Knowledge of the thermodynamic potential in terms of the independent variables allows to characterize the macroscopic state of the system. However, in practice, it is difficult to access this ...potential experimentally due to irreversible transitions that occur between equilibrium states. A showcase example of sudden transitions between (meta)stable equilibrium states is observed for soft porous crystals possessing a network with long-range structural order, which can transform between various states upon external stimuli such as pressure, temperature and guest adsorption. Such phase transformations are typically characterized by large volume changes and may be followed experimentally by monitoring the volume change in terms of certain external triggers. Herein, we present a generalized thermodynamic approach to construct the underlying Helmholtz free energy as a function of the state variables that governs the observed behaviour based on microscopic simulations. This concept allows a unique identification of the conditions under which a material becomes flexible.
In this paper, three barostat coupling schemes for pressure control, which are commonly used in molecular dynamics simulations, are critically compared to characterize the rigid MOF-5 and flexible ...MIL-53(Al) metal–organic frameworks. We investigate the performance of the three barostats, the Berendsen, the Martyna–Tuckerman–Tobias–Klein (MTTK), and the Langevin coupling methods, in reproducing the cell parameters and the pressure versus volume behavior in isothermal–isobaric simulations. A thermodynamic integration method is used to construct the free energy profiles as a function of volume at finite temperature. It is observed that the aforementioned static properties are well-reproduced with the three barostats. However, for static properties depending nonlinearly on the pressure, the Berendsen barostat might give deviating results as it suppresses pressure fluctuations more drastically. Finally, dynamic properties, which are directly related to the fluctuations of the cell, such as the time to transition from the large-pore to the closed-pore phase, cannot be well-reproduced by any of the coupling schemes.
The flexibility of three MIL-47(V)-type materials (MIL-47, COMOC-2, and COMOC-3) has been explored by constructing the pressure versus volume and free energy versus volume profiles at various ...temperatures ranging from 100 to 400 K. This is done with first-principles-based force fields using the recently proposed QuickFF parametrization protocol. Specific terms were added for the materials at hand to describe the asymmetry of the one-dimensional vanadium-oxide chain and to account for the flexibility of the organic linkers. The force fields are used in a series of molecular dynamics simulations at fixed volumes but varying unit cell shapes. The three materials show a distinct pressure–volume behavior, which underlines the ability to tune the mechanical properties by varying the linkers toward different applications such as nanosprings, dampers, and shock absorbers.
A force field is proposed for the flexible metal–organic framework MIL-53(Al), which is calibrated using density functional theory calculations on nonperiodic clusters. The force field has three ...main contributions: an electrostatic term based on atomic charges derived with a modified Hirshfeld-I method, a van der Waals (vdW) term with parameters taken from the MM3 model, and a valence force field whose parameters were estimated with a new methodology that uses the gradients and Hessian matrix elements retrieved from nonperiodic cluster calculations. The new force field predicts geometries and cell parameters that compare well with the experimental values both for the large and narrow pore phases. The energy profile along the breathing mode of the empty material reveals the existence of two minima, which confirms the intrinsic bistable behavior of the MIL-53. Even without the stimulus of external guest molecules, the material may transform from the large pore (lp) to the narrow pore (np) phase Liu et al. J. Am. Chem. Soc. 2008, 120, 11813. The relative stability of the two phases critically depends on the vdW parameters, and the MM3 dispersion interaction has the tendency to overstabilize the np phase.
Abstract
Soft porous crystals (SPCs) are widely known for their intriguing properties and various counterintuitive phenomena such as negative linear compression, negative thermal expansion and ...negative gas adsorption (NGA). An intriguing case is the adsorption of methane in DUT-49 for which experimentally a drop in the amount of adsorbed particles was observed under increasing vapor pressure. It is yet unknown which specific systems can exhibit NGA under which thermodynamic conditions. Herein, a semi-analytical thermodynamic model is applied to determine the conditions required for NGA, including their sensitivity towards various system-specific parameters, and investigate the correlation with pressure-induced breathing. As such, it is found that certain non-breathing materials may exhibit breathing with NGA under application of a fixed mechanical pressure. Such meticulous control of multiple triggers for NGA can open the way to new applications such as tunable gas detection and pressure amplification.
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•Adsorption of linear pentenes in H-ZSM-5 at 323K yields an almost equally stable π-complex and covalently bound alkoxide.•The transformation from the π-complex to the chemisorbed ...complex is activated by a free energy in the range of 33–42kJ/mol.•The stability has been unravelled by contemporary static and dynamic first principle methods.•Theoretical calculations can predict the stability of elusive and reactive intermediates in zeolite catalysis.
Adsorption of linear pentenes in H-ZSM-5 at 323K is investigated using contemporary static and molecular dynamics methods. A physisorbed complex corresponding to free pentene, a π-complex and a chemisorbed species may occur. The chemisorbed species can be either a covalently bonded alkoxide or an ion pair, the so-called carbenium ion. Without finite temperature effects, the π-complex is systematically slightly more bound than the chemisorbed alkoxide complex, whereas molecular dynamics calculations at 323K yield an almost equal stability of both species. The carbenium ion was not observed during simulations at 323K. The transformation from the π-complex to the chemisorbed complex is activated by a free energy in the range of 33–42kJ/mol. Our observations yield unprecedented insights into the stability of elusive intermediates in zeolite catalysis, for which experimental data are very hard to measure.
A new semi-analytical mean-field model is proposed to rationalise breathing of MIL-53 type materials. The model is applied on two case studies, the guest-induced breathing of MIL-53(Cr) with CO
2
and ...CH
4
, and the phase transformations for MIL-53(Al) upon xenon adsorption. Experimentally, MIL-53(Cr) breathes upon CO
2
adsorption, which was not observed for CH
4
. This result could be ascribed to the stronger interaction of carbon dioxide with the host matrix. For MIL-53(Al) a phase transition from the large pore phase could be enforced to an intermediate phase with volumes of about 1160-1300 Å
3
, which corresponds well to the phase observed experimentally upon xenon adsorption. Our thermodynamic model correlates nicely with the adsorption pressure model proposed by Coudert et al. Furthermore the model can predict breathing behaviour of other flexible materials, if the user can determine the free energy of the empty host, the interaction energy between a guest molecule and the host matrix and the pore volume accessible to the guest molecules. This will allow to generate the osmotic potential from which the equilibria can be deduced and the anticipated experimentally observed phase may be predicted.
A new semi-analytical mean-field model is proposed to rationalise breathing of MIL-53 type materials. The model is applied on two case studies, the guest-induced breathing of MIL-53(Cr) with CO ...sub(2) and CH sub(4), and the phase transformations for MIL-53(Al) upon xenon adsorption. Experimentally, MIL-53(Cr) breathes upon CO sub(2) adsorption, which was not observed for CH sub(4). This result could be ascribed to the stronger interaction of carbon dioxide with the host matrix. For MIL-53(Al) a phase transition from the large pore phase could be enforced to an intermediate phase with volumes of about 1160-1300 Aa super(3), which corresponds well to the phase observed experimentally upon xenon adsorption. Our thermodynamic model correlates nicely with the adsorption pressure model proposed by Coudert et al. Furthermore the model can predict breathing behaviour of other flexible materials, if the user can determine the free energy of the empty host, the interaction energy between a guest molecule and the host matrix and the pore volume accessible to the guest molecules. This will allow to generate the osmotic potential from which the equilibria can be deduced and the anticipated experimentally observed phase may be predicted.
The aluminum fumarate MOF A520 or MIL-53-FA is revealed to be a promising material for mechanical energy-related applications with performances in terms of work and heat energies which surpass those ...of any porous solids reported so far. Complementary experimental and computational tools are deployed to finely characterize and understand the pressure-induced structural transition at the origin of these unprecedented levels of performance.
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