(87a) The Role of the Intermolecular Potential on the Dynamics of C2H4 Confined in Cylindrical Nanopores

The confinement of fluids in nanoporous solids can be accompanied by striking effects on the molecular dynamics,¹ which do not necessarily possess an analogy in the bulk phase. Upon confinement, molecules interact with the solid walls to an extent that markedly depends on the chemical nature of the solid and its corresponding pore size. Bhatia et al.² studied the transport of CH₄ adsorbed into armchair single-walled carbon nanotubes (SWCNTs), and concluded that the diffusion coefficient decreases with adsorbate density. The dynamics of CH₄ and C₂H₆ inside a zig-zag SWCNT have been studied by Krishna et al.³ The diffusivity of gases and liquids confined in carbon nanotubes is far from being thoroughly understood and, furthermore, results are sometimes conflicting. We aim herein to understand the effect of the level of detail used in the description of the fluid's energetics, upon the effective observed dynamics. Much can be gained or lost in terms of computational effort and physical detail by coarse-graining (CG) molecular models; Depa et al. showed that by CG the intermolecular potential of polymers,⁴ the bulk fluid would exhibit faster dynamics than the corresponding atomistic representations, and related this to the enhanced softness of the CG potential. It is the purpose of this work to study the influence of the intermolecular potential on the dynamical behavior of C₂H₄, in a bulk phase, and also confined inside a (16,0) SWCNT (D_eff ≈ 9.1 Å). This issue has been partially addressed by Mao and Sinnott⁵ and Cruz and Müller.⁶ We employ molecular dynamics (MD) simulations with five distinct intermolecular potential models, whose level of CG corresponds to different degrees of detailing the C₂H₄ molecule; including a fully atomistic representation of ethylene (AA-OPLS), validated by comparison against bulk experimental data,⁷ but also simpler models with varying degrees of CG ranging down to a single isotropic Lennard-Jones sphere (1CLJ). The capabilities and drawbacks of each of these different molecular descriptors are explored in a wide range of densities (ρ ≤ 15.751 mol/L) and temperatures (220 ≤ T (K) ≤ 340).

II. Results and Discussion

The effect of confinement on the self-diffusion coefficient, D, of ethylene, is observed to be dependent on the particular potential model employed, in a manner which is different than in bulk, where the calculated D values are rather independent of the potential used. As C₂H₄ is confined, differences between molecular potentials are enhanced resulting in discrepancies in the observed self-diffusivities. It is generally argued that coarse-graining intermolecular potentials results in increased self-diffusivities. In the present case, if the AA-OPLS model is used as benchmark, it becomes clear that the effect of CG is unpredictable, and an appropriate and accurate parameterization may faithfully reproduce self-diffusion data. Furthermore, the existence of explicit electrostatic details in the potential seems to induce short-range order in the confined fluid, resulting in a slowing down of molecular mobility. The radial distribution function for the simple 1CLJ potential exhibits a sharp peak at r = 4.73 Å and a second (less intense) long-range peak located at r = 8.73 Å, indicating that molecules are densely packed together with almost no free volume between them (σ ≈ 4.6 Å). When the fluid model is increasingly refined, a different picture is obtained. If the C₂H₄ molecule is described with the TraPPE potential, not only does the initial g(r) peak becomes much broader, with an half-width length of Δr ≈ 1.95 Å, but it also appears closer at r = 4.48 Å; the second peak observed in the 1CLJ model is no longer clearly observable. If electrostatics are now explicitly added to the fluid molecules, via atomic partial charges (AA-OPLS), a further refinement of the initial peak takes place. The r = 4.48 Å peak of the TraPPE potential essentially gets split into two contributions, r = 4.03 Å and r = 4.78 Å, suggesting the insurgence of a very short-range ordered arrangement of molecules in the AA-OPLS model, that is absent in the other potentials.

In spite of the marked anisotropy introduced by the solid, both the bulk fluid and anisotropic systems data are observed to roughly collapse onto a same master curve, in this work described as a simple power-law dependency of the self-diffusion coefficient with molecular density, D = D₀ρ^λ (–1.269 ≤ λ ≤–0.943). The isochors show that the confined fluid response to temperature is similar, either above or bellow the critical value, T_c=282.35 K, and in all cases obeys the Arrhenius law, D = Aexp(-E_a/RT). At constant density, it was observed⁷ that the self-diffusion coefficients are remarkably dependent of the particular potential model, D (1CLJ) < D (AA-OPLS) < D (TraPPE). From the Arrhenius fits, it becomes clear that for each potential studied, regardless of its own specificities and degree of molecular detail, the activation energy (E_a/R) decreases monotonically with increasing molecular density. Because molecules in the dense fluid are highly packed, with little free volume between them, exchange of momentum via molecular collisions is highly efficient, thus dramatically increasing the self-diffusional process. We are unaware of experimental work reporting self-diffusion data for confined ethylene. Nonetheless, in order to probe the simultaneous effect of confinement and T on the fluid dynamics, we compare our results with bulk experimental data⁸ using the AA-OPLS model as benchmark. It then becomes clear that, when the solid is saturated with fluid (15.024 mol/L), the D coefficients show a similar response to applied temperature, both in bulk and under confinement. The activation energies obtained from the Arrhenius plots, (E_a/R)^bulk = 214.12 K and (E_a/R)^SWCNT = 242.85 K, suggest that confinement exerts a major influence on the absolute values of D, but not so much on their intrinsic dependence on temperature. To a reasonable approximation, the self-diffusivity differences between the bulk and confined phases are roughly constant over the entire temperature domain, (D^bulk/ D^SWCNT)^[220K-340K] = 2.52 ± 0.13. A totally different picture results when density is lowered, and the existence of free volume becomes a relevant parameter. For the isochor at 5.331 mol/L, free volume inside the solid is more than 50 % of total available volume, and therefore a sharp discrepancy can be observed in the slope of the corresponding bulk system (5 mol/L), leading to activation energies that are quite different between the bulk and confined fluid, (E_a/R)^bulk = 301.64 K and (E_a/R)^SWCNT = 533.96 K. For those lower densities, the self-diffusivities ratio increases dramatically to (D^bulk/ D^SWCNT)^[220K-340K] = 10.2 ± 0.5. One can extrapolate the previous observations to a very dilute fluid, and postulate that as the free volume inside the solid increases, so do the differences in the corresponding activation energies between the bulk and confined fluid.

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