(231ak) Thermodynamic Stability of Capillary Condensation in Ordered Mesoporous Silica with Surface Roughness

The ordered　mesoporous silica materials such as MCM-41 and SBA-15 have attracted much attention because of their potential use as catalyst supports, separation, and drug delivery, etc. They are also considered as the most suitable model adsorbent for a fundamental adsorption study of capillary condensation. Phase behavior of fluids confined in the siliceous mesorporous materials have been extensively studied by experiments, theory and molecular simulations, and the experimental studies reveal that high temperature and large pore diameter lead to disappearance of adsorption hysteresis loop. However, the mechanism of the adsorption hysteresis dissipation has still been a missing piece of the puzzle since MCM-41 appeared in 1992, because cylindrical pore models with smooth and structureless wall have been used to understand the capillary condensation behavior. Recent theoretical and simulation studies have shown that surface roughness of pore wall affects adsorption and capillary condensation [1,2]. We therefore constructed an atomistic silica pore model, which has molecular-level surface roughness, with the aid of the electron density profile (EDP) of MCM-41 and SBA-15 obtained from X-ray diffraction data, and performed the molecular simulations to understand the thermodynamic stability of vapor-liquid transition and the mechanism of the adsorption hysteresis.

      Molecular dynamics simulation was used for constructing amorphous fused silica blocks with the BKS type potential. The system was equilibrated in the canonical ensemble at 4000 K, and subsequently, the fused silica blocks were quenched from 4000 K to room temperature. To obtain atomistic MCM-41 and SBA-15 models, the amorphous silica blocks were carved out to coincide with the experimental determined EDP [3]. Adsorption isotherms of Lennard-Jones argon on the atomistic MCM-41 and SBA-15 models at 75 K, 80 K and 87 K were calculated by the grand canonical Monte Carlo (GCMC) method and the gauge cell Monte Carlo (MC) method [4]. Moreover, adsorption isotherms of argon on MCM-41 (pore diameter 3 nm and 4 nm) and SBA-15 samples (pore diameter 7 nm) at 75 K, 80 K and 87 K were measured by an adsorption apparatus consisting of a cryostat with a helium closed-cycle refrigerator and BELSORP-max (BEL, Japan) to compare with the simulation results.

      The GCMC isotherms of argon on the atomistic MCM-41 models at 75 K, 80 K and 87 K are in good agreement with the experimental data, which suggests that our models provide a good description of the surface roughness of MCM-41. Then, the simulated equilibrium capillary condensation pressures correspond to the experimental desorption branches, which indicates that the experimental desorption branch comes from thermodynamic equilibrium vapor-liquid transition. However, a large difference in the adsorption branch between the experiment and simulation was observed in all the cases. This suggests that the energy fluctuation of the system to overcome an energy barrier for the vapor-liquid transition is different between the experiment and the GCMC simulation. We therefore calculated a work required for the state change from a multilayer adsorption state to a capillary condensation state by integrating a sigmoidal adsorption isotherm obtained from the gauge cell MC method [5]. The obtained work shows that the height of the energy barrier for the capillary condensation decreases with increasing vapor pressure. If the system cannot overcome the energy barrier at the thermodynamic equilibrium transition pressure, spontaneous capillary condensation should occur at a higher pressure than the equilibrium transition pressure, resulting in the emergence of adsorption hysteresis. The energy barrier obtained from a comparison with the experimental adsorption branch of argon for MCM-41 (pore diameter 3 nm) at 75 K was 0.154 kT per adsorbate molecule. We assumed it as an energy fluctuation of the system at the spontaneous capillary condensation pressure, and predicted the capillary condensation pressure of argon on the atomistic MCM-41 model at 80 K and 87 K. The predicted spontaneous condensation pressures are in good agreement with the experimental data. We also determined the spontaneous condensation pressures of argon for the other atomistic MCM-41 model at all the temperatures, by setting the energy fluctuation of the system, 0.154 kTper adsorbed molecule, and succeeded in obtaining excellent agreement with the experimental adsorption branches for the corresponding MCM-41 (pore diameter 4 nm).

      As is the case with MCM-41, the GCMC isotherms of argon on the atomistic SBA-15 models (pore diameter 7 nm) at 75 K, 80 K and 87 K are in close agreement with the experimental data. The calculated thermodynamic equilibrium transition pressures, however, correspond not to the experimental desorption branches but to the experimental adsorption ones differently from MCM-41. The calculated work profiles of SBA-15 model at the three temperatures show that the height of the energy barriers is exactly lower than the energy fluctuation 0.154 kTper adsorbate molecule, which ensures that the capillary condensation transition is the thermodynamic equilibrium transition. A previously-reported corrugated pore structure of SBA-15 [6] would cause the ink-bottle effect around the pore entrance, thereby leading to a liquid-vapor evaporation transition at lower pressures than the equilibrium transition pressures. Our results for SBA-15 contradict a widely-accepted understanding [7] that the evaporation process is the thermodynamic equilibrium one while the condensation process is the state change from a metastable state. Hence more careful examinations, such as measuring scanning loops to confirm the ink-bottle effect, should be required for verification of our results.

[1] B. Coasne et al., Langmuir, 22, 194 (2006).

[2] N. Muroyama et al., J. Phys. Chem. C, 112, 10803 (2008).

[3] H. Tanaka et al., Adsorption, 19, 631 (2013).

[4] A. V. Neimark and A. Vishnyakov, Phys. Rev. E, 62, 4611 (2000).

[5] A.Vishnyakov and A. V. Neimark, J. Phys. Chem. B, 110, 9403 (2006).

[6] G. A. Tompsett et al., Langmuir, 21, 8214 (2005)

[7] A. V. Neimark et al., Phys. Rev. E, 62, 1493 (2000)