The Role of Temperature and Adsorbate on Negative Gas Adsorption in the Mesoporous Metal-Organic Framework DUT-49

Role of Negative Gas In this contribution, we present an extensive investigation of adsorption of a range of different gases at various temperatures in DUT-49, a metal-organic framework which features a negative gas adsorption (NGA) transition. Adsorption experiments at temperatures ranging from 21 to 308 K, were used to identify, for each guest, a critical temperature range in which NGA occurs. The experimental results were complemented by molecular simulations that rationalize the absence of NGA at elevated temperatures and the non-monotonic behavior observed upon temperature decrease. Abstract 12 Unusual adsorption phenomena, such as breathing and negative gas adsorption (NGA), are rare 13 and challenge our understanding of the thermodynamics of adsorption in deformable porous 14 solids. In particular, NGA appears to break the rules of thermodynamics by exhibiting a 15 spontaneous release of gas accompanying an increase in pressure. This apparent anomaly is in fact 16 due to long-lived metastable states, and a fundamental understanding of this process is required 17 for the discovery of new materials with this exotic property. Interestingly, NGA was initially 18 observed upon adsorption of methane in the metal-organic framework DUT-49 at relatively low 19 temperature, close to the respective standard boiling point of the adsorptive, and no NGA was 20 observed in the same host/guest system at higher temperatures. In this contribution, we present 21 an extensive investigation of adsorption of a range of different gases at various temperatures in 22 DUT-49, a material which features an NGA transition. Experiments at temperatures ranging from 23 21 to

https://doi.org/10. 26434/chemrxiv.11733408.v1 In this contribution, we present an extensive investigation of adsorption of a range of different gases at various temperatures in DUT-49, a metal-organic framework which features a negative gas adsorption (NGA) transition. Adsorption experiments at temperatures ranging from 21 to 308 K, were used to identify, for each guest, a critical temperature range in which NGA occurs. The experimental results were complemented by molecular simulations that rationalize the absence of NGA at elevated temperatures and the non-monotonic behavior observed upon temperature decrease.
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Introduction 5
Structural flexibility and softness in porous crystals has generated new adsorption phenomena 6 beyond the classified types of isotherms known for rigid adsorbents. 1 While gradual swelling of 7 soft porous solids upon adsorption of fluids has been known for decades 2 , cooperative well-8 defined structural transformations in soft porous crystals have led to predefined adsorption 9 behavior, governed by reversible crystal-to-crystal structural transformations. 3 Especially in the 10 field of metal-organic frameworks (MOFs), adsorption-induced flexibility frequently gives rise to 11 stepwise isotherms governed by single or multiple steps and wide hysteresis dictated by expansion 12 or contraction of the pores. 4 Due to their uncommon adsorption behavior, these materials are 13 being discussed as alternative adsorbents in the area of gas sensing 5, 6 , storage 7 or separation 8-11 . 14 In early examples of adsorption-induced transitions in MOFs, it was shown that the pores in a 15 condensed framework can be expanded upon application of gas pressure. In this phenomenon, 16 called gate-opening, the adsorbate stabilizes the presence of the open pores (op), which 17 subsequently collapses upon reduction in gas pressure and subsequent desorption of the gas 18 molecules from the pores. 12 However, attractive solid-fluid and fluid-fluid interactions can also 19 result in large-scale contraction of the pores upon adsorption. This was first demonstrated in the 20  in which the open pore (op) channels are found to undergo contraction upon 21 adsorption of gases at intermediate pressure. 13 Accompanying a further increase in gas pressure, 22 the contracted pores (cp) are reopened to the initial op structure via structural expansion, and 23 these successive transitions in MIL-53 where thus referred to as breathing. 14 In both gate-opening 24 and breathing materials, the experimentally observable isotherms represent a mixture of the 25 single component isotherm of each structural phase with transition regions, which represent a 26 mixture present in the corresponding pressure range. The step-wise isotherms, and switching of 27 the solid, is caused by highly inelastic transformations due to an anharmonic Helmholtz free 28 energy profile upon deformation ( ( ), where represents a deformation). 15 In recent years, 29 several computational studies have demonstrated that adsorption-induced structural transitions 30 stem from a complex interplay between the structural flexibility of the MOF and the solid-fluid and 31 fluid-fluid interactions. [16][17][18] Beyond the nature of the solid and fluid, temperature effects were 32 found to have a large impact on the presence of breathing, observed in the systems MIL-53 19, 20 1 and ZIF-8 21 , however little experimental and computational work has been performed beyond 2 these systems. 3 In 2016, we discovered the phenomenon of negative gas adsorption (NGA), initially observed in 4 the MOF DUT-49 22 (Dresden University of Technology No. 49), which is characterized by a negative 5 step in the adsorption isotherm originating from adsorption-induced structural contraction of the 6 pores 23 . This adsorption behavior is unique for both rigid and flexible adsorbents, although large-7 scale adsorption induced-structural contraction is known to occur in other solids, such as  Computational analysis has revealed that the formation of a metastable adsorption state is a 9 prerequisite for NGA 24 . The op-cp transition is energetically driven by an increase in adsorption 10 interactions in the reduced pore volume, well reflected by an increase in adsorption enthalpy 11 upon contraction, which was investigated both experimentally and computationally 25 . The excess 12 amount of adsorbate present in the pores of the op state before contraction (n op ) and excess of 13 the amount of adsorbate present in the cp phase after contraction (n cp ) defines the amount of gas 14 released upon NGA, further termed Δn NGA . (1) 15 The structural contraction strongly depends on the softness of the framework and we recently 17 found that shortening of the ligand backbone increases stability and consequently prevents NGA. 18 While elongation increases softness, resulting in the discovery of the second NGA material,  . Although this study demonstrated a design principle for the synthesis of other materials 20 capable of NGA, the initial discovery and experimental adsorption conditions used in previous 21 studies, such as methane adsorption at 111 K, were very much serendipitous. These conditions 22 were originally chosen for instrumental reasons, to be able to record the full relative pressure 23 range below ambient pressure and avoid the application of high pressure. Interestingly, the 24 occurrence of NGA upon adsorption of other gases, such as n-butane (298 K) 23 , nitrogen (77 K) 27 , 25 and xenon (200 K), 28,29 was observed at temperatures close to the respective standard boiling 26 point of the adsorptive while no structural contraction, or NGA, was found at elevated 27 temperatures and pressures (methane 298 K, xenon 273 K). In addition, structural contraction 28 without the presence of NGA (breathing behavior, similar to adsorption behavior of 20 ) is 29 observed upon adsorption at reduced temperatures for some gases (n-butane at 273 K, xenon at 30 165 K). Consequently, three distinct adsorption trajectories have been identified for DUT-49: 31 structural contraction without NGA, structural contraction with NGA, and no adsorption-induced 1 structural contraction (Fig. 1).  As previously observed, Δn NGA values extracted from the isotherms in the range of 91-130 K show 10 as a function of temperature a non-monotonic trend, with a maximum of 6.15 mmol g -1 at 100 K. in the range of 91-135 K exhibit an inverse hysteresis around the NGA step in which the desorption 18 branch undercuts the adsorption branch ( Fig. 2 c,d). This indicates a structural contraction 19 following isothermal desorption from the pores. In the temperature range of 140-190 K no 20 hysteresis was observed indicating an absence of structural transitions (Supplementary Figure 3). 21 Consequently, recovery of guest free DUT-49op after NGA could be achieved by increasing the 22 temperature at a pressure beyond 300 kPa, beyond 160 K, and subsequently removing the 23 methane in vacuum. This allows for cycling NGA by subsequently performing adsorption at 24 reduced temperatures in the range of 91-130 K. 7 To investigate whether the non-monotonic evolution of Δn NGA as a function of temperature is 1 universal, the study of methane adsorption was first extended by analysing a series of 2 hydrocarbons and hydrogen at or below their respective standard boiling points (Supplementary 3 Figure 1). Among the adsorptive/temperature combinations tested, hydrogen is the only 4 adsorptive to neither show contraction nor NGA. Methane (111 K) and ethene (169 K) exhibit NGA 5 while the rest of the series exhibit contraction and hysteresis without the presence of NGA. As 6 previously observed for n-butane, 23 NGA was found to occur with increasing adsorption 7 temperature. Thus, isotherms at temperatures above the boiling point were recorded for ethene, 8 ethane, propane, and n-butane. Increasing temperature, from 169 to 199 K, Δn NGA increases from 9 1.23 to 8.08 mmol g -1 for the adsorption of ethene (Supplementary Figure 4) and the Δn NGA value 10 recorded at 199 K is the highest observed for all hydrocarbons investigated in this study. NGA is 11 observed for the adsorption of ethane in the range of 200 to 240 K, and Δn NGA reaches a maximum 12 of 4.03 mmol g -1 at 220 K. No NGA occurs above 220 K and in the range of 184 to 220 K structural 13 contraction without NGA is observed (Supplementary Figure 5). NGA at 230 and 240 K occurs at 14 132 and 216 kPa, which represents pressure amplification well above ambient pressure that is 15 required for air bag-type or pneumatic applications. The series of experiments was further 16 extended by adsorption of propane in the temperature range of 231 to 298 K (Supplementary 17 Figure 6). At these investigated temperatures, NGA is only observed at 261 K, with a respective 18 Δn NGA value of 1.77 mmol g -1 , and no contraction is observed at 298 K. The shape of the adsorption 19 branch indicates that structural contraction occurs at all temperatures except at 298 K, however 20 without NGA. To further characterize the nature of the structural transition we employed in situ 21 PXRD upon adsorption of propane at 231 K (Supplementary Figure 17) and ethane at 185 K 22 (Supplementary Figure 18). In comparison to the structural contraction following methane 23 adsorption at 111 K and n-butane at 298 K, which was previously analysed 23 , a similar cp formation 24 is observed for ethane and propane (Supplementary Figure 19). However, severe peak broadening 25 and the presence of an additional peak at lower diffraction angles, for cp formation upon propane 26 adsorption, indicate the formation of a more disordered state, which might explain the difference 27 in adsorption behaviour compared to other hydrocarbons. Nevertheless, in all other cases DUT-49 28 responds in a comparable fashion allowing the direct comparison of the isotherms and NGA 29 transitions. Including the previously published adsorption data of n-butane in the arrange of 273-30 308 K 23 an interesting trend can be observed: For each gas a non-monotonic evolution of Δn NGA 31 with temperature is observed (Fig. 3). 3 highest experimentally observed temperature at which NGA occurs referred to as maximum T NGA (black line).

4
As described above, for each gas a low temperature limit is observed for which DUT-49 is found to 5 contract with an absence of NGA, referred to as T low (the minimal T for which Δn NGA > 0). With 6 increasing temperature Δn NGA is found to increase, reaching a maximum at a temperature, T NGA . 7 Following a further increase in temperature, a decrease in Δn NGA is observed and an increase in 8 uptake in the plateau after structural contraction is observed, which was previously assigned to 9 incomplete structural contraction of the bulk sample demonstrated by in situ PXRD 27 . At a certain 10 upper temperature limit, referred to as T high (the maximum T for which Δn NGA > 0), no structural 11 contraction and reversible adsorption/desorption behaviour is observed. In the following, we thus 12 define the temperature T = T NGA at which Δn NGA reaches a maximum for a given adsorbate, T = T low 13 for the low temperature limit of NGA, T = T high for the high temperature limit of NGA and T high -T low 14 thus defines the range where NGA is observed for a respective adsorptive. Although all gases are 15 hydrocarbon-based, their increase in chain length suggests that the observed behaviour is of more 16 general nature and not a factor of chemical composition. In fact, the same evolution of Δn NGA was 17 previously found upon adsorption of xenon used as a probe molecule for in situ NMR 18 experiments 28,29 . To test whether this observation is supported for other noble gases, a series of 19 adsorption experiments were conducted using argon and krypton in the temperature range of 77-20 110 K and 120-160 K, respectively. A comparable temperature dependent evolution of Δn NGA is 21 obtained for both gases with argon reaching a maximum of 10.5 mmol g -1 at 95 K and krypton 22 6.3 mmol g -1 at 140 K. Interestingly, no NGA and structural contraction where observed upon 23 adsorption of argon at 105 K, however structural contraction and inversed hysteresis were 24 observed upon desorption in the low pressure range. This indicates that the activation barrier for 25 adsorption-induced contraction is lower upon desorption compared to the adsorption process and 1 might provide further insight to the irreversible contraction upon desorption of other adsorbates. 2 Most importantly, the experiments conducted demonstrate that NGA in DUT-49 can be obtained 3 in the a wide temperature range of 77-310 K by selecting the appropriate adsorbate. This is an 4 important fundamental observation and might also be relevant for the utilization of NGA for 5 practical applications in pneumatic devices or others. However, the experiments also raise two 6 fundamental questions: first, is there a generalizable correlation for a family of adsorbates that 7 enables prediction of the temperature range where there is presence of Δn NGA , and secondly, what 8 properties govern this observed temperature dependence of NGA? 9

Empirical correlation of T C with T NGA 11
In cylindrical mesoporous solids semi-empirical correlation of the pore critical temperature and 12 the melting point depression with the critical temperature of the fluid are found for a variety of 13 different pore sizes. [30][31][32] Shrinkage and disappearance of the hysteresis loop at the hysteresis 14 critical temperature reflects the temperature dependence of capillary condensation 33 known to be 15 related to NGA in DUT-49 26 . To probe the presence of a correlation, we plotted T high , T low , T NGA , 16 and the whole temperature range for which NGA is observed against physical properties of the 17 applied gases, such as the standard boiling point the critical temperature and their ratio 18 (Supplementary Figure 15). In fact, the temperature range in which NGA is observed for each guest 19 shows a linear correlation with the critical temperature, T c , of the fluid and is expressed in 20 in which the parameters i and j can be fitted to experimental data. This linear correlation is 22 observed for the three different temperature T high , T low , T NGA , as well as the whole temperature 23 range for which NGA is observed (Fig. 4).

5
Parameters i and j were determined to be i = 0.74 and j = -6.43 K for T high , and i = 0.82 and j = -6 54.1 K for T low , thus setting the limits for T NGA that is fitted with parameters of 0.78 and -26.1 K, 7 respectively. The similarity of the slopes i demonstrate that the temperature range of NGA for 8 these gases is governed by a universal correlation. The difference in j parameter obtained for both 9 fits shows the average deviation of around 20 K between T high , T low , and T NGA . This variation is 10 within the temperature steps of 10 K of the performed adsorption experiments and shows that 11 the resolution of the experiments is high enough to detect NGA for other gases, not explored in 12 this study. The correlation of T c with T NGA is particularly useful, as it can be used to predict the 13 temperature range where NGA can be expected to occur, and peak, for other gases. Because 14 structural contraction with the absence of NGA did occur at or below the standard boiling point for 15 long chain hydrocarbons, we can use equation 2, and the derived parameters, to estimate T NGA for 16 other adsorptives. For example, n-pentane with a critical temperature of 469.6 K is expected to 17 show NGA at 340 K, n-hexane (T c = 507.6 K) at 369 K and n-heptane (T c = 540.6 K) at 394 K. 18 Hydrogen, with a critical temperature of 33.1 K, is expected to show NGA at 8.5 K, a temperature, 19 which is 13 K below the investigated temperature where no structural contraction was observed. 20 Not only can equation 2 provide an estimate of the temperature region where NGA occurs but 21 also the temperature range where Δn NGA reaches a maximum. This is demonstrated for the 22 adsorption of C 4 hydrocarbons, n-butane, 1,3-butadiene, 2-methylpropane with T c of 425.2 K, 23 425.1 K, and 407.7 K, respectively, where Δn NGA for the adsorption of n-butane and 1,3-butandien 24 at 298 K is comparable at around 1.3 mmol g -1 but over doubled for the adsorption of 25 methylpropane. Although it is observed that Δn NGA decreases with increasing molar volume of the 26 condensed fluid, at the given adsorption temperature and saturation pressure (p/p 0 =1), which 27 correlates in part with T c , no direct correlation was found to estimate the magnitude of Δn NGA , as a 28 function of temperature, based on the performed experiments. Total uptake of condensed fluid in 1 the pores of DUT-49op and cp can be estimated at saturation using the pore volume of the 2 structures and the molar volume of the fluid, but the magnitude of Δn NGA is primarily dictated by 3 how much the op phase can be overloaded, beyond the intersection of the op/cp isotherms. This 4 point of structural transition not only correlates to a specific loading of fluid, it is also correlated to 5 a specific p NGA , the absolute pressure at which NGA occurs. Because adsorption isotherms, as a 6 function of absolute pressure, are strongly impacted by the adsorption temperature, comparison 7 of the relative pressure obtained from division with the vapour pressure, p 0 , at a given 8 temperature permits comparison of isotherms at different temperatures and at the same relative 9 pressure range. In all experiments performed, structural contraction and NGA were found to be in 10 the relative pressure region of 0.09 to 0.19, which correlates to the pressure range where 11 mesopore filling occurs, as previously analysed by in situ neutron diffraction 26 . Accompanying 12 increasing T and Δn NGA not only the absolute pressure of transition at which NGA occurs, p NGA , but 13 also the relative transition pressure, p NGA /p 0 , is shifted to higher pressures. Similar to the 14 correlation between T c and T NGA , the relative transition pressure p NGA /p 0 was found to linearly 15 grow with the critical pressure p c of the fluid (Supplementary Figure 16). To estimate an empirical 16 correlation similar to the study of temperature dependence of Δn NGA , values of p NGA /p 0 were taken 17 at T NGA for the series of gases previously discussed. The upper temperature limit of NGA for some 18 gases has not been reached, because Δn NGA as a function of T was analysed in 10 K steps. This is 19 expected to impact the accuracy of the pressure more drastically than for the previous correlation 20 with temperature. Thus, an error for p NGA /p 0 was estimated based on the resolution of the 21 pressure range obtained from the conducted experiments. By using equation (3), p NGA can be 22 estimated for different gases using the vapor pressure p 0 as a function of T NGA . 23 Due to the relatively low number of adsorption experiments around the upper temperature limit, 24 the empirically estimated factor l of 0.032 is expected to underestimate p NGA . However, it does 25 provide an estimation of the transition pressure at which contraction and NGA are to be expected, 26 and thus present another tool of narrowing the conditions where NGA transitions are expected for 27 a given adsorptive in  29 Canonical ensemble for determination of high temperature limit (T high ) 30 Although the empirical correlations above provide guidelines for the discovery of NGA transitions 31 in DUT-49 in defined temperature and pressure ranges, we sought to provide an analysis of the 32 fundamental thermodynamic and kinetic aspects responsible for the non-linear evolution of Δn NGA properties of the op and cp phase in DUT-49. As the metastable region in the isotherm that 1 represents the NGA transition is difficult to capture using existing experimental and computational 2 techniques, as a first approximation we consider the presence of adsorption-induced structural 3 contraction as a prerequisite for NGA to occur. Coudert et al. were previously successful in 4 simulating the p,T phase-diagram of methane adsorption in MIL-53 using the osmotic ensemble, 5 ∆ ( , ), as a function of adsorption temperature, T, and pressure, p, the free energy 6 difference between the open and contracted state, F op-cp , and change in volume, V op-cp , the 7 adsorbed amount, n ads , as well as the molar fluid volume V m , described in equation (4). 8 Although a detailed analysis of structural transition for DUT-49 has been performed 24 , the 9 temperature dependence of the adsorption energetics have not been fully characterized yet. To 10 analyze the adsorption-induced structural transition upon adsorption of methane in DUT-49, we 11 thus simulated a series of isotherms for the op and cp phase in the temperature range of 91-190 K 12 with 10 K increments using grand canonical Monte Carlo (GCMC) simulations, i.e. with rigid 13 description of the host material for each phase. These simulations complement the previously 14 discussed experimentally recorded isotherms. In general, we find good agreement between the 15 simulated and experimental adsorption isotherms and capture the intersection of the isotherms of 16 both phases with high accuracy validating the computational analysis and derived adsorption 17 energetics. As primary condition for the occurrence of NGA, we take the structural contraction of 18 the op phase beyond the crossing point of the op and cp isotherms: this crossing point 19 corresponds to an adsorbed amount n op-cp and pressure p op-cp . From the simulated isotherms these 20 values can easily be defined and Δf i can now be expressed as a function of Δn NGA using Equation 5: 21  The difference in osmotic potential not only can characterize the energetic conditions for 5 temperature dependent adsorption-induced contraction in DUT-49, but it can also indicate the 6 free energy difference upon contraction as a function of Δn NGA , thus defining the limits of 7 structural contraction. The p,n region in which Δf exceeds the free energy required for structural 8 contraction (∆ − , ca. 900 kJ mol -1 ) 24 matches well with the experimentally observed presence 9 of structural contraction upon adsorption of methane (91-130 K). Please note we make a constant 10 approximation for the free energy of structure contraction, ∆ − , as entropy was previously 11 reported to have a negligible contribution to the guest-free framework transition. This obtained 12 thermodynamic analysis of the evolution of Δn NGA , in particular the increase with decreasing 13 temperature, is in contrast to the experimental observations. In fact, from an equilibrium 14 thermodynamic standpoint it is impossible to predict the temperature dependence. One could 15 argue, that Δn NGA is expected to decrease with decreasing temperature because |Δf|, the 16 thermodynamic driving force for the transition, increases with decreasing temperature. In this 17 case Δn NGA could exhibit negative values, which would indicate a sudden jump towards higher 18 adsorbed amount in the isotherm ( Fig. ). However, this analysis is complicated by two important 19 aspects intrinsically connected to NGA, the metastability of the transition and the desorption of 20 gas upon structural contraction. Both features are not captured by the above methodology and 21 thus don't allow to draw any conclusion in the evolution of Δn NGA with temperature. The 22 conducted thermodynamic characterisation, however, does capture and rationalize the upper 23 temperature limit, T high , for structural contraction very accurately and supports the empirical 24 correlation of T c and T NGA . In the next section, we rationalise the non-monotonic NGA behaviour 1 and estimate Δn NGA based on a different theoretical model, a mechanical model based on 2 adsorption-induced stress. 3 Adsorption-stress model for determination of low temperature limit (T low ) 4 Analyzing the adsorption mechanism via in situ neutron diffraction and GCMC simulations, we 5 concluded that the adsorption-induced stress occurring from adsorption in the larger pores in the 6 DUT-49 framework precedes the structural contraction. In fact, several studies on ordered 7 mesoporous silicates show that the adsorption-induced stress on the host material reaches a 8 maximum value before capillary condensation occurs in the mesopores 2, 34 . This phase transition in 9 the fluid phase is characterized by a hysteresis, depending on diameter of the pore. The activation 10 barrier with decreasing adsorption temperature for capillary condensation is reported to increase 11 and a widening of the hysteresis is observed 31,35,36  DUT-49 using a series of classical molecular dynamics simulations in the NVT ensemble. We 24 employed these simulations for methane adsorption at three temperatures at which NGA was 25 experimentally observed namely 91, 111 and 130 K (Fig. 6).  This adsorption-induced stress follows non-monotonic behavior characteristic of many 5 mesoporous materials 2, 38 . Although structural contraction and the presence of a metastable state 6 beyond the crossing point of the isotherm (n op = n cp ) are required for NGA, and strongly influenced 7 by the mechanical properties of the framework, prior to this the mechanical role of the adsorbate 8 has not been investigated. We observe that the process of methane adsorption can produce 9 considerable adsorption-induced stress. Notably the minimum between -30 and -40 MPa 10 compares well to the experimental transition pressures, previously reported by hydrostatic 11 compression 25 . Since the structural contraction is found to be independent of temperature effects, 12 especially in such a small temperature range, the critical stress for contraction might be assumed 13 the same for all investigated temperatures. Similar to our previous analysis of the free energy 14 change as a function of n op -n cp the adsorption stress isotherms can also be transferred as a 15 function of n op -n cp (Fig. 7).

4
Although the slope of the stress isotherms as a function of n op -n cp are comparable, they exhibit an 5 offset towards increased Δn NGA values with increasing temperatures. To reproduce the Δn NGA 6 observed experimentally, Δn NGA at 91K is estimated at 50 CH 4 per unit cell (calculated 2.6 mmol g -1 , 7 experimental 1.36 mmol g -1 ), 150 CH 4 per unit cell (calculated 7.9 mmol g -1 , experimental 8 6.1 mmol g -1 ) at 111 K and 200 CH 4 per unit cell (calculated 10.5 mmol g -1 , experimental 9 0.2 mmol g -1 , estimated for complete op-cp transition 8.3 mmol g -1 ) at 130 K, the corresponding 10 critical stress is in the range of -25 MPa to -20 MPa. This critical stress is in the same numerical 11 range of the transition pressure (35 MPa) measured by mercury intrusion thus supporting the 12 validity of this adsorption-stress model, which was initially tested on a very different material, 13 namely the breathing MIL-53. 39 Changes in adsorption temperature will influence the adsorption 14 in both phases and as a result the crossing point is shifted towards decreasing relative pressure 15 with a decrease in temperature. Consequently, at lower temperature the critical adsorption stress 16 occurs at a pressure where structural contraction is thermodynamically possible but at a pressure 17 closer to the crossing point of the op-cp isotherms, which in consequence leads to inferior Δn NGA . 18 With increasing temperature, the transition region is shifted to higher pressure as well as higher 19 n op beyond the intersection of the isotherms and thus results in enhancement of Δn NGA . 20

Conclusion 22
In conclusion, we have demonstrated the presence of negative gas adsorption transitions upon 1 adsorption of a series of hydrocarbons and noble gases in DUT-49 in defined temperature and 2 pressure ranges. For each adsorptive NGA was observed in a limited temperature range T high -T low , 3 which linearly correlates with the critical temperature of the adsorptive. An empirical correlation 4 was determined to be universal for hydrocarbons, and noble gases, and predicts the temperature 5 range where NGA is expected to occur in DUT-49 for fluids not investigated in this study. A non-6 monotonic evolution of Δn NGA with temperature was observed from the experimental isotherms, 7 with a high temperature and low temperature limit. The thermodynamic interactions responsible 8 for these limits were further characterised by computational methods using methane adsorption 9 as an example. First, the high temperature limit of adsorption-induced structural contraction was 10 analysed using the osmotic ensemble on a series of GMCM modelled isotherms. It was found that 11 beyond a certain temperature limit the change in adsorption energetics between the op and cp 12 state no longer allows for the compensation of the energy required for structural contraction. 13 Although the computationally predicted upper temperature limit correlates well with 14 experimental observations and thus provides a novel tool to predict structural contraction in the 15 DUT-49 system ab initio, it provides no information on the experimentally observed lower 16 temperature window and the evolution of Δn NGA with temperature. Because kinetic analysis of 17 adsorption in a large system like DUT-49 is so far not accessible we instead decided to characterise 18 the temperature dependence of the adsorption-induced stress, responsible for structural 19 contraction. The stress minimum is found to be shifted with decreasing temperature to lower 20 adsorption relative pressure, closer to the intersection of the isotherms of DUT-49op and cp. 21 Consequently, Δn NGA is found to decrease with decreasing temperature. The predicted transition 22 pressures from the stress-based analysis correlate well with the experimental observations and 23 allow to replicate the evolution and to some extent the magnitude of Δn NGA , consequently 24 providing an explanation for the observed non-monotonic NGA behaviour. 25 This present study, on the role of temperature on NGA transitions, addresses important questions. 26 It mainly demonstrates that NGA is a physical phenomenon dictated by the combination of solid-27 fluid and fluid-fluid interactions and is observed for a wide array of different gases in different 28 temperature regimes. However, this study raises two questions: First, is the empirically derived 29 correlation between T NGA and T c valid for other adsorptives that exhibit enhanced solid-fluid and 30 fluid-fluid interactions such as CO 2 or other very polar gases? Secondly, is the analysis valid for can a more general correlation link these material parameters to the physical gas properties 1 identified in the present study? Ideally, such correlations can be identified purely ab initio by the 2 use of computational analysis. However so far, we were not able to compute the full energy 3 landscape of gas adsorption in DUT-49 at different temperatures involving both entropic and 4 enthalpic factors, occurring by the release of gas upon NGA, and the evolution of kinetic barriers, 5 known to be responsible for NGA. These computations might also help to identify novel NGA-6 capable porous solids. For now, rather simplistic thermodynamic, stress-based, and empirical 7 correlations derived from experimental analysis provide a conceptual guideline for the 8 temperature range in which NGA is to be expected, possibly in systems other than DUT-49. For 9 example, generally lower adsorption temperatures benefit structural contraction, by enhanced 10 adsorption-induced stress, and thus present one of the prerequisites for NGA to occur.

Conflicts of interest 40
There are no conflicts to declare.

Materials and methods 1
The synthesis and characterization of this DUT-49 sample used in the presented experiments is in 2 detail described in reference 1 where it is labelled as DUT-49(4). All samples used in the conducted 3 study originate from the same batch of DUT-49 crystals with an average crystal size distribution of 4 4.26 µm. The following gases were used: 5

Low pressure adsorption experiments (<110 kPa) 1
Low pressure (p < 110 kPa) volumetric adsorption experiments were carried out on a BELSORP-max 2 instrument by MICROTRACBEL CORP. and the measuring routine of BELSORP-max control software was 3 used. In general, equilibration conditions for each point were 1% pressure change within at least 4 350 s. For adsorption experiments below the standard boiling point of the adsorptive 1% within 5 500 s was chosen. The dead volume was routinely determined using helium. Values for the 6 adsorbed amount of gas in the framework are all given at STP and were recalculated to mmol g -1 . 7 Prior to the measurement the samples were degassed at 373-423 K for at least 5 h in dynamic 8 vacuum (p < 10 -4 kPa). 9 Vapor adsorption experiments were conducted at 298 K using the BELSORP-max routine for 10 degassing and characterization of vapors. Equilibration criteria were increased to 0.5% pressure 11 change within at least 550 s due to the low pressures and relatively slow equilibration in these 12

experiments. 13
Several methods for reaching the desired adsorption temperatures were used: For analysis at 295 K 14 or higher temperatures a JULABO thermostat was used. For analysis at 273 K ice was used as a 15 coolant. To reach adsorption temperatures not achievable by these techniques in the range of 16 300 K -10 K a closed cycle helium cryostat was used. The cryostat DE-202AG was operated by a 17 temperature controller LS-336 (LAKE SHORE) and the heat produced by the cryostat is removed from 18 the system by a water-cooled helium compressor ARS-2HW. The sample was placed in a custom 19 made cell consisting of a 3 cm long rod-shaped copper cell of 1 cm diameter, sealed by a copper 20 gasket from the exterior with a copper dome and insulated by dynamic vacuum (p < 10 -4 kPa), and 21 connected to the BELSORP-max adsorption instrument with a 0.5 mm copper capillary. The samples 22 were degassed prior to the measurement at room temperature for at least 1 h in dynamic vacuum 23 (p < 10 -7 kPa). 24

High pressure adsorption experiments (1 kPa< p < 8 MPa) 1
High pressure (1 kPa< p < 8 MPa) volumetric adsorption experiments were carried out on a 2 BELSORP-HP instrument by MICROTRACBEL CORP. and the measuring routine of BELSORP-HP control 3 software was used. In general equilibration conditions for each point were 1% pressure change 4 within at least 350 s (exceptions are mentioned specifically). The dead volume was routinely 5 determined using helium at 298 K and at the desired adsorption temperature. The adsorption 6 temperatures in the range of 300 K -10 K were achieved by using the same closed cycle helium 7 cryostat described in detail above. The sample was placed in a custom-made cell consisting of 3 cm 8 long copper-mantled VCR-sealed stainless-steel SWAGELOK cell of 0.5 cm inner diameter and 9 connected to the BELSORP-HP adsorption instrument with a 0.5 mm stainless steel capillary. The 10 cell was insulated by dynamic vacuum (p < 10 -4 kPa), and the samples were degassed prior to the 11 measurement at room temperature for at least 1 h in dynamic vacuum (p < 10 -5 kPa). Adsorbed 12 amounts are given as excess amount adsorbed in mmol g -1 . 13

Routine for sample recycling 1
In our previous studies on NGA the transition upon desorption was found to be irreversible 2 . 2 Consequently, for each adsorption measurement a new sample of DUT-49 had to be used to record 3 individual isotherms. To overcome this extensive usage of sample amount a routine was developed 4 to cycle DUT-49 even when NGA is present. This procedure was previously described in two 5 references 2, 3 and was primarily applied in the characterization of methane and ethane for which 6 experiments were first conducted at elevated temperatures and then stepwise decreased until 7 structural transitions were observed and then after desorption the regeneration protocol applied. 8 In general, some adsorbed molecules can be removed from the pores of DUT-49 if the guest 9 molecules are in a supercritical state. This fact is used in the initial supercritical activation of DUT-49 10 using carbon dioxide. When analyzing the adsorption behavior upon adsorption of methane it 11 becomes obvious that the isotherms become reversible at temperatures beyond the critical point 12 (for methane around 150 K). Thus, methane can be removed from the pores of DUT-49op by 13 increasing the temperature beyond this point while maintaining saturation pressure in the 14 measuring cell. This method of regeneration has some experimental limitations: The increase in 15 temperature while maintaining saturation pressure of the adsorptives can lead to high pressures. 16 Thus, this method of regeneration could only be performed in high pressure equipment. For 17 experiments conducted at pressures below 100 kPa in the BELSORP-max instrument, each 18 experiment was performed on a fresh sample. In addition, this recycling technique was found to be 19 not applicable to adsorption of krypton, propane, n-butane (due to limitations of upper 20 temperature limit of the instrument) and ethene. 21 22 23

Adsorption isotherms 1
In the following figures adsorption isotherms of different gases/vapors and recorded at different 2 temperatures are depicted. In each isotherm filled symbols correspond to the adsorption, empty 3 symbols to the desorption carried out subsequently.       6. Empirical analysis of NGA parameter 1 NGA parameter were derived from the previously shown isotherms. In the table below numerical 2 values relevant for the discussion of the manuscript are provided in Supplementary Table 3. It is 3 important to note that adsorption experiments may suffer from errors primarily caused by 4 variations in the sample amount and inaccurate weighing caused by the preparation under inert 5 atmosphere. A second inaccuracy originated from the resolution of the isotherms which, in the case 6 of high pressure isotherms, strongly relies on the sample amount used in the experiment. This 7 inaccuracy is expected to result in an underestimation of Δn NGA. Temperature accuracy in the 8 conducted experiments was determined by internal calibration via condensation of the fluid at 9 saturation pressure. The instrument itself provides a high temperature stability and accuracy of 10 0.01 K. 11 Supplementary Table 3. Numerical values to describe NGA properties derived from the recorded 12 isotherms. contains the adsorption temperature, T, the adsorbed amout in the op phase before 13 NGA, n op (NGA), the adorbed amount in the cp phase after NGA, n cp (NGA), the amount of gas 14 expelled upon NGA expressed as Δn NGA , as well as the pressure at which NGA occurs, p NGA , recorded 15 at n op (NGA). 16 n cp (NGA) (mmol g -1 ) Δn NGA (mmol g -1 )

In situ PXRD Experiments 1
PXRD experiments in parallel to adsorption were performed at BESSY II light source, KMC-2 2 beamline of Helmholtz-Zentrum Berlin für Materialien und Energie 4 using the recently established 3 experimental setup. 5 The diffraction experiments were performed in transmission geometry using a 4 sample holder with a thickness of 2 mm. Monochromatic radiation with energy of 8048 eV 5 (λ = 1.5406 Å) was used for all experiments. The diffraction images were measured using 2θ scan 6 mode and a Vantec 2000 area detector system (BRUKER) in the range of 2 -50° 2θ. A synchrotron 7 beam with dimensions of 0.5 x 0.5 mm was used for the experiments. Corundum powder with a 8 crystallite size of 5 µm was used as an external standard. The image frames were integrated using 9 Datasqueeze 2.2.9 software 6 and processed using Fityk 0.9.8 program 7 . 10 To control the gas loading the BELSORP-max setup was used. The adsorption chamber was sealed 11 with an X-ray transparent beryllium dome and connected to the BELSORP-max via a 0.5 mm copper 12 capillary. The adsorption cell was isolated by a second beryllium dome and insulating dynamic 13 vacuum (p < 10 -5 kPa). Different gas loadings were dosed to the cell and equilibrated by using either 14 the automated BELSORP software while automatically recording a full isotherm or by manually 15 dosing. The gas pressure was equilibrated for at least 400 s before a PXRD pattern was recorded in 16 both cases. The adsorption temperature was controlled by a closed cycle helium cryostat. The 17 cryostat DE-202AG was operated by a temperature controller LS-336 (LAKE SHORE) and the heat 18 produced by the cryostat is removed from the system by a water-cooled helium compressor ARS-19

2HW. 20
Temperature dependent PXRD experiments were performed in a closed chamber under dynamic 21 vacuum of 10 -4 mbar in the temperature range of 100 -725 K with steps of 25 K on a PANALYTICAL 22 X'PERT PRO with λ = 0.15405 nm in Bragg-Brentano-geometry. The temperature was raised with 5 K 23 min -1 starting at 100 K. For each temperature three PXRD patterns were collected under isothermal 24 conditions in the 2Ѳ range from 2.5 up to 22 °, with a step size of 0.028 ° and 40 s per step.