Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter (O) February 15, 2019

Phonons in deformable microporous crystalline solids

  • Bogdan Kuchta EMAIL logo , Filip Formalik , Justyna Rogacka , Alexander V. Neimark and Lucyna Firlej


Phonons are quantum elastic excitations of crystalline solids. Classically, they correspond to the collective vibrations of atoms in ordered periodic structures. They determine the thermodynamic properties of solids and their stability in the case of structural transformations. Here we review for the first time the existing examples of the phonon analysis of adsorption-induced transformations occurring in microporous crystalline materials. We discuss the role of phonons in determining the mechanism of the deformations. We point out that phonon-based methodology may be used as a predictive tool in characterization of flexible microporous structures; therefore, relevant numerical tools must be developed.

Award Identifier / Grant number: 2015/17/B/ST8/00099

Funding source: AVN

Award Identifier / Grant number: 1834339.

Funding statement: BK, FF and JR acknowledge support from the Polish National Science Center (NCN, grant no. 2015/17/B/ST8/00099). AVN acknowledges support from the NSF grant No 1834339.


[1] M. Born, K. Huang, Dynamical Theory of Crystal Lattice, Oxford University Press, 1954.Search in Google Scholar

[2] S. Kitagawa, K. Uemura, Dynamic porous properties of coordination polymers inspired by hydrogen bonds. Chem. Soc. Rev.2005, 34, 109.10.1039/b313997mSearch in Google Scholar PubMed

[3] S. Horike, S. Shimomura, S. Kitagawa, Soft porous crystals. Nature Chem.2009, 1, 695.10.1038/nchem.444Search in Google Scholar PubMed

[4] G. Férey, C. Serre, Large breathing effects in three-dimensional porous hybrid matter: facts, analyses, rules and consequences. Chem. Soc. Rev.2009, 38, 1380.10.1039/b804302gSearch in Google Scholar PubMed

[5] M. Alhamami, H. Doan, C. H. Cheng, A review on breathing behaviors of metal-organic-frameworks (MOFs) for gas adsorption. Materials (Basel)2014, 7, 3198.10.3390/ma7043198Search in Google Scholar PubMed PubMed Central

[6] J. Wieme, L. Vanduyfhuys, S. M. J. Rogge, M. Waroquier, V. Van Speybroeck, Exploring the flexibility of MIL-47(V)-type materials using force field molecular dynamics simulations. J. Phys. Chem. C2016, 120, 14934.10.1021/acs.jpcc.6b04422Search in Google Scholar PubMed PubMed Central

[7] A. U. Ortiz, A. Boutin, A. H. Fuchs, F. X. Coudert, Investigating the pressure-induced amorphization of zeolitic imidazolate framework ZIF-8: mechanical instability due to shear mode softening. J. Phys. Chem. Lett.2013, 4, 1861.10.1021/jz400880pSearch in Google Scholar PubMed

[8] A. Phan, C. J. Doonan, F. J. Uribe-Romo, C. B. Knobler, M. O’Keeffe, O. M. Yaghi, Synthesis, structure, and carbon dioxide capture properties of zeolitic imidazolate frameworks. Acc. Chem. Res.2010, 43, 58.10.1021/ar900116gSearch in Google Scholar PubMed

[9] A. Schneemann, V. Bon, I. Schwedler, I. Senkovska, S. Kaskel, R. A. Fischer, Flexible metal-organic frameworks. Chem. Soc. Rev.2014, 43, 6062.10.1039/C4CS00101JSearch in Google Scholar PubMed

[10] C. R. Murdock, B. C. Hughes, Z. Lu, D. M. Jenkins, Approaches for synthesizing breathing MOFs by exploiting dimensional rigidity. Coord. Chem. Rev.2014, 258, 119.10.1016/j.ccr.2013.09.006Search in Google Scholar

[11] A. Ghoufi, G. Maurin, G. Férey, Physics behind the guest-assisted structural transitions of a porous metal-organic framework material. J. Phys. Chem. Lett.2010, 1, 2810.10.1021/jz1011274Search in Google Scholar

[12] A. Ghoufi, K. Benhamed, L. Boukli-Hacene, G. Maurin, Electrically induced breathing of the MIL-53(Cr) metal-organic framework. ACS Cent. Sci.2017, 3, 394.10.1021/acscentsci.6b00392Search in Google Scholar PubMed PubMed Central

[13] Y. Liu, J. Her, A. Dailly, A. J. Ramirez-cuesta, Reversible structural transition in MIL-53 with large temperature hysteresis. J. Am. Chem. Soc.2008, 130, 11813.10.1021/ja803669wSearch in Google Scholar PubMed

[14] I. Beurroies, M. Boulhout, P. L. Llewellyn, B. Kuchta, G. Férey, C. Serre, R. Denoyel, Using pressure to provoke the structural transition of metal-organic frameworks. Angew. Chem. Int. Ed.2010, 49, 7526.10.1002/anie.201003048Search in Google Scholar PubMed

[15] D. Fairen-Jimenez, S. A. Moggach, M. T. Wharmby, P. A. Wright, S. Parsons, T. Düren, Opening the gate: framework flexibility in ZIF-8 explored by experiments and simulations. J. Am. Chem. Soc.2011, 133, 8900.10.1021/ja202154jSearch in Google Scholar PubMed

[16] T. Loiseau, C. Serre, C. Huguenard, G. Fink, F. Taulelle, M. Henry, T. Bataille, G. Férey, A Rationale for the large breathing of the porous aluminum terephthalate (MIL-53) upon hydration. Chem. A Eur. J.2004, 10, 1373.10.1002/chem.200305413Search in Google Scholar PubMed

[17] F. Millange, N. Guillou, R. I. Walton, J. M. Grenèche, I. Margiolaki, G. Férey, Effect of the nature of the metal on the breathing steps in MOFs with dynamic frameworks. Chem. Commun.2008, 4732.10.1039/b809419eSearch in Google Scholar PubMed

[18] C. Serre, F. Millange, C. Thouvenot, M. Noguès, G. Marsolier, D. Louër, G. Férey, Very large breathing effect in the first nanoporous chromium(III)-based solids: MIL-53 or CrIII(OH)·{O2C-C6H4-CO2}·{HO2C-C6H4 -CO2H}x·H2Oy. J. Am. Chem. Soc.2002, 124, 13519.10.1021/ja0276974Search in Google Scholar PubMed

[19] S. Bourrelly, P. L. Llewellyn, C. Serre, F. Millange, T. Loiseau, G. Férey, Different adsorption behaviors of methane and carbon dioxide in the isotypic nanoporous metal terephthalates MIL-53 and MIL-47. J. Am. Chem. Soc.2005, 127, 13519.10.1021/ja054668vSearch in Google Scholar PubMed

[20] Y. Liu, S. Couck, M. Vandichel, M. Grzywa, K. Leus, S. Biswas, D. Volkmer, J. Gascon, F. Kapteijn, J.F.M. Denayer, M. Waroquier, V. Van Speybroeck, P. Van Der Voort, New VIV-based metal−organic framework having framework flexibility and high CO2 adsorption capacity. Inorg. Chem.2013, 52, 113.10.1021/ic301338aSearch in Google Scholar PubMed

[21] M. T. Wharmby, S. Henke, T. D. Bennett, S. R. Bajpe, I. Schwedler, S. P. Thompson, F. Gozzo, P. Simoncic, C. Mellot-Draznieks, H. Tao, Y. Yue, A. K. Cheetham, Extreme flexibility in a zeolitic imidazolate framework: porous to dense phase transition in desolvated ZIF-4. Angew. Chem. Int. Ed.2015, 54, 6447.10.1002/anie.201410167Search in Google Scholar PubMed

[22] D. Bousquet, F. X. Coudert, A. G. J. Fossati, A. V. Neimark, A.H. Fuchs, A. Boutin, Adsorption induced transitions in soft porous crystals: an osmotic potential approach to multistability and intermediate structures. J. Chem. Phys.2013, 138, 174706.10.1063/1.4802888Search in Google Scholar

[23] S. Krause, V. Bon, I. Senkovska, U. Stoeck, D. Wallacher, D. M. Többens, S. Zander, R. S. Pillai, G. Maurin, F. X. Coudert, S. Kaskel, A pressure-amplifying framework material with negative gas adsorption transitions. Nature2016, 532, 348.10.1038/nature17430Search in Google Scholar

[24] F. X. Coudert, A. Boutin, A. H. Fuchs, A. V. Neimark, Adsorption deformation and structural transitions in metal – organic frameworks: from the unit cell to the crystal. J. Phys. Chem. Lett.2013, 4, 3198.10.1021/jz4013849Search in Google Scholar

[25] U. Stoeck, S. Krause, V. Bon, I. Senkovska, S. Kaskel, A highly porous metal-organic framework, constructed from a cuboctahedral super-molecular building block, with exceptionally high methane uptake. Chem. Commun.2012, 48, 10841.10.1039/c2cc34840cSearch in Google Scholar

[26] D. Li, K. Kaneko, Hydrogen bond-regulated microporous nature of copper complex-assembled microcrystals. Chem. Phys. Lett.2001, 335, 50.10.1016/S0009-2614(00)01419-6Search in Google Scholar

[27] P. A. Fleury, The effects of soft modes on the structure and properties of materials. Annu. Rev. Mater. Sci.1976, 6, 157.10.1146/ in Google Scholar

[28] B. Kuchta, T. Luty, R. J. Meier, The α-β phase transition in solid oxygen. J. Phys. C Solid State Phys.1987, 20, 585.10.1088/0022-3719/20/4/009Search in Google Scholar

[29] B. Kuchta, T. Luty, Lattice dynamics of solid nitrogen with an ab initio intermolecular potential. II. Anharmonic librations in the α phase. J. Chem. Phys.1983, 78, 1447.10.1063/1.444887Search in Google Scholar

[30] F. Formalik, M. Fischer, J. Rogacka, L. Firlej, B. Kuchta, Effect of low frequency phonons on structural properties of ZIFs with SOD topology. Micropor. Mesopor. Mater.2018, 0. doi:10.1016/j.micromeso.2018. in Google Scholar

[31] P. L. Llewellyn, G. Maurin, T. Devic, S. Loera-Serna, N. Rosenbach, C. Serre, S. Bourrelly, P. Horcajada, Y. Filinchuk, G. Férey, Prediction of the conditions for breathing of metal organic framework materials using a combination of X-ray powder diffraction, microcalorimetry, and molecular simulation. J. Am. Chem. Soc.2008, 130, 12808.10.1021/ja803899qSearch in Google Scholar PubMed

[32] C. Serre, S. Bourrelly, A. Vimont, N. A. Ramsahye, G. Maurin, P. L. Llewellyn, M. Daturi, Y. Filinchuk, O. Leynaud, P. Barnes, G. Férey, An explanation for the very large breathing effect of a metal-organic framework during CO2 adsorption. Adv. Mater.2007, 19, 2246.10.1002/adma.200602645Search in Google Scholar

[33] A. V. Neimark, F. X. Coudert, A. Boutin, A. H. Fuchs, Stress-based model for the breathing of metal-organic frameworks. J. Phys. Chem. Lett.2010, 1, 445.10.1021/jz9003087Search in Google Scholar PubMed

[34] C. Triguero, F. X. Coudert, A. Boutin, A. H. Fuchs, A. V. Neimark, Mechanism of breathing transitions in metal-organic frameworks. J. Phys. Chem. Lett.2011, 2, 2033.10.1021/jz2008769Search in Google Scholar

[35] P. Hohenberg, W. Kohn, Inhomogeneous electron gas. Phys. Rev.1964, 136, B864.10.1103/PhysRev.136.B864Search in Google Scholar

[36] W. Kohn, L. J. Sham, Self-consistent equations including exchange and correlation effects. Phys. Rev.1965, 385.10.1103/PhysRev.140.A1133Search in Google Scholar

[37] R. P. Feynman, Forces in molecules. Phys. Rev.1939, 56, 340.10.1103/PhysRev.56.340Search in Google Scholar

[38] K. Parlinski, Ab initio determination of anharmonic phonon peaks. Phys. Rev. B2018, 98, 1.10.1103/PhysRevB.98.054305Search in Google Scholar

[39] A. Togo, I. Tanaka, First principles phonon calculations in materials science. Scr. Mater.2015, 108, 1.10.1016/j.scriptamat.2015.07.021Search in Google Scholar

[40] K. Parlinski, Z. Q. Li, Y. Kawazoe, First-principles determination of the soft mode in cubic ZrO2. Phys. Rev. Lett.1997, 78, 4063.10.1103/PhysRevLett.78.4063Search in Google Scholar

[41] K. Parlinski, Calculation of phonon dispersion curves by the direct method. AIP Conf. Proc.1999, 479, 121.10.1063/1.59457Search in Google Scholar

[42] G. Kresse, J. Hafner, Ab initio molecular dynamics for liquid metals. Phys. Rev. B1993, 47, 558.10.1016/0022-3093(95)00355-XSearch in Google Scholar

[43] G. Kresse, J. Furthmuller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B1996, 54, 11169.10.1103/PhysRevB.54.11169Search in Google Scholar PubMed

[44] G. Kresse, D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B1999, 59, 1758.10.1103/PhysRevB.59.1758Search in Google Scholar

[45] S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. I. J. Probert, K. Refson, M. C. Payne, First principles methods using CASTEP. Z. Kristallogr.2005, 220, 567.10.1524/zkri.220.5.567.65075Search in Google Scholar

[46] P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. De Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari, R. M. Wentzcovitch, QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter.2009, 21, 395502.10.1088/0953-8984/21/39/395502Search in Google Scholar PubMed

[47] R. Dovesi, A. Erba, R. Orlando, C. M. Zicovich-Wilson, B. Civalleri, L. Maschio, M. Rérat, S. Casassa, J. Baima, S. Salustro, B. Kirtman, Quantum-mechanical condensed matter simulations with CRYSTAL, Wiley Interdiscip. Rev. Comput. Mol. Sci.2018, 8, 1.Search in Google Scholar

[48] X. Gonze, Perturbation expansion of variational principles at arbitrary order. Phys. Rev. A1995, 52, 1086.10.1103/PhysRevA.52.1086Search in Google Scholar PubMed

[49] S. Baroni, P. Giannozzi, A. Testa, Greens-function approach to linear response in solids. Phys. Rev. Lett.1987, 58, 1861.10.1103/PhysRevLett.58.1861Search in Google Scholar PubMed

[50] M. Fischer, Structure and bonding of water molecules in zeolite hosts: benchmarking plane-wave DFT against crystal structure data. Zeitschrift Fur Krist. – Cryst. Mater. 2015, 230, 325.10.1515/zkri-2014-1809Search in Google Scholar

[51] M. Fischer, F. O. Evers, F. Formalik, A. Olejniczak, Benchmarking DFT-GGA calculations for the structure optimisation of neutral-framework zeotypes. Theor. Chem. Acc.2016, 135, 1.10.1007/s00214-016-2014-6Search in Google Scholar

[52] M. Fischer, R. J. Angel, Accurate structures and energetics of neutral-framework zeotypes from dispersion-corrected DFT calculations. J. Chem. Phys.2017, 146, 174111.10.1063/1.4981528Search in Google Scholar PubMed

[53] F. Formalik, M. Fischer, J. Rogacka, L. Firlej, B. Kuchta, Benchmarking of GGA density functionals for modeling structures of nanoporous, rigid and flexible MOFs. J. Chem. Phys.2018, 149, 064110.10.1063/1.5030493Search in Google Scholar PubMed

[54] D. Nazarian, P. Ganesh, D. S. Sholl, Benchmarking density functional theory predictions of framework structures and properties in a chemically diverse test set of metal-organic frameworks. J. Mater. Chem. A2015, 3, 22432.10.1039/C5TA03864BSearch in Google Scholar

[55] S. Grimme, Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem.2006, 27, 1787.10.1002/jcc.20495Search in Google Scholar PubMed

[56] K. Lee, É. D. Murray, L. Kong, B. I. Lundqvist, D. C. Langreth, Higher-accuracy van der Waals density functional. Phys. Rev. B – Condens. Matter Mater. Phys.2010, 82, 3.10.1103/PhysRevB.82.081101Search in Google Scholar

[57] J. K. Bristow, J. M. Skelton, K. L. Svane, A. Walsh, J. D. Gale, A general forcefield for accurate phonon properties of metal-organic frameworks. Phys. Chem. Chem. Phys.2016, 18, 29316.10.1039/C6CP05106ESearch in Google Scholar

[58] M. R. Ryder, B. Civalleri, T. Bennett, S. Henke, S. Rudić, G. Cinque, F. Fernandez-Alonso, J. C. Tan, Identifying the role of terahertz vibrations in metal-organic frameworks: from gate-opening phenomenon to shear-driven structural destabilization. Phys. Rev. Lett.2014, 113, 1.10.1103/PhysRevLett.113.215502Search in Google Scholar PubMed

[59] J. Hutter, M. Iannuzzi, F. Schiffmann, J. Vandevondele, CP2K: atomistic simulations of condensed matter systems. Wiley Interdiscip. Rev. Comput. Mol. Sci.2014, 4, 15.10.1002/wcms.1159Search in Google Scholar

[60] A. Krylov, A. Vtyurin, P. Petkov, I. Senkovska, M. Maliuta, V. Bon, T. Heine, S. Kaskel, E. Slyusareva, Raman spectroscopy studies of the terahertz vibrational modes of a DUT-8 (Ni) metal-organic framework. Phys. Chem. Chem. Phys.2017, 19, 32099.10.1039/C7CP06225GSearch in Google Scholar

[61] L. Vanduyfhuys, S. M. J. Rogge, J. Wieme, S. Vandenbrande, G. Maurin, M. Waroquier, V. Van Speybroeck, Thermodynamic insight into stimuli-responsive behaviour of soft porous crystals. Nature Commun.2018, 9, 1.10.1038/s41467-017-02666-ySearch in Google Scholar PubMed PubMed Central

[62] A. Ghysels, L. Vanduyfhuys, M. Vandichel, M. Waroquier, V. Van Speybroeck, B. Smit, On the thermodynamics of framework breathing: a free energy model for gas adsorption in MIL-53. J. Phys. Chem. C2013, 117, 11540.10.1021/jp311601qSearch in Google Scholar

[63] C. L. Hobday, R. J. Marshall, C. F. Murphie, J. Sotelo, T. Richards, D. R. Allan, T. Düren, F. X. Coudert, R. S. Forgan, C. A. Morrison, S. A. Moggach, T. D. Bennett, A computational and experimental approach linking disorder, high-pressure behavior, and mechanical properties in UiO frameworks. Angew. Chem. Int. Ed.2016, 55, 2401.10.1002/anie.201509352Search in Google Scholar PubMed PubMed Central

[64] F. X. Coudert, The osmotic framework adsorbed solution theory: predicting mixture coadsorption in flexible nanoporous materials. Phys. Chem. Chem. Phys.2010, 12, 10904.10.1039/c003434gSearch in Google Scholar PubMed

[65] M. Witman, S. Ling, S. Jawahery, P. Boyd, M. Haranczyk, B. Slater, B. Smit, The influence of intrinsic framework flexibility on adsorption in nanoporous materials. J. Am. Chem. Soc.2017, 139, 5547.10.1021/jacs.7b01688Search in Google Scholar PubMed PubMed Central

[66] P. G. Yot, Z. Boudene, J. Macia, D. Granier, L. Vanduyfhuys, T. Verstraelen, V. Van Speybroeck, T. Devic, C. Serre, G. Férey, N. Stock, G. Maurin, Metal-organic frameworks as potential shock absorbers: the case of the highly flexible MIL-53(Al). Chem. Commun.2014, 50, 9462.10.1039/C4CC03853CSearch in Google Scholar

[67] N. Y. Tan, M. T. Ruggiero, C. Orellana, T. Tian, A. D. Bond, T. M. Korter, D. Fairen-Jimenez, J. A. Zeitler, Investigation of the terahertz vibrational modes of ZIF-8 and ZIF-90 with terahertz time-domain spectroscopy. Chem. Commun.2015, 51, 16037.10.1109/IRMMW-THz.2015.7327716Search in Google Scholar

[68] A. S. Munn, A. J. Ramirez-Cuesta, F. Millange, R. I. Walton, Interaction of methanol with the flexible metal-organic framework MIL-53(Fe) observed by inelastic neutron scattering. Chem. Phys.2013, 427, 30.10.1016/j.chemphys.2013.05.017Search in Google Scholar

[69] M. Ptak, B. Zarychta, D. Stefanska, A. Ciupa, W. Paraguassu, Novel bimetallic MOF phosphors with imidazolium cation: structure, phonons, high-pressure phase transitions and optical response. Dalton Trans.2019, 48, 242.10.1039/C8DT04246BSearch in Google Scholar

[70] J. Wieme, K. Lejaeghere, G. Kresse, V. Van Speybroeck, Tuning the balance between dispersion and entropy to design temperature-responsive flexible metal-organic frameworks. Nature Commun.2018, 9, 4899.10.1038/s41467-018-07298-4Search in Google Scholar PubMed PubMed Central

[71] P. G. Boyd, S. M. Moosavi, M. Witman, B. Smit, Force-field prediction of materials properties in metal-organic frameworks. J. Phys. Chem. Lett.2017, 8, 357.10.1021/acs.jpclett.6b02532Search in Google Scholar PubMed PubMed Central

[72] J. C. Tan, T. D. Bennett, A. K. Cheetham, Chemical structure, network topology, and porosity effects on the mechanical properties of Zeolitic Imidazolate Frameworks. PNAS2010, 107, 9938.10.1073/pnas.1003205107Search in Google Scholar PubMed PubMed Central

[73] J. C. Tan, A. K. Cheetham, Mechanical properties of hybrid inorganic-organic framework materials: establishing fundamental structure-property relationships. Chem. Soc. Rev.2011, 40, 1059.10.1039/c0cs00163eSearch in Google Scholar PubMed

[74] T. D. Bennett, S. Cao, J. C. Tan, D. A. Keen, E. G. Bithell, P. J. Beldon, T. Friscic, A. K. Cheetham, Facile mechanosynthesis of amorphous zeolitic imidazolate frameworks. J. Am. Chem. Soc.2011, 133, 14546.10.1021/ja206082sSearch in Google Scholar PubMed

[75] M. E. Casco, Y. Q. Cheng, L. L. Daemen, D. Fairen-Jimenez, E. V. Ramos-Fernández, A. J. Ramirez-Cuesta, J. Silvestre-Albero, Gate-opening effect in ZIF-8: the first experimental proof using inelastic neutron scattering. Chem. Commun.2016, 52, 3639.10.1039/C5CC10222GSearch in Google Scholar PubMed

[76] A. E. J. Hoffman, L. Vanduyfhuys, I. Nevjestić, J. Wieme, S. M. J. Rogge, H. Depauw, P. Van Der Voort, H. Vrielinck, V. Van Speybroeck, Elucidating the vibrational fingerprint of the flexible metal-organic framework MIL-53(Al) using a combined experimental/computational approach. J. Phys. Chem. C2018, 122, 2734.10.1021/acs.jpcc.7b11031Search in Google Scholar PubMed PubMed Central

[77] W. Zhou, H. Wu, T. Yildirm, J. R. Simpson, A. R. Hight Walker, Origin of the exceptional negative thermal expansion in metal-organic framework-5 Zn4O(1,4-benzenedicarboxylate)3. Phys. Rev. B2008, 78, 054114.10.1103/PhysRevB.78.054114Search in Google Scholar

[78] L. H. N. Rimmer, M. T. Dove, A. L. Goodwin, D. C. Palmer, Acoustic phonons and negative thermal expansion in MOF-5. Phys. Chem. Chem. Phys.2014, 16, 21144.10.1039/C4CP01701CSearch in Google Scholar

[79] N. Lock, M. Christensen, Y. Wu, V. K. Peterson, M. K. Thomsen, R. O. Piltz, A. J. Ramirez-Cuesta, G. J. McIntyre, K. Norén, R. Kutteh, C. J. Kepert, G. J. Kearley, B. B. Iversen, Scrutinizing negative thermal expansion in MOF-5 by scattering techniques and ab initio calculations. Dalton Trans.2013, 42, 1996.10.1039/C2DT31491FSearch in Google Scholar

[80] M. R. Ryder, B. Civalleri, G. Cinque, J. C. Tan, Discovering connections between terahertz vibrations and elasticity underpinning the collective dynamics of the HKUST-1 metal-organic framework. CrystEngComm.2016, 18, 4303.10.1039/C5CE02347ESearch in Google Scholar

[81] E. Cockayne, Thermodynamics of the flexible metal-organic framework material MIL-53(Cr) from first-principles. J. Phys. Chem. C2017, 121, 4312.10.1021/acs.jpcc.6b11692Search in Google Scholar PubMed PubMed Central

[82] K. L. Svane, J. K. Bristow, A. Walsh, Anharmonic origin of giant thermal displacements in the metal-organic framework UiO-67. J. Phys. Chem. C2017, 121, 22010.10.1021/acs.jpcc.7b04757Search in Google Scholar

[83] J. L. C. Rowsell, E. C. Spencer, J. Eckert, J. A. K. Howard, O. M. Yaghi, Gas adsorption sites in a large-pore metal-organic framework. Science2005, 309, 1350.10.1126/science.1113247Search in Google Scholar PubMed

[84] D. Dubbeldam, K. S. Walton, D. E. Ellis, R. Q. Snurr, Exceptional negative thermal expansion in isoreticular metal – organic frameworks. Angew. Chem. Int. Ed.2007, 46, 4496.10.1002/anie.200700218Search in Google Scholar PubMed

[85] S. S. Han, W. A. Goddard, Metal−organic frameworks provide large negative thermal expansion behavior. J. Phys. Chem. C2007, 111, 15185.10.1021/jp075389sSearch in Google Scholar

[86] J. S. O. Evans, Negative thermal expansion materials. J. Chem. Soc. Dalton Trans.1999, 3317.10.1039/a904297kSearch in Google Scholar

Received: 2018-11-29
Accepted: 2019-01-31
Published Online: 2019-02-15
Published in Print: 2019-07-26

©2019 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 10.12.2023 from
Scroll to top button