9824 Phys. Chem. Chem. Phys., 2011, 13, 9824–9830 This journal is c the Owner Societies 2011 Cite this: Phys. Chem. Chem. Phys., 2011, 13, 9824–9830 Quantum fluctuations increase the self-diffusive motion of para-hydrogen in narrow carbon nanotubesw Piotr Kowalczyk,* a Piotr A. Gauden, b Artur P. Terzyk b and Sylwester Furmaniak b Received 21st January 2011, Accepted 24th March 2011 DOI: 10.1039/c1cp20184k Quantum fluctuations significantly increase the self-diffusive motion of para-hydrogen adsorbed in narrow carbon nanotubes at 30 K comparing to its classical counterpart. Rigorous Feynman’s path integral calculations reveal that self-diffusive motion of para-hydrogen in a narrow (6,6) carbon nanotube at 30 K and pore densities below B29 mmol cm À3 is one order of magnitude faster than the classical counterpart. We find that the zero-point energy and tunneling significantly smoothed out the free energy landscape of para-hydrogen molecules adsorbed in a narrow (6,6) carbon nanotube. This promotes a delocalization of the confined para-hydrogen at 30 K (i.e., population of unclassical paths due to quantum effects). Contrary the self-diffusive motion of classical para-hydrogen molecules in a narrow (6,6) carbon nanotube at 30 K is very slow. This is because classical para-hydrogen molecules undergo highly correlated movement when their collision diameter approached the carbon nanotube size (i.e., anomalous diffusion in quasi-one dimensional pores). On the basis of current results we predict that narrow single-walled carbon nanotubes are promising nanoporous molecular sieves being able to separate para-hydrogen molecules from mixtures of classical particles at cryogenic temperatures. Introduction Confinement of classical and quantum particles at the nano- scale has attracted a lot of attention in recent years from a fundamental point of view as well as its relevance to nano- technology, material science, biology, geology, astronomy, etc. 1–10 The physical properties of confined particles and the diffusion rate in reduced dimensionality exhibit a number of peculiarities in comparison with the bulk phase. 11–20 Among novel nanomaterials, single-walled carbon nanotubes (SWNTs) are excellent carbon nanomaterials providing a quasi-one dimensional nanoscale confinement. 21 It is well- known that for classical particles anomalous single-file diffusion (SFD) occurs when the individual nanopores of the medium are so narrow that the particles are unable to pass each other. 22–29 As a result, the sequence of particles remains the same over a long time. Because the movements of individual particles are highly correlated, the mechanism of molecular diffusion in quasi-one dimensional nanopores is different from that observed for isotropic diffusion in the bulk system. Experimental and theoretical results collectively indicate that poorer mixing of adsorbed classical particles (i.e. traffic at the nanoscale) in narrow carbon nanotubes results in slow self-diffusive motion. 22–29 To the best of our knowledge the self-diffusive motion of light particles (e.g. 4 He, para-H 2 , ortho-D 2 ) adsorbed in quasi- one dimensional channels of carbon nanotubes at cryogenic temperatures has not been studied experimentally so far. It is not surprising since both quasielastic neutron scattering and pulsed-field gradient-nuclear magnetic resonance measure- ments of self-diffusion at cryogenic temperatures in narrow carbon nanotubes are very complicated. Individual carbon nanotubes of various sizes with metal contaminates and defects self-assemble into a stable bundle structure. 21,30,31 This complex structure consists of different adsorption sites, including internal and interstitial channels, grooves, and rounded surface of the bundle. Thus, the measured overall self-diffusion constant of adsorbed particles does not correspond to this inside a defect-free carbon nanotube. Other experimental difficulties result from the instability of narrow carbon nanotubes characterized by a high graphene curvature as well as a poor experimental signal from light particles. Rigorous theoretical calculations and computer experiments offer an alternative tool for the investigation of the self- diffusive motion of light particles in narrow carbon nanotubes a Nanochemistry Research Institute, Department of Chemistry, Curtin University of Technology, P.O. Box U1987, Perth, 6845 Western Australia, Australia. E-mail: Piotr.Kowalczyk@curtin.edu.au; Tel: +61 8 9266 7800 b Department of Chemistry, Physicochemistry of Carbon Materials Research Group, N. Copernicus University, Gagarin St. 7, 87-100 Torun, Poland. E-mail: gaudi@uni.torun.pl, aterzyk@chem.uni.torun.pl, sf@chem.umk.pl w Electronic supplementary information (ESI) available: Snapshots of p-H 2 and its classical counterpart adsorbed in studied carbon nanotubes (6_6mov1, 6_6mov2, class_mov1, class_mov2). Theory, methods, and simulation details with additional Fig. 1S–5S. It should be noted that all movies in the ESI were created using the VMD program. 70,71 PCCP Dynamic Article Links www.rsc.org/pccp PAPER Downloaded by Uniwersytet Mikolaja Kopernika on 19 September 2011 Published on 18 April 2011 on http://pubs.rsc.org | doi:10.1039/C1CP20184K View Online