(424a) The Role of the Intermolecular Potential On the Dynamics of C2H4 Confined In Cylindrical Nanopores

The Role of the Intermolecular
Potential on the Dynamics of C₂H₄ Confined in Cylindrical
Nanopores

Fernando
J.A.L. Cruz,¹ Erich A. Muller,² Jose P.B. Mota¹

¹Requimte/CQFB, Dept. Chemistry, Universidade Nova de Lisboa,
2829-516 Caparica, Portugal. ² Dept. Chem. Eng.,
Imperial College London, South Kensington Campus, London SW7 2AZ, UK.

fj.cruz@fct.unl.pt

I. Introduction

     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 ). This issue has been partially addressed by Mao and Sinnott⁵
and Cruz and Muller.⁶ We employ molecular dynamics (MD) simulations
with five distinct intermolecular potential models (Fig.1), 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 (< 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 (Fig.2), 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 (Fig.3), resulting in a slowing down of molecular mobility. The radial
distribution function (Fig.3) for the simple 1CLJ potential exhibits a sharp
peak at r = 4.73  and a second (less
intense) long-range peak located at r
= 8.73 , indicating that molecules are densely packed together with almost no
free volume between them (Sigma = 4.6
). 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 ca. 1.95 , but
it also appears closer at r = 4.48 ;
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 (magnification inset of Fig.3). The r = 4.48  peak of the TraPPE potential essentially gets split into two
contributions, r = 4.03  and r = 4.78 , 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 (Fig.2), in this work described as a simple power-law dependency of the
self-diffusion coefficient with molecular density, D = D₀r^l (–1.269 < l < –0.943). The isochors in Fig.4 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 in Fig.5 our results with bulk experimental data⁸ using the
AA-OPLS model as benchmark. It is clear from Fig. 5 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 isochore at 5.331 mol/L
(Fig.5), 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.

FIG. 1 The five different intermolecular potentials used in the MD simulations; each sphere represents a pseudo-atom with a characteristic Lennard-Jones pair (s, e),  di is the partial electrostatic charge on particle i, Q is the molecular quadrupole corresponding to the 2CLJQ force-field, and L is the chemical bond length between two CH2 pseudo-atoms.

FIG.2 Influence of potential CG upon bulk and confined C2H4 (T = 300K). Symbols are MD data and lines correspond to a power-law, D=D0rl(–1.269 ² l ²–0.943); AA-OPLS (black), 2CLJQ (blue), TraPPE (red), UA-OPLS (purple) and 1CLJ (green).	FIG.3 Radial distribution functions, g(r), of confined C2H4 (T=300 K): AA-OPLS (black, 15.024 mol/L), TraPPE (red, 15.024 mol/L) and 1CLJ (green, 11.632 mol/L).

FIG.4 Temperature dependence of the confined fluid self-diffusion coefficient (220 ² T (K) ² 340). Symbols represent MD results and lines correspond to Arrhenius fits, D=Aexp(-Ea/RT).	FIG.5 Temperature dependence of the fluid self-diffusion coefficient (220 ² T (K) ² 398.15). Symbols represent bulk experimental data8 and lines correspond to the Arrhenius equation for the bulk (dashed) and confined (full) phases using the AA-OPLS potential.

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