Under pressure: Quasi-high pressure effects in nanopores

doi:10.1016/j.micromeso.2011.07.017

Microporous and Mesoporous Materials

Volume 154, 15 May 2012, Pages 19-23

https://doi.org/10.1016/j.micromeso.2011.07.017 Get rights and content

Abstract

Phenomena that occur only at high pressures in bulk phases are often observed in nanopores, suggesting that the pressure in such confined phases is large. We develop two models to study the pressure tensor of an argon nanophase confined in carbon micropores by molecular simulation, and show that the in-pore tangential pressure is positive and on the order of 10⁴ bar, while the normal pressure can be positive or negative depending on pore width, with a magnitude of ∼10³ bar at ambient bulk pressure. We find that the in-pore tangential pressure is very sensitive to the bulk pressure, suggesting that it should be possible to control the former over wide ranges in laboratory experiments. We also report results for porous materials other than carbon, and show that the pressure enhancement is smaller for pores with weakly attractive walls (e.g. silica and oxides), but larger for more strongly attractive walls (e.g. mica).

Graphical abstract

Highlights

► Pressure tensors for argon in carbon slit pores from molecular simulation. ► The tangential component of the pressure is enhanced by a factor of 10⁴–10⁷. ► A small increase in bulk pressure causes a huge increase in tangential pressure. ► Pressure enhancement arises from compression of adsorbate due to attractive wall. ► The sign oscillation of enhanced normal pressure expands or compresses the pore.

Introduction

Phases confined in micropores and mesopores often exhibit physical and chemical properties that are dramatically different from those of the bulk phase [1]. Such confinement effects arise from the reduced dimensionality and the strong interaction between the confined phase and the porous material. These effects find numerous applications, e.g. in the purification of water and air streams, heterogeneous catalysis, drug delivery, sensors, energy storage, in fabrication of nanomaterials such as nanowires, as insulators in microcircuits and as electrodes for fuel cells and supercapacitors.

Phenomena that occur only at very high pressures (e.g. ∼10⁴ bar) in the bulk phase are often observed to occur in the confined phase at pressures (the pressure of the bulk phase in equilibrium with the confined phase) of the order of 1 bar [2], [3]. Examples of such phenomena include high pressure chemical reactions, high pressure solid phases, high pressure effects in solid–liquid equilibria and effects on spectral properties. The well-studied nitric oxide dimer reaction, $2 NO ⇌ (NO)_{2}$ , provides an illustration of a high pressure reaction that occurs in the porous material at low pressure. In the bulk gas phase it has a very low yield with less than 1 mol% dimer at 300 K and 1 bar pressure, but in activated carbon fibers (average pore width of 0.8 nm) the mole fraction of dimers is 99%, measured by magnetic susceptibility [4]. Fourier transform infrared spectroscopy experiments on this reaction in single walled carbon nanotubes (1.35 nm in diameter) similarly show ∼100% dimers [5], and molecular simulation results [6] for NO dimerization in slit-shaped carbon pores and carbon nanotubes agree with these experiments qualitatively. A simple thermodynamic calculation finds that a dimer mole fraction of 98–99 mol% would only be obtained in the bulk phase at pressures between 12,000 and 15,000 bar at the experimental temperatures. In addition, phases that occur only at high pressure in the bulk material are often observed in nanopores [7], [8], [9], [10], [11], [12], [13]. Surface force apparatus experiments have observed liquid–solid transitions of nanophases confined between mica surfaces for several substances at temperatures well above their normal melting points, T_mp. For example, cyclohexane [7], [8], [9] (T_mp = 279 K) freezes at 296 K (bulk phase freezes at ∼440 bar at 296 K) and n-dodecane [10] (T_mp = 263.4 K) freezes at 300 K (bulk phase freezes at ∼1860 bar at 300 K) when confined between mica surfaces in the surface force apparatus. Molecular simulations [13] for dodecane between mica surfaces are in agreement with the experimental data. Neutron diffraction studies show evidence of high pressure ice phases in carbon nanopores at ambient conditions [14]. Finally, we note that several experimental small-angle X-ray scattering studies show significant effects of the adsorption of a confined phase on the pore width and interlayer atomic spacing of the pore walls [11], [12], indicating a strong positive or negative pressure normal to the walls.

With the aim of providing fundamental understanding of these apparently unconnected effects in confined nanophases, we report a molecular simulation study of the pressure tensor for argon within simple slit-pore models of nanoporous carbons and other materials.

Section snippets

Simulation details

The effects of pore width H and bulk phase pressure P_bulk on the density and pressure profiles were examined in two different slit pore models at 87.3 K (the boiling point of argon). In Model I (Fig. 1a), the slit pore is finite in length, and the pore walls are fully atomistic and semi-flexible. The pore is symmetric about z = 0 and formed by two opposing graphitic walls that lie parallel to the xy-plane. Each of the two walls consists of three stacked layers of graphene that are infinite along

Results and discussion

Fig. 2a shows the in-pore density and pressure profiles in Model I for the reduced pore width $H_{e}^{*} = H_{e} / σ_{ff} = 3.0$ (1.02 nm) at 87.3 K and 1 bar bulk pressure. Fig. 2b and c, respectively, show the density and tangential pressure profile under the same condition in a series of pores with reduced pore widths ranging from 2.0 to 5.0 in increments of 0.5.

The two peaks in the density profile indicate two layers of argon molecules in the pore of $H_{e}^{*} = 3.0$ (Fig. 2a), which is the well-known layering effect in

Conclusions

Our calculations show that very high tangential (of the order 10⁴ bar or more) and normal (of order 10³ bar or more) pressures are expected in carbon micropores and small mesopores. These high in-pore pressures unify a wide range of previously unconnected phenomena, such as the observation of high pressure phases and high pressure reactions in nanoporous materials, and provide a connection between the behavior of confined phases and the bulk phase at high pressure. Such a relationship could

Acknowledgments

We thank K. Kaneko for helpful discussions. We also thank the National Science Foundation (grant No. CBET-0932658) for support of this research. Computational time was provided through a Teragrid Research Allocation by the U.S. National Science Foundation (Grant No. CHE080046N).

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Under pressure: Quasi-high pressure effects in nanopores

Abstract

Graphical abstract

Highlights

Introduction

Section snippets

Simulation details

Results and discussion

Conclusions

Acknowledgments

Surf. Sci.

Surf. Sci.

Carbon

Carbon

Phys. Lett. A

Phys. Chem. Chem. Phys.

Rep. Prog. Phys.

J. Phys. Condens. Matter

Langmuir

J. Phys. Chem. B

J. Chem. Phys.

J. Chem. Phys.

J. Chem. Phys.

Science

Phys. Rev. Lett.

Phys. Rev. Lett.