Low Temperature Calorimetry Coupled with Molecular Simulations for an In-Depth Characterization of the Guest-Dependent Compliant Behavior of MOFs.

In this study adsorption microcalorimetry is employed to monitor the adsorption of four probes (argon, oxygen, nitrogen, and carbon monoxide) on a highly flexible mesoporous metal-organic framework (DUT-49, DUT = Dresden University of Technology), precisely measuring the differential enthalpy of adsorption alongside high-resolution isotherms. This experimental approach combined with force field Monte Carlo simulations reveals distinct pore filling adsorption behaviors for the selected probes, with argon and oxygen showing abrupt adsorption in the open pore form of DUT-49, in contrast with the gradual filling for nitrogen and carbon monoxide. A complex structural transition behavior of DUT-49 observed upon nitrogen adsorption is elucidated through an isotherm deconvolution in order to quantify the fractions of the open pore, contracted pore, and intermediate pore forms that coexist at a given gas pressure. Finally, the heat flow measured during the guest-induced structural contraction of DUT-49 allowed an exploration of complex open-contracted pore transition energetics, leading to a first assessment of the energy required to induce this spectacular structural change.

Introduction

Framework rigidity upon adsorption is still a common assumption applied to porous materials. Although adsorbate-induced structural changes of host frameworks were revealed more than 90 years ago,[1] the advent of precisely tunable compliant adsorbents which can respond to diverse stimuli such as guest loading,[2−4] temperature,[5] or mechanical pressure[6−9] has sparked tremendous scientific curiosity. The family of porous hybrid materials, namely metal–organic frameworks (MOFs), has been instrumental in furthering the possibility space of flexible adsorbents,[10−13] in part due to the structural control afforded by their building blocks and regular crystalline nature. Various flexible behaviors of their architectures such as gate opening,[14] pore collapse,[15] breathing,[16] and swelling[17] have been observed.

DUT-49 (Dresden University of Technology No. 49) is a member of the flexible MOF family, constructed of metal–organic polyhedra (MOP) interconnected in an fcu topology, resulting in a hierarchical pore size distribution and a high surface area (in excess of 5400 m2/g).[18] Besides these structural features, DUT-49 has shown the ability to suddenly switch from its initial open pore (op) form to a contracted pore (cp) version upon gas adsorption, simultaneously ejecting part of the guest molecules from its crystal structure, as illustrated in Figure . This behavior leads to an increase of gas pressure in the containing enclosure and has been dubbed “negative gas adsorption”, or NGA, owing to its counterintuitive nature.[19] The micromechanical and energetic principles underpinning this unexpected behavior were identified computationally[20−22] as adsorption stress-induced linker buckling, leading to a structural transition between metastable equilibrium states. More recently, several derivative materials were synthesized through an isoreticular approach, with longer central struts shown to increase the predisposition toward flexibility,[23] and more general rules for adsorption-induced contraction were investigated in a simplistic slit-pore model.[22] However, a complete understanding of the system has yet to be achieved, in particular regarding the guest and temperature dependence of the structural contraction, with both variables being intimately linked to the strength of the host/guest interactions as well as to the energetics of the structural transition, insofar never determined experimentally.

Figure 1

Schematic of the DUT-49 open pore (op) transition upon gas adsorption to a closed pore (cp) phase, accompanied by expulsion of guest adsorbate from pores, followed by gradual reopening at higher pressures. Also represented are the three pore families: octahedral (orange), tetrahedral (blue), and the cuboctahedral metal–organic polyhedron (green), as well as the corresponding linker shape in the two phases.

Microcalorimetry is a powerful technique which allows a direct in situ monitoring of the energetics of adsorption as a function of guest uptake. Here, the differential enthalpy of adsorption is evaluated concurrently with the isotherm, permitting an accurate assessment of combined host/guest and guest/guest interactions. When the porous material undergoes a guest-induced structural transition, the additional energy generation or consumption of the host transition contributes to the total heat flow, increasing or lowering the amount of heat recorded by the microcalorimeter, respectively.[24] For DUT-49 it is known that the increased interactions between the guests and the cp phase due to a more confined environment allow for its stabilization, at least until the penalty of guest expulsion becomes too high.[20] However, these factors have not been captured experimentally due to the complex energetic landscape. In the following work microcalorimetry and molecular simulations are combined to investigate this limit, alongside an in-depth characterization of adsorption, pore filling, and energetics.

Microcalorimetric studies on DUT-49 and its analogues have been solely reported at 303 K for n-butane.[23,25] The strong guest–temperature dependence of the op–cp structural transition previously observed[19,23] calls for the selection of multiple probes which would allow for a comparison of the MOF switching behavior outside the temperature range of a conventional calorimeter. Here, four model probes (argon, oxygen, nitrogen, and carbon monoxide) with distinct intrinsic properties were considered at cryogenic temperatures, a range where N2 and Ar have been previously shown to induce the contraction of DUT-49.[23] A home-built Tian–Calvet calorimeter which can operate in these conditions was used,[26] in conjunction with a continuous, quasi-equilibrium, adsorbate introduction method, allowing for subtle changes in the differential enthalpy of adsorption as well as transient phenomena to be observed experimentally.

Using this setup, we were able not only to obtain high-resolution isotherms of all studied probes on DUT-49 but also to precisely measure the corresponding differential enthalpy of adsorption for each probe. These experimental findings were corroborated by force field Monte Carlo (MC) simulations to reveal the similarity and specificity of the probes in terms of adsorption behaviors. Additionally, the continuous introduction method employed in tandem with the MC calculations allowed us to determine for the first time the enthalpy of transition between the guest-loaded open and contracted forms of DUT-49 and to evidence its guest-dependence. We demonstrate that this enthalpy is indeed a function of the difference in integral enthalpy of adsorption between the two loaded op–cp conformations, shedding further light on the complex energetic landscape of DUT-49 and its host–guest chemistry.

Materials and Methods

Material

DUT-49 samples used in this study were taken from the same batch, with the synthesis, activation, and characterization described in detail in a previous publication,[27] where it is labeled as DUT-49(4). After supercritical CO2 activation, samples were stored and transferred under inert atmosphere in an Ar-filled glovebox.

Adsorption Microcalorimetry

Adsorption microcalorimetry at temperatures below ambient was performed by using a homemade calorimeter in a diving-bell configuration, first described by Rouquerol[26] and further detailed elsewhere.[28] In short, the setup consists of a Tian–Calvet differential calorimeter which is immersed in a cryogenic bath at its boiling point (liquid nitrogen for 77 K or argon for 87 K). The bath is refilled as required, to maintain a constant fluid level throughout the experiment. The upper part of the system, containing the automated gas dosing apparatus, is kept in a temperature-controlled enclosure at 303 K. The adsorbent is placed in a J-shaped cell made of borosilicate glass to minimize thermal expansion stress and introduced into the fluid filled Dewar and through the bottom of the differential calorimeter. Good thermal equilibrium between the cell and surrounding thermopile is ensured using a helium blanket in the calorimetric enclosure, kept under a small positive pressure through a continuous nominal flow. The experiment starts when the calorimeter signal recedes to baseline (5 μW). A schematic and depiction of the apparatus is provided in Figure S1.

As observed in previous experiments with DUT-49 and nitrogen, argon, methane, and n-butane,[23,25] the commonly employed stepwise dosing method makes difficult an accurate pressure control around the critical transition uptake. A possible alternative might be the use of very small dosing steps. However, this approach would increase the experimental duration and decrease the resolution of each step as consecutive doses introduce a cumulative error in the pressure measurement. Furthermore, the local pressure variations during dosing may induce a premature structural transition. To alleviate this concern, we have instead used a continuous adsorbate introduction method.[28] In brief, the flow of adsorbate into the cell is kept constant by a restriction in the pipe diameter which is strict enough to allow the gas to enter via a sonic flow regime. Above a certain pressure differential, the sonic nozzle allows the flow rate to become purely a function of upstream pressure and environmental temperature. As a steady flow rate is only possible with a pressure difference above 3 bar (gas dependent), the desorption branch cannot be measured.

For each experiment, a small amount (10 to 20 mg) of DUT-49 was introduced in the cell while maintained under an inert gas flow. The amount of material represents a trade-off between isotherm/enthalpy accuracy and experimental duration. The cell was then sealed with an oxybutane torch prior to evacuation, leak check, and sample activation at 420 K under dynamic vacuum (down to 10–4 mbar) for at least 8 h. Any repeat measurements on the same material were performed with an identical thermal reactivation procedure. A separate calibration step was carried out at the start of each experiment to determine the adsorbate flow rate and the dead volume before the entrance to the cell. Experimental flow rate was maintained between 1 to 3 mmol h–1, low enough to consider the system at quasi-equilibrium. This assumption was verified by conducting multiple experiments at different upstream pressures. A perfect overlap of the measured isotherms confirms that the experiments took place at equilibration times below the dead time of the calorimeter (Figure S4). The complete data set is available in the SI in Figure S2 and Figure S3.

Computational Details

Grand canonical Monte Carlo (GCMC) simulations were carried out at 77 K to compute the adsorption isotherms and enthalpies for argon, oxygen, nitrogen, and carbon monoxide in DUT-49 cp and op forms by employing the Complex Adsorption and Diffusion Simulation Suite (CADSS) code.[29] Additional calculations were performed for argon at 87 K while the adsorption isotherms for nitrogen were equally computed for the ip form (structure from ref (27)). The simulation box was made of 1 conventional unit cell for all DUT-49 phases with atomic coordinates taken from the previous study.[19] The fugacities for all adsorbates at a given thermodynamic condition were computed using the Peng–Robinson equation of state. For each state point, 108 Monte Carlo steps were used for both equilibration and production runs. The guest/DUT-49 and guest/guest interactions were treated using a van der Waals contribution with a cutoff of 12 Å. The Lennard-Jones (LJ) potential parameters for the atoms of the inorganic and organic parts of the DUT-49 framework were derived from the universal force field (UFF)[30] and DREIDING,[31] respectively. Argon was represented by a single LJ site described by the OPLS force field. The other adsorbates were modeled as two-LJ sites with associated potential parameters taken from the work of ref (32) for CO and from the TraPPE force field[33] for N2 and O2. Lorentz–Berthelot (LB) combination rules were used to calculate the cross LJ potential parameters (Table S2).

Results and Discussion

Probe Dependence of the Adsorption Isotherm

Recorded isotherms at 77 K for the four probes are depicted in Figure and compared with the GCMC simulated isotherms for the open and contracted pore forms of DUT-49. It should be noted that the selected probes differ in their physicochemical properties, such as size, shape, and polarity (with several of these parameters given in Table S1). Three isotherm regions can be clearly distinguished for Ar and O2 and are archetypal of the NGA behavior. Initial loading occurs in the op form, until contraction of the hierarchical pore network leads to expulsion of the adsorbed guest and a decrease of the adsorbed amount around p/p0 = 0.1. After this step a plateau is observed, as the cp form is fully saturated with the probe. Finally, a gradual reopening of the cp form is observed, until the material is completely regenerated. In sharp contrast, carbon monoxide does not appear to induce a structural contraction in DUT-49, with adsorption occurring purely in the op form. The transition occurring in the nitrogen isotherm is more complex and will be further discussed in a later section.

Figure 2

Experimental (black) and GCMC-simulated isotherms on DUT-49 op (red) and cp (blue) at 77 K for argon, oxygen, nitrogen, and carbon monoxide. Shaded regions highlight ranges in which the material has undergone transitions and is not in an op phase.

In all cases, the GCMC simulated data for the cp and op forms capture well the distinct regions of the experimental adsorption isotherms. Total uptake in the op form (as the uptake at p/p0 = 0.6) and in the cp form (as the uptake at p/p0 = 0.3 after contraction) is nearly identical to the experimental findings. Furthermore, the pore filling steps coincide similarly well, which validates the force field parameters used to describe all present interactions.

A three-step adsorption isotherm is expected in the simulated op isotherms, as the framework is characterized by a trimodal hierarchical pore size distribution. The cuboctahedral pore at the center of the MOP is completely filled at low pressures, followed by slow multilayer-like filling of the tetrahedral and octahedral larger pores, as was previously shown experimentally though in situ neutron diffraction.[23] However, subtle features emerge when comparing the condensation step in the tetrahedral and octahedral pores with different probes. Figure shows that with O2 and Ar, this step is sharp, corresponding to an abrupt pore filling. In contrast, the isotherm is smoother for CO and even more so for N2, with the pores being filled gradually. A careful analysis of MC snapshots during adsorption reveals that compared to Ar and O2, both CO and N2 are more homogeneously distributed within the whole porosity at initial and intermediate pressures (shown in Figure S5), likely owing to the difference between the adsorption temperature and the boiling point of the respective adsorbates (values in Table S1). This scenario indicates that a substantial reorganization of N2 and CO is required to accommodate the subsequent molecules when the gas pressure increases, leading to a gradual pore filling. The predicted probe-dependent pore filling mechanism is reminiscent to that previously reported for the same probe molecules in the pore-gating ZIF-8.[34] Regarding adsorption in the cp form, the octahedral and tetrahedral voids are greatly reduced in volume, resulting into a filling of all these pores at very low pressures.

Figure 3

Breakdown of simulated adsorption isotherms on the op phase into fraction of probe uptake in each pore type: octahedral (orange), tetrahedral (blue), and cuboctahedral (green). The assignment of a probe into a cavity was performed based on a radial distribution from the center of each pore type.

Specific Case of Nitrogen Adsorption

The different steps observed in the experimental nitrogen isotherm (Figure ) are unlike the transition mechanics exhibited by argon and oxygen. While guest ejection is still observed at p/p0 = 0.1, the total uptake after NGA does indicate a fully contracted phase, as evidenced by the large difference between the experimental and GCMC simulated uptakes in the cp existence range. Furthermore, the nitrogen induced reopening of DUT-49 is characterized by three distinct steps, as opposed to one with other adsorbates. This behavior is also encountered in the results of ref (27), where crystal size is responsible for the shift from nonflexible to switching, with new intermediate phases observable in between. Thus, we can expect that a fraction of the MOF undergoes (i) an incomplete transition to an intermediate pore form (ip) that was previously identified,[27] which (ii) reopens partially as a larger pore intermediate form (ip) and then (iii) fully. It can therefore be assumed that nitrogen adsorption takes place near the lower limit of favorable transition energetics, where particulate surface effects can have a high influence on the energy barrier of transition, prohibiting a direct access to the op form.

An estimation of the fraction of sample that undergoes each type of structural transformation is essential for drawing conclusions on the evolution of DUT-49. For this purpose, we assumed that the total adsorption uptake can be described as a linear combination of the simulated uptake in the existing phases in each pressure range. Figure graphically exemplifies isotherm deconvolution for the (cp + ip) and (cp + op) ranges, from which it can be estimated that 44% of the sample undergoes a complete contraction. Thus, the amount of material which undergoes a full op – cp contraction is a modest ratio of the total amount of sample.

Figure 4

(top) Depiction of different phase mixtures [1–4] and phase transformations [a–d] throughout the nitrogen adsorption isotherm of DUT-49. (bottom) The simulated isotherms of the different phases in the highlighted region are linearly combined to obtain the different contribution of each phase when there is a (left) cp + ip coexistence and (right) cp + op coexistence. For the displayed isotherm 44% of the material undergoes complete transition to the cp phase.

We have observed that sequential nitrogen isotherms recorded on the same cell lead to a reduction of the amount of material undergoing complete op–cp transition (Figure S6). In the case of the cell in Figure , the op–cp conversion fraction drops from 44% to 17% in a second experiment. However, subsequent isotherms are repeatable and do not induce further degradation. The resulting trends from all experiments are presented in Table S3 and are consistent with the previous observation. We can tentatively surmise that the initial structural contraction may lead to the fragmentation and suppression of complete transition in a fraction of crystallites, likely those above a certain size threshold. Previously published SEM images before and after an adsorption cycle[27] appear to support this hypothesis. While very small particles appear to fully lose their compliance,[27] no proportion of DUT-49 in our experiments remains static, thus only very large crystals undergo stress-induced attrition. It should be mentioned that in the case of other probes, such as argon and oxygen, cycling appears to also induce a progressive amorphization of the material, as can be observed in Figure S8.

Adsorption and Structure Contraction Energetics

We turn to the differential enthalpy of adsorption as measured through microcalorimetry to delve deeper into the interactions of all adsorbate/DUT-49 systems. Enthalpy curves of the four probes are presented in Figure , together with GCMC simulated adsorption enthalpy for both op and cp structures. The sharp vertical discontinuities in the experimental curves are indicative of NGA, while the sudden large increase in differential enthalpy at the saturation pressure is explained through the loss of resolution when the adsorbed amount decreases as the isotherm plateaus. The general shape of the enthalpy curve is reminiscent of what was previously observed for n-butane at 303 K,[23,25] suggesting an identical energetic landscape throughout pore filling with all probes. Two regions of the enthalpy curves can be further highlighted for analysis: the region below 0.1 fractional loading, which can be ascribed to the initial interactions of the probe with the MOF framework, and the plateau after structural contraction, where the amount adsorbed is also accompanied by a progressive framework reopening.

Figure 5

Comparison between simulated and measured enthalpy curves at 77 K for all probes. Fractional loading is defined as uptake divided by maximum loading and is represented on the x axis. The dotted vertical line indicates structural contraction; in this range curves have been trimmed above 15 kJ mol–1 for clarity.

For Ar and O2, the experimental and simulated enthalpy profiles have a near-perfect overlap in the low-pressure range. The adsorbate/DUT-49 interactions can be described purely through dispersion interactions and are in the region of 10–11 kJ mol–1. The slight increase in Δadsh upon further uptake can be associated with the increased guest/guest interactions during the complete filling of the MOP pore. Dissimilarly, a deviation is present for the CO enthalpy curve, as the measured initial Δadsh is around 30 kJ mol–1 vs 11–14 kJ mol–1 by GCMC simulations. This is consistent with the formation of Cu(II)···CO adducts as seen in similar paddlewheel based MOFs such as HKUST-1[35] which cannot be accurately described using the generic force field parameters considered here. Indeed, a visual examination of the carbon monoxide saturated DUT-49 (Figure S7) shows a pronounced color change and suggests a change in the coordination sphere of the copper atoms. As the sample is brought to ambient temperature, the cyan color disappears, attesting to the labile nature of the interaction, in contrast to stable Cu(I)···CO coordination compounds. The initial enthalpy of nitrogen adsorption (15 kJ mol–1) is also higher than the value predicted for the op form (10 kJ mol–1), although to a lesser extent than CO, likely due to similar phenomena. It is worth mentioning that both CO and N2 interactions occur only at low fractional loadings, below the range in which NGA has been observed to occur. The enthalpy of adsorption after this region is comparable to the simulated value. Therefore, while specific host/guest interactions may be present at open metal sites, they seem to play a negligible role in the global mechanism of adsorption.

On the other hand, the influence of guest properties such as polarity on the thermodynamic feasibility of transition is less apparent. Preliminary evidence suggests that the temperature limits for NGA existence are correlated to intensive thermodynamic properties of the guest, like the critical point, when considering nonspecific adsorbates.[36] The behavior of carbon monoxide would then buckle this trend, as one would expect NGA transition at the same temperature as nitrogen. It is then reasonable to assume that strong host–guest interactions will shift the energy difference between the op and cp loaded phases, leading to a corresponding shift in the contraction temperature range. Unfortunately, a complete picture is difficult to obtain, as other adsorbates characterized by strong guest–guest interactions, such as water and ethanol[3] also attack the metal-linker bond, destroying the framework.

The enthalpies of adsorption recorded at higher partial pressures for Ar and O2, corresponding to simultaneous adsorption and structural reopening, are remarkably similar to the simulated values for the same loading in the op form. It is expected that any further adsorption in a filled cp–op intermediate pore system would have a much higher Δadsh, comparable with what is predicted for the cp form (14–16 kJ mol–1). We can therefore conclude that a part of the energy of adsorption must be required for structural reopening, offsetting the total measured enthalpy through microcalorimetry.

As a consequence of continuous adsorbate introduction, we can precisely monitor the heat output during the op–cp transition step, analogous to a differential scanning calorimeter (DSC). Examples of time-resolved curves can be seen in Figure S9, with a complex peak observed during structural contraction. The transition of any crystallite is likely to trigger a cascade effect, where local increases in guest pressure induce contraction of neighboring particles. As such, deconvolution of the signal into individual contributions is nearly impossible, since minute factors such as diffusion effects, cell geometry, sample amount, or flow rate can drastically change its signature. However, by integrating the heat evolved Q, a cumulative enthalpy of transition for the guest/DUT-49 system (ΔHexp) may be obtained. It should be noted that while the flow of adsorbate is not stopped throughout structural transition, the flow rate is minimal, to the point of negligible impact.

During contraction, three main components of the total enthalpy as measured by calorimetry (ΔHexp) can be rationalized:which can be represented mathematically with the following approximation:

Energy required for structural transition, ΔH, as the op form is more stable than the cp form;[19]

Energy required to desorb and expel the guest from the material pores, ΔHdes;

Energy associated with the increased interaction strength between the adsorbed guest and the smaller pores of the cp phase with respect to the op phase, ΔHinter;

The first component only depends on the host, while the latter two are a function of the guest as well. It is also apparent that the last term is the only exothermic component and thus must overcome the former two in order for the transition to be exothermic. Here, we approximate the combined contribution of the last two components as the difference between the integral enthalpy of adsorption of the op and cp form, at the transition uptake for each phase (or ΔΔHads), an assumption based on guest desorption during NGA occurring from a completely op form:

As a measurement of the enthalpy of adsorption on a pure op or cp phase is physically impossible, we rely on the simulated enthalpy curves, in view of their validation in the previous sections, while taking nop and ncp from the experimental isotherms. A graphical overview of the calculation procedure is depicted in Figure . It is obvious that the energy available to overcome the enthalpic cost of structural transition sharply decreases as a larger amount of guest is adsorbed in the op phase, ultimately becoming endothermic. As the amount of “guest overload” was found to be a function of temperature by Krause and co-workers,[19,23] this method predicts an upper threshold for exothermic NGA.

Figure 6

(top) Graphical representation of the calculation of ΔΔHads for argon and nitrogen starting from simulated enthalpy curves of the op (red) and cp (blue) phases. Shaded regions correspond to integral enthalpy of adsorption (ΔadsH) for the two phases. Integration limits are between 0 and the transition uptake taken from experimental isotherms in Figure as nop and ncp, respectively. ΔΔHads is the difference between the two areas. The experimental curve is represented in light gray. (bottom) Calculated ΔΔHads as a function of uptake at transition. Below the curve minima, nop = ncp and no desorption would take place during a transition. Afterward, ncp is limited by the pore volume of the cp phase. Dotted line shows the calculated value for the above case.

Nitrogen appears to still induce a contraction beyond this limit (as seen in Figure ). Indeed, the microcalorimetry peak observed during transition shows an endothermic process (Figure S9), unlike any other probe at 77 K. Two observations may be made for this counterintuitive behavior. First, it highlights that the increase in entropy generated by the expulsion to the gas phase of a large amount of guest from the material pores can also offset the Gibbs free energy of the transition so that the transition is spontaneous. Second, while the recorded signal is endothermic, its integral is significantly lower than what is predicted through GCMC calculations of ΔΔHads (332 kJ mol–1 vs 1877 kJ mol–1, per unit cell). As the NGA step leads to the simultaneous formation of two phases, the exothermic transition to the ip phase can offset the endothermic transition to the cp phase. Indeed, a direct correlation is found between the fraction of ip phase formed and the enthalpy of the transition step (Figure S10).

Due to the complex behavior upon N2 adsorption, the previous effects cannot be separated. Thus, to observe the evolution of enthalpy with temperature, the Ar/DUT-49 system was selected owing to its unambiguous guest-induced op–cp transition (see Figure and Figure ) and good correspondence to in silico enthalpies. Separate isotherms and enthalpy curves were obtained at 87 K with the same experimental setup and computational methodology (Figure S11). At this temperature, a larger NGA step is observed, as the system is further loaded before contraction. It is seen that the measured and simulated differential enthalpy curves are not impacted by the change in temperature, thus the calculated ΔΔHads curve in Figure can be considered interchangeable at 87 K. However, the NGA event becomes endothermic, similar to nitrogen at 77 K (Figure S12). Therefore, we can conclude not only that ΔΔHads is a good predictor of transition energetics but also that entropy is a critical variable that controls the feasibility range of the structural contraction. As the difference in entropy between a gas phase and a liquid phase (as assumed to exist in the pores of DUT-49) decreases with temperature, the combined effect of increasing ΔΔHads and decreasing TΔSads offers a rationalization for the disappearance of NGA at higher temperatures. Such entropic contributions due to phase transitions in both the solid and fluid phase are unprecedented in any guest-responsive system and clearly demonstrate the complexity that NGA imposes on such responsive systems.

Finally, ΔΔHads is related to the experimental enthalpy measured during NGA (ΔHexp) by an offset corresponding to the enthalpy of structural contraction. This method is similar in concept to the DSC/TGA experiments previously employed for determining the enthalpy of structural transition for MIL-53,[37] with the scanning performed in terms of adsorbate pressure rather than temperature. By substituting in eq :

The ΔH term can be obtained from the free energy difference between the guest-free op and cp phases previously calculated by ref (20). The two values can be equated directly if we assume that (i) the entropy difference between the two phases is negligible,[20,38] (ii) the pressure on the material is sufficiently small, and (iii) there is little to no temperature dependence of these quantities. If ΔH is taken as 900 kJ mol–1 (per unit cell) and ΔΔHads as calculated in Figure , the two sides of the equation take the values in Table .

Table 1

Comparison for Experimental and Simulated Enthalpy Contributions in DUT-49

	ΔHexp(kJ mol–1)	ΔΔHads + ΔHop–cp(kJ mol–1)
77 K	–1033	–481
87 K	19	581

At both 77 and 87 K, the two values are remarkably similar in magnitude and sign. While the offset can be attributed to contributions from the assumptions made, the experimental error, and simulation parameters, it is the first time that the two methodologies can be directly compared and validated for the enthalpy contributions of the transition event in a compliant material such as DUT-49.

Conclusion

Low temperature adsorption microcalorimetry was used to perform an in-depth study of the adsorption of argon, nitrogen, oxygen, and carbon monoxide in the flexible DUT-49 system. When combined with molecular simulations, the setup employed in a quasi-equilibrium introduction mode appears as a powerful approach to shed light not only on the mechanism of adsorption in compliant solids but also on the subtle and transient energetics of the structural transition step itself. We can draw the following conclusions:

The enthalpy of transition for the system is a function of the amount of op phase overloading, with higher loadings leading to an increased NGA amount and an increased energetic cost. Transition entropy change can offset this cost, but only to a point. Furthermore, for the first time, a direct comparison of the experimental and simulated enthalpy contributions of structural contraction can be made, with good agreement between the two methods.

The complex behavior exhibited throughout nitrogen adsorption can be deconvoluted by using contributions of simulated adsorption isotherms to obtain the fraction of material undergoing contraction to each phase (cp–op or cp–ip). Material cycling is seen to decrease the fraction of complete cp–op contraction, as expected from a batch of small crystal DUT-49, therefore providing evidence for crystal fragmentation.

The mechanism of adsorption strongly depends on the probe molecules. It was demonstrated that the pore filling differs with the physicochemical properties of the adsorbates leading to a progressive smearing of the condensation step in the large pores of DUT-49 from O2 to N2. Strongly interacting guests, such as CO may shift the existence range of the NGA transition.

We consider our findings in this work as a key step toward understanding the energetic and entropic contributions that occur during NGA. They not only provide direct experimental access to parameters previously only captured computationally, they also demonstrate the complexity of the interplay between adsorption-induced structural transitions and subsequent gas release upon NGA. In particular the estimation of entropic contribution but also internal heat management[24] occurring upon structural contraction will further help toward application of the phenomenon of NGA as well as support the design of other porous solids with NGA transitions.