Article pubs.acs.org/JPCC
Cryogenic Noble Gas Separation without Distillation: The Effect of Carbon Surface Curvature on Adsorptive Separation Piotr Kowalczyk,*,† Piotr A. Gauden,‡ and Artur P. Terzyk‡ †
Nanochemistry Research Institute, Department of Chemistry, Curtin University of Technology, P. O. Box U1987, Perth, 6845 Western Australia, Australia ‡ Department of Chemistry, Physicochemistry of Carbon Materials Research Group, Nicolaus Copernicus University, Gagarin Street 7, 87-100 Torun, Poland ABSTRACT: Applying a novel self-consistent Feynman− Kleinert−Sesé variational approach (Sesé, L. M. Mol. Phys. 1999, 97, 881−896) to quantum thermodynamics and the ideal adsorbed solution theory, we studied adsorption and equilibrium separation of 20Ne−4He mixtures in carbonaceous nanomaterials consisting of flat (graphite-like lamellar nanostructures) and curved (triply periodic minimal carbon surfaces) nanopores at 77 K. At the infinite mixture dilution, Schwarz P-carbon and Schoen G-carbon sample represents potentially efficient adsorbents for equilibrium separation of 20Ne−4He mixtures. The equilibrium selectivity of 20Ne over 4He (αNe−He) computed for Schwarz P-carbon and Schoen G-carbon sample is very high and reaches 219 and 163 at low pore loadings, respectively. Graphite-like lamellar nanostructures with interlamellar spacing (Δ) less than 0.6 nm are also potential adsorbents for equilibrium separation of 20Ne−4He mixtures at cryogenic temperatures. Here, αNe−He of 80 is predicted for Δ = 0.46 nm at low pore loadings. The quantum-corrected molar enthalpy of 20Ne adsorption strongly depends on the curvature of carbon nanopores. For Schwarz P-carbon sample, it reaches 8.2 kJ mol−1, whereas for graphite-like lamellar nanostructures the maximum enthalpy of 20Ne physisorption of 5.6 kJ mol−1 is predicted at low pore loadings. In great contrast, the quantum-corrected molar enthalpy of 4He adsorption is only slightly affected by the curvature of carbon nanopores. The maximum heat released during the 4He physisorption is 3.1 (Schwarz P-carbon) and 2.7 kJ mol−1 (graphite-like lamellar nanostructure consisting of the smallest flat carbon nanopores). Interestingly, for all studied carbonaceous nanomaterials consisting of curved/flat nanopores, αNe−He computed for the equimolar composition of 20Ne−4He gaseous phases is still very high at total mixture pressure up to 1 kPa. This circumstance is indicative of the possibility of carrying out the adsorption separation of 20Ne−4He mixtures at pt < 1 kPa and 77 K that do not require high-energy consumption. Presented potential models and simulation methods will further enhance the accuracy of modeling of confined inhomogeneous quantum fluids at finite temperatures. separation of 20Ne−4He mixtures is a challenging problem for both experimentalists and theoreticians. 20 Ne has been extracted from the atmosphere as a byproduct in air separation plants. Typical analysis of 20Ne stream after complete H2 removal consists of the following: N2 (70%), 20Ne (23%), and 4He (7%).1 By passing the mixture at a pressure of around 50 bar through a reflux exchanger surrounded by a bath of liquid N2, it is fairly easy to remove the bulk of N2.1 A bed of activated charcoal (or other ordinary porous carbon) can adsorb the remaining traces of N2.1 In contrast to N2 capture, the separation of 20Ne from 4He is very difficult and expensive. Because the critical temperature of 20Ne is 44.41 K and that of 4 He is 5.2 K, the use of liquid H2 as a refrigerant is necessary. Meissner succeeded in separating 20Ne−4He mixture on a fairly large scale by using H2 in the early 1930s.1 This treatment,
I. INTRODUCTION High-purity noble gases, including 20Ne and 4He, are very important for lasers, light bulbs, scuba diving lights, etc.1−3 Apart from its use in fluorescent light fixtures, 20Ne has also found application in high-energy physics and military.1 On the other hand, liquid 4He is an important cooling agent used in nuclear plants, basic scientific research, medical imaging, and other cryogenic systems.1−3 Because the electron shells of noble gases are completely filled, they are inert, that is, do not normally form chemical compounds.4 Moreover, 20Ne and 4He exhibit significant quantum effects throughout their liquid range.5−22 As has been shown by Beenakker et al.23 and others,24−26 nanoscale confinement additionally impacts the space/momentum localization of quantum particles, which amplify the importance of quantum effects at finite temperatures. Thus, the accurate treatment of the phase behavior of these fluids under strong confinement must include quantum effects. Taking into account the quantum nature of 20Ne and 4 He atoms, as well as their chemical inertness, we argue that the © 2012 American Chemical Society
Received: June 7, 2012 Revised: August 24, 2012 Published: August 26, 2012 19363
dx.doi.org/10.1021/jp305613f | J. Phys. Chem. C 2012, 116, 19363−19371
The Journal of Physical Chemistry C
Article
⎧ 1 4 4 ⎪ VLJ(r ) − A (β , r )∇ VLJ(r ) 8 ⎪ 1/2 ⎫ ⎧ ⎪ + 3 ln⎨ sinh[β ℏΩ(β , r )/2μ ] ⎬, ⎪ β ⎩ β ℏΩ(β , r )/2μ1/2 ⎭ ⎪ 2 ⎪ Ω >0 ⎪ 1 4 (β)∇4 VLJ(r ), Ω2 = 0 VFKS(β , r ) = ⎨ VLJ(r ) − A GFH 8 ⎪ ⎪ 1 ⎪ VLJ(r ) − A̅ 4 (β , r )∇4 VLJ(r ) 8 ⎪ 3 ⎧ sin[β ℏ|Ω(β , r )| /2μ1/2 ] ⎫ ⎪ ⎬, ⎪ + β ln⎨ ⎩ β ℏ|Ω(β , r )| /2μ1/2 ⎭ ⎪ ⎩ Ω2 < 0
however, presents a problem because the boiling point of H2 is 20.4 K and that of 20Ne is 27.2 K. The triple point of 20Ne on the other hand is 24.6 K, which is above the boiling point of H2. Thus, care has to be exercised to make sure that the 20Ne does not solidify and block the tube (see ref 1 for other details). The separation factor, αNe−He, which is simply relative volatility for distillation, is not high for cryogenic separation of 20Ne−4He mixtures.1 Therefore, novel concepts and technologies are needed in order to develop/improve the 20Ne−4He separation processes. In recovering of 20Ne from 20Ne−4He mixtures, the separation by adsorption systems seems to be a very attractive alternative to costly and energy-intensive cryogenic distillation operations.1−3 However, as pointed out by Ruthven and others,27−30 a highly selective nanoporous material is a key to achieve the high adsorption selectivity of 20Ne over 4He. For equilibrium-driven separation, the intrinsic selectivity of nanoporous materials at infinite dilution of gaseous mixture is simply given by the ratio of the equilibrium constants (Henry’s law constants), αNe−He = KNe/KHe.31,32 It is expected that nanoporous material has the adsorption preference toward 20 Ne, i.e., KNe/KHe > 1. This is because the strength of the van der Waals interactions between adsorbed noble gases and nanoporous materials is higher for larger adsorbed atoms. Simply, as polarizability increases, dispersion forces also become stronger.4 Carbonaceous nanomaterials, including ordinary porous carbon, activated carbon fibers, ordered porous carbons, carbon nanotubes, and recently synthetized graphitic nanoribbons,33,34 are promising and fascinating nanostructures that can be potentially used in adsorption separation of 20 Ne−4He mixtures at 77 K (note that the selected operating temperature is a boiling point of N2, which is easily achievable1). These carbonaceous nanomaterials consist of various flat/curves nanopores that represent strong adsorption centers with high adsorption capacity.33,34 In order to optimize the αNe−He, we need to understand the impact of the nanopore curvature on the cryogenic adsorption of noble gas mixtures. For graphite-like lamellar nanostructures we need to tune the interlamellar spacing in order to get high αNe−He. As shown by Gogotsi and co-workers,33 tunable nanoporous carbons can be produced from metallic carbides by chemically removing the metallic element, leaving a systematic array of pores on the nanometer level. How αNe−He varies with the curvature of carbon nanopores, what is the optimal interlamellar spacing for 20 Ne−4He mixture adsorptive separation, and how αNe−He varies with the total pressure of equimolar 20Ne/4He mixtures at 77 K are key questions that we would like to answer, and this is the primary goal of the current work.
(1)
where Ω (β, r), a (β, r), and VLJ(r) are computed from 2
Ω 2 (β , r ) =
2
35
1 2 1 ∇ VLJ(r ) + a 2(β , r )∇4 VLJ(r ) 3 6
(2)
⎧ 1 ⎪ A2 (β , r ) = 2 ⎪ β Ω (β , r ) ⎪ ⎡ ⎤ ⎛ β ℏΩ(β , r ) ⎞ ℏΩ ( , β β r) ⎪ ⎢ ⎥, ⎟ ⎜ cosh − 1 ⎪ ⎢⎣ 2μ1/2 ⎥⎦ ⎝ 2μ1/2 ⎠ ⎪ 2 ⎪ Ω >0 ⎪ 2 2 a (β , r ) = ⎨ A GFH (β) = β ℏ2 /12μ , Ω2 = 0 ⎪ ⎪ 1 ⎪ A̅ 2 (β , r ) = 2 β Ω (β , r ) ⎪ ⎤ ⎪ ⎡ β ℏ|Ω(β , r )| ⎛ β ℏ|Ω(β , r )| ⎞ ⎪ ⎢ ⎟ − 1⎥ , cot⎜ 1/2 1/2 ⎥⎦ ⎠ ⎝ 2μ ⎪ ⎢⎣ 2μ ⎪ 2 ⎩ Ω
