J. Phys. Chem. C 2008, 112, 20549–20559
20549
Atomistic Simulation of Micropore Structure, Surface Area, and Gas Sorption Properties for Amorphous Microporous Polymer Networks Abbie Trewin,*,† David J. Willock,‡ and Andrew I. Cooper*,† Department of Chemistry and Centre for Materials DiscoVery, UniVersity of LiVerpool, Crown Street, LiVerpool L69 3BX, United Kingdom, and Cardiff Catalysis Institute, School of Chemistry, Cardiff UniVersity, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom ReceiVed: July 20, 2008
A series of hyper-cross-linked polymer network models was generated based on the self-condensation of dichloroxylene (DCX). In this study, we present a new method for the automated construction of simulated polymer networks in which the chain conformation is continually adjusted using a Monte Carlo approach. In addition, we demonstrate a nonarbitrary method for simulating gas sorption properties in microporous polyDCX networks by taking into account the solvent-accessible surface areas. Exploring the effects of the simulated bulk density reveals a good fit between the scaled simulated gas sorption isotherms and the measured experimental isotherms for H2 and N2 gases using a modeled polymer density of 0.8 g/cm3. Introduction Microporous materials (with pore sizes of 0.95). The peak simulated H2 sorption energy (-9.5 kJ/mol at a simulation density of 0.8 g/cm3; Figure 10a) is higher than the measured isosteric heat value of between -7.0 and -7.5 kJ/mol.14 This might stem from the presence of small highenergy pockets40 of free volume associated with the Connolly surface that contribute to the H2 sorption simulation (see discussion above and Figure 11) but that are not present (or at least, not physically accessible to the sorbate) in the real polymer system. Conclusions The data presented in this work suggest a simple and nonarbitrary scaling methodology for estimating the gas sorption properties of amorphous microporous polymers. The best fit between the scaled simulated gas sorption isotherms and the measured isotherms occurs for the H2 and N2 simulations with a modeled polymer density of 0.8 g/cm3, that is, very close to the measured polymer density of 0.78 g/cm3.14 At this bulk density, the simulated BET surface area (1553 m2/g) is comparable to the experimentally determined BET surface area of 1370 m2/g, whereas the solvent-accessible surface area (727 m2/g) is somewhat lower. The average sorption energy is slightly overestimated (-9.5 kJ/mol), probably because of high-energy pores that do not contribute to gas sorption in the real polymer sample. These simulations are much more representative of the real physical system than models built around the “unscaled” Connolly surface. In practical terms, the use of the solventaccessible surface is far more convenient (and less computationally expensive)24 than the application of the BET theory to simulated isotherms produced by GCMC simulations, especially in this case, where the larger cluster models seem to be the most physically representative. These models might be useful for simulating the behavior of other sorbates and also for probing the potential effects of changes to the polymer structure, for example, the introduction of substituents or high-energy “binding sites”,41 provided that a suitable force field is employed. There are, however, several challenges in using this methodology in a predictive manner for new, as-yet-unknown materials. First, a large number of nontrivial experimental data are required to produce these polymer models. These include
20558 J. Phys. Chem. C, Vol. 112, No. 51, 2008
Trewin et al.
Figure 12. Simulated (a) H2 and (b) N2 sorption isotherms for a range of densities compared with the experimental isotherms with a measured density of 0.78 g/cm3 (red). A scaling factor corresponding to the ratio between the Connolly surface area and the solvent-accessible surface area in each case has been applied to the simulated data.
bulk density determination, solid-state 13C NMR measurements, elemental analyses, and gas sorption isotherms.14,29 In particular, there is a strong dependence of simulated surface area and sorption properties on bulk density (Figures 8-12). It is critical, therefore, that an appropriate simulated density be used, and this is a property that is very hard to predict ab initio for these amorphous polymers. The sensitivity of the simulations to the cluster size (Figure 6) is also problematic because this is hard to probe by methods such as solid-state 13C NMR spectroscopy but might, in principle, be explored, by wide-angle X-ray scattering.44 Again, the iterative fitting of simulations by exploring a wide range of possible cluster sizes is very timeconsuming. Lastly, hyper-cross-linked polymers present some specific challenges, as these materials are known to swell significantly in even very poor solvents.15,16,45,46 As such, although the use of static-density polymer sorbent models for H2 at 77.3 K and 1.1 bar might be reasonable, this approach would almost certainly fail for liquids (including nonsolvents such as H2O) where pronounced swelling would occur. It is also possible that swelling effects might occur with liquefied gases such as N2 or argon. To summarize, we have shown that accessible surface areas can be employed in simulations for amorphous polymers much as demonstrated for MOFs.24 The lack of a definitive crystal structure, however, necessitates much more empirical fitting and the use of multiple indirect characterization techniques to produce plausible models. This approach might therefore be less
helpful in a predictive sense for amorphous microporous polymers, at least in terms of anticipating wholly new systems. These methods are useful, however, in rationalizing and predicting the structure and behavior of new microporous PIMs,11,27 HCPs,12,13,15,16 and CMPs17-21,28 as they are discovered and characterized. Acknowledgment. The authors are grateful to EPSRC (EP/ C511794/1) for funding. We thank Dr Colin Wood for assistance with the BET calculations. Supporting Information Available: Plots of surface area against the grid spacing and probe radius used in the calculation of the respective geometric surface area. Plots of H2 uptake against Connolly surface area and density and the simulated H2 isotherms for a range of densities. This material is available free of charge via the Internet at http://pubs.acs.org References and Notes (1) Schu¨th, F.; Sing, K. S. W.; Weitkamp, J. Handbook of Porous Solids. Wiley: New York, 2002. (2) Cheetham, A. K.; Fe´rey, G.; Loiseau, T. Angew. Chem., Int. Ed. 1999, 38, 3268–3292. (3) Eddaoudi, M.; Kim, J.; Rosi, N.; Vodak, D.; Wachter, J.; O’Keeffe, M.; Yaghi, O. M. Science 2002, 295, 469–472. (4) Yaghi, O. M.; O’Keeffe, M.; Ockwig, N. W.; Chae, H. K.; Eddaoudi, M.; Kim, J. Nature 2003, 423, 705–714.
Atomistic Simulation of Microporous Polymer Networks (5) Zhao, X. B.; Xiao, B.; Fletcher, A. J.; Thomas, K. M.; Bradshaw, D.; Rosseinsky, M. J. Science 2004, 306, 1012–1015. (6) Kitagawa, S.; Kitaura, R.; Noro, S. Angew. Chem., Int. Ed. 2004, 43, 2334–2375. (7) Coˆte´, A. P.; Benin, A. I.; Ockwig, N. W.; O’Keeffe, M.; Matzger, A. J.; Yaghi, O. M. Science 2005, 310, 1166–1170. (8) El-Kaderi, H. M.; Hunt, J. R.; Mendoza-Cortes, J. L.; Coˆte´, A. P.; Taylor, R. E.; O’Keeffe, M.; Yaghi, O. M. Science 2007, 316, 268–272. (9) Budd, P. M. Science 2007, 316, 210–211. (10) Budd, P. M.; Ghanem, B. S.; Makhseed, S.; McKeown, N. B.; Msayib, K. J.; Tattershall, C. E. Chem. Commun. 2004, 230–231. (11) McKeown, N. B.; Gahnem, B.; Msayib, K. J.; Budd, P. M.; Tattershall, C. E.; Mahmood, K.; Tan, S.; Book, D.; Langmi, H. W.; Walton, A. Angew. Chem., Int. Ed. 2006, 45, 1804–1807. (12) Lee, J. Y.; Wood, C. D.; Bradshaw, D.; Rosseinsky, M. J.; Cooper, A. I. Chem. Commun. 2006, 2670–2672. (13) Germain, J.; Hradil, J.; Fre´chet, J. M. J.; Svec, F. Chem. Mater. 2006, 18, 4430–4435. (14) Wood, C. D.; Tan, B.; Trewin, A.; Niu, H. J.; Bradshaw, D.; Rosseinsky, M. J.; Khimyak, Y. Z.; Campbell, N. L.; Kirk, R.; Sto¨ckel, E.; Cooper, A. I. Chem. Mater. 2007, 19, 2034–2048. (15) Tsyurupa, M. P.; Davankov, V. A. React. Funct. Polym. 2002, 53, 193–203. (16) Tsyurupa, M. P.; Davankov, V. A. React. Funct. Polym. 2006, 66, 768–779. (17) Jiang, J. X.; Su, F.; Trewin, A.; Wood, C. D.; Campbell, N. L.; Niu, H.; Dickinson, C.; Ganin, A. Y.; Rosseinsky, M. J.; Khimyak, Y. Z.; Cooper, A. I. Angew. Chem., Int. Ed. 2007, 46, 8574–8578. (18) Jiang, J.-X.; Su, F.; Trewin, A.; Wood, C. D.; Niu, H.; Jones, J. T. A.; Khimyak, Y. Z.; Cooper, A. I. J. Am. Chem. Soc. 2008, 130, 7710– 7722. (19) Jiang, J. X.; Su, F.; Niu, H.; Wood, C. D.; Campbell, N. L.; Khimyak, Y. Z.; Cooper, A. I. Chem. Commun. 2008, 486–488. (20) Dawson, R.; Su, F. B.; Niu, H. J.; Wood, C. D.; Jones, J. T. A.; Khimyak, Y. Z.; Cooper, A. I. Macromolecules 2008, 41, 1591–1593. (21) Weber, J.; Thomas, A. J. Am. Chem. Soc. 2008, 130, 6334–6335. (22) Lin, X.; Jia, J. H.; Zhao, X. B.; Thomas, K. M.; Blake, A. J.; Walker, G. S.; Champness, N. R.; Hubberstey, P.; Schroder, M. Angew. Chem., Int. Ed. 2006, 45, 7358–7364. (23) Vitillo, J. G.; Ricchiardi, G.; Spoto, G.; Zecchina, A. Phys. Chem. Chem. Phys. 2005, 7, 3948–3954.
J. Phys. Chem. C, Vol. 112, No. 51, 2008 20559 (24) (a) Du¨ren, T.; Millange, F.; Fe´rey, G.; Walton, K. S.; Snurr, R. Q. J. Phys. Chem. C 2007, 111, 15350–15356. (b) Walton, K. S.; Snurr, R. Q. J. Am. Chem. Soc. 2007, 129, 8552–8556. (25) Garberoglio, G. Langmuir 2007, 23, 12154–12158. (26) Connolly, M. L. Science 1983, 221, 709–713. (27) McKeown, N. B.; Makhseed, S.; Budd, P. M. Chem. Commun. 2002, 2780–2781. (28) Weder, C. Angew. Chem., Int. Ed. 2008, 47, 448–450. (29) Wood, C. D.; Tan, B.; Trewin, A.; Su, F.; Rosseinsky, M. J.; Bradshaw, D.; Sun, Y.; Zhou, L.; Cooper, A. I. AdV. Mater. 2008, 20, 19116–1921. (30) Lewis, D. W.; Willock, D. J.; Catlow, C. R. A.; Thomas, J. M.; Hutchings, G. J. Nature 1996, 382, 604–606. (31) Lewis, D. W.; Sankar, G.; Wyles, J.; Willock, D. J.; Catlow, C. R. A.; Thomas, J. M. Angew. Chem., Int. Ed. 1997, 36, 2675–2677. (32) Maple, J. R.; Hwang, M.-J.; Stockfisch, T. P.; Dinur, U.; Waldman, M.; Ewig, C. S.; Hagler, A. T. J. Comput. Chem. 1994, 15, 162–182. (33) Sun, H. J. Phys. Chem. B 1998, 102, 7338–7364. (34) Surble´, S.; Millange, F.; Serre, C.; Du¨ren, T.; Latroche, M.; Bourrelly, S.; Llewellyn, P. L.; Fe´rey, G. J. Am. Chem. Soc. 2006, n/a. (35) Ahn, J. H.; Jang, J. E.; Oh, C. G.; Ihm, S. K.; Cortez, J.; Sherrington, D. C. Macromolecules 2006, 39, 627–632. (36) Sherrington, D. C. Chem. Commun. 1998, 2275–2286. (37) Hebb, A. K.; Senoo, K.; Bhat, R.; Cooper, A. I. Chem. Mater. 2003, 15, 2061–2069. (38) Cooper, A. I.; Holmes, A. B. AdV. Mater. 1999, 11, 1270–1274. (39) Li, J.; Favis, B. D. Polymer 2001, 42, 5047–5053. (40) Panella, B.; Hones, K.; Muller, U.; Trukhan, N.; Schubert, M.; Putter, H.; Hirscher, M. Angew. Chem., Int. Ed. 2008, 47, 1–6. (41) Trewin, A.; Darling, G. R.; Cooper, A. I. New J. Chem. 2008, 32, 17–20. (42) Lochan, R. C.; Head-Gordon, M. Phys. Chem. Chem. Phys. 2006, 8, 1357. (43) Hubner, O.; Klopper, W. J. Phys. Chem. A. 2007, 111, 2426–2433. (44) Sankar, G.; Okubo, T.; Fan, W.; Meneau, F. Faraday Discuss. 2007, 136, 157–166. (45) Davankov, V. A.; Pastukhov, A. V.; Tsyurupa, M. P. J. Polym. Sci. B: Polym. Phys. 2000, 38, 1553–1563. (46) Pastukhov, A. V.; Tsyurupa, M. P.; Davankov, V. A. J. Polym. Sci. B: Polym. Phys. 1999, 37, 2324–2333.
JP806397F
