Contribution of restricted rotors to quantum sieving of hydrogen isotopes

Hathorn, Bryan C.; Sumpter, Bobby G.; Noid, D. W.

doi:10.1103/physreva.64.022903

Cited by 44 publications

(79 citation statements)

References 17 publications

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“…When the pore size of the adsorbents was small, the successive adsorption stage, after initial surface diffusion and pore diffusion, was governed by quantum sieving stemming from different zero-point energies, and the translational and rotational confinements of the hydrogen isotope molecules. The results in this study agreed well with the quantum sieving effect on adsorbents with small pores, which were reported from various studies [16,20,42,43,[50][51][52]. The quantum effect on the CMS contributed to the successive adsorption stages as discussed in Figs.…”

Section: Comparison Between Equilibrium Selectivity and Breakthrough supporting

confidence: 93%

Adsorption dynamics of hydrogen and deuterium in a carbon molecular sieve bed at 77K

Chu

Cheng

Zhao

et al. 2015

Separation and Purification Technology

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Section: Comparison Between Equilibrium Selectivity and Breakthrough supporting

confidence: 93%

Adsorption dynamics of hydrogen and deuterium in a carbon molecular sieve bed at 77K

Chu

Cheng

Zhao

et al. 2015

Separation and Purification Technology

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“…Recent work by Hathorn et al has examined rotational states of H 2 isotopomers confined in model nanotubes in the dilute adsorption limit. 42 Their work indicates that rotational effects enhance the overall selectivity of the heavier isotope. Thus, the selectivities observed in our results, which arise purely from the quantization of translational degrees of freedom, should most accurately be interpreted as lower bounds to the exact selectivity of these systems.…”

Section: Resultsmentioning

confidence: 99%

Adsorption and separation of hydrogen isotopes in carbon nanotubes: Multicomponent grand canonical Monte Carlo simulations

Challa

Sholl

Johnson

2002

The Journal of Chemical Physics

172

202

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Adsorption isotherms of hydrogen isotopes from molecular simulations in carbon nanotubes and interstices are presented. The adsorption of pure isotopes follows Henry’s law up to moderate coverages. A modified path integral grand canonical Monte Carlo (PI-GCMC) technique for mixture adsorption is presented and applied to adsorption of isotope mixtures in carbon nanotubes. Adsorption isotherms of H2–T2 mixtures in nanotubes and interstices are determined at 20 and 77 K. Selectivities for T2 over H2 are calculated over a range of pressures. Selectivity in the nanotubes and interstices increases with pressure until the nanotube is saturated. Comparison of simulation results with predictions based on ideal adsorbed solution theory (IAST) shows good agreement up to moderate loadings. At higher loadings, selectivities determined from multicomponent simulations remain roughly constant, whereas IAST predicts continued increase in selectivities. Isotherms for H2–D2 and the selectivities of D2 over H2 are determined for adsorption in (10,10) nanotubes and in the interstitial channels of closed (10,10) nanotubes.

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“…(5) describe the free geodesic motion on S 2 , the standard spherical harmonics will occasionally be termed to as wave functions of the free geodesic motion on S 2 . The rigid rotator is commonly used as a tool in the description of diatomic molecules [8]- [10], a field that has recently enjoyed a significant boost through the progress in ultra-cooling techniques. The introduction of a potential in eq.…”

Section: The Quantum Rigid Rotatormentioning

confidence: 99%

Rotational symmetry and degeneracy: a cotangent-perturbed rigid rotator of unperturbed level multiplicity

Alvarez-Castillo¹,

Compean²,

Kirchbach³

2011

Molecular Physics

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Abstract:We predict level degeneracy of the rotational type in diatomic molecules described by means of a cotangent-hindered rigid rotator. The problem is shown to be exactly solvable in terms of non-classical Romanovski polynomials. The energies of such a system are linear combinations of t(t + 1) and 1/[t(t + 1) + 1/4] terms with the non-negative integer principal quantum number t = n + | m| being the sum of the order n of the polynomials and the absolute value, | m|, of the square root of the separation constant between the polar and azimuthal angular motions. The latter obeys with respect to t same branching rule, | m| = 0, 1, ..., t, as does the magnetic quantum number with respect to the angular momentum, l, and in this fashion the t quantum number presents itself formally indistinguishable from l. In effect, the spectrum of the hindered rotator has the same (2t + 1)-fold level multiplicity as the unperturbed one. For low t values wave functions and excitation energies of the perturbed rotator differ from the ordinary spherical harmonics, and the l(l + 1) law, respectively, while approaching them asymptotically with the increase of t. In this fashion the breaking of the rotational symmetry at the level of the representation functions is opaqued by the level degeneracies. The model furthermore provides a tool for the description of rotational bands with anomalously large gaps between the ground state and its first excitation. Relationship between symmetry and degeneracy:Introductory remarks.The relationship between the rotational symmetry of the central potentials and the degeneracy in their spectra is a complex one. One expects that due to rotational symmetry the spectra of the central potentials will show the (2l + 1)-fold degeneracy with respect to the magnetic quantum number, which they really do, though not alone. Matters are complicated by the circumstance that various exactly solvable radial potentials (see ref.[1] for a compilation) have more symmetries than the rotational symmetry of the angular motion. The reason for this is that in the process of the reduction of the radial part of the separated Schrödinger equation down to the hypergeometric differential equation by an appropriate point-canonical transformation, the energy always emerges as a combination, known as principal quantum number, of l, and the order n of the polynomial. In many cases the radial wave equation can be transformed to a power series of the Casimir operator of some Lie group different from SO(3) and the principal quantum number can be associated with the corresponding eigenvalues of the group invariant. A prominent example in that regard is the fundamental inverse distance problem, where this combination appears as, N = l + n + 1, the positive integer N being known as the principal quantum number. Summing up the (2l + 1) fold degeneracies for all l = 0, 1, 2, .. (N − 1), a larger N −1 0 (2l + 1) = N 2 -fold level degeneracy occurs with respect to both l and m. The rotational (2l + 1)-fold multiplicity is of course at the ver...

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Contribution of restricted rotors to quantum sieving of hydrogen isotopes

Cited by 44 publications

References 17 publications

Adsorption dynamics of hydrogen and deuterium in a carbon molecular sieve bed at 77K

Adsorption dynamics of hydrogen and deuterium in a carbon molecular sieve bed at 77K

Adsorption and separation of hydrogen isotopes in carbon nanotubes: Multicomponent grand canonical Monte Carlo simulations

Rotational symmetry and degeneracy: a cotangent-perturbed rigid rotator of unperturbed level multiplicity

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