Nuclear Quantum Effects in the Layering and Diffusion of Hydrogen Isotopes in Carbon Nanotubes Piotr Kowalczyk,* ,† Artur P. Terzyk, ‡ Piotr A. Gauden, ‡ Sylwester Furmaniak, ‡ Katsumi Kaneko, ∥ and Thomas F. Miller, III ⊥ † School of Engineering and Information Technology, Murdoch University, Perth, Western Australia 6150, Australia ‡ Faculty of Chemistry, Physicochemistry of Carbon Materials Research Group, Nicolaus Copernicus University in Toruń, Gagarin Street 7, 87-100 Toruń, Poland ∥ Center for Energy and Environmental Science, Shinshu University, Nagano 380-8553, Japan ⊥ Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States * S Supporting Information ABSTRACT: Although recent experimental studies have demon- strated that H 2 and D 2 molecules wet the inner surface of supergrowth carbon nanotubes at low temperatures, characterization of the structural and dynamical properties in this regime is challenging. This Letter presents a theoretical study of self-diffusion in pure and binary H 2 ,D 2 , and T 2 contact monolayer films formed on the inner surface of a carbon nanotube. Our results show that monolayer formation and self-diffusion both in pure hydrogen isotopes and in H 2 /T 2 and H 2 /D 2 isotope mixtures is impacted by nuclear quantum effects, suggesting potential applications of carbon nanotubes for the separation of hydrogen isotopes. U nderstanding how nuclear quantum effects (i.e., zero- point motion and tunneling) influence the dynamics and structure of confined molecular hydrogen isotopes is an important problem in surface science, due to the role of such effects in adsorptive separation processes. 1−3 Experimental measurements of hydrogen isotope diffusion in nanomaterials have generally been limited to high temperatures for which the confined hydrogen is a supercritical fluid. 1−10 Only recently, Contescu et al. 11 used quasielastic neutron scattering to study the self-diffusion of pure H 2 and D 2 adsorbed in narrow nanopores (<0.7 nm) of polyfurfuryl alcohol-derived activated carbon (PFAC) at subcritical temperatures in the range of 10− 40 K. In this work, the measured self-diffusion coefficient for pure D 2 was 76 times higher than that of pure H 2 , revealing a pronounced inverse isotope effect. Steric hindrance in narrow carbon nanopores caused by the higher excluded volume of H 2 was used to explain its slower self-diffusion (i.e., the Chudley− Elliott jump-diffusion mechanism), whereas D 2 was found to exhibit liquid-like self-diffusion. 11 Similarly, the impact of nuclear quantum effects on diffusion of gases from single- carbon nanotubes has been studied experimentally, 12, 13 revealing that H 2 diffuses out of the interior of carbon nanotubes at significantly faster rates than D 2 . Taken together, these works illustrate the importance of nuclear quantum effects in nanoconfined environments and motivates a more complete analysis of the range of phenomenology that may be observed in nanoconfined mixtures of H 2 and D 2 . Recent progress in the synthesis of pure, structurally homogeneous, and relatively wide carbon nanotubes via the supergrowth (SG) method 13,15 has triggered new experimental studies of quantum molecular sieving of H 2 and D 2 at low temperatures. 16 It was shown that single-component H 2 and D 2 adsorption isotherms have a steep uptake at low pressures, indicating formation of contact monolayer films on the concave inner surface of SG carbon nanotubes at 20 K. 16 However, the formation of the H 2 monolayer is more gradual and shifted to lower pressures compared to D 2 . These experimental results further suggest an interesting role for nuclear quantum effects in the structure and dynamic of molecular hydrogen in pure and binary contact monolayer films. In this work, we present a theoretical study of H 2 ,D 2 , and T 2 dynamics in pure and binary films that line the interior of relatively wide (2.72 nm pore diameter 16 ) carbon nanotubes at 25 K, a temperature at which my previous studies of liquid para-H 2 have been previously performed. 17−20 We use ring- polymer molecular dynamics (RPMD) 21−23 to provide a quantized description of the molecular dynamics, using n = 32 ring polymer beads for the imaginary-time path-integral discretization in the NVT ensemble. Interactions between hydrogen isotopes are modeled using the spherically symmetric Silvera−Goldman potential. 24 The interactions between hydro- gen isotopes and an infinitely long, cylindrically symmetric carbon nanotube are computed using 25 Received: July 20, 2015 Accepted: August 7, 2015 Letter pubs.acs.org/JPCL © XXXX American Chemical Society 3367 DOI: 10.1021/acs.jpclett.5b01545 J. Phys. Chem. Lett. 2015, 6, 3367−3372 Downloaded by UNIWERSYTET MIKOLAJA KOPERNIKA on August 27, 2015 | http://pubs.acs.org Publication Date (Web): August 13, 2015 | doi: 10.1021/acs.jpclett.5b01545