: July 29, 2013 Revised: September 17, 2013 Published: September 30, 2013 12982

dx.doi.org/10.1021/la402630s | Langmuir 2013, 29, 12982−12989

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Scheme 1. Schematic Overview on the Problem of Low-Pressure Hysteresisa

a

Exemplary N2 adsorption/desorption isotherm showing a pronounced hysteresis upon desorption (left-hand side) and schematic drawing of the two possibilities commonly discussed as the origin of the hysteresis, namely formation of new pores (volume-swelling) of kinetically hindered filling of existing pores upon adsorption.

Figure 1. schematic overview of the swelling experiment (PIM-1 in argon). The film was fixed at the lower end and covered by a foil to avoid delamination from the millimeter paper. Photographs (with enlarged insets) show the film during the experiment, no swelling could be observed in liquid Ar.

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MATERIALS AND METHODS

RESULTS AND DISCUSSION

Macroscopic Approach. The first example is a macroscopic analytical approach, namely the investigation of the potential swelling of a film of a polymer of intrinsic microporosity (PIM-1) under cryogenic conditions.6,18 PIM-1 is considered to be a glassy polymer with no detectable glass transition temperature.6 Nevertheless, analysis of PIM-1 by nitrogen adsorption at 77.4 K does usually result in a pronounced hysteresis down to low pressures (see SI). The hysteresis cannot be attributed fully to the presence of mesopores. It was suggested that the effect could be due to matrix swelling.18 From a polymer science point of view, swelling can occur if a polymer (network) is subjected to a (thermodynamically) reasonably good solvent; that is, the polymer−solvent interaction should be large enough to overcome polymer−polymer interactions. In the present example of PIM-1, which is a glassy and highly rigid polymer, we do not expect chain stretching like it is observed in rubbery networks. Hence, any potential macroscopic deformation would be expected to originate from the creation of new or growth in size of existing pores, both processes require the breaking of polymer−polymer interactions. Nitrogen (as well as argon) can however be regarded as poorly interacting solvents

The betulin based polyester network Bet-1 was prepared according to a recently published procedure and obtained after freeze-drying from dioxane.32 PIM-1 membranes were prepared following literature protocols.33,34 Precipitated PIM-1 was obtained by precipitation of a filtrated PIM-1 solution (THF) into methanol. Gas adsorption experiments were performed with an Autosorb-1 MP (Quantachrome Instruments) machine. Measurements at 77.4 K were performed using a dewar filled with liquid N2 for cooling. Temperatures of 87.3 and 195 K were adjusted using the Optistat DN cryostat (2nd generation) of Oxford Instruments/Quantachrome Instruments. A tyemperature of 273.15 K was established using a thermostatted water/ethylene glycol mixture. Initial data analysis was performed using either the AS1Win or the Quadrasorb 5.05 software package (Quantachrome Instruments). Measurements were conducted using an equilibration time setting of 3 min (the time interval, in which the pressure change must be below the allowed difference, typically Δp < 0.0008 atm) if not stated otherwise. An equilibration time of 3 min is a commonly used “default” value of the Autosorb-1 machine of Quantachrome Instruments. High-purity gases were used throughout the experiments. Samples were degassed using the built-in outgasser of the Autosorb-1 MP machine (turbomolecular vacuum pump) at either 70 °C (Bet-1) or 100 °C (PIM-1) for at least 20 h before analysis. 12983


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Figure 2. (a) Chemical structure of the betulin based network Bet-1; (b) 3D representation (space-filling) of the structure shown in panel a; (c) N2 (77.4 K), Ar (87 K, cryostat), and CO2 (195 K, cryostat) adsorption/desorption isotherms of freeze-dried Bet-1 (absolute pressure).

equilibrium state or whether the outcome of the measurement depends largely on the experimental conditions. Detailed Gas Adsorption Experiments. A set of gas adsorption experiments (N2 and Ar adsorption at 77.4 and 87 K, CO2 at 195 and 273 K) was performed on another microporous polymer system in order to understand the phenomenon somewhat better. Betulin based microporous polyester networks (Bet-1) do also show a significant hysteresis when being analyzed by N2 physisorption at 77.4 K and were chosen for these experiments. The networks were prepared by polycondensation of betulin (a natural triterpene) and 1,3,5triacid trichloride benzene and obtained by freeze-drying according to a reported method.32 Figure 2a shows the chemical structure of the betulin networks and a typical N2 adsorption−desorption isotherm obtained at 77.4 K is depicted in Figure 2c together with Ar and CO2 isotherms (see below). A significant hysteresis between adsorption and desorption of N2 is observed, which does not close at low p/p0. An obvious feature of the N2 adsorption isotherm is the fact that the initial steep uptake at very low relative pressures is followed by a linear increase of volume with increasing relative pressure, typically in the range between 0.2 < p/p0 < 0.8. This behavior was also observed for other microporous polymers showing low-pressure hysteresis previously and was initially interpreted as some kind of dual-mode adsorption feature.17 We were interested if the linear increase is generally observed upon gas adsorption at the condensation temperature of the respective gas. Hence, we measured also the argon and carbon dioxide adsorption isotherms of Bet-1 at 87.3 and 195 K, respectively. Figure 2c shows the adsorption/desorption isotherms together with the N2 adsorption data. The argon adsorption follows the N2 isotherm very closely. The CO2 adsorption isotherm showed also a linear increase, which was somewhat steeper. All isotherms had also a pronounced low-pressure hysteresis in common. In summary, the adsorption isotherms obtained at the respective condensation temperatures of the adsorbates are comparable at least on a qualitative level. Argon adsorption at 87.3 K is very useful for the analysis of micropores, as it undergoes less specific interactions and it is generally also believed to be less affected by diffusional, i.e.,

(LONDON interactions mainly) and significant swelling is rather unexpected given that the polymer−polymer interactions involve also stronger dipole interactions. The volume difference between the adsorption and desorption branch of the N2 isotherm of a PIM-1 film at a relative pressure p/p0 = 0.2 amounts to ∼85 cm3 g−1 STP, which relates in turn to a potential uptake of ∼0.13 cm3 of liquid N2 per gram of PIM-1. This corresponds to a volume increase of ΔV/V0 = 0.127 (12.7%) of the polymer film, if the difference can be attributed to swelling (assuming a PIM-1 density of ∼1.1 g/cm3). This is much larger than a volume change of 0.5% (calculated based on molecular modeling), which arises as a consequence of relaxation events in PIM-1 at 77K and 0.1 bar N2 pressure18 and seems rather unlikely. Nevertheless, the possibility of volume-swelling was checked using a macroscopic approach as described in the following. A film of PIM-1 (20 × 5 × 0.05 mm) was degassed at 70 °C under dynamic vacuum and cooled to 77.4 K, and argon was condensed into the sample cell subsequently (see Figure.1). Under the assumption of isotropic swelling (i.e.ΔV/V0 ≈ 3ΔL/ L0) and taking the higher density of liquid argon compared to N2 into account, the volume change would have accounted for an increase in film length of ∼0.6−0.7 mm (see SI for details). The length change of the film was monitored, but no significant increase was observed in liquid Ar. As a crosscheck, we subjected the film to liquid ethanol, which is a nonsolvent, but can penetrate the pores. In this case, significant volume expansion was observed (see SI). Hence, it can be concluded that volume-swelling is possible if the polymer/polymer interactions can be overcome by a sufficiently strong interacting adsorbate such as ethanol. The absence of volume-swelling in liquid argon can however be considered as a first macroscopic proof that volume-swelling is not alone the cause of the hysteresis observed in common gas adsorption experiments. This leads us however straightforward to the question, whether there is another explanation for the observed hysteresis. Indeed, it was suggested that such hysteresis could also be due to kinetic effects.7 At this point, it becomes interesting whether the adsorption isotherms do represent an 12984


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Figure 3. (a) N2 adsorption/desorption isotherm on Bet-1 at 87.3 and 77.4 K; (b) hysteresis scan of Bet-1, using different equilibration settings, namely 2 or 10 min (note: different batch of Bet-1); (c) cumulative pore volume distribution of a Bet-1 material, derived from CO2 adsorption at 273 K (GCMC model, carbon slit pores),21,43 N2 adsorption/desorption at 77.4 (QSDFT, carbon slit micropores, cylindrical mesopores, adsorption or equilibrium model, respectively);25 (d) fictional PSD (cartoon), showing nonaccessible free volume (dark gray), an intermediate fraction (light gray) corresponding to restricted access pores) and open pores (white) together with a schematic drawing of the pore morphology and the associated filling process (e).

kinetic restrictions during the measurement.35,36 The fact that the experimentally obtained Ar adsorption isotherm (at 87K) is however very much comparable to the N2 adsorption isotherm can be regarded as another indication that the hysteresis effect is not solely due to the experimental conditions but that there could be other (molecular and topological) reasons for the hysteresis.

If swelling would occur, i.e., the expansion of existing and/or formation of new pores according to Scheme 1, this could find reflection in the isosteric heat of adsorption.37 The N2 adsorption/desorption isotherm of Bet-1 was hence measured at 87 K in order to determine the isosteric heat of adsorption (see Figure 3a). The uptake of N2 was however enhanced at 87.3 K compared to the uptake at 77.4 K, and no heats of adsorption were determined consequently.38 This implies that 12985


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Figure 4. Schematic illustration of the pore filling mechanism of a restricted-access pore. Parts of the pore get filled at low p/p0, creating a solvation pressure, which is negative, hence leading to compaction of the narrow passage, which makes it impassable (pseudoequilibrium). As the relative pressure increases during the measurement, the solvation pressure gets larger, causing elastic expansion finally, which allows passage and pore filling. Likely, higher temperatures are also expected to yield less contraction and hence easier pore filling.

The effect manifests in an isotherm shape, which is phenomenological similar to a solution effect (Henry-type behavior). This provides at least partial explanation for the often observed dual-mode type adsorption profiles of microporous polymers, which, as we saw from the macroscopic example cannot be attributed to volume-swelling only.17,41 If the pore filling occurs by this way, reversing the isotherm at intermediate p/p0, should result in a comparable fraction of fluid remaining within the material. A hysteresis scan experiment was consequently done, where the adsorption was reversed at p/p0 = 0.75. This experiment could also exclude effects due to fluid condensation within in the large mesopores/ macropores of freeze-dried Bet-1 samples (Figure 3b). In case of volume-swelling, one would expect that the N2 condensation within the large meso/macropores would lead to even stronger swelling of the micropores and consequently to a higher amount of trapped N2.42 The isotherms do however unify at low p/p0, indicative of an equal amount of adsorbate trapped within the open and restricted micropores of Bet-1. Hence, we are confident that there is no strong swelling and that the hysteresis is indeed related to the irregular topology of the present micropores, which results in some ill-defined connectivity. The findings are summarized schematically in Figure 3d,e. Pores which are well-connected can be filled very fast, whereas pores with a very narrow opening or even nominally closed pores cannot be filled easily (restricted-access). As the pressure increases, the acting solvation pressure σ leads to the filling of restricted-access pores. This process manifests in a fashion comparable to dissolution in the matrix but has a different background. Upon desorption, there is no thermodynamic reason for the fluid to be desorbed from these pores until very low relative pressure is reached. This results ultimately in the observed hysteresis. At higher temperatures the pores fill more easily as evidenced by the measurement of N2 adsorption at 87 K. This result is in accordance with previous results on carbons using N2 adsorption at 77.4 and 90 K.39 The exact reasons, why the filling at 87 K is easier are not yet clear. Often it is simply argued that the measurements at 77.4 K are “kinetically hindered”, but no deeper reason is known to us. The

the adsorption (at least at or near the condensation temperature) follows an activated diffusion mechanism (sometimes also referred to as solution-diffusion mechanism). Easily accessible, i.e., open, micropores will be filled at low p/p0 according to classic theories. This could also be interpreted as the formation of so-called liquid plugs or islands, which block very narrow throats, which are the connection to other pores. The passage of such narrow openings is expected to be easier at higher T, which is in accordance with the experimental observations.39 Microporous polymers can be described generally as highly irregular (amorphous) materials. The statistical coexistence of very small pores along with larger micropores is reasonable, resulting in a rather broad pore size distribution (see Figure 3d). If the hypothesis on the formation of liquid plugs is reasonable, it is worth having a look at the thermodynamics of confined fluids, which might provide a better understanding of the adsorption behavior at intermediate p/p0. It is well understood that fluids condensed in narrow pores exhibit solvation pressures σ (for larger pores known within the framework of the Young−Laplace theory). These solvation pressures can be positive or negative, depending on the exact thermodynamic parameters and the pore size. A recent work by Neimark and co-workers showed that for (topologically) heterogeneous pores σ is positive for extremely small pores in the whole pressure range, while it is negative for pores larger than 0.45 nm at low p/p0 but increases finally also for those pores with increasing p/p0 > 0.01.29,30,40 This would suggest that, except for the most narrow pores (of 0.3 nm size), a contraction is expected at low relative pressure. This contraction can reduce the throat size down to sizes, which do not allow gas to pass through, i.e., the formation of liquid plugs. However, the pressure σ associated with the liquid plugs increases finally with p/p0. This increase allows relaxation of the contraction and as σ > 0, and some small elastic expansion settles in at intermediate p/p0, allowing gas molecules to pass through finally (see also Figure 4). We propose hence that the increasing solvation pressure could be the driving force for the filling of pores with restricted access, i.e., pores that are present already in the material and which are not to be newly created. 12986


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We note that the results presented here are somewhat contradictory to previous explanations, which assumed swelling as one of the main sources of the hysteresis.14 Rearrangements of the polymeric matrix are however still thinkable within the gas adsorption experiment and even expected as a consequence of the solvation pressure. They should however be low in quantitative impact, if one considers the fact that polymer (networks) far below their glass-transition are considered. Hence, we believe that the picture developed within this study is more congruent. BET surface areas and pore volume data were finally calculated from the adsorption and desorption branches of Bet-1 (Table 1). Comparison of the specific surface areas

temperature dependence of the solvation pressure might be regarded but was not yet analyzed in detail for N2 in this temperature range. A study by Gubbins et al on methane adsorption on carbon showed however that the contraction (magnitude of the negative solvation pressure) is lower at higher T.44 This might be one reason for the easier passage, but more knowledge is needed here for a final statement. The argumentation assumes that the isotherms at the respective condensation temperatures are pseudoequilibrium isotherms; that is, the pores cannot fill at the time-scale of the experiment at all (no matter how long we wait) but are only filled upon pressure increase.45 Support for this hypothesis comes from the fact that a change in the equilibration settings toward significantly longer equilibration times of the gas adsorption experiment did not show a major impact on the gas uptake (Figure 3b), which is in accordance with experiments conducted by Zukal and co-workers on aromatic microporous polymers.41 Taking all those findings into account, the question appears, whether the desorption branch does represent a state more closely related to “equilibrium” (taking the amount of pore filling into account) and could be used for porosity analysis. The better differentiation between filled micropores and potentially present broadly distributed mesopores would be a supportive argument for its use in porosity analysis. Apparently, the adsorption branch cannot differentiate between them, as it represents an overlay of both: mesopore filling and filling of restricted-access micropores within the intermediate p/p0 range. To further answer this question, we performed CO 2 adsorption measurements at 273 K on Bet-1 (see SI, Figure S1). Indeed, the analysis of the CO2 isotherms collected at 273 K did not show strong hysteresis, which is indicating that they indeed represent equilibrium isotherms.46 The cumulative pore volume of pores up to ∼1.2 nm in diameter in Bet-1 can be determined from the CO 2 isotherms making use of commercialized GCMC or NLDFT models.21,43 QSDFT analysis of either the adsorption or desorption branch of the N2 adsorption isotherms of Bet-1 was also done and the cumulative pore volume is plotted in Figure 3c together with the GCMC analysis of the CO2 adsorption. It can be clearly seen that the GCMC analysis merges nicely with the QSDFT results obtained from the desorption branch, while the analysis of the adsorption branch underestimates the micropore volume dramatically (∼50%). Hence, we suggest making use of the desorption branch for analysis of microporous materials additionally in case they show significant low-pressure hysteresis, which is not of kinetic origin. A prerequisite of such analysis would be the absence of swelling and/or significant rearrangements. We are confident that these processes do contribute indeed only little to the hysteresis. In fact, dilation of microporous materials is observed upon gas adsorption due to elastic response to the acting solvation pressure, but it is typically of rather low magnitude. Indeed, volume changes of ΔV/V0 < 1% have been reported for hard carbonaceous materials,47,48 but values much smaller than the initial calculated 10−13% have been also reported for soft polymeric materials such as PIM-1 at low/near-ambient pressures.18,49 This dilation is based on the elastic response of the material to the acting solvation pressures, and it should hence not contribute significantly to the hysteresis but be reversed upon micropore emptying.

Table 1. Porosity Characteristics of a Bet-1 Material Determined by Various Methodsa

a

Bet-1

SBET/ m2 g‑1

Sμ‑pore (CO2)/ m2 g‑1

Sμ‑pore (QSDFT)/ m2 g‑1

Vμ‑pore (CO2)/ cm3 g‑1

Vμ‑pore (QSDFT)/ cm3 g‑1

adsorption desorption

354 408

310 310

166 227

0.117 0.117

0.075 0.112

μ-pore defines as pores with a width of less than 2 nm.

obtained from CO2 adsorption and N2 desorption (BET) still shows some difference, which can be attributed to meso/ macropores which are also present within Bet-1 but cannot be analyzed by CO2 adsorption. Hence the BET surface areas are larger than the micropore surface areas as determined by CO2. When micropore surface areas determined by either GCMC analysis of CO 2 adsorption or QSDFT analysis of N 2 adsorption/desorption are compared, it becomes clear that analysis of the adsorption branch of the N2 isotherm does underestimate the microporosity significantly, whereas the desorption data compares better with the CO2 results.

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CONCLUSIONS Within this study, we presented a framework to explain the lowpressure hysteresis in cryogenic gas adsorption, which is often observed for microporous polymers. Although the findings presented within this manuscript are based on the gas adsorption investigation of one specific material, we are confident that they are quite general (please see SI for exemplary analysis of a PIM-1 sample and other materials). We provide evidence that the low-pressure hysteresis is not primarily due to volume-swelling. Macroscopic swelling experiments showed that PIM-1 cannot swell in liquid Ar due to insufficient adsorbate/adsorbent interactions. Instead, the low− pressure hysteresis is expected to arise as a consequence of interplay between elastic changes of the polymer segment positions and acting solvation pressures, which ultimately lead to diffusion problems. We expect that both the topology of the pores present in microporous polymers and the overall softness of the materials determine the shape of the cryogenic gas adsorption isotherms, which can accordingly give first information on the pore connectivity. We define two different types of micropores (open and restricted-access), which can be present in amorphous microporous polymers. The entrance to the restricted pores, which is thought of as a narrow passage, gets impassable at low relative pressure, when the negative solvation pressure leads to a compaction of the material, hence leading to an even more narrow passage that cannot be passed at the respective thermodynamic state. The presence of 12987


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restricted-access pores is hence most likely responsible for the observed low-pressure hysteresis. Their filling seems to appear only within the course of the experiment as a consequence of the changed thermodynamic parameters that are leading to changes in the solvation pressure and corresponding elastic response of the materials (see Figure 4 for a graphical summary of the process). The presence of a pronounced low-pressure hysteresis, which does show up even after proper degassing and at experiment conditions that allow enough equilibration time,50 is hence a hint toward the presence of ill-connected pores. Such information could be rather important for the performance of microporous polymers in various adsorption related applications (which typically benefit from well-connected pores). In the case that there is no significant difference, i.e., no strong hysteresis, the micropores can be regarded as well connected and accessible. A higher elastic modulus of the material is expected to be supportive for easy pore filling, as the deformation of narrow channels is expected to occur at lower magnitude and less pore-filling restrictions are expected. This might be one of the reasons why such hysteresis is hardly observed in microporous hard matter such as carbons or zeolites, which are based on highly condensed structures. Based on this results, we suggest to use the desorption branch in addition to the adsorption branch of the cryogenic isotherms in order to access BET surface areas, micropore volumes, and pore size distributions of microporous polymers. The difference between the two branches is probably related to the amount of restricted-access pores. Finally, it was shown again that CO2 adsorption at 273.15 K is a versatile tool, which can provide a lot of information on the micropore region. Typically, it is much less flawed by diffusional limitations and should hence be employed more regularly. We hope, that the present work can define a valid framework (or initiate such at least) for the analysis of microporous polymeric materials. This will serve a better comparability of the different materials under development nowadays and can significantly enhance understanding of their performance in various applications.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

Additional adsorption/desorption isotherms and gas adsorption data analysis. 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]. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Jessica Brandt is acknowledged for lab assistance. Inspiring discussions with Prof. Markus Antonietti are highly appreciated. Funding by the Max Planck Society is acknowledged. 12988


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(40) Yang, K.; Lin, Y.; Lu, X.; Neimark, A. V. Solvation forces between molecularly rough surfaces. J. Colloid Interface Sci. 2011, 362, 382−388. (41) Zukal, A.; Slováková, E.; Balcar, H.; Sedlácě k, J. Polycyclotrimers of 1,4-Diethynylbenzene, 2,6-Diethynylnaphthalene, and 2,6-Diethynylanthracene: Preparation and Gas Adsorption Properties. Macromol. Chem. Phys. 2013, 214 (18), 2016−2026. (42) Capillary condensation in mesoporous materials is known to be affected by deformations as well. These are however typically lower in magnitude. See ref 47 for exemplary measurements. (43) Vishnyakov, A.; Ravikovitch, P. I.; Neimark, A. V. Molecular Level Models for CO2 Sorption in Nanopores. Langmuir 1999, 15, 8736−8742. (44) Balbuena, P. B.; Berry, D.; Gubbins, K. E. Solvation pressures for simple fluids in micropores. J. Phys. Chem. 1993, 97, 937−943. (45) This would be in line with reported N2 adsorption experiments on PIMs, which took up to 380 h hysteresis (see ref 8). (46) It could be argued that CO2 does condense within very narrow micropores at 273 K, and the above-mentioned solvation pressure effects and respective hysteresis should be seen as well. Too little is however known on the temperature dependency of the solvation pressure. The absence of a hysteresis does however indicate that pore filling is not hindered at 273 K, which might be a consequence of the overall higher temperature (higher thermal energy of both: adsorbate and adsorbent). (47) Balzer, C.; Wildhage, T.; Braxmeier, S.; Reichenauer, G.; Olivier, J. P. Deformation of Porous Carbons upon Adsorption. Langmuir 2011, 27, 2553−2560. (48) Kowalczyk, P.; Furmaniak, S.; Gauden, P. A.; Terzyk, A. P. Carbon Dioxide Adsorption-Induced Deformation of Microporous Carbons. J. Phys. Chem. C 2010, 114, 5126−5133. (49) Hoelck, O. Gas Sorption and Swelling in Glassy Polymers Combining Experiment, Phenomenological Models and Detailed Atomistic Molecular Modeling. Ph.D. Thesis; TU Berlin, 2008; available online via OPUS-IDN/1771 at http://opus.kobv.de/tuberlin/ volltexte/2008/1771/. (50) Silvestre-Albero, A. M.; Juárez-Galán, J. M.; Silvestre-Albero, J.; Rodríguez-Reinoso, F. Low-Pressure Hysteresis in Adsorption: An Artifact? J. Phys. Chem. C 2012, 116, 16652−16655.

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