J. Phys. Chem. C 2009, 113, 14953–14962
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Quantum Effect-Mediated Hydrogen Isotope Mixture Separation in Slit Pore Nanoporous Materials Yang Wang and Suresh K. Bhatia* DiVision of Chemical Engineering, The UniVersity of Queensland, Saint Lucia, Brisbane, Queensland 4072, Australia ReceiVed: May 13, 2009; ReVised Manuscript ReceiVed: June 26, 2009
We use path integral simulations to investigate the separation of H2 and HD, as well as H2 and D2, in carbon slit pores of various sizes using a new improved set of carbon-hydrogen interaction parameters determined in our laboratory. As expected, the selectivity of HD over H2 is lower than that of D2 over H2 at the same conditions due to the smaller mass of HD molecules and hence larger quantum effects. In the pressure range of 0.1-10.0 bar, the selectivity is not sensitive to the pressure at the temperature of 77 K. At 40 K the selectivity shows a positive relation to the adsorbed phase density. We also report an unusual crossover effect in which the selectivity in a pore of width 0.85 nm exceeds that in a smaller pore (0.69 nm) at high densities due to enhanced quantum confinement effects when a second layer forms in the larger pore. The optimal pore widths for HD/H2 separations were identified to be 0.56-0.57 nm, with operating pressures of 10.0 and 0.1 bar for the two pore sizes, respectively. We also simulate equilibrium separation in the commercial Takeda 3 Å carbon molecular sieve, based on a slit-like pore model with a distribution of pore sizes, but find only modest equilibrium selectivity for HD over H2. It is suggested that while quantum effects are small within the pore bodies, narrow pore entrances must lead to significant quantum effects on the dynamics in order to explain literature data of faster uptake of D2 compared to H2 at 77 K in this material. Thus, kinetic molecular sieving at narrow necks, for which this material is well established, maybe a more attractive option than equilibrium separation. Alternatively, materials with controlled smaller pore sizes are needed for more efficient equilibrium HD/H2 separation. The ideal adsorption solution theory (IAST) is also examined for prediction of the binary hydrogen isotope mixture isotherms in the presence of quantum effects and is found to match simulations at all operating conditions investigated. Introduction The heavier isotope of hydrogen, deuterium, is a useful resource, which has numerous applications, such as in nuclear fusion, neutron scattering techniques, nonradioactive isotopic tracer methods, hydrogen nuclear magnetic resonance spectroscopy, lighting as well as a host of others. It has a very low natural abundance in the oceans, where it forms ∼0.015% of all naturally occurring hydrogen. Currently, the production of deuterium is largely via various isotope separation techniques such as cryogenic distillation, centrifugal enrichment, and electromagnetic mass spectrometry. Due to the very similar thermodynamic properties of hydrogen and deuterium, these techniques are very expensive and high in energy cost. Over the past decade, there has been increased interest in newer more cost-effective hydrogen separation methods. Quantum isotope separation in nanoscale materials is one of the alternatives that has recently attracted much attention.1-16 Hydrogen and deuterium have significant difference in the magnitude of quantum effects at low temperature due to the mass of deuterium being twice the mass of hydrogen. Nanoscale porous materials can exploit this difference if the pore sizes are close to the dimension of the hydrogen molecules, as the greater uncertainty in the position of the center of mass of the lighter hydrogen leads to greater steric hindrance for this molecule. This difference in the quantum behaviors of the isotopes leads to difference in * To whom correspondence should be addressed. Email: s.bhatia@ uq.edu.au.
their adsorption behavior in nanoporous materials at low temperature, which can be utilized to separate the two isotopes more efficiently. Beenakker and his co-workers were the first to demonstrate the possibility of hydrogen isotope quantum separation in nanoscale pores.17 On the basis of a simple hardsphere model, their work showed preferential adsorption of deuterium in cylindrical pores due to larger quantum uncertainty of the hydrogen. Several subsequent investigations, both theoretical and experimental, have confirmed this effect.5,6,8-10 In addition to the difference in adsorption, Bhatia et al. have shown a more striking kinetic feature, that the heavier deuterium diffuses faster than lighter hydrogen in zeolite molecular sieves at low temperature.2,18 This effect has later been experimentally confirmed by Zhao et al.19 using a 3 Å carbon molecular sieve and raises the possibility of kinetic molecular sieving of the isotopes in narrow pore materials at low temperature. Therefore, microporous materials may offer promise for hydrogen isotope separations. Our recent study, among the few focusing on binary mixture isotope separation, has shown that slit-shaped microporous carbons have the potential to be a good medium for hydrogen isotope mixture separations at low temperature.13 Optimal operation conditions have been determined for the most efficient separation process. At present, all of the isotope mixture separation simulations take account of H2 and D2 mixtures. However, the isotope deuterium, which exists in trace amount in nature, mostly takes the form of hydrogen deuteride, a molecule consisting of a deuterium atom and a hydrogen atom
10.1021/jp9044397 CCC: $40.75 2009 American Chemical Society Published on Web 07/16/2009
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J. Phys. Chem. C, Vol. 113, No. 33, 2009
Wang and Bhatia
(HD). Therefore, experimental and even industrial processes must deal with the separation of H2 and HD mixtures. In this paper, we investigate binary HD/H2 mixture adsorption in carbon slit pores by performing equilibrium simulations. We employed a new set of carbon atom parameters, by which the experiment H2 and D2 adsorption data on carbons are successfully reproduced,20 to perform the calculations. We report the effects of temperature, pressure as well as pore size on the equilibrium HD/H2 separation. We also report the difference between the selectivities of HD over H2 and D2 over H2. In addition, we perform a series of calculations to simulate the isotope separation on a real commercial microporous carbon material, Takeda 3 Å. We note that the selectivity of HD over H2 has never been reported before. It is also the first time that equilibrium isotope separation simulations have been performed on a practical nanoporous material. These studies are therefore of importance in the search for an efficient nanoporous medium for practical hydrogen isotope separation processes. We also apply the ideal adsorbed solution theory21 (IAST) to predict the selectivity of binary hydrogen isotope mixtures and demonstrate that the theory can be successfully used, with results closely matching simulations.
Vsf(z) ) Vsf(z) + Vsf(h - z)
(4)
where h is the center-to-center distance between carbon atoms on the opposing surfaces, measured along the normal. The quantum effects are incorporated into the simulations by the Feynman path integral (PI) formalism.25,26 This method models a single molecule as a ring of multiple beads, which are connected via harmonic springs. The spring constant, k, is calculated using
k)
Pm (βp)2
(5)
where P is the number of beads per molecule, m is mass, β ) 1/kBT (kB is the Boltzmann constant), and p is Planck constant divided by 2π. The total fluid-fluid energy is given by N
P
∑∑
1 UPI(r) ) k 2 i)1
R)1
(ri(R) - ri(R+1))2 +
1 P
P
∑ ∑ U(rij(R)) i
